KAERI/TR-2935/2005

SAS4A/SASSYS-1 ^33^KALIMER-150 ^71-

Evaluation of the Inherent Safety of the KALIMER-150 Design Using the SAS4A/SASSYS-l Computer Code

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Summary

In order to evaluate the passive characteristics of the advanced safety design features of KALIMER-150, the plant responses and safety margins during typical ATWS events were investigated using the system transient code SAS4A/SASSYS-1 developed by Argonne National Laboratory. The key characteristic necessary for passive safety and inherent self-protection is an overall negative reactivity feedback response to reactor accident initiators. Because the passive safety mechanisms are the result of tightly coupled thermal, hydraulic, neutronic, and mechanical physical phenomena, analysis and investigation methods employing detailed computational models of the phenomena and geometry are required to permit accurate quantification of effects.

Three ATWS events as the most relevant for evaluation of passive safety design features were selected. These are unprotected transient overpower (UTOP), unprotected loss of flow (ULOF), and unprotected loss of heat sink (ULOHS). The ATWS events are extremely unlikely event category in the KALIMER-150 design, however; they are considered in establishing the design bases for KALIMER-150. The events selected in this category have the potential for a large release of radioactive material, core melt, or reactivity excursion. The KALIMER-150 design should have capability to ensure that adequate prevention or protection is furnished for these events.

The analysis results by the SAS4A/SASSYS-1 code shows that the KALIMER-150 design has inherent safety characteristics and is capable of accommodating ATWS events. The passive safety mechanism in the KALIMER-150 design makes the core shutdown with sufficient margin and the passive removal of decay heat and matching power to heat sink by passive self-regulation is successful. The self-regulation of power without scram is mainly due to the inherent and passive reactivity feedback.

In the first chapter, general design features of the passive safety system in the innovative sodium cooled reactors are discussed. In the next chapter, the design features of KALIMER-150 are briefly described from the system safety point of view. The state-of- the-art models and computational methods used in SAS4A/SASSYS-1 are reviewed in the chapter 3. The KALIMER-150 modeling by SAS4A/SASSYS-1 for the safety analysis is presented in chapter 4. Detailed hand calculations for the code input preparation and the list of the code input deck are presented in Appendix A and B, respectively. Safety analysis results for the selected ATWS events are discussed to evaluate the safety margins of the KALIMER-150 design in chapter 5.

The SAS4A/SASSYS-1 analyses were carried out by the primary author during his stay at ANL for an International Nuclear Energy Research Initiative collaboration supported by the Korean Ministry of Science and Technology and the U.S. Department of Energy.

Table of Contents

Table of Contents ................................................................................................... iList of Tables........................................................................................................... iiList of Figures ........................................................................................................ iii

1. Introduction ...................................................................................................... 11.1 Containment and Shielding ............................................................................. 11.2 Passive Self-regulation of Power ................................................................... 21.3 Passive Removal of Decay Heat .................................................................... 2

2. Design Features of KALIMER-150 ............................................................. 52.1 Reactor Core.................................................................................................. 72.2 Reactor Coolant and Heat Removal Systems.................................................. 8

3. Features of SAS4A/SASSYS-1.........................................................................133.1 Core and Fuel Treatment...................................................................................143.2 Reactivity Feedback Models............................................................................. 163.3 Primary and Intermediate Heat Transport Systems........................................ 203.4 Steam Generator Model ....................................................................................223.5 RVACS Heat Removal Model..........................................................................22

4. Modeling of KALIMER by SAS4A/SASSYS-1 ............................................244.1 Core and Fuel ...................................................................................................... 254.2 Primary Heat Transport System .......................................................................294.3 Passive Safety Decay Heat Removal System ................................................. 314.4 Intermediate Heat Transport System and Steam Generator .......................... 334.5 Safety Criteria.....................................................................................................35

5. Analyses Results.................................................................................................375.1 Steady State of SAS4A/SASSYS-1 ............................................................... 375.2 Unprotected Over Power Transient (UTOP) .................................................. 425.3 Unprotected Loss of Flow (ULOF) ................................................................. 465.4 Unprotected Loss of Heat Sink (ULOHS) ...................................................... 545.5 Combined ULOF/LOHS.................................................................................... 595.6 Combined UTOP Cases................................................................................... 61

6. Summary............................................................................................................. 67References ..................................................................................................................... 68

Appendix A. SAS4A/SASSYS-1 Input Preparation for KALIMER-150...............A1Appendix B. List of Input Deck.................................................................................. B1

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List of Tables

Table 2.1 KALIMER-150 Plant Performance............................................................ 6Table 2.2 KALIMER Design Parameters....................................................................7

Table 4.1 PRIMAR-4 model of the KALIMER: compressible volumes................. 29Table 4.2 PRIMAR-4 model of the KALIMER plant (cont.)....................................33Table 4.3 PRIMAR-4 model of the KALIMER plant: temperature elements......... 34

Table 5.1 Major plant parameters at steady-state condition..................................... 38

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List of Figures

Fig. 2.1 KALIMER nuclear steam supply system..................................................... 5Fig. 2.2 Breakeven core loading pattern......................................................................8Fig. 2.3 KALIMER reactor vessel and internal structures..........................................9Fig. 2.4 Reactor core and supporting structures...........................................................9Fig. 2.5 Intermediate heat transport system................................................................ 11Fig. 2.6 Residual heat removal systems...................................................................... 12

Fig. 3.1 Core channel node structure........................................................................... 15Fig. 3.2 General heat transport system geometry........................................................21Fig. 3.3 RVACS model.................................................................................................23

Fig. 4.1 Schematic of the SAS4A/SASSYS-1 Model of the KALIMER plant....... 24Fig. 4.2 Power and flow distribution in an 1/6 assembly............................................ 26Fig. 4.3 SAS4A axial zones and fuel node for KALIMER code............................. 28

Fig. 5.1 Normalized power (steady state) .................................................................... 38Fig. 5.2 Pool temperatures (steady state) ................................................................... 39Fig. 5.3 Reactivity components (steady state)............................................................39Fig. 5.4 Flow distribution (steady state)......................................................................39Fig. 5.5 Fuel temperatures (steady state).................................................................... 40Fig. 5.6 PSDRS temperatures (steady state)............................................................... 40Fig. 5.7 Radial fuel temperature in the hot assembly (steady state)...........................40Fig. 5.8 Radial fuel temperature in the driver assembly (steady state)......................41Fig. 5.9 Radial fuel temperature in the inner blanket assembly (steady state)........ 41Fig. 5.10 Normalized power and flow during UTOP.................................................45Fig. 5.11 Reactivity feedback components during UTOP......................................... 45Fig. 5.12 Fuel temperatures during UTOP..................................................................46Fig. 5.13 KALIMER primary pump coastdown curve.............................................. 47Fig. 5.14 Normalized power and flow during ULOF.................................................49Fig. 5.15 Reactivity feedback components during ULOF.......................................... 50Fig. 5.16 Fuel temperatures during ULOF.................................................................. 50Fig. 5.17 Normalized power and flow during ULOF with 1 pump

coastdown failure........................................................................................... 51Fig. 5.18 Fuel temperatures during ULOF with 1 pump coastdown failure..............51Fig. 5.19 Fuel temperatures during ULOF with 2 pumps coastdown failure............52Fig. 5.20 Fuel temperatures during ULOF with 2 pumps coastdown failure............52Fig. 5.21 Normalized power and flow during ULOF with 3 pumps coastdown

failure............................................................................................................ 53Fig. 5.22 Fuel temperatures during ULOF with 3 pumps coastdown failure......... 53Fig. 5.23 Normalized power and flow during ULOHS............................................... 55Fig. 5.24 Reactivity feedback components during ULOHS..................................... 56Fig. 5.25 Fuel temperatures during ULOHS................................................................ 56Fig. 5.26 Normalized power and flow during ULOHS (long term period)............... 57

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Fig. 5.27 Reactivity feedback components during ULOHS (long term period).......... 57Fig. 5.28 Fuel temperatures during ULOHS (long term period)....................................58Fig. 5.29 Heat balance between core power and PSDRS heat removal......................... 58Fig. 5.30 Temperature distribution in the PSDRS.......................................................... 59Fig. 5.31 Normalized power and flow during ULOF/LOHS..........................................60Fig. 5.32 Reactivity feedback components during ULOF/LOHS................................. 60Fig. 5.33 Fuel temperatures during ULOFLOHS.......................................................... 61Fig. 5.34 Normalized power and flow during UTOPLOHS..........................................62Fig. 5.35 Reactivity feedback components during UTOPLOHS.................................. 63Fig. 5.36 Fuel temperatures during UTOPLOHS.......................................................... 63Fig. 5.37 Normalized power and flow during UTOPLOF............................................ 64Fig. 5.38 Reactivity feedback components during UTOPLOF..................................... 64Fig. 5.39 Fuel temperatures during UTOPLOF............................................................. 65Fig. 5.40 Normalized power and flow during UTOPLOFLOHS................................ 65Fig. 5.41 Reactivity feedback components during UTOPLOFLOHS.........................66Fig. 5.42 Fuel temperatures during UTOPLOFLOHS LOHS..................................... 66

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Chapter 1. Introduction

The strategy to meet the basic safety functions of nuclear power plants employs traditional defense in depth: Multiple barriers to prevent release of radiation, highly reliable systems for controlling and protecting the plant, high quality construction and rigorous maintenance. In addition, the safety strategy of the advanced liquid metal fast reactors (LMFR) goes beyond those traditional measures. Their system consisting of the reactor heat source and balance-of-plant (BOP) heat engine is configured to provide the needed safety functions by exploiting the natural laws of physics to the maximum degree achievable. The passive safety approach of the advanced sodium-cooled reactors is described in this section.

The passive safety approach assures safe response even if the engineered safety systems fail, or if there are multiple, compounding failures and human errors. The advanced LMFR design can accommodate all credible malfunctions or unplanned initiators passively, without damaging to cladding or structure. Severe accident initiators, even if they were to damage the fuel cladding, would be accommodated passively without challenging the integrity of the reactor vessel.

Passive safety of the advanced sodium-cooled fast reactors such as KALIMER [1] and IFR [2] is based on the following characteristics: large margins between the operating conditions and physical safety limits, reliance on passive processes to hold power production in balance with heat removal, and totally passive removal of decay heat independent of the equipment and structures in the BOP. Should equipment in the BOP or control system fail, reactors will passively regulate their own power so as to remain undamaged for all such initiators, even in the anticipated transient without scram (ATWS) scenarios. Decay heat is removed through a heat transport path driven by natural convection in a passive manner.

1.1 Containment and Shielding

The advanced LMFR approach to containing and shielding the radio reactivity in the fuel is the classical one, which is three diverse and redundant layers of protection. The alloy fuel is inside steel cladding, which is in turn in the reactor vessel, and the reactor vessel is in the reactor containment. Within the reactor vessel, shielding surrounds the core on all sides to keep the secondary sodium in the heat exchangers from being activated by neutrons. The steam generators emit no radiation unlike current PWRs. In the EBR-II, which has operated as an IFR prototype power plant, personnel access to the reactor head and the steam generators is unrestricted and routine while the reactor is at power.

Even with random failures of fuel elements, the chosen fuel, cladding, and coolant are chemically compatible. Running the reactor with breached cladding leads neither to low density corrosion products that could choke off flow, nor to exothermic or hydrogen-

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producing reaction between fuel and coolant. Second, the zirconium-containing fuel alloy has been found to retain iodine. Iodine is the largest contributor to the fission product component of source terms for early release of radioactivity in an accident. Passive removal of decay heat and matching power to heat sink by passive self-regulation have been so successful that all operational and design basis events (DBE) lead to a fully benign response, in which even the cladding remains intact. Finally, the integrity of the reactor vessel is maintained even for those extremely unlikely situations where the integrity of the cladding cannot be guaranteed.

1.2 Passive Self-regulation of Power

The power demanded by the BOP is potentially subject to anomalous fluctuations caused by equipment failure or human error. However if the reactor is made to adjust its power to the heat sink in the anomalous condition, the troubles in the BOP cannot cause the reactor to overheat and release radioactivity. Passive self-regulation is achieved by matching heat generation rate to the available heat sink rate. In the analysis a quasi-static reactivity balance is used to calculate the new asymptotic power by considering the innate reactivity feedbacks. The effectiveness of designing for passive self-regulation has been proven in demonstration tests with the EBR-II reactor.

The end state of the protected accident transient is subcritical because control rods are scrammed. The passive response without scram may result in an end state that is neutronically critical at a low power and low flow rate. The stability of such passive shutdown equilibrium states must be assessed because of the potential for dynamic oscillations caused by coupling between neutronics and thermal hydraulics - at least partially the same feedback mechanisms that permit favorable passive self-regulation of power.

Two oscillation modes can be identified. A higher frequency mode associated with the reactor core itself and a lower frequency mode involving both the core and the primary heat transport loop. In the reactor-only mode, oscillations in the reactor power induces slightly delayed oscillations in the temperature of the coolant at the reactor outlet, which causes reactivity changes via radial dilation of the core and axial expansion of the control rod driveline - closing the feedback loop by affecting the power. In the mode where the feedback loop is the primary heat transport circuit, oscillations in the reactor power induce perturbations in the outlet temperature of the coolant; with a longer time delay, those oscillations are propagated around the primary coolant circuit back to the reactor inlet, where they introduce reactivity changes through radial expansion of the grid plate and axial elongation of the reactor vessel wall - again closing the feedback loop by affecting the power.

1.3 Passive Removal of Decay Heat

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Passive self-regulation could not be exploited to relax the requirement the BOP equipment and structures for regulating reactor power be safety-grade unless there were also an alternative path for removing decay heat.

To assure the presence of the heat removal fluid without relying on engineered safety systems, the IFR and KALIMER-150 approach is place the reactor core and its cooling fluid in a double-walled reactor vessel at ambient pressure. With the primary coolant system at ambient pressure, storing energy in the form of high-pressure coolant can be avoided and there is no opportunity to lose the coolant by flashing it to vapor.

The second element of the strategy for passively removing decay heat is to arrange for buoyancy-driven natural circulation to carry the heat out of the chain-reacting region to an ultimate heat sink. There are two innate phenomena pertaining to the matter. First, the diminishing decay-heat power level, from about 1/20 full power immediately after shutdown to less than 1/100 full power within a day or so, allows the designer to trade off a smaller capacity decay heat removal channel against a large thermal storage capacity in the reactor vessel itself, so as to safely store the initial excess of heat that is generated during the short period when the decay heating rate exceeds the transport capacity of the channel.

Second, the decay heat is to be transported to the external ambient atmosphere as an ultimate heat sink, rather than to the BOP heat engine. The temperature of the ambient heat sink in the world at large is about 30 °C, which is opposed to the Rankin cycle’s feedwater heat sink temperature of about 300 °C. The naturally occurring 300 °C increase in temperature drop between the surface of the fuel cladding and the ultimate heat sink, when combined with the naturally occurring 20 to 100 % reduction in power output, together compensate for the decrease in mass flow rates and increase in thermal impedance of the heat transport path that occur when the flow velocity diminishes in the transition from forced to natural convection.

The requirement for passive, buoyancy-driven flow to convect the decay heat out of the core determines the internal layout of the primary convection loop. The same primary- coolant flow path through the core that is used in the power range serves also under natural circulation as the first link in the passive-decay-heat removal channel. Even though at full power the convective loops rely on forced circulation to achieve the required mass and energy fluxes, the layout of thermal centers and primary convective loop’s low resistance to flow make it possible for natural circulation to handle the decay heat.

The decay heat that is transported away from the fuel by the buoyancy-driven flow in the primary coolant circuit increases the temperature of the mass of coolant and structural material inside the primary system. The subsequent links in the passive heat transport path from this heat reservoir to the ultimate ambient heat sink are matters of design detail

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that depend in part on the plant’s heating rate. For low enough heat ratings (1000 MWt or less), the surface-to-volume ratio of the vessel is large enough to support natural-draft cooling of the vessel’s exterior by ambient air. At large heat ratings, more effective means are required. A chain of dedicated natural convection loops, starting with heat exchangers immersed in the primary vessel as topological extension of its separation barrier. The loops in the chain have interfaces at the vessel and at the containment separation barrier, and the heat crosses these barriers by conduction to reach the final link, which rejects the heat through natural-draft ambient-air heat exchangers.

In all cases, the capability for passive heat removal is rated at less than 1% of pull power, and the process is fully passive in that it is powered by natural convection; moreover, it runs all the time. The revenue lost from continuously dumping 1% of the heat directly to ambient, rather than through the heat engines, is offset in part by not needing safety-grade construction of the main heat transport loops nor of the heat rejection components of the Rankin cycle heat engine.

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Chapter 2. Design Features of KALIMER-150

The conceptual plant design selected for safety evaluation in this study is the KALIMER reactor design developed by the Korea Atomic Energy Research Institute (KAERI). The KALIMER design is depicted in Fig. 2.1. KALIMER is a pool-type, sodium-cooled, metallic-fuelled fast reactor that serves as a prototypic demonstration for future commercial liquid metal-cooled reactor (LMR) designs. The principal design objectives for KALIMER are enhanced safety, competitive economics, proliferation resistance, and environmental friendliness. The plant performance characteristics of KALIMER are summarized in Table 2.1, and the KALIMER design parameters are given in Table 2.2.

The KALIMER plant design life is thirty years. The selected design life is a compromise between longer component life and high thermal efficiency. The higher operating temperature associated with high thermal efficiency sets design limits on the integrity of reactor structures. To facilitate siting flexibility, the KALIMER design utilizes seismic isolation, which simplifies plant seismic design, enhances structural safety, and reduces construction costs.

The safety design philosophy of KALIMER emphasizes inherent safety mechanisms for protection of public health and safety and of plant investment. This philosophy places maximum reliance on passive responses to abnormal and emergency conditions, and minimizes the need for active, engineered safety systems. Plant capital costs are reduced by substitution of passive safety mechanisms for active systems.

The KALIMER design includes features to protect against accident propagation. The use of liquid metal coolant promotes heat transfer, and provides for removal of decay heat by natural circulation. Metallic fuel operates at low temperature compared to ceramic fuels, reducing stored heat and the associated stored reactivity. The large heat capacity of the

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Table 2.1 KALIMER-150 plant performance

Item Specification Rationale

Plant thermal efficiency

Net efficiency > 38%Higher thermal efficiency means higher utilization of fuel and less environmental impact.

Plant availability >= 89%

Average availability over the plant design life considering planned outages of 30 days per 18 months, forced outages of 5 days per year and major outages of 45 days every 3 years.

Refueling interval >=18 monthsMinimum cycle length of 18 months is necessary for the prototypic demonstration of a commercial LMFR.

Spent fuel storage capacity in the reactor vessel

>= 1 cycle dischargeCapability of storage of the spent fuel in the reactor vessel facilitates spent fuel handling design and handling.

Load rejection capacity

Should be able to accommodate 100% off-site load rejection without plant trip

The capability of 100% load rejection capability is required to mitigate consequences of rapid transients and to relax thermal impact on plant systems.

Operation, maintenance and serviceability

Minimize the required number of operators.

Simplicity of plant operation yields reduction of operational cost and possibility of human error.

Major equipment should be replaceable.

Major equipment lives that impact the plant lifetime should be replaceable for investment protection.

Optimal level of automation

Automation improves plant availability by minimizing the need for operator intervention.

Automatic inspection and diagnosis

Automatic inspection and diagnosis minimize testing and maintenance errors.

Human centered design

A functional task analysis ensures a consistent design. VDU(Visual Display Unitj-based design improves human system interface, thus reduces human errors.

Reliance on a safety grade diesel generator

The plant should not require any safety grade diesel generators.

Reliance on safety grade diesel generators is costly and contrary to the main safety design philosophy of KALIMER.

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Table 2.2 KALIMER design parameters

OVERALLNet Plant Power, MWe 150Core Power, MWt 392.2Gross Plant Efficiency, % 41.5Net Plant Efficiency, % 38.2Reactor Pool TypeNumber of IHTS Loops 2Safety Shutdown heat Removal

PSDRS

Seismic DesignSeismic Isolation

Design

PHIS

Reactor Core I/O Temp., “C 386.2/530.0Total PHTS Flow Rate, kg/s 2143.1Primary Pump Type ElectromagneticNumber of Primary Pumps 4

IHTSIHX I/O Temp., °C 339.7/511.0IHTS Total Flow Rate, kg/s 1803.6IHTS Pump Type ElectromagneticNumber of IHXs 4Number of SGs 2

COREBreeding Ratio 1.05Core Configuration HeterogeneousCore Height, mm 1000Axial Blanket, Thickness, mmCore Diameter, mm 3373Fuel Form U-TRU-10% ZrFeed Fuel Enrichment (Total TRU) for Equilibrium Core, %

30.0

Assembly Pitch, mm 161Fuel/Blanket Pins per Assembly 271/127Cladding Material HT9Refueling Interval, months 18

STEAM SYSTEMSteam Flow Rate, kg/s 175.5Steam Temperature 483.2Steam Pressure, MPa 15.50

pool-type primary system provides long times for evolution of system transients and increases the time margins for emergency response. The reactor is designed to have a negative power reactivity coefficient during all modes of plant operation. The reactor is equipped with multiple, diverse shut-down and heat removal mechanisms to attain a high level of accident protection.

2.1 Reactor Core

The KALIMER reactor core loading pattern is shown in Fig. 2.2. Metallic fuel is selected as the most proper fuel for KALIMER due to its in-reactor performance, nuclear characteristics, and inherent safety performance.

In the analysis of the fuel isotopic inventory for fuel recycle, metal fuel pyroprocessing treatment was applied. It was assumed that the pyroprocessing treatment returns 99.9% of TRU to the core and loses 0.1% to the waste stream. In addition, 5% of the rare-earth (RE) fission products are recycled and all other fission products go to the waste stream. As the result of searching the most suitable core configuration and design parameters satisfying the objective and ground rules for design, it was shown that the effective core

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o □r>/eiTL?l 5Lo interrai Slants 2<-s Radial jlanKftle Cc/tU Red f.S3 U35 1

Gttf ri-J Re"le:tor 16# rLC6hle J 5 £o IV 9e Shield rj

7ma! 367

Fig. 2.2 Breakeven core loading pattern

height is 100 cm. The TRU enrichment for feed driver fuel is 30.0% and the desired breeding ratio is 1.05 considering computational uncertainty. The breakeven core configuration is shown in Fig. 2.2.

2.2 Reactor Coolant and Heat Removal Systems

The KALIMER reactor coolant outlet temperature is 530 °C and the outlet pressure is near atmospheric. This allows the reactor vessel to be designed as a thin shell structure considering creep-fatigue, thermal fatigue, thermal stripping and ratcheting phenomena. The reactor head supports the intermediate heat exchangers (IHX), the primary coolant pumps, the reactor vessel, and the rotating plug supports the upper internal structure and the in-vessel transfer machine (IVTM). Figure 2.3 shows the arrangement of the KALIMER coolant systems and the reactor vessel and internal structures.

KALIMER reactor internals consist of a fixed internal support structure, a fixed shield structure, and the upper internal structure (UIS). The internal support structure is exposed to a high radiation environment, and is designed to maintain structural integrity for the whole plant lifetime. The control rod drive mechanism (CRDM) suspends the control rod through the shroud tube of the UIS. The arrangement of the KALIMER reactor core and supporting structures is shown in Fig. 2.4.

The function of the primary heat transport system (PHTS) is to transfer the heat generated from the reactor core to the intermediate heat transport system (IHTS). Sodium coolant flowing at 2143.1 kg/s enters the reactor core at 385 °C, and is heated to 530 °C as it flows through the reactor. The coolant then flows to the intermediate heat exchanger (IHX) where it transfers heat to the sodium of the secondary system. Cold pool sodium is circulated through the sodium distribution space and core by the primary electromagnetic pumps (BMP). The EM pump voltage and frequency are regulated to control coolant flow through the primary heat transport system.

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Rotating Plug -Positioning of IVTM

for Replacement and Installation of Core Assemblies

Reactor Head -Thickness: 30 cm - Seals KV and CV -Supports IHTS and EMP -Provides Holes for ISI

Reactor Support Structure -Integral Support Ring Type -AllowsThermal Expansion

Using Self .Lubricating Plate

CRDM- Number 6 CRDM. 1 SASS- Multi Rx Shutdown Function

. Motor Driving TypeElectromagnetic Type

Reactor Vessel- 316 SS- Thickness :5 cm. Length : 1843 cm.

Outside Diameter 702 cm

Containment Vessel- 2(l/4)Cr-l Mo- Thickness : 2.5 cm Length 1868 cm

Outside Diameter ' 737 cm

Air Separator- PSDRS Air Flow for Decay Heat Removal

Reactor Vault■■ Provides Reactor Support Wall- Provides PSDRS Air Flow

Fig. 2.3 KALIMER reactor vessel and internal structures

Nosepiece & Receptacle- Installation of Core Assemblies- Guide the Sodium Cedant Into

the Duct- Constrain the Horizontal and

Vertical Displacements of Core Assemtiies

OCore Former Ring -Constram i'loncdrital Large Displacement at Upper Part

Core Assemblies- Hexagonal i3undle type- Total Number : 367

Flow Inlet Plenum- Upper & Lower Grids, receptacles- Installation of Core- Distnbubofl of Sodium Coolant into

the Core

Fig. 2.4 Reactor core and supporting structures

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The PHTS is filled with sodium to a level below the reactor head, with a free surface exposed to the cover gas space. The sodium volume of the PHTS is designed so that the reactor core remains covered in the event of a vessel leak or rupture, and reactor cooling is maintained. Helium gas, which is inert chemically, is used as cover gas to control the pressure change due to thermal expansion of sodium. The cover gas is maintained at atmospheric pressure during operation to prevent the release of contaminated radioactive materials to the environment.

Bounded by the reactor vessel, the reactor head, and the IHX, the PHTS serves as a defense-in-depth barrier to prevent release of contaminated sodium to the next barrier provided by the containment system. The containment system as shown in Fig. 2.1, which consists of the containment dome and the containment vessel, is designed as a defense-in-depth barrier to protect against leakage through the reactor head or vessel. The containment vessel is a cylindrical structure surrounding the reactor vessel. The annular space between two vessels is filled with argon gas to prevent air-sodium reactions due to accidental sodium leakage from the reactor vessel. The containment vessel is designed so that all structure surfaces have high emissivity for effective radiation heat transfer.

An EM pump is used to simplify the piping arrangement in the pool type primary heat transport system, and to facilitate effective recovery of heat generated by the pump in the coolant. KALIMER has four primary EM pumps installed along with the two intermediate heat exchangers in the annular space at the top of reactor. Since EM pumps do not have heavy rotating shafts and impellers like mechanical pumps, the coolant flow rate falls rapidly if electrical power is lost. To compensate, the KALIMER primary coolant EM pumps are equipped with a supplementary inertial device to provide the transition from forced to natural circulation core cooling in the event of a loss of pump power supply.

The functions of the IHX are to deliver the heat transferred from the primary sodium to the secondary sodium in the IHTS, and to provide physical separation between the radioactive primary sodium and the non-radioactive sodium of the intermediate system. The cylindrically shaped IHX is installed vertically within the hot pool of the reactor vessel. The IHX is a counter-flow shell and tube type heat exchanger with a straight tube bundle. The IHX design arrangement provides proper relative vertical height from the core to promote heat transfer by natural circulation. Two IHX's are connected in parallel in each of the two IHTS loops.

The arrangement of the IHTS is shown in Fig. 2.5. The KALIMER conceptual design includes two IHTS loops. The functions of the IHTS are to transfer the heat delivered from the primary system through the IHX to the steam generation system, and to serve as a physical barrier to prevent the accidental spread of radioactive contamination due to chemical reaction between sodium and water in the steam generation system. With the capability to provide natural circulation between the IHX and the elevated steam

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generator, the KALIMERIHTS design can also remove core decay heat. The KALIMER IHTS design includes a sodium drain tank and a rupture disk to mitigate sodium-water reactions, to separate the reaction products initiated by steam generator tube leaks, and to relieve sodium-water reaction pressures.

The KALIMER steam generation system (SGS) converts feed water to super-heated steam for use in generating electricity in a turbine/generator set. The SGS controls the flow rate of the feed water to prevent over pressurization. Since the KALIMER steam generator is an integral, once-through type, flow instability may occur during low power and low flow rate operation. To circumvent this, it is necessary to re-circulate feed water at low power, and a recirculation pump and auxiliary water tank are provided. In the recirculation mode, saturated steam is not supplied to the turbine but is sent to the condenser to protect the turbine from erosion. In the once-through mode, superheated steam is sent to the turbine to generate electricity. The steam generator tube bundle consists of a number of helical coil tubes with water and steam flow inside the tubes. The gas region above the free sodium surface is filled with inert cover gas and is designed to accommodate sodium expansion by the sodium temperature change of the IHTS. At the bottom region of the steam generator, a rupture disk is installed to relieve the pressure spike should there be a sodium-water reaction due to a tube leak.

Fig. 2.5 Intermediate heat transport system

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The KALIMER residual heat removal system (RHRS) is shown in Fig. 2.6. The RHRS consists of the passive safety decay heat removal system (PSDRS) and the steam generator auxiliary cooling system (SGACS). The PSDRS is a passive safety grade decay heat removal system and consists of the reactor vessel, the containment vessel, the air separator, and the air flow stacks. The PSDRS is a fully passive system that requires neither operator action nor any active component actuation. Cold air enters the air inlet at the top of the stack. After turning 180° at the bottom of the air separator, the air flows upward through the hot air riser provided by the space between the air separator and the containment vessel. As the air flows upward, it removes heat and is discharged from the air outlets at the top of the air stack to the final heat sink, the environment. The driving force of this natural circulation process is the air density difference. The PSDRS is designed to operate continuously for the plant life time. Since heat removal during normal power operation is heat loss from the point of view of plant efficiency, the PSDRS is designed to minimize heat loss by maintaining sodium level so low as to reduce heat loss during normal operation. On the other hand, in the event that the normal heat removal paths are unavailable, the temperature of the primary sodium increases. The expansion of sodium raises its surface level to the overflow slots on the reactor baffle. When the sodium level reaches the overflow slot and overflows it, natural circulation of the primary sodium through the annular space between the reactor baffle and the reactor vessel commences, effectively increasing the heat transfer area and the heat transfer through the reactor vessel. The SGACS is a non-safety grade RHRS that removes heat from the wall of the steam generator during plant power operation or PSDRS operation.

Fig. 2.6 Residual heat removal systems

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Chapter 3. Features of SAS4A/SASSYS-1

The SAS4A and SASSYS-1 computer codes were separately developed at Argonne National Laboratory in the IFR Program for transient analysis of LMFRs. The earlier versions of SAS were developed to analyze severe hypothetical core disruptive accidents involving extensive melting of pins, high power levels and short time scales ranging from milliseconds to a few seconds. The reactor core is treated in great detail, but the thermal- hydraulics of the primary loop outside the reactor vessel is treated in a simple way to drive the subassembly coolant dynamic simulations.

In contrast, SASSYS-1 was originally designed to address the consequences of loss-of- decay-heat-removal accidents, SASSYS-1 evolved into a tool to analyze passive safety response mechanisms in anticipated transients without scram (ATWS), and as a margin assessment tool for design basis accidents. To fulfill this role, the latest version of SAS4A/SASSYS-1 [3] contains the same models as the SAS4A computer code for fuel element heat transfer and single and two-phase coolant hydraulics. In addition, SAS4A/SASSYS-1 has the capability to provide a detailed thermal/hydraulic simulation of the primary and secondary coolant circuits, as well as the BOP steam/water circuit.

The liquid metal and steam circuit models include component models for heat exchangers, pumps, valves, steam generators, turbines, and condensers, and thermal/hydraulic models of pipes and plena. SAS4A/SASSYS-1 also contains a control system model, which provides digital representations of reactor control system, pump, and valve controllers and their response to input signal changes. SAS4A/SASSYS-1 served as the computational engine in a multi-tasking, workstation-based simulator for the EBR-II power plant.

The original role for SAS4A/SASSYS-1 required extensive analysis capabilities and flexibility, and it required numerical methods and coding that were efficient enough to run long transients in a reasonable amount of computer time. The result was a code that is capable of handling a wide range of transients, from minor operational transients through hypothetical ATWS. Currently ATWS analysis is only one of the many uses of SAS4A/SASSYS-1. In addition to nominal natural circulation cases, the code can handle off-normal situations leading to coolant flow reversal or stagnation or boiling in the core.

The SAS4A/SASSYS-1 code was developed to analyze any LMFR design, loop or pool type reactors. Also, the control system model in SAS4A/SASSYS-1 is flexible enough to handle any control system. Thus, not only can any new LMFR design be analyzed, but experimental results from older, existing reactors can be used to validate the SAS4A/SASSYS-1 models that are then used to analyze new designs. A great deal of flexibility is provided in the amount of detail used to model a component, from simple, fast running treatments to detailed, but slower running treatments. An arbitrary

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arrangement of components can be in the primary and intermediate heat transport systems. The code can handle loop or pool designs, hot leg or cold leg pumps, and once-through steam generators or evaporator-superheater combinations. Additional flexibility is provided by the modular design of the code which makes it easy to modify or replace the treatment for one component without affecting the rest of the code. Computing speed is obtained by using semi-implicit or full implicit numerical schemes that allow the use of large time steps, especially in long, slow transients.

SAS4A/SASSYS-1 was designed to be comprehensive, flexible, and fast running. Even though it was designed mainly for analyzing shut-down heat removal transients, the code is quite capable of handling a very wide range of cases, from minor operational transients through hypothetical core disruptive accidents. The code runs fast enough to do extended transients of one day or more. On most of these computers the code can run considerably faster than real time. This chapter provides an overview of advanced model in the SAS4A/SASSYS-1 computer code.

3.1 Core and Fuel Treatment

The SAS4A/SASSYS-1 core treatment is taken from the SAS4A [4], In addition to heat transfer, coolant flow, and reactor power level calculations, the core treatment contains the SAS4A modules for treating severe accidents. These modules include the sodium boiling module, the molten clad relocation module, a fuel pin mechanics module for predicting pin failure, and modules for treating the motion of molten fuel after pin failure in voided or unvoided assemblies. Many of these modules are bypassed in a typical SAS4A/SASSYS-1 run, but they are available if needed.

The SAS4A/SASSYS-1 core is a multi-channel treatment in which each channel contains a pin, its associated coolant, and a structure [5], The structure represents wrapper wires and/or a representative fraction of the subassembly duct wall. Usually an average pin within a subassembly is modeled, but it is possible to represent a hot pin instead. A channel represents a subassembly or a group of similar subassemblies.

In general, finite differencing in both space and time is used in SAS4A/SASSYS-1. Up to 36 axial modes are used to represent a channel. Fig. 3.1 shows the radial and axial mesh used for temperature calculations in a channel. The whole length of the subassembly, from coolant inlet to coolant outlet, is usually represented by a channel. The coolant and structure nodes run the whole length of the channel. More radial nodes are used in the core and blanket regions than in the rest of the channel.

For each axial node in the core or blankets, between four and eleven radial nodes are used in the fuel, three are used in the cladding, one in the coolant, and two in the structure. In the gas plenum region a single temperature is calculated for the gas; and at each axial node there is one cladding node, one coolant node, and two structure nodes. In the

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reflector regions above and below the fuel pin there are two reflector nodes, one coolant node, and two structure nodes for each axial node. The coolant nodes are staggered with respect to the fuel, cladding, structure, and reflector nodes. The gas plenum can be either above or below the core.

For the pre-boiling temperature calculations, the fuel, clad, coolant, and duct wall temperatures for an axial node are solved for simultaneously, using a semi-implicit or fully implicit time differencing scheme that is numerically stable for large time steps. Temperature-dependent thermal properties are used. After boiling starts, the fuel pin heat transfer calculations stop at the clad surface, and the clad surface heat flux is used to couple with the boiling calculation.

The coolant flow in a channel is driven by inlet and outlet plenum pressures. All channels use the same inlet and outlet plenum pressures; so as the flow rates change, flow redistribution between channels is automatically accounted for. The coupling of all channels to common inlet and outlet plenums provides for hydraulic coupling between channels. The onset of boiling and inlet flow reversal in one channel can lead to a temporary rise in the inlet plenum pressure and an increase in flow in other channels. Either turbulent or laminar friction factors are used for a channel, depending on the

Fig. 3.1 Core channel node structure

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Reynolds number. The pre-boiling calculations use incompressible flow. Friction, inertia, orifice pressure drops, and grid-spacer pressure drops are accounted for. Also, the gravity head is re-calculated for every time step using the current coolant temperatures.

SAS4A/SASSYS-1 uses a point kinetics treatment for the neutron flux and fission power level. For its neutronics calculations SAS4A/SASSYS-1 treats detailed reactivity feedback from each channel. SAS4A/SASSYS-1 uses a decay heat treatment similar to that normally used for delayed neutron precursors. Up to six decay heat precursor groups are used, each with its own yield and decay constant. The time-dependent decay heat can be computed internally by the code as a function of burn-up and power history.

3.2 Reactivity Feedback Models

The key characteristic necessary for passive safety and inherent self-protection is an overall negative reactivity feedback response to reactor accident initiators. Because the passive safety mechanisms are the result of tightly coupled thermal, hydraulic, neutronic, and mechanical physical phenomena, analysis and investigation methods employing detailed computational models of the phenomena and geometry are required to permit accurate quantification of effects. Therefore, the evaluation of reactivity feedback effect is of a major consideration for all of the unprotected events in the advanced LMFR which adopts inherent and passive safety concept.

SAS4A/SASSYS-1 uses a point kinetics approximation for the neutron flux and fission power level. At any time, the net reactivity is the sum of a number of individual reactivity feedbacks that are determined by the transient thermal, hydraulic, mechanical, and neutronic state of the reactor. The feedback reactivities normally considered are fuel Doppler, coolant density, fuel and cladding axial expansion, radial core expansion, and control rod driveline thermal expansion. Reactivity feedbacks from fuel heating and coolant heating are tracked with first order perturbation theory.

The net reactivity is composed of nine reactivity feedback components:

dk(t) = dkp{t) + dkcs{t) + dkD{t) + dkd{t) + dkNa(t) + dkre(t)

+ (f) + W + A,/ W

where 5kp(t) = the user-defined reactivity5kcs(t) = control system reactivity5kD(t) = fuel Doppler feedback reactivity5kd(t) = fuel and cladding axial expansion feedback reactivity5kNa(t) = control density or voiding feedback reactivity5kre(t) = core radial expansion feedback reactivity5kcr(t) = control rod drive expansion feedback reactivitySkfu(t) = fuel relocation feedback reactivity

(1)

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5kci(t) = cladding relocation feedback reactivity

Global reactivity feedback coefficients resulting from Doppler effect, uniform radial core expansion, uniform fuel axial expansion, and sodium voiding in the equilibrium core were utilized, including expansion of the control drive line and reactor vessel.

Ill User-Defined ReactivityThis reactivity is intended for use when explicit reactivity feedback model is not available. Examples of the user-defined reactivity are a control rod insertion or withdrawl, or the dropping of fuel assembly during reloading.

For this option, IPOWER (Block 1, location 18) is set to 0 and the number of pairs of values of programmed reactivity and time inputs is entered in NPREAT (Block 1, location 18) > 0. The reactivity array is entered in PREATB (Block 12, location 29) and time input is entered in PREATM (Block 12, location 49). A maximum of 20 pairs may be entered in PREATB and PREATM. IFIT (Block 1, location 95) specifies the type of fits to use of the curve.

(2) Control System ReactivityThis reactivity is the value supplied by the reactivity control signal (JTYPE=-1) generated by the control system model INCONT (Block 5).

(3) Fuel Doppler Feedback ReactivityThe fuel Doppler feedback is calculated from the spatially dependent fuel temperature distribution and the input spatial distribution of the fuel Doppler reactivity coefficient. In each single-pin channel, the axial distribution of the radial pin-average fuel temperature is used to calculate the reactivity feedback.

The Doppler reactivity feedback in a subassembly is estimated from

SkD(t) = aD In7)(0)

(2)

where aD is the local fuel Doppler coefficient and is determined by adjusting linearly between the coolant-in and coolant-out values to correct for the effect of coolant voiding on neutron leakage. The coolant-in and coolant-out Doppler coefficients are entered in ADOP and BDOP (Block 62, location 62 and 63), and the axial weighting of the Doppler coefficients is input in WDOPA (Block 62, location 64).

(4) Fuel and Cladding Axial Expansion Feedback ReactivityThe DEFORM-4 (oxide fuel) and DEFORM-5 (metallic fuel) fuel behavior models are available in SAS4A/SASSYS-1 to predict transient fuel and cladding axial dimension changes, and in each single-pin channel, the reactivity feedback associated with fuel and cladding axial expansion are computed from first order perturbation theory.

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The fuel contribution to axial expansion feedback from node j is calculated from

= /»/(;) Ry(7)K(7 + l)-z^(;)]/A^(;)

+ m/U) #/(7) (7 +1) - z^ (;)] / A^r (;) - /My (;) Ry (7)(3)

where znf(j) and z0(j) are old and new fuel axial meshes, and AznHj) = zn±<j+l) - zn±<j)

A similar equation is used to calculate the cladding contribution to axial expansion feedback except that new clad axial meshes, ZnC(j) replace znHj).

The total reactivity change is then calculated from

= far (4)j

where sex is an effective axial expansion multiplier. The summation is only over the core nodes and the axial blankets are ignored in the fuel expansion feedback. In order to obtain an accurate value for the axial expansion reactivity feedback, the fuel worths input for the upper axial blanket nodes must be the worth of core fuel in the blanket region.

The cladding and fuel worths are input in arrays CLADRA and FUELRA (Block 62, locations 160 and 208). The effective axial multiplier is input in EXPCFF (Block 63, location 79). The simple axial expansion reactivity model is invoked by IAXEXP (Block 51, location 181).

151 Coolant Density or Voiding Feedback ReactivityThe coolant density reactivity feedback is calculated from the spatially dependent coolant density distribution and the input distribution of the coolant density reactivity coefficient calculated from perturbation theory. The reactivity feedback data is entered as a coolant void worth (the negative of the coolant mass worth), and the coolant density feedback reactivity is calculated from the time-dependent axial density distribution in each single­pin channel.

The reactivity feedback from coolant density change or two-phase coolant boiling are calculation from

(5)i J

where(pc)ji = coolant void worth in axial segment j of channel I Oji = average coolant void fraction in segment j of channel I (pc)ji are input in array VOIDRA (Block 62, location 112).

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(6) Core Radial Expansion Feedback ReactivityThe detailed radial core expansion model in SAS4A/SASSYS-1 accounts for radial core expansion due to thermal expansion of the hexcan load pads, thermal expansion of the core support grid plate, and transient bending of the core subassemblies due to radial temperature gradients and constraints imposed by radial restraint rings at the load pad elevations. Reactivity feedback is then calculated from the computed core dimension change and an input linear reactivity coefficient based on stand-alone neutronics eigenvalue calculations.

In the simple radial expansion feedback model, the radial growth of the core is determined by the expansion of the lower grid support structure and by the expansion of the duct walls at the above core load pads. The expansion of the lower grid support structure is assumed to be proportional to the rise is the subassembly inlet temperature above its initial steady-state value. The expansion at the location of the above core load pads is assumed to be proportional to the change in the average structure temperature at this location.

The radial expansion reactivity feedback is calculated from

('JATin + XMC(ATslp

%4C (6)

wheret = time, secondtl = time at the end of first main time step, second Tm(t) = coolant inlet temperature, K Cre = coefficient, $/K ATln = T;n(t) -Tin(tl), KXMC = distance from nozzle support point to core midplane, m XAC = distance from nozzle support point to above core load pad, m Tslp (i,t) = structure temperature (outer structural radial node) in channel i at the

axial node corresponding to the above core load pad Tslp (t) = TSLp(i,t) averaged over the channel i ATslp = TSLp(t) -TSLp(tl), K

The simple radial expansion model is invoked by specifying IRADEX (Block 1, location 36). Cre and XMC/XAC are entered as input variables RDEXPC and XMCXAC (Block 12, locations 78 and 79).

171 Control Rod Drive Expansion Feedback ReactivityFor the control rod driveline feedback model, it is assumed that the control rod drivelines are washed by the outlet coolant from the core. Thermal expansion of the drives due to a rise in core outlet temperature will cause the control rods to be inserted further into the core, providing a negative reactivity component. On the other hand, if the control rod drives are supported on the vessel head, and if the core is supported by the vessel walls, then heating the vessel walls will either lower the core or raise the control rod drive

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supports, leading to a positive reactivity component. Both the control drive expansion and the vessel wall expansion are accounted for in SAS4A/SASSYS-1.

The control drive expansion reactivity feedback is calculated from

= Ocr Az^ (7)

whereAzn = Azcr - AzvAzcr = the axial expansion of control driveAzv = the axial expansion of vessel wallaor, bcr = inputs entered in Block 12, locations 73 and 74

(8) Fuel and Cladding Relocation Feedback ReactivityThis component of reactivity feedback is computed from

(8)

wheremij(t) = the material mass at axial node j in channel i(Ak/Am)ij = the material reactivity worth in axial node j of channel i

(Ak/Am)ij are input in CLADRA and FUELRA (Block 62, location 160 and 208), whose curve may be input on the fuel (MZ) mesh or the coolant (MZC) mesh according to the input value of IRE AC A (Block 51, location 365).

3.3 Primary and Intermediate Heat Transport Systems

For the primary and intermediate loop thermal hydraulics calculations, SAS4A/SASSYS- 1 uses a generalized geometry as indicated in Fig. 4.2. A number of compressible volumes are connected by liquid or gas segments, and each liquid segment can contain one or more elements. This treatment allows SAS4A/SASSYS-1 to be used for and arbitrary arrangement of components, since compressible volumes and segments can be connected in an arbitrary manner.

Various types of elements can be used to make up a liquid segment. Liquid segments are characterized by incompressible flow, with the possible exception of the core element. The reactor core is a special element that is handled by the core channel treatment. Compressible volumes are characterized by pressures which drive the flows through the liquid and gas segments. If a compressible volume does not contain a cover gas, then the liquid is treated as compressible. All gas segments are treated as pipes. The gas flow through a pipe is calculated using an isothermal treatment by Shapiro [6],

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For solving the hydraulic equations for the primary and intermediate heat transport loops, the use of semi-implicit or fully implicit time differencing is more difficult to implement than explicit forward differencing, especially when using a generalized geometry with an arbitrary number of compressible volumes, segments, and elements. With an implicit scheme, the pressures and flows for all connected compressible volumes and segments must be solved for simultaneously. By linearizing the hydraulic equations for each time step, SAS4A/SASSYS-1 obtains a semi-implicit or fully implicit solution for the hydraulics equations without iterating.

Linearized semi-implicit or fully implicit methods are most useful for long transients in which temperatures and flows are changing slowly, since in such cases accurate results can be obtained with large time steps as long as the step sizes are small enough that changes during a step are small. For more rapid transients, the step size must be reduced, even with a fully implicit method; and for fast transients accuracy considerations may require comparable step sizes for any type of time differencing.

In principle, the coolant flows for all core channels could be calculated simultaneously, along with the primary loop hydraulics; but after the onset of boiling this would unduly complicate the boiling model. Instead, a somewhat relaxed coupling scheme is used to couple the core flow calculations with the primary loop hydraulics at the inlet and outlet coolant plenums. First, the primary loop hydraulics calculations for a time step are made before the channel flow calculations. Second, after the primary and intermediate loop hydraulics calculations are complete, the core channel coolant dynamics routines compute the actual channel flows for each channel independently, using the newly

Fig. 3.2 General heat transport system geometry

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calculated inlet and outlet coolant plenum pressures as boundary conditions. Third, the difference between the estimated core flow and the actual computed core flow for a time step is used to adjust the coolant masses in the inlet and outlet coolant plenums before the start of the calculations for the next time step.

3.4 Steam Generator Model

SAS4A/SASSYS-1 contains two steam generator options. One is a very simple option in which the user specifies the sodium-side temperature drop as a function of time. The other option [7] is a moderately detailed, but fast running, model. The transients of interest for SASSYS-1 usually do not involve rapid steam generator transients that would require a very detailed model that would consume large amount of computer time.

The moderately detailed model for an evaporator or a once-through steam generator was developed using an approach similar to that of Bein and Yahalom [8], This model uses moving nodal boundaries. Each axial node represents a well defined physical region with smooth, slowly varying water properties within the region.

For each of four regions in the evaporator, an energy equation and a continuity equation is written for the water. These equations include terms for the moving boundaries. For each region, an average heat transfer coefficient is evaluated in order to obtain the heat flux to the water. On the sodium side, single phase incompressible flow is assumed, and only an energy equation is used for each region. In addition, an overall loop momentum equation is used for the sodium in the evaporator plus any pipes attached to it. A separate model is used for the superheater. This model is simpler and faster running, since it does not use moving boundaries or deal with phase changes. A quasi-static approximation used for the stream side energy equation provides a very stable solution algorithm.

3.5 RVACS Heat Removal Model

In a RVACS, heat is transferred from hot sodium inside the reactor vessel through the vessel wall by conduction, to the guard vessel mainly by radiation, and to air flowing between the guard vessel and an outer shell. The air flows by natural convection. Figure3.3 shows the general RVACS model and nodding scheme. Wall temperature nodes are used for the reactor vessel, guard vessel, outer shell of collector cylinder (inside and outside), outer wall, and a constant temperature deep in the concrete or the ground. Air nodes are included for the down-comer and for the up-flow section. An air inlet section and an outlet stack are also included. Either vertical or non-vertical sections of vessel wall can be treated.

The reactor vessel wall can be made up of SAS4A/SASSYS-1 components, including a hot pool wall, a cold pool wall, a pipe wall, or an annular flow element wall. The annular flow element is a new type of liquid of flow element that has recently been added to

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SAS4A/SASSYS-1, mainly for modeling the RVACS. Both radiative and convective heat transfer from the guard vessel are modeled. Radiation from the guard vessel to the outer shell as well as convective heat transfer to air from the guard vessel and the outer shell are treated. The outer shell or collector cylinder is assumed to be insulated, but less-than- perfect insulation can be treated. Temperatures on both sides of the insulation are calculated. Heat transfer from the inside of the outer shell to the outside, and from the outside of the outer shell to the incoming air, is treated. Radiation from the outer shell to the outer wall is treated as well as convective heat transfer from the outer wall to the incoming air. Also, conduction from the outer wall to a constant temperature node deep in the concrete or in the ground is handled. As indicated in Fig. 3.3, one axial node is included above the liquid level in the vessel. This node is included to account for heat transfer through the outer shell between incoming and outgoing air. For this node, the heat transfer coefficient between the reactor vessel and the guard vessel is set to zero.

Inlet

node n+ 1 iquid level

node

3.3 RVACS model

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Chapter 4. Modeling of KALIMER by SAS4A/SASSYS-1

The input deck of SAS4A/SASSYS-1 for the KALIMER rector plant was prepared to perform the steady-state analysis. The base input deck contains all the data required for initializing the plant conditions prior to any particular transient. A majority of the design data was taken from the KALIMER design with breakeven equilibrium core. The method and assumptions used for the analysis follow the conventional guideline of SAS4A/SASSYS-1 code. The SAS4A/SASSYS-1 calculation utilized the same data source for the KALIMER breakeven core design [9] as used for the SSC-K analyses [10]. The generation of the base input data for the KALIMER breakeven core along with any assumptions used in the SAS4A/SASSYS-1 run is documented in Appendix A of this report. The numerical details for generating the input date for KALIMER are presented in this document

An overall plant component schematic was developed for modeling of the KALIMER design, as shown in Fig. 4.1, where major components are represented by appropriate SAS4A/SASSYS-1 modules. The model schematic closely represents the actual

He gas

PSDRS

Hot Pool

CCiRECold Pool

Inlet Plenum

Fig. 4.1 Schematic of the SAS4A/SASSYS-1 Model of the KALIMER plant

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KALIMER reactor design. The components of reactor vessel, IHTS and SG are represented by various volumes and flow elements in the model. The primary circuit contains all of the sodium which flows through the core in the reactor vessel. The sodium travels from the core into the hot pool, then through the IHX for the intermediate heat transport system. The sodium flows out of the IHX into the cold pool, then primary pump sucks the sodium through the flow guide surrounding the core. The circuit is completed by the sodium flowing back through the discharge pipe of EM pump into the inlet plenum and uthrough the core assemblies.

4.1 Core and Fuel

For the whole-core model, each of the SAS4A/SASSYS-1 channels represents a single, average pin in a subassembly, and several subassemblies are grouped together, so that a single channel may represent all the pins in a number of subassemblies. Pins with similar geometrical dimensions, power, flow, enrichment, burn-up, thermo-physical properties, and performance characteristics (reactivity feedback, mechanical, thermal, fluid dynamics) are grouped for modeling by a single channel. In this way, all of the pins in the KALIMER reactor were modeled with a multiple channel model.

The core of the KALIMER is represented according to the SAS4A modeling. According to the previous SAS4A/SASSYS-1 practice, it is sufficiently accurate to represent the core within the boundary of the first row of radial blanket assemblies except for control assemblies by three channels for analyzing the typical ATWS events. However the radial blanket assembly was included in the core model in the present analysis because the small core of KALIMER does not burden computer with heavy computation load. Therefore the KALIMER core is represented by four channels in SAS4A.

The grouping of the subassemblies into channels is done according to the following arrangement: One channel is selected for the hot assembly. The hot assembly is expected to have the highest temperature during any particular transient and it is most likely to be the assembly to reach any given failure threshold. The criteria for selecting the hot assembly are the highest power-to-flow ratio with a correspondingly high average power. All remaining drivers assemblies in the core are included in a single channel, and all internal blankets and all radial blankets are included in separate single channels. The subassemblies exterior to the row of radial blanket assemblies, such as control rod, reflector, and shield assemblies etc. are considered in the PRIMAR-4 model of the primary system. This way turns out to be computationally more efficient, without any real loss in accuracy.

The layout of the KALIMER metallic fueled core is shown in Fig. 2.2 and the assembly assignment in it's 1/6 core is shown in Fig. 4.2. There are 36 different individual assembly locations in the 16 core, including control rods, GEMs, and USS. The assemblies need to be grouped into a relatively small number of channels for the SAS4A

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core model as mentioned before. A detailed description of the assembly including assembly assignment number, flow grouping, and assembly power is given in Fig. 4.2. Assemblies located at (3,1) and (3,3) have the highest average power per assembly while assemblies located at (6,3) and (6,4) have the highest power-to-flow ratio. The later assemblies have a low average power per assembly compared with the first one. It was determined that the driver assembly located in the third row of the core (3,1) was the hottest assembly.

In the multiple channel whole-core model, each channel represents a single fuel pin and the associated coolant and structure. The structure field may be used to represent some part of the hex-can and the pin spacers. The four core channels are modeled by flow segment 1 (SI) as shown in Fig. 4.1. The driver and internal and radial blanket subassemblies are represented by the detailed SAS4A channel model. PRIMAR-4 sets all of the SAS4A channels to be represented by liquid element 1 (El), connecting compressible volumes CV1 and CV2, which simulates the core inlet plenum and hot pool, respectively. The SAS4A channels are set to be always the first liquid segment SI in PRIMAR-4. The core channel of El consists of four channels. The peak power channel (channel 1) is used to calculate a hot channel response. Average of the remaining driver fuel assemblies are grouped into the channel 2. Channel 3 is an average of the internal blanket assemblies. Channel 4 is an average of the radial blanket assemblies.

rFig. 4.2 Power and flow distribution in an 1/6 assembly

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The remainder of the core assemblies is represented using more liquid elements between CV1 and CV2. As shown in Fig. 2.2, the KALIMER core includes 6 control rod, 48 reflector, 54 B4C shield, 54 IVS, and 72 radial shield assemblies, which are not represented by the SAS4A core channels.

The control rod assemblies are represented by three liquid elements, E2, E3, and E4, where E2 and E4 are pipe elements with characteristics of the pin section of the assembly below and above E3. E3 is represented as the power producing region, which is called as a term "bypass channel" element in PRIMAR-4. This type of element is designed for simulating the power producing regions of the core which may exist outside of the SAS4A channels. Since all control rod assemblies are considered to be identical, the 6 control assemblies are represented with 1 set of these 3 elements duplicated 6 times. This is controlled by the multiplicity factors for the liquid segments. The pipe and "bypass channel" elements in PRIMAR-4 uses the same equation for calculating the liquid flow rate, so that the elements E2, E3, and E4 can be combined into one liquid segment (S2). However, the heat transfer calculations are different, so three temperature groups Tl, T2, and T3 are required for E2, E3, and E4, respectively.

In the same manner as for the control rod assemblies, the reflector and B4C shield assemblies are simulated by one set of three elements. The total flow areas of these assemblies are represented by only one flow segment (S3), consisting of three liquid elements of E5, E6, and E7, and corresponding temperature groups, T4, T5, and T6. Another set of three liquid elements is used to simulate the IVS, radial shield assemblies and the core bypass flow. The core bypass flow is associated with leakage at the grid plate and subassembly connection. This sodium flows up to the hot pool in the gaps between the subassemblies. Since this region does not have a defined geometry, small flow rates just large enough to ensure stability of the heat transfer calculation in PRIMAR-4 are assumed. These three elements E8, E9 and E10 are in liquid segment S4 and in temperature groups T7, T8, and T9.

Figure 4.3 shows representations of the core channel by SAS4A. The SAS4A channel model assumes a single pin geometry for the calculation, which extends from the bottom to the top of the subassembly. The single pin is divided into a number of axial zones, where fuel including sodium bond, gas plenum, and upper and lower reflector zones are represented. The axial nodes used for the KALIMER analysis are total 7 nodes in the lower reflector, 20 in the active fuel, 4 in the sodium bond, 6 in the gas plenum, and 4 in the upper reflector.

Radial and axial meshes specified by user are used for temperature calculations in a channel. For each axial node in the core, 11 radial nodes are used in the fuel, 3 are used in the cladding, 1 in the coolant, and 2 in the structure. In the gas plenum region a single temperature is calculated for the gas; and at each axial node there is 1 cladding node, 1 coolant node, and 2 structure nodes. In the reflector regions above and below the fuel pin,

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there are 2 reflector nodes, 1 coolant node, and 2 structure nodes for each axial node. The coolant nodes are staggered with respect to the fuel, cladding, structure, and reflector nodes. The scheme of calculation node is presented in Fig. 3.1. A specified fraction of the total reactor power is generated in fuel, cladding, blanket and sodium. The axial variation of power generation is governed by an input axial power profile.

The gap between the fuel and cladding is computed as a function of time. When the gap is closed, a direct input of the contact conductance is required. Since the metallic fuel has a tendency to contact with the cladding during its initial phase of irradiation, the gap was assumed to be close throughout the entire calculation time. The constant gap conductance of 1.324*105 W/m2K was used as done in the SSC-K analysis.

The neutronics data, including fuel and cladding worthies, coolant worthies, and Doppler, are averaged for each channel to form the neutronics characteristics of each channel. The average is weighted based on the number of each assembly in the core. The average

axial elevation (m)

4 segments

segments

.200

.000

-0.5585

-1.1170

Fig. 4.3 SAS4A axial zones and fuel nodes for KALIMER core

-28-

coolant flow rate is calculated in the same manner for each channel. The fuel temperature coefficient due to the Doppler effect at BOEC is on the basis of 1/T142 variation. The sodium void worths for the total voiding in the active core are 3.99 dollars at BOEC. For the partial voiding, all the regions have a positive sodium void worth. The radial expansion coefficients are -564 pcm/(% radial expansion). The total control rod worths are invariantly about 22.71 dollars during an operation cycle.

Six GEM assemblies are added to KALIMER in order to supplement the negative reactivity feedback that develops once the pumps have been tripped. When the pumps trip and the pressure drops, the sodium within the GEMs at the active core elevation is displaced by expanding helium gas, thus increasing the leakage of neutrons from the core. The induced negative reactivity (2.55 dollars) from GEM activation only is not enough to bring the core subcritical in any sodium-voided conditions. It should be noted that, due to the state of insufficient knowledge about the core during the KALIMER conceptual design, the uncertainties for the reactivity components are large.

4.2 Primary Heat Transport System

The input data to support the PRIMAR-4 model are contained in input block 3, INPMR4, and block 18, PMR4IN. Basically, INPMR4 covers the data governing the overall arrangement of all of the components in the model, while PMR4IN contains the associated geometrical, flow, and heat transfer data. Tables 4.1 and 4.2 list the PRIMAR- 4 models for the KALIMER reactor system. The liquid flow elements are grouped into flow segments for the fluid flow calculations and into temperature groups for the heat transfer calculations, as indicated in Table 4.3.

Compressible volume 1 (CV1) is the core inlet plenum. The hot pool is modeled by one volume, CV2, which contains hot sodium and cover gas. Most of the sodium flow leaves

Table 4.1 PRIMAR-4 model of the KALIMER: compressible volumes

VOLUME TYPE DESCTIPTION

PRIMARY LOOPS

1 1 Core inlet plenum2 7 Hot pool, plenum with cover gas3 8 Cold pool, pool with cover gas4 4 Annulus volume

INTERMEDIATE LOOPS

5 4 Intermediate loop pipe (hot side)6 9 Intermediate loop pipe (cold side)7 4 Intermediate loop pipe (cold side)

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CV2 through the IHX. KALIMER has 2 identical IHTS loops, each with its own steam generator (SG). The current PRIMAR-4 model of KALIMER is developed with one lumped IHX and its associated intermediate loop out to the SG. Flow segment of S5 represents the primary sodium of the IHX tube side. The elements of Ell, El 2, and El 3 represent the sodium flow on the shell side of the IHX, where E12 covers the active heat transfer section between the primary sodium and the intermediate loop. Ell and El3 are piping elements with characteristics simulating the inlet and outlet sections of the IHX. All three elements are in the same liquid segment, S5, but three temperature groups are required, T10, Til, and T12 for heat transfer calculation. The sodium leaving E13 flows into the cold pool, CV3.

The sodium is taken from the cold pool through the flow guide by the primary EM pumps. KALIMER has 4 EM pumps in the reactor vessel and two group pumps are modeled in Fig. 4.1. The first group represents 3 pump loops, while the other group represents one of the pump loops. This would be useful if the effect of the failure of one pump were to be analyzed, or if the effect of the breaking of 1 out of 4 the discharge pipes are to be investigated. The first group pump contains a flow path from El4 through El7 in liquid segment S6, going from CV3 to CV1. E14 and El 5 are the flow guide and the upward flow channel within the EM pump body, respectively. Pump discharge pipe feeding sodium into the core inlet plenum, CV1, consists of E16 and E17. E16 is associated with the vertical section of the discharge pipe coming down from the pump, and El7 with the horizontal section going into the core inlet plenum. The liquid elements El4 and El5 are in a lumped temperature group T13, and E16 and E17 are in a T14. This grouping of elements and temperature groups are repeated for E18 and E19 (T15), E20 and E21 (T16) for the second group pump (liquid segment S7). The EM pump representation was simplified for the present analysis because the KALIMER design was not detailed enough to be modeled by SASSYS-1. Therefore a simple pump model was utilized and the primary system flow rate was controlled as function of time by the user input.

KALIMER reactor design has a vertical liner near the reactor vessel wall, which is called reactor baffle. The height of the reactor baffle is such that during normal operation the baffle is higher than the sodium level in the hot pool, and the sodium in the annulus between the baffle and the vessel wall is stagnant. During a loss of heat sink event, the sodium in the system heats up and expands enough to spill over the top of the baffle opening a new flow path along the vessel wall and bypassing the IHX. Since heat flow from the hot pool through the baffle is modeled, some of heat removal to the vessel wall and the PSDRS is accounted for even before overflow of the baffle.

The annular boundary region dividing the hot and cold pools was modeled. Four IHXs and four EM pumps are located in the annular region. The reactor baffle on the top of the annular region and the separation plates on the bottom of the annular region allow flow from the hot pool and the cold pool, respectively, into the annular region, but this is greatly restricted by the close fit of the plates to the vessel components. The annular

-30-

region is represented by CV4, with each connected to the larger pool by a short pipe section of E22 and E23, respectively. This allows sodium to enter or leave the buffer region in response to temperature changes in the sodium. This volume is particularly important in long-term transients as it provides a considerable heat sink to moderate the temperature rise of the hot and cold pools. The heat transfer can be represented by the component-to-component heat transfer model specially provided by PRIMAR-4. The liquid element E22 between CV2 and CV4 is in the temperature group T17, and E23 between CV3 to CV4 is in T18.

4.3 Passive Safety Decay Heat Removal System

SAS4A/SASSYS-1 contains a model for transient analysis of heat removal by a RVACS (Reactor Vessel Auxiliary Cooling System) or a DRAGS (Direct Reactor Auxiliary Cooling System) in an LMFR. This model has been validated by comparing the model prediction against experimental data from a large scale RVACS/DRACS simulation experiment programmed at ANL [11].

Passive Safety Decay heat Removal System (PSDRS) in the KAIMER design has the same function as the RVACS. The PSDRS is modeled by the flow path connecting CV2 and CV3 over the reactor baffle. PSDRS is represented by one liquid segment of S10, consisting of two liquid elements of E24 and E25. Each element has individual temperature group T19 and T20. A fictitious valve element E25 is additionally modeled at the exit of the overflow path. This allows the PSDRS to be shut off during normal operation of the reactor, and activated when the sodium level in the hot pool rises above the top of the reactor baffle. When the sodium heats up, expands, and spills over the top of the liner, the sodium flows down the vessel wall and then into the cold pool bypassing the IHX. This direct contact of hot pool sodium on the vessel wall increases the heat removal rate by PSDRS.

The nominal heat removal capacity of PSDRS is considered to initialize the heat balance of the KALIMER plant. PSDRS begins the transient calculations operating at its full rated capacity for nominal power reactor conditions. Since the nominal power of PSDRS is only 1.3 MW, in comparison to the total reactor power of 392.2 MW, this has a negligible effect on the course of the transients until the SG is lost and power is reduced to decay heat level.

In the SAS4A/SASSYS-1 model, both radiative and convective heat transfers from the reactor vessel to the containment vessel are modeled. Radiation from the containment wall to the separation wall as well as convective heat transfer to air from the containment wall and the separation wall are treated. The separation wall is assumed to be insulated, but the conductive heat transfer in the separation wall can be treated. Temperatures on both sides of the insulation are calculated. Radiation from the outer separation wall to the concrete silo as well as convective heat transfer from the outer separation wall to the incoming air is considered. With perfect insulation on the separation wall and little heat transfer into the concrete, the calculation of air and wall temperatures on the down-comer

-31 -

side would be unnecessary. The air flow rate of natural circulation is computed based on the air gravity and the air flow pressure losses.

Table 4.2 PRIMAR-4 model of the KALIMER plant: liquid element

Liquid Flow Liquid Flow Liquid Flow TemperatureComponent Element Segment GroupPrimary Heat Transport System

Core 1 1 -

Control Rod Assembly:Lower section 2 2 1Blanket section 3 2 2Upper section 4 2 3

Reflector, B4C Shield Assemblies: Lower section 5 3 4Blanket section 6 3 5Upper section 7 3 6

Radial Shield IVS Assemblies:Lower section 8 4 7Blanket section 9 4 8Upper section 10 4 9

IHX:Inlet section 11 5 10Tube section 12 5 11Outlet section 13 5 12

Pump Group 1Pump inlet pipe 14 6 13Pump 15 6 13Pump outlet pipe 16 6 14Pump outlet pipe 17 6 14

Pump Group 2Pump inlet pipe 18 7 15Pump 19 7 15Pump outlet pipe 20 7 16Pump outlet pipe 21 7 16

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Table 4.2. PRIMAR-4 model of the KALIMER plant (cont.)

Liquid Flow Liquid Flow TemperatureComnonent Element Segment GroupAnnulus Volume

Hot pool side 22 8 17Cold pool side 23 9 18

PSDRSInlet section 24 10 19Outlet valve 25 10 20

Intermediate Heat Transport System

Vertical suction pipe 26 11 21Pump 27 11 21Pump discharge pipe 28 11 22IHX downcomer 29 12 23IHX tube side 30 12 11Vertical outlet pipe 31 12 24Horizontal pipe 32 13 25SG shell side 33 13 26Horizontal suction pipe 34 13 27

4.4 Intermediate Heat Transport System and Steam Generator

KALIMER has two IHTS which take heat from the PHTS out to the steam generators (SGs). The IHTS is a conventional pipe system transporting sodium between the IHXs and the SGs. These are modeled as identical loops, represented by the one loop. Each IHTS loop contains the shell side of IHX, intermediate loop pump, the sodium side of SG, and all necessary piping. The water side of SG is not modeled, but a simplified treatment is used instead. The pump in the cold return section of the IHTS loop is modeled in PRIMAR-4, which is represented by E27. The sodium flows through a long horizontal pipe from the SG building into the containment building, E28. The sodium then flows vertically down into the reactor vessel through the IHX central downcomer, E29. The intermediate sodium is on the tube side of the heat exchanger, E30, and flows vertically upward out of the IHX through E31. Another long horizontal section takes the sodium back to SG, E32. Since the IHX heat transfer section is already included in temperature group Til, the element E30 has the same temperature group T11.

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The SG uses the simple model available in PRIMAR-4. It is assumed that the SG rejects heat at their nominal full power capacity during the steady-state. The normalized temperature drop across the SG, E33, is specified as a function of time. This is easily changed to the other option, which specifies the SG outlet temperature as a function of time, if desired for a particular accident. The sodium flows out of the SG and returns to

Table 4.3 PRIMAR-4 model of the KALIMER plant: temperature elements

Liquid Comp.Vol. Temp. Elem. Elem.See. In Out Groun No. Tyne Description

1 1 2 0 1 1 Core subassemblies

2 1 2 1 2 3 Pipe2 3 2 Bypass channel3 4 3 Pipe

3 1 2 4 5 3 Pipe5 6 2 Bypass channel6 7 3 Pipe

4 1 2 7 8 3 Pipe8 9 2 Bypass channel9 10 3 Pipe

5 2 3 10 11 3 Pipe11 12 6 IHX, shell side12 13 3 Pipe

6 3 1 13 14 3 Pipe13 15 5 Pump impeller14 16 3 Pipe14 17 3 Pipe

7 3 1 15 18 3 Pipe15 19 5 Pump impeller16 20 3 Pipe16 21 3 Pipe

8 2 4 17 22 3 Pipe9 3 4 18 23 3 Pipe

10 2 3 19 24 13 Annular element20 25 11 Valve

11 6 7 21 26 3 Pipe21 27 5 Pump impeller22 28 3 Pipe

12 7 5 23 29 3 Pipe11 30 7 IHX, tube side24 31 3 Pipe

13 5 6 25 32 3 Pipe26 33 8 SG (sodium side)27 34 3 Pipe

-34-

the pump through the simple pipe, E34. The intermediate loops between CV6 and CV7 are represented by Sll and the loop from E29 to E31 is represented with one liquid segment, S12. The remaining loop between CV5 and CV6 is represented by S13.

4.5 Safety Criteria

The evaluation of the reactor safety uses four sets of acceptance criteria: reactor shutdown, shutdown heat removal, radiation exposure to plant personnel and offsite radiological dose. The acceptance criteria are based on the premise that if appropriate fuel design and coolable geometry limits are not exceeded and if radiological releases are limited so that the dose guidelines presented in 10 CFR 100 are not exceeded for the postulated site suitability source term, then the public health and safety are adequately protected. Temperature limits are established for the reactor core cladding, core sodium, PHTS sodium coolant boundary, and fuel centerline. Specific temperature limits for the PHTS are based on the type of materials used in KALIMER [12].

KALIMER has top-level design requirements for safety. Conservatively quantifiable criteria are set based on current knowledge of irradiated metal fuel and HT9 pin behavior to insure that these design requirements are met. These criteria are based on physical phenomena that govern the safety and reliability. Especially, the acceptance criteria for the anticipated transients without scram (ATWS), are: (1) no sodium boiling, (2) no structural integrity violation, (3) no cladding failure, (4) no fuel melting. The temperature limits are dependent on the specific KALIMER fuel and cladding compositions and are subjected to revision as additional experimental test data become available. Although the temperature limits may be modified somewhat over time, the phenomenological safety criteria are not expected to change. The following temperature limits for the safety acceptance criteria are taken from Ref. [12].

No sodium boilingProtection of the reactor structures is provided by limiting the potential for ATWS events to progress into energetic HCDA events. Because U-Pu fueled core has positive coolant voiding reactivity coefficient over much of the active core length, significant boiling must be avoided. Local boiling in the core may also result in an increased cladding failure rate as cladding and fuel-cladding interface temperature increase. The sodium boiling temperature depends on the pressure, which varies with sodium depth and pumping. In KALIMER, the in-core sodium boiling temperature is about 1343 K (1070 °C) if the pumps are operating and 1233 K (960 °C) if the pumps are off.

Maintain structure integrityThe ASME Code Level D limits are 1033 K (760 °C) over the short term (less than one hours) or 973 K (700 °C) over the longer term, i.e., more than one hour. The structural temperature will be similar to the average core outlet sodium temperature although they will lag sodium temperature significantly during the early portion of a transient.

-35-

No cladding failureCadding rupture is the principal fuel mechanism that release fission products and fuel into the coolant. Failure by cladding creep rupture, with cladding thinning by fuel-cladding liquid phase formation, is the appropriate mechanistic cladding breach criterion. This criterion is simplified for the conceptual design into a cladding temperature limits that serve to limit the cladding creep strain to magnitudes less than that associated with cladding rupture. The ferritic alloy HT9 has significant degradation in creep strength at elevated temperature. For the conceptual design phase of KALIMER, a simplified temperature limit of 790 °C (1063 K) at the cladding mid-wall has been selected to preclude early cladding rupture (less than 2 hours).

No fuel meltingSeveral tests have demonstrated that extensive fuel melting doest not affect the basic pin failure mechanism. Based on the aggregate of metal fuel tests, centerline fuel melting, even extensive melting exceeding 80% of a given cross-section, is not a problem and does not result in pin failure. Fuel melting temperature is well above the minimum temperature for formation of fuel-cladding liquid phase, except for the case of extremely high coolant temperature.

Even though the centerline molten fuel at the overpower transient does not contribute to the cladding failure, limitation of the amount and time duration of molten fuel is given. Fuel melting should be less than 50% of pin cross-sectional area for less than 2 minutes. Equivalent fuel temperature greater than 1070 °C (1343 K) for less than 2 minutes eliminates the potential of the fuel motion reactivity effect.

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Chapter 5. Analyses Results

5.1 Steady State

The base input deck of SAS4A/SASSYS-1 was set up to perform the steady-state analysis and is listed in the appendix A of this report. The base input deck contains all the data required for initializing the plant conditions prior to any particular transient. A majority of the design data was taken from the KALIMER design with breakeven equilibrium core [9], and the remaining data were deduced from conservative engineering judgment.

For this analysis, the steady-state option provided by SAS4A/SASSYS-1 was intentionally not used. Instead, a null transient calculation was made for steady state conditions at full power. The steady-state run is executed until either the specified numbers of steps have been run or until the maximum fractional change from step to step in component-to-component heat transfer is less than the specified convergence criterion. After the completion of the steady-state run, the reactivity components are set to zero before the start of the regular transient calculation.

The major system parameters at the full power steady-state conditions, obtained from the null-transient calculation, are compared with the design data in Table 5.1. The SAS4A/SASSYS-1 code predicts well the steady state conditions of the KALIMER design. In the table, the sodium temperatures at the SG inlet and outlet are not available, because SAS4A/SASSYS-1 used the simple option in which the user specifies the sodium-side temperature drop as a function of time.

The dynamic behaviors of important system parameters during the full power normal operation are shown in Figs. 5.1 through 5.6. The normalized core power calculated by SAS4A/SASSYS-1 is shown in Fig. 5.1. The sodium temperatures in the hot and the cols pools are indicated in Fig. 5.2. The variations of reactivity feedback components in Fig.5.3 are so small that their propagations into the transient case are negligible. The flow fraction in each core channel is shown in Fig. 5.4. Temperature distributions of the in- core assemblies and PSDRS are illustrated in Figs. 5.5 and 5.6, respectively.

Figs. 5.7 through 5.9 indicate the radial temperature distributions in the fuel slug along the active core of 1 m for channels 1 through 3, respectively. The fuel region consists of 20 axial nodes and each axial node is divided into 11 equal distance segments in the radial direction. The highest fuel centerline temperature in the driver assembly occurs at the 12th node from the bottom of fuel because of a cosine-shape axial power. The peak fuel centerline temperature of the hot assembly calculated by SAS4A/SASSYS-1 is 938.43 K.

-37-

Table 5.1 Major plant parameters at steady-state condition

Plant Parameters Design SAS4A/SASSYS-1

Core Power, MWt 392.2 392.2

Primary flow rate, kg/s 2143.1 2143.1

Core inlet temperature, °C 386.2 385.25

Core outlet temperature, °C 530.0 529.95

IHX inlet temperature, °C 529.8 529.85

IHX outlet temperature, °C 385.0 384.85

Cover gas pressure, Pa 10133 10133

Cover gas temperature, °C NA 522.85

Cold pool level, m 10.63 10.687

Hot pool level, m 15.63 15.697

Pump head, m 83.61 83.61

Intermediate flow, kg/s 1803.6 1803.6

SG outlet temperature, °C 339.0 NA

SG inlet temperature, °C 511.0 NA

1.2

1.0

o

% 08

<D$ 0.6

CL

roEoZ 0.2

0.00 500 1000 1500 2000

Time, sec

Fig. 5.1 Normalized power (steady state)

total power decay heat

-38-

900

800-

700Q.E<D

CL 600-

500

< 0

2000

Time, sec

Fig. 5.2 Pool temperature (steady state)

500

DoppleraxialradialCRDLsodium

1500 20001000

Time, sec

Fig. 5.3 Reactivity components (steady state)

1000-

100-

o 10

.channel 1

IHTS loop

IHX primary

. channel 3 channel 4

- channel 2

-l-------1-------'-------1-------'-------r500 1000

Time, sec

1500 2000

Fig. 5.4 Flow distribution^steady state)

-39-

1000

950-

900-

700-

Fuel centerline

500 15001000

Time, sec

Fig. 5.5 Fuel temperature (steady state)

2000

800

700

2 600

cl 500E

f—£ 400□COCL

300

2000 500 1000 1500 2000

Time, sec

Fig. 5.6 PSDRS temperature (steady state)

1 1 1 I 1 I 1

^ Reactor vessel

^/Containment

pinner separator -

Air outlet -

^/ Outer separator Outer wall

Air inlet

i | i | i | i

Fuel centerline

900-

850-

800-

750-

Fuel boundary700-

Hot Assembly

Axial elevation, m

Fig. 5.7 Radial fuel temperature in the hot assembly (steady state)

-40-

950

Fuel centerline900-

850-

800-

750-

Fuel boundary700-

Driver Fuel Assembly

-------- 1------- 1------- 1------- 1------- 1------- 1------- 1------- 1------- 1-------0.0 0.2 0.4 0.6 0.8 1.0

Axial elevation, m

Fig. 5.8 Radial fuel temperature in the driver assembly (steady state)

Fuel centerline

Fuel boundary

Inner Blanket Assembly

Axial elevation, m

Fig. 5.9 Radial fuel temperature in the inner blanket assembly (steady state)

-41 -

5.2 Unprotected Over Power Transient (UTOP)

One of the traditional accidents that has been analyzed is the unprotected transient overpower (UTOP) and this event results when positive reactivity is inadvertently inserted into the core and there is a complete failure of reactor protection system (RPS). The limiting case assumption is that all the control rods are accidentally removed. This event is bounded by the amount of reactivity available in the control rods. Doppler feedback is the usual mechanism to limit an overpower event of the core. But the metallic fueled core has small Doppler feedback due to hard neutron spectrum, and the UTOP can be a very challenging event for the KALIMER core.

In the case of the KALIMER plant, which operates at near atmospheric pressure, there is no available driving force for removing a control rod faster than its normal drive speed. In order to account for uncertainties and to be conservative, a total of 30 cents has been adopted as the UTOP initiator for the analysis. It is also assumed that the shim motors withdraw the control rods at the rate of 2 cents per second, corresponding to the maximum speed of the shim motor. Thus, the UTOP is assumed to insert 2 cents per second for 15 seconds. This relatively low control rod reactivity worth is due to the high thermal conductivity of metallic fuel, and the low cold-to-hot reactivity swing necessary for ascension to power.

For this analysis, it is further assumed that the primary and secondary sodium flows remain at the rated conditions for the UTOP event and that the feedwater is sufficient to keep the sodium outlet temperature from the SG constant. Thus, the four EM pumps are assumed to continue to operate at nominal conditions. No plant protection system action was taken during this transient so that the reactor power changes only in response to passive feedback of reactivity as the transient evolves.

The main concern of the UTOP analysis is to evaluate the system response by nuclear- kinetic and thermal-hydraulic effects that involve inherently shutting the core down to acceptable power levels, which precludes coolant boiling and fuel damage. Since such severe situation occurs during the initial period extending over the initial several hundred seconds of the transient, the SAS4A/SASSYS-1 calculation was terminated at 10 minutes by the user.

In the SAS4A/SASSYS-1 analysis, the initial reactivity insertion leads to a power increase, which raises the fuel, coolant, and structural temperatures. The power and flow transients during the initial 600 seconds are shown in Fig. 5.10. The reactor power reaches a peak of 1.50 times the rated power at 15.0 seconds and then slowly decreases to seek equilibrium with the available heat sink provided by the coolant system heat capacity and the heat rejection by the steam generators. The power begins to level off at1.05 times the rated power by 600 seconds. The core flow stays constant as shown in the figure.

The temperature increases in the fuel, coolant and structures bring reactivity feedbacks due to the fuel Doppler effect, fuel and cladding axial thermal expansion, coolant density

-42-

decrease, radial core dilation by structural thermal expansion at the above-core load pad (ACLP) plane, and thermal expansion of the control rod drivelines. The evolution of these reactivities is depicted in Fig. 5.11. The net reactivity, which is the sum of the assumed reactivity insertion and the feedbacks, rises initially with the inserted reactivity, but soon peaks and falls as the negative feedbacks counter the only positive feedback from coolant density decrease. The net reactivity eventually decreases to near zero, and in the long term, begins a slow, low amplitude, negative-to-positive oscillation as the reactor adjusts to the heat rejection provided by the steam generators.

The rise in fuel temperatures first increases the Doppler absorption of the neutrons and then triggers the fuel’s elongation. Doppler feedback is the fastest acting feedback mechanism. Fuel temperature is instantly affected by the core power level and is a practically instantaneous indicator of the power excursion. Metallic fuel expands significantly as it heats. The axial expansion of the fuel is controlled by the expansion of the cladding, since the metallic fuel has less strength than the cladding.

Thermal expansion of the sodium coolant produces a reactivity feedback effect. Higher sodium temperatures create a harder neutronic spectrum, which generates a positive reactivity feedback as shown in figure. For the KALIMER reactor with sodium-cooled and mixed plutonium-uranium core, the net feedback effect from the coolant thermal expansion is positive. It should be pointed out that sodium density feedback is the only positive reactive feedback.

The higher sodium temperatures cause the thermal expansion of the control rod driveline and radial expansion, which are negative feedbacks. The control rod drivelines have a large time constant and are slow to act compared to core radial expansion. The code result shows the transient of vessel expansion, which withdraws the control rods and results in decreasing of negative reactivity, at about 70 seconds and gradually increases after then.

The radial core dilation due to thermal expansion at the ACLP plane adds negative reactivity that eventually limits the power increase and contributes to the power reduction that follows. The radial dimension of the core is determined largely by assembly spacing. The spacing is determined by the grid plate at the bottom of the core and by the ACLP at the above the active core. Radial thermal expansion of the core support structure is a relatively slow feedback mechanism, because the hot fuel must increase the cladding temperature first and then the coolant. The coolant must then transport the heat to the load pad planes and heat the ducts/load pads. As a result, spreading of the core leads to a negative reactivity feedback. For the present SAS4A/SASSYS-1 analyses, a detail mechanistic model for calculating the radial displacement due to thermal expansion was used.

Although the reduced power decreases the worth of Doppler, axial expansion, the control rod driveline and radial expansion effects cause the total reactivity to become slightly negative and re-stabilize the power.

-43 -

The fuel temperature is an important parameter for fast transients, on the order of seconds to a few minutes. If the fuel temperature exceeds the solidus temperature then there is the possibility that the resulting molten fuel region may influence the fuel relocation. Figure 5.12 shows the coolant inlet and peak fuel, cladding, and coolant temperatures in the nominal, in hottest fuel element channel during the UTOP accident. Also shown is the minimum coolant boiling temperature (“saturation”) at the top of the reactor core, the location of the peak coolant temperature. It should be pointed out that the fuel and cladding temperatures are taken from the 14th axial node, and the coolant temperature are from the 21th axial node in the hot channel assembly, which means those temperatures may not be the highest values into the transient. The peak fuel centerline temperature predicted by SAS4A/SASSYS-1 is 784 °C, and it is 286 °C below the fuel temperaturein criteria (1070 °C).

The cladding temperature is an important parameter for slow transients, on the order of several minutes to hours. The eutectic penetration occurs over time at specific temperature. The cladding temperature predicted by SAS4A/SASSYS-1 reaches maximum level of 633 °C, which is substantially below the threshold for eutectic formation (790 °C) and provide a large safety margin. Therefore no cladding damage is expected during UTOP.

The sodium coolant temperature is another important parameter for slow transients. The ability to remove decay heat through the PSDRS, to maintain structural integrity, is dependent on the coolant temperature. The peak sodium temperature in the hot channel calculated by SAS4A/SASSYS-1 is 614 °C, which temperature is also significantly below sodium boiling point (1070 °C). At all times in the transient, the margin to coolant boiling is greater than 450 °C. The average core outlet temperature reaches a peak of 580 °C, which is also below the acceptance criteria of 760 °C.

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NO

RM

ALI

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POW

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R FL

OW

KALIMER-i GO UTOP

» tgt.ji- ^ ?.c_-/_r-j0£>_j _rLyyv •.utcMxyvyLN

ano vTIME. SEC,

Fig. 5.10 Normalized power and flow during UTOP

KALiMER-150 UTOP

* t-.L~ = c-op^Lcn ■■■ r.'.d, cxr ■ ccqu'.nii HRQGRAViUED ■ JSftEHP. j "PDL EXF. ■ PUD.

TIME. SEC.10U.C

Fig. 5.11 Reactivity feedback components during UTOP

-45-

KALIMEA-150 UTOP

O - ^^TL'R.'.T-QN =_ (^LV.D- INLET

x o.u luu.o yuLi.u so; o 4000 ooo.c swo° TIME: SEC.

Fig. 5.12 Fuel temperatures during UTOP

5.3 Unprotected Loss of Flow (ULOF)

In the KALIMER-150 design, the coolant pumps are specified as an electromagnetic (EM) design equipped with synchronous motor-generator (MG) sets to provide inertia for flow coast down. Power to the MG sets is provided by a source external to the unit. The initiator for the unprotected loss of flow (ULOF) accident is assumed to be a failure of the normal power supply for the primary and intermediate loops coolant pumps. The offsite power supply for the EM pump is not a safety-grade system, thus a loss of flow event is of high probability to be considered “anticipated” in the KALIMER design.

The reduced primary coolant flow normally leads to a reactor scram due to a high flux-to- ftow ratio. For this event to be interested, it is assumed that the RPS fails to detect the mismatch or that the control rods fail to insert. The ULOF is assumed to start with a trip and coastdown of all of the primary pumps. The accident sequence is driven by the loss of forced coolant flow in a reactor operating initially at full power. Power level is determined by inherent reactivity feedbacks and GEM during the entire transient.

A loss of power supply to all primary pumps may occur while the reactor is operating in the power mode. Then the flow rate in the primary loop coasts down while the forced circulating flow in the intermediate loop maintains. The normal heat removal through the IHXs and SGs is available in this event. Also the natural circulation in the PHTS in conjunction with the PSDRS effectively removes the core decay heat.

- 46 -

For a loss of flow accident, the power to flow ratio is the key parameter that determines the consequences of the accident. As long as enough coolant flow is available to remove the generated heat, the fuel temperature can be maintained at acceptable levels. Therefore the pump coastdown plays an important role for the plant safety and depends on the capacity of the pump synchronous generator. Since the detailed design data for the KALIMER EM pump was not available to date, the EM pump model provided by the SAS4A/SASSY-1 code could not be used in this analysis. Instead the coastdown curve of the KALIMER EM pump was directly used as input data in the tabular format of flow vs. time. Therefore the pump flow rate behaves the coastdown characteristic curves after the pump trip, as shown in Fig. 5.13. This is the same way used in the SSC-K calculation.

Figure 5.14 shows that the reactor power level decreases with the flow rate during the initial 600 seconds. Trip of the primary pumps at 0 seconds causes a rapid flow reduction with a decrease of reactor power level. The coastdown flow rate gradually decays following pump trip during the initial 100 seconds. Over the longer term, the core flow is driven by natural circulation in the PHTS. The natural circulation flow rate by SAS4A/SASSYS-1 is 4.9 % of the rated flow at 600 seconds. The power immediately begins to drop and reaches decay heat level by about 90 seconds since there is enough negative reactivity insertion due to OEMs. In the KALIMER-150 design, the six GEM subassemblies are located in a high leakage region on the core. The power level drops to about 2.8% of the nominal power by the end of 600 seconds.

The changes in the reactivity by SAS4A/SASSYS-1 are shown in Figs. 5.15. The GEM reactivity (“PROGRAMMED”) clearly overwhelms all other reactivity effects and provides a negative shutdown margin. The GEMs reach their full worth at about -224 0 in about 55 seconds, and the worth remains throughout the entire transient. The fast insertion of negative reactivity reduces the power keeping the power-to-flow ratio

flowratehead

0.6 -

0.4 -

0.2 -

Time, seconds

Fig. 5.13 KALIMER primary pump coastdown curve

-47-

favorable. At the end of 600 seconds, the net reactivities predicted by SAS4A/SASSYS-1 is -1.73 $. During the first 600 seconds of the event, the positive feedbacks are offset by the GEM negative feedback and the core maintains a subcritical shutdown.

The ULOF condition indicates the core is over-cooled compared to the reference temperature at the nominal operating condition. The Doppler feedback shows a positive response because the fuel actually cools down. Doppler feedback is the fastest acting feedback mechanism. The usual positive reactivity feedback from sodium density becomes negative after 16 seconds into the transient because of core over-cooling by GEMs. The CRDL/RV reactivity feedback turns slightly positive due to vessel expansion. The reactivity feedbacks for the axial and radial expansion are slightly negative in the early transient but they soon become positive since their temperatures become lower than the reference ones.

The sodium pool temperatures slowly change by the big thermal sink due to the large primary sodium inventory and the metal mass. The hot pool temperature slightly risen during the early period of the transient gradually decreases, because the heat removal through natural circulation by the IHTS and PSDRS is available. The neutronic feedbacks, which reduce the power, are related to the power-to-flow ratio, which determines the sodium temperature in the core.

Figure 5.16 illustrates the temperature distribution at the twelfth fuel node from bottom of the core in the hot assembly. In the figure the temperatures of the fuel center line, clad, and sodium at the exit of the hot channel are shown. The rapid insertion of the negative reactivity reduces the power, keeping the power-to-flow ratio favorable, so that the heat generated in the fuel can be removed without damaging the fuel. The rapid increase of the fuel temperatures in the first few seconds is attributed to the power-to-flow mismatch, and subsequent rapid drops of those temperatures result from the quick negative feedback of the GEMs. The fuel temperatures rise again due to the power-to-flow mismatch and reach in the equilibrium condition when the natural circulation flow is established at the decay heat power level. The reactor heat is transported to the heat capacity provided by the primary and intermediate coolant systems inventory in natural circulation mode. Heat is also rejected by the PSDRS.

The highest peak fuel temperature at the beginning of the transient is 676 °C at 5 seconds. There is substantial safety margin for the ULOF event. The peak clad temperature predicted is 594 °C and it is substantially below the threshold for eutectic formation. The duration of the elevated temperature is very short. It provides a large safety margin and no cladding damage is expected. As seen in Fig. 5.13, the peak sodium temperatures in the hot driver calculated is 585 °C. The temperature is also significantly below sodium boiling point. Over the long term, The peak average core outlet temperature is 556 °C and no challenge to the structural integrity is expected.

The absence of pump coastdowns can be a major safety concern because the passive reactor shutdown requires some time to bring the fission power down. Sensitivity study on the pump coastdown failure mode was conducted to find the maximum allowable

-48-

number associated with pump coastdown failure satisfying the safety acceptance criteria. Analyses were carried out by the SAS4A/SASSYS-1 code to investigate the pump coastdown failure case.

Figures 5.17 and 5.18 indicate the transients of normalized power and flow, and the fuel temperature distribution in the hot assembly during the ULOF with one pump coastdown failure, respectively. Figures 5.19 and 5.20 indicate the same parameters as presented in Figs 5.17 and 18 for the ULOF with two pumps coastdown failure. For these two coastdown failure cases, the fuel centerline temperatures predicted by SAS4A/SASSYS-1 are below the melting temperature of fuel (1343 K). The clad temperatures for two cases are also below the threshold for eutectic formation (1063 K). Therefore a large safety margin and no cladding damage are expected during these transients.

Figures 5.21 and 5.22 indicate the normalized power and flow transients, and the temperature distribution in the hot assembly during the ULOF cases with three pumps coastdown failure, respectively. In the case with three pump coastdown failure, the fuel centerline temperature rapidly increased to melting point at 11 seconds and the clad reached 1063 K at 3.5 seconds. The sodium coolant started boiling at about 8 seconds.

KALIMER-150 ULOF

* TO":''- =T;'i.VEr Cl \X\ j!_-J _ J J_l_OVV i_7izOAVL™'E5.

300.0TIME. SEC.

Fig. 5.14 Normalized power and flow during ULOF

-49-

CH

AN

NEL

1 TEM

PER

ATU

RE.

DEG

. CKALIMER-150 ULOF 6/ 1

> :Jtr □ nor^LEn ^ had. ex;1. . cjo.amGRAMME 1CFL3-EKP.

-2.0LI

-s.ond.g 100.U o yuu.o ■ius.u ioo.o eco.o

TIME, SEC.Fig. 5.15 Reactivity feedback components during ULOF

KALIMER-150 ULOF

1MM - Q 1:UL)0-_J;LhL_________ “ r>Lhl

&56.0 -

300.0TIME. SEC.

Fig. 5.16 Fuel temperatures during ULOF

-50-

NO

RM

ALI

ZED

POW

ER O

R FL

OW

KALIMER-I50 ULOF-M COAST FAILURE

■ iQiAi.ho mz BsitiALsmi™

Fig. 5.17 Normalized power and flow during ULOF with 1 pump coastdown failure

SAS4A/SASSYS-1 1 pump failureFuel centerline

900-

Fuel boundary

800-

Coolant

700-

Time, sec

Fig. 5.18 Fuel temperatures during ULOF with 1 pump coastdown failure

-51 -

NO

RM

ALI

ZED

POW

ER O

R FL

OW

KALI ME R-150 ULOF+2 COAST FAILURE

5DD.0

Fig. 5.19 Normalized power and flow during ULOF with 2 pumps coastdown failure

SAS4A/SASSYS-1 2 pumps failureFuel centerline1000-

Fuel boundary

- Clad— Coolant

800-'

700-

Time, sec

Fig. 5.20 Fuel temperatures during ULOF with 2 pumps coastdown failure

-52-

KALIMER-150 ULOF+3 COAST FAILURE 7/5/04

* tq-ai p^Ea fctitifcBLJJElfflUL. ■SL^Y±(^EE:4

TIME, SEC,

Fig. 5.21 Normalized power and flow during ULOF with 3 pumps coastdown failure

KALI ME R-150 ULOF+3 COAST FAILURE

u ■. saimaumi ilml" NLz6 hUbL

40.0TIME. SEC.

Fig. 5.22 Fuel temperatures during ULOF with 3 pumps coastdown failure

-53-

5.4 Unprotected Loss of Heat Sink (ULOHS)

The ULOHS is assumed to start with loss of heat rejection capability at all of the SGs, with primary and intermediate loop pumps continuing to run. The only heat removal is conducted by the passive heat removal system of PSDRS. Further, it is assumed that no plant protection system action including reactor scram is taken during this transient, so that the power level is changed in response to the thermal reactivity feedbacks. The course of the accident is determined by the reactivity feedback due to the higher temperatures and the capability of the PSDRS to absorb the power generated.

The ULOHS tends to be a longer-term transient than the others, because it does not end until the system temperatures have increased to the point where the fission process is shut down, leaving only decay heat generated in the core, and where the decay heat generation rate is within the capability of the PSDRS. For the first few minutes, at least until low- power equilibrium is established, the decay heat greatly exceeds the heat removal capability of the PSDRS, so the entire sodium inventory of the reactor vessel heat up until the thermal feedback reduces reactivity, causing the power to decline. The time it takes to reach the equilibrium temperature at which power has fallen to match the capability of the PSDRS to reject heat passively is determined by the heat capacity of the reactor vessel itself and the sodium and structures it contains. The larger the reactor vessel, the longer it is before heat removal must take over to keep temperatures from becoming unacceptable, and the smaller the needed capacity of the passive heat removal system.

The power history plot in Fig. 5.23 indicates that negative reactivity associated with the inlet temperature rise is sufficient to reduce the reactor power to decay heat level within the first hour of the accident. The power gradually decrease and reaches to the decay heat level by about 2500 seconds into the transient.

With full reactor power being transferred to the coolant, the primary and intermediate coolant systems heat, and the reactor inlet temperature rises. This introduces multiple reactivity effects, but the overall inlet temperature coefficient is negative, and the rising inlet temperature reduces reactor power. Fig. 5.24 shows the reactivity feedbacks computed by SAS4A/ASSYS-1 for the ULOHS accident. As shown in the figure, positive reactivity feedbacks result from heating of the reactor vessel that effectively withdraws CRDL, and from the net temperature increase of the coolant in the reactor. But the negative reactivity contributions from fuel Doppler effect, fuel axial expansion, and thermal expansion of the core support structure cause the net reactivity to be negative. This acts to reduce the reactor power level as the system attempts to reach thermal equilibrium with the only available heat sink.

Fig. 5.25 shows that the associated collapse of the reactor temperature rise tends to equilibrate all temperatures just above the original average temperature. SAS4A/SASSYS-1 predicts the peak transient coolant temperature in the ULOHS accident is 617 °C at 2400 seconds and all temperatures converge to about 615 °C after then. The temperature reached are nearly 300 °C below the sodium boiling temperature,

-54-

and about 150 °C below the temperature which could cause long-term damage to full element integrity.

During the initial period, the sodium pool heat sink absorbs the decay heat that exceeds the capacity of the PSDRS, without reaching temperatures that damage the core. The KALIMER eventually cools until it becomes neutronically critical again, at a power matched to the capacity of the PSDRS. Figures 5.26 through 5.28 show the normalized power history, reactivity feedback transient, and fuel temperature distribution in the hottest channel by 40,000 seconds (11.1 hours) for the ULOHS accident. It is apparently shown that all system parameters reach to a stable condition, which means the core decay heat is well removed by the PSDRS in the long term-cooling phase.

Figure 5.29 shows the heat generation rate in the core and the heat removal rate through the PSDRS. Since the fission power is not saved in the code output after the decay heat fraction becomes greater than the fission power, it’s plot after 12500 seconds does not appear in the figure. The heat removal capacity by the PSDRS reaches to 5.25 MWt at about 4000 seconds and it stays constant after then. The PSDRS heat capacity exceeds the decay heat rate at about 5100 seconds and the reactor system begins to be cooled in the long-term cooling mode. Figure 5.30 indicates the temperatures of the reactor vessel, containment wall, separator wall, and air at the outlet during the operation of the PSDRS. The 20 °C cold air entered the chimney of the PSDRS is heated by about 160 °C at the outlet channel.

KALIMER-150 ULOHS

"PT.-M pp'-vm u C: iANNC, I r.OVi * decay ruwin

u.O -mtrn.n sctiao

TIME. SEC.Fig. 5.23 Normalized power and flow during ULOHS

-55-

CH

AN

NEL

1 TEM

PER

ATU

RE,

DEG

. C

REA

CTI

VIT

Y $

KALI MEM 50 BLOWS

• .NET........................ d_I?grRtgfl_ ^ HAJ. bX.-1. - COJUJt.■j PPOGAAMMEB a CXI7 f enpLEXp.

no 101X.L1 2000.0 sloo.u 40&0.0 oooo oTIME, sec;

Fig. 5.24 Reactivity feedback components during ULOHS

KALIMER-150 ULOHS

« s..'',runAT cr-j <2_ cl-d_____■■ INLZ~

0.0 1(100.0 20UU.L UCUU.O -1(100.0 L. 000.0

TIME. SEC.Fig. 5.25 Fuel temperatures during ULOHS

-56-

FiEA

CTI

VilY

, S

FOR

MA

LIZE

D PO

WE

R O

h FLO

W

KAL:MERD50 ULOHS

* TO "A ^p;V~R g r: ANNF 1 FI Ci'.'V ■ DEMY P(TW?R

Ij.tixltf b.DHltf .Ck Li' if £.Uk 1C £ Lv;1u' iS.tolti S.-L-xOYtaH)TIME: SEC.

Fig. 5.26 Normalized power and flow during ULOHS (long term period)

KAUMER-150 ULOHS

................... 2_!^TL=1^_ - i.^u. txr. ■' oojlw ilj.2D™DAL'L=P.. iiLEX': - ci:=xr \ FufeL ,..

1.5X1P 2.UMC

TIME, SEC.Fig. 5.27 Reactivity feedback components during ULOHS (long term period)

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CH

AN

NEL

1 TEM

PER

ATU

RE.

DEG

. CKALI ME R-150 ULOHS

*.SAiudAjm._ d cl* j0_hUEL________ i iNL-T

Li.Uxltfb.talU* l.'LXC 'J I.Linlt1 £.CVi10 a.GisIC 3.0k" 'j

TIME, SEC.

Fig. 5.28 Fuel temperatures during ULOHS (long term period)

— fission power • • • decay heat- -PSDRS

0.1 -heat balance at 5100 s

0.01 -

Time, s

Fig. 5.29 Heat balance between core power and PSDRS heat removal

-58-

800-

700-

600-

— reactor vessel— containmnetwall

exit air— inner separator -•••outer separator

500

400-

20000 30000

Time, s

Fig. 5.30 Temperature distribution in the PSDRS

10000 40000

5.5 Combined ULOF/LOHS

The ULOF/LOHS is a combined ATWS accident with multiple failures. It is assumed that the transient is initiated from full power conditions, as defined in Section 5.3. The transient is initiated by all EM pumps tripping and beginning to coastdown, while the IHXs stop removing heat from the primary system. The reactor does not scram. The PSDRS is only available to remove the core heat during the entire transient.

Figure 5.31 shows that the reactor power decrease with the flow rate and drops to about the decay heat level by 300 seconds. The automatic feedbacks are related to the power- and-ftow ratio. The reactivity feedback transients are shown in Fig. 5.32. The net reactivity is about -1.7 $ at 1000 seconds. The dominant feedback during this event is the negative feedback from the GEMs, as shown in the figure. The positive CRDL reactivity feedback caused from the reactor vessel expansion is apparently shown in this event, which is compare with the only ULOF case in Fig. 5.15.

In Fig. 5.33, the fuel temperatures drop very quickly at the core center. The peak fuel temperatures during the early transient are almost same as the only ULOF case. The peak temperatures shift to the core exit, where the peak sodium temperatures cause the highest fuel temperature. Significant margins to fuel melting, cladding-fuel eutectic penetration, and sodium boiling are maintained throughout the entire transient. The coolant margin to boiling may decreases, depending on the duration of the heatup.

-59-

NO

RM

ALI

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POW

ER O

R FL

OW

KALIM ER -150 U LO F/LOH S

' C' I.AL I ■OV-.'b : 6 CHAWCL 1 ELQV/ "-DECAYTOWCn1.?0 -------------------- l--------- ---------

o.fln

0.1 D

0.0 1000.0 2000.0 0000.0 <#00.0 5000.0TIME, SEC.

Fig. 5.31 Normalized power and flow during ULOF/LOHS

K ALIM ER-150 ULOF/LOHS

..................... □ CiO^P .EF " PAD. EXP. 7 IjOOL.^N'tXP. " O+iUL bXJ,.. \ PUL.

TIME. SEC.Fig. 5.32 Reactivity feedback components during ULOF/LOHS

-60-

KALI MER-150 ULOF/LOH5

o » Ij^.T~A~IQN g_C>.D* mo i\m INI F"

3.0 1000 3 233-3.0 3000.0 4039 0 =000 0

TIME. SEC.Fig. 5.33 Fuel temperatures during ULOF/LOHS

5.6 Combined UTOP Cases

Various UTOP cases are analyzed to investigate the combined effects of loss of flow and/or loss of heat sink. The peak power and peak temperatures during the UTOP event occur mainly due to the reactivity feedback in the early period of the transient. Therefore the loss of heat sink does not affect the UTOP results until 15 seconds when the control rods are completely withdrawn. As expected, it was found that the peak fuel temperatures during the UTOP/LOHS are the same as the only UTOP case. But the system transients after the peak power during the UTOP/LOHS case are very different from the only UTOP case, because only the PSDRS is available to remove the core heat. The normalized power, reactivity feedbacks, and peak fuel temperatures during the UTOP/LOHS case are shown in Figs. 5.34 through 5.36, respectively.

The UTOP cases combined with loss of flow are also investigated. Once the primary pumps trip and begin costdown operation, the negative reactivity feedback by OEMs is immediately inserted into the core. As shown in Fig. 5.15, the whole negative reactivity of GEM is completely inserted into the core within the initial 50 seconds into the transient and the GEM reactivity is very large compared with other reactivity feedback components during ULOF. Therefore more negative reactivity feedback due to GEMs significantly affects the UTOP transient. The peak fuel centerline temperature calculated by SAS4A/SASSYS-1 during the UTOP/LOF case is 764 °C compared with 784 °C for the only UTOP case.

-61 -

But the temperatures of the cladding and the sodium within the assembly are 671 °C and 658 °C, respectively, which are higher than the corresponding temperatures of 633 °C and 614 °C for the only UTOP case. It can be expected because less core heat is removed by the decreased pump flow rate in the combined UTOP/LOF transient. The normalized power, reactivity feedbacks, and peak fuel temperatures during the UTOP/LOF case are shown in Figs. 5.37 through 5.39, respectively.

The analysis results of the combined UTOP with both LOF and LOHS case are presented in Figs. 5.40 through 5.42. The peak fuel temperatures during the UTOP/LOF/LOHS are the same as those for the UTOP/LOF case because of the same reason explained before.

KALIMEM50 UTOP/L0M5

U.CI 2zC 0 5CD.C 750.CI 10DD.C 12SD.H tSgfrD 17fG. D 2CCG. 3

TIME. SEC.Fig. 5.34 Normalized power and flow during UTOP/LOHS

-62-

CH

AN

NEL

1 TEM

PER

ATU

RE.

DEG

. CKALI MER -1 SO UTOP/LC HS

* .. C DOPPI FR ■■ RAD FkP ? CO01 A'tT- AHEjF. ■■■ CRLIL B-;K ■ -.J=L

7% o irioci'1; -?k-o 1.3000 i7ro.o?ccc.oTIME. SEC.

Fig. 5.35 Reactivity feedback components during UTOP/LOHS

KALIMER-150 UTOR/L.OHS

n._R£OJRATIO\ □ Ol AD

............. " COOUN7 b IHI.ET

.30 0 1000 0 15:30 0 1=300.0 17500^000 0TIME, SEC.

Fig. 5.36 Fuel temperatures during UTOP/LOHS

-63 -

R £

AC

TIV

ITY

. 5

NO

R M

A L

i ZED

PO

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R O

R F L

OW

KALlMER-150 UTDF.'LOF

■ r.M.^L l-OS'li- »_L4-.AHN_= L J_hL.__ ■ ktCA^UWcR.

1 ™.n 17S n.rTIM E, EE: j,

Fig. 5.37 Normalized power and flow during UTOP/LOF

KALIMER-l50 UTOP/L.OF

‘.Nh.i.................. - q/.n. ~x°. ? ooo AMTpnocnwtiMED i A%. r>;^. $ KIEL

li.u 2zo.o sao.c 757).c, toin.o i2fin.o i fiooc 17o0.0time, sec,

Fig. 5.38 Reactivity feedback components during UTOP/LOF

- 64 -

KALIMER-15Q UTOR/LOF

O ■ SA UIIh.I rjr-j L

Io

U.Cv 2i£ J 5CC 0 750.0

TIME. SEC.Fig. 5.39 Fuel temperatures during UTOP/LOF

D IZiC.n 1500.0 17j0.fi

KALIMER-150 UTOR/LOF/LOHS

■ iQiAL MO'.vkh ?„L:y.<rjNhL.„:„hiyvv__ -F_:cA>_EPWLR

250 a moo.r;TIME. SEC.

Fig. 5.40 Normalized power and flow during UTOP/LOF/LOHS

-65-

CH

AN

NEL

1 TEM

PER

ATU

RE.

DEC

. CKALIMER-150 UTOP/LOF/LOHS

O < LI.Ic

....................... fLP=T^n_ i.f.n. r>:F ? o<X>\ 4N~:-...7fL™.nAvvj:D__ i_/.x [XF.__ - a-. =y* ■■■■■ fue.

] 1000.0TIME, SEC.

2!>o.n i~no.o 1750 0?ono.0

Fig. 5.41 Reactivity feedback components during UTOP/LOF/LOHS

KALIMER-1 50 UTCP/LOF/L.CHS

■ s.u.TIJRhT ;'jN c C AD ___»_Fy_FJ_________ - coy A\T r. !f.J| =-

750.0 1C0C0 1750.0 1500.0 v'jo.o .2000.0

TIME, SEC.Fig. 5.42 Fuel temperatures during UTOP/LOF/LOHS

- 66 -

Chapter 6. Summary

In order to evaluate the passive characteristics of the advanced safety design features of KALIMER-150, the plant responses and safety margins during typical ATWS events were investigated using the system transient code SAS4A/SASSYS-1, which was developed by Argonne National Laboratory.

Three ATWS events as the most relevant for evaluation of passive safety design features were selected. These are unprotected transient overpower (UTOP), unprotected loss of flow (ULOF), and unprotected loss of heat sink (ULOHS). The ATWS events are extremely unlikely event category in the KALIMER-150 design, however; they are considered in establishing the design bases for KALIMER-150. The events selected in this category have the potential for a large release of radioactive material, core melt, or reactivity excursion. The KALIMER-150 design should have capability to ensure that adequate prevention or protection is furnished for these events.

It was shown that the KALIMER-150 design has inherent safety characteristics and is capable of accommodating ATWS events. The passive safety mechanism in the KALIMER-150 design makes the core shutdown with sufficient margin and the passive removal of decay heat and matching power to heat sink by passive self-regulation is successful. The self-regulation of power without scram is mainly due to the inherent and passive reactivity feedback. The inherent safety features of the KALIMER-150 core are strongly dependent on the reactivity feedback effects such as the Doppler, sodium void, core radial expansion, fuel axial expansion, control rod expansion, and GEM. The GEM effect during ULOF appears to be highly effective and helpful during such an event. Analyses results with the SAS4A/SASSYS-1 computer code predict that the severe accident conditions are prevented by wide margins.

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References

[1] Dohee Hahn et al, “KALIMER Preliminary Conceptual Design Report,” KAERI/TR-1636/2000, KAERI, 2000.

[2] C. E. Till, Y. I. Chang, and W. H. Hannum, “The Integral Fast Reactor - An Overview,” Progress in Nuclear Energy, Vol.31, p.3, 1997.

[3] J. E. Cahalan, et al., “Advanced LMR Safety Analysis Capabilities in the SASSYS-1 and SAS4A Computer Codes,” Proceedings of the Int. Topical Meeting on Advanced Reactors Safety, Pittsburgh, Pennsylvania, 17-21 April, TUNS,1994.

[4] J. E. Cahalan et al., “The Status and Experimental Basis of the SAS4A Accident Analysis Code System,” Proc. Int. Meeting on Fast Reactor Safety Technology, Seattle, Washington, pp.603-614, 1979.

[5] F. Dunn, “Integrated Intra-Subassembly Treatment in the SASSYS-1 LMR Safety System Analysis Code,” ANL/CP-74685, NURETH-5, Salt Lake City, Utah, 1992.

[6] A. H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol.l, Ch.6., The Ronald Press Co., New York, 1953.

[7] P. A. Pizzica, “An Improved Steam Generator Model for the SASSYS Code,” ANS Winter Meeting Session on Thermal-Hydraulic Aspects of Passive Safety and New Generation Reactors, CONE-891140-2, 1989.

[8] M. Bein and B. S. Singer, “Dynamic Simulation of an LMFBR Steam Generator,” Proceedings of the Second Power Plant Dynamics, Control and Testing Symposium, Knoxville, Tenn., 1975.

[9] Y. M. Kwon, “Design Data for the Plant Safety Analysis for KALIMER Design,” LMR/SA121-DO-01/2001, Rev.00, KAERI, 2001.

[10] Y. M. Kwon, “SSC-K Basedeck for KALIMER Breakeven Core Safety Analysis,” LMR/SA121-CN-01/01, Rev.01, KAERI, 2001.

[11] F. E. Dunn, “Validation of the RVACS/RACS Model in SASSYS-1,” Trans. Am. Nucl. Soc., Vol.55, p.723, 1987.

[12] Y. M. Kwon, “Safety Related Design Bases Events for KALIMER,” LMR/SA11 l-AB-01/01, Rev.01, KAERI, 2001.

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SAS4A/SASSYS-1 INPUT PREPARATION FOR KALIMER-150 (BOEC Core)

The numerical details for generating the input date for KALIMER -150 are presented in this document. Design date are converted into the appropriate SAS4A/SASSYS-1 input as required. The SAS4A/SASSYS-1 input data deck for the steady-state of KALIMER-150 is listed in Appendix.

The generation of the SAS4A/SASSYS-1 input data deck is done block-by-block. The basis for each value is given along with calculations required to derive the input value. Background information needed to be known for preparing the input data is also provided.

General integer input and optionsBlock 1 INPCOM General integer input dataBlock 11 OPCIN Controls for time step size and convergence criteriaBlock 51 INPCHN General integer input data for selecting general channel

dependent input options

Core geometryBlock 61 GEOMIN Geometrical data for SAS4A channel models

Reactivity worth tablesBlock 12 POWINA general neutronics data for core modeling Block 62 POWINC Channel dependent neutronics input data

Thermophysical propertiesBlock 13 PMATCMBlock 63 PMATCHBlock 65 FUELIN

Coolant flowBlock 3 INPMR4Block 14 PRIMIN

Block 64 COOLINBlock 18 PMR4IN

General channel independent fuel and cladding properties Properties for each channel Only one entry

Integer input data for model option of PRIMAR-4 Coolant flow and temperatures in the primary loop (for PRIMAR-4 and boiling model)Coolant flow information for each channel Floating-type input data for PRIMAR-4

- A1 -

Channel Modeling of the CoreKALIMER-150 design is illustrated in Fig. A, which has a 150 MWth metallic fueled core, sodium-cooled pool-type reactor. The core is modeled with channels in SAS4A. Each channel represents one or more subassemblies. Whole core is represented by grouping of similar subassemblies into a representative channel. For each channel, the appropriate data for the geometry, neutronics, thermophysical properties, and coolant flow parameters are required, which reflect the average of the group.

According to the previous SAS4A/SASSYS-1 practice, it is sufficiently accurate to represent the core within the boundary of the first row of radial blanket assemblies except for control assemblies by three channels for analyzing the typical ATWS events. However the radial blanket assembly is included in the core model in the present analysis because the small core of KALIMER-150 does not burden computer with heavy computation load. Therefore the KALIMER-150 core is represented by four channels in SAS4A. For the comparison analysis with SSC-K calculation, the number of core channel needs to be consistent with that of SSC-K. The radial blanket assembly is modeled as a separate core channel in SSC-K.

The grouping of the subassemblies into channels is done according to the following arrangement: One channel is selected for the hot assembly. The hot assembly is expected to have the highest temperature during any particular transient and it is most likely to be the assembly to reach any given failure threshold. The criteria for selecting the hot assembly are the highest power-to-flow ratio with a correspondingly high average power. All remaining drivers assemblies in the core are included in a single channel, and all internal blankets and radial blankets are included in separate single channels. The subassemblies exterior to the row of radial blanket assemblies, such as control rod, reflector, and shield assemblies etc. are considered in the PRIMAR-4 model of the primary system. This way turns out to be computationally more efficient, without any real loss in accuracy.

The layout of the KALIMER-150 metallic fueled core is shown in Fig. B and the assembly assignment in it's 1/6 core is shown in Fig. C. There are 36 different individual assembly locations in the 1/6 core, including control rods, GEMs, and USS. The assemblies need to be grouped into a relatively small number of channels for the SAS4A core model as mentioned before. A detailed description of the assembly assignment number, flow grouping, assembly power and flow, and relative power-to-flow ratio is given in Table A. Two assembly types are candidates for the hottest channel. Assemblies (3,1) and (3,3) have the highest average power per assembly while assemblies (6,3) and (6,4) have the highest power-to-flow ratio. However, the later assemblies have a low average power per assembly compared with the first one. Therefore the driver assembly located in the third row of the core (3,1) is selected as the hottest assembly. The remaining assemblies are grouped as indicated in Table A.

The neutronics data, including fuel and cladding worthies, coolant worthies, and Doppler, will be averaged for each channel to form the neutronics characteristics of each channel. The average is weighted based on the number of each assembly in the core. The average coolant flow rate is calculated in the same manner for each channel.

-A2-

Steam Generator

Containment Dome

IHX

Conlainmnl Vessel

Core EM Pump

Reactor Support Wall

Reactor Vessel

Fig. A KALIMER-150 Reactor Plant

& Driver Fuel 54• Internal Blanket 24• Radial Blanket 48• Control Rod 60 USS 1

GEM 6# Reflector 48# BXC Shield 540 IVS 54# Shield 72

Total 367

Fig. B KALIMER-150 Core Layout

• A4 -

Fig. C Assembly Assignment for the Power and Flow Distributions (1/6 Core Symmetry)

- A5-

Table. A SAS4A Channel/Assembly Parameter at BOEC for KALIMER-150 Metal Core

Assembly Assembly SAS4A Orifice Total Power Flow RelativeNumber Type Channel Zone Assembly (MWth) (kg/s) Pwr/Flw Note

(3,1) DR 1 1 3 6.62 35.0: 0.18914(3,2) DR 2 1 6 6.55 35. Oj 0.18714:(3,3) DR 2 1 T 8 6.62 35.0 0.189145

(5,1) DR 2 2 3: 5.9 32.2 0.18323(5,2) DR 2 2 .......... 65 6.13 32.2: 0.19037(5,4) DR 2 2 6i ..6.13 " 32.2: 6.19037

5__(S,5) DR 2 2 3' 5.9 32.2; 0.18323

(6,2) DR 2 3 65' 4.995 27.2: 0.18346(6,3) DR 2! 3 .....6 ' 5.22 27.2 0.19191

! (6,4) DR | 25 ....3 ..................6' ....5.22 27.25 0.19191: (6,5).... ...... DR........ i --gj ......3 6 ' 4:99 27.2 6.18346

: 12,1)........ IB.

3 4 3: 1.69: .....10.2 0.16569(2,2) IB 3| _ 4I________ % 1.69 10.2i 0.16569(4,2) !B ■" 31 A 6; "1.68 10.2' 0.16471

:.... J4,3)...... iB : ..... 3 ......4:..

1^68 : 10.2! 0.16471n~r~i i(5,3) ! JB......... ' , .................3 :................._5 6: 1.55 9.4i 6.16489

(7,3) ......RB ... 4: ................6 65 0.98 ;................ s.'g; 0.16610(7,4) RB..... .......... 4 6 6.99 5:95 0.16780

L . (7,5) _ ......4 I 6 '............... 6; 0 98 r_ ^ 5.9 i 0.16610 :i ............ ; | ;

: (7,2) RB 4 7 ........................65 6.85 | 5.15 0.166675.... (7,6) RB ......4 7 i 6 0.85 5.15 0.16667

: (7,D RB 4 ; 8 ......... 3: 6.57 I 3.4; 0.16765;L... (7,7) ...RB.... 4 ... 8 ............. .3. 0.57 : 3.4: 0.16765:

(8,4) ' RB 4 9 6: 0.38 .......... 2.35 6.16522I "(8,5) RB 4 9 65 ....6.38 ..2.35 0.16522

-A6-

Basic Plant Parameters of KALIMER-150

Thermal power POWER := 392.2 MWth

Total core flow rate Wcore := 2143.1 kg/sec

Core temperature

Tcorein := 386.2 + 273.15 Tcorein = 659.35 K

Tcoreout := 530 + 273.15 Tcoreout = 803.15 K

Tcoreavg := 0.5 x (Tcorein + Tcoreout) Tcoreavg = 731.25 K

Power and flow fractions of subassemblies (BOEC condition)

Power Flow

Hot driver PWRhot := 0.01686 x (6) F_hotassy := 0.016 x (6)

PWRhot = 0.10116 F_hotassy = 0.096

Remaining driver PWRdr := 0.78842 - PWRhot

PWRdr = 0.68726

Inner blanket

Radial blanket

Control rod

Reflector

B4C shield

IVS

Radial shield

PWRib := 0.09926

PWRrb := 0.08981

PWRcr := 0.000975

PWRrf := 0.002880

PWRbcs := 0.00362

PWRivs := 0.00563

PWRrs := 0.000153

F_DRassy := 0.77 - F_hotassy

F_ DR assy = 0.674

F_IBassy := 0.11

F_RBassy := 0.1

F„CRassy := 0.005

PWRsum := PWRhot + PWRdr + PWRib + PWRrb + PWRcr + PWRrf + PWRbcs ... + PWRivs + PWRrs

PWRsum = 0.990748

F_sum := F_hotassy + F_DRassy + F_IBassy + F_RBassy + F_CRassy

F_sum = 0.985

- A7-

Subassembly data

Number of subassemblv

Pin number per subassemblv

Hot driver NhotAssy := 6 N_Dpin := 271

Remaining driver NdrAssy := 48

Inner blanket NibAssy := 24 N_Bpin := 127

Radial blanket NrbAssy := 48

Control rod NcrAssy := 6 N_Cpin := 61

Reflector NrfAssy := 48 N_Rpin := 61

B4C shield NbcsAssy := 54 N_BSpin := 7

IVS NivsAssy := 54

Radial shield NrsAssy := 72 N_RSpin := 61

USS NussAssy := 1

GEM NgemAssy := 6

Sum NsumAssy := NhotAssy + NdrAssy + NibAssy+ NrfAssy + NbcsAssy + NivsAssy + NrsAssy + NussAssy + NgemAssy

NsumAssy = 367

Dimensions of driver and blanket subassemblies

Driver

Assembly lattice pitch (m)

Duct inner flat-to-fiat (m)

Duct outer flat-to-flat (m)

Pin outer diameter (m)

Clad inner diameter (m)

Clad thickness (m)

Wire wrap diameter (m)

Pitch_Dasy := 0.161

L_Dinflat := 0.1496

L_Doutflat := 0.157

OD_Dpin := 0.0074

ID_Dclad := 0.0063

t_Dclad := 0.00055

D Dwire := 0.0014

Blanket

Pitch_Basy := 0.161

L_Binflat := 0.1496

L_Boutflat := 0.157

OD_Bpin := 0.012

ID_Bclad ;= 0.01092

t_Bclad := 0.00054

D Bwire := 0.00095

- A8-

Assembly lattice pitch (m)

Duct inner flat-to-flat (m)

Duct outer flat-to-flat (m)

Pin outer diameter (m)

Clad inner diameter (m)

Wire wrap diameter (m)

Assembly lattice pitch (m)

Duct inner flat-to-flat (m)

Duct outer flat-to-flat (m)

Pin outer diameter (m)

Clad inner diameter (m)

Control rod

Pitch_Casy := 0.161

L_Cinflat := 0.1496

L_Coutflat := 0.157

OD_Cpin := 0.016

ID_Cclad := 0.013

D_Cwire := 0.001

BaC shield

Pitch_BSasy := 0,161

L_BSinflat := 0.1496

L_BSoutflat := 0.157

OD_BSpin 0.0546

ID_BSclad := 0.04871

Reflector

Pitch_Rasy := 0.161

L_Rinflat := 0.1496

L_Routflat := 0.157

OD_Rpin := 0.0188

Radial shield

Pitch_RSasy := 0.161

L_RSinflat := 0.1496

L_RSoutflat := 0.157

OD_RSpin := 0.0188

- A9-

BLOCK 1, INPCOM

The integer input for the core model is contained in 2 input blocks. Block 1 contains the integer input which applies on a core-wide basis, while Block 51 integer input data applies to each channel.

Block 1 contains general integer input data which is channel independent for the core model of SAS4A. It include time step controls for printing, restart files and problem times. Many selection flags for model options are also set in this input block. Only nonzero values are discussed unless a value of zero has a particular meaning.

Location 1, NCHANThe number of core channels used to represent the core

= 4 as discussed before.

Location 2. IDBUGOChannel independent debug flag

= 0 No debugging prints2 Steady state coolant debug prints3 More steady state coolant debug prints

Location 3. IFUEL1Number of fuel types used in the channel modelsThis is used to set the number of fuel property tables in Block 13.

= 5

Location 4, ICLAD1Number of cladding types used in the channel models,This is used to set the number of cladding property tables in Block 13.

= 1

Location 5, IPLUPFlag selecting the location of the fission gas plenum

- 0 Fuel-pin gas plenum above the cores 1 Fuel-pin gas plenum above the cores

- A10-

Location 7,1TKELTemperature scale for SSPRNT and TSPRNT print routines and TSPLOT plotting routines

= 0 Temperatures in Kelvins > 0 Temperatures in degrees centigrade

Location 8. IPOWERPower driver option. This flag selects the option of specifying a table of reactivity as a function of time to be input to the calculation. This table is in Block 12 and is used mainly for the reactivity insertion in a transient overpower accident.

= 0 External reactivity vs. time from the table 1 Power vs. time from table

Location 9. IPOWOP= 0 Steady-state power in the peak axial segment is calculated from

total reactor power (see POWTOT)> 0 Steady-state total reactor power is calculated from the peak

axial segment (see POW)

Location 11, MAXSTPMaximum number of main time steps for the transient calculations This is rather arbitrary, selected by the user depending on the length of transient desired. It is also possible to use maximum problem time, Block 11, Loc. 7, for the same purpose, in which case MAXSTP is set to a large value.

If only a steady-state calculation is to be done, the value of MAXSTP is 0. Several values of MAXSTP are typically used, depending on the accident; 400 seconds for LOF, 800 seconds for TOP, and 3000 seconds for LOHS events, respectively. This input value must be reset for controlling the length of the calculation in the continuous transient.

= 0 for steady-state

Location 12. IPONumber of main time step between full printouts before IBLPRT or coolant boiling This integer selects the frequency of printing the full printout, based on the time step number, and is arbitrary. Typically the following values are used: 20 for LOF and 50 for TOP and LOHS.

= 0 for steady-state

- A11 -

Location 13, IPOBlTime step between prints after IBLPRT or coolant boiling

The same as Loc. 12, but for printing after the initiation of boiling. The value in Loc. 12 are repeated for this study.

= 0 for steady-state

Location 14, IBLPRTMain time step number for switch of full printout interval from IPO to IPOBOI. If IBLPRT = 0, switch occurs at coolant boiling.

= 0 for steady-state

Location 15, NSTEPRestart file save option

= 0 No restart file saved> 0 Restart file saved every NSTEP main time steps

This integer selects the frequency of writing a restart file on logical unit 17, and is arbitrary. If a restart file is desired, the file on logical unit 17 must be created by either making a new file or overwriting an existing file during job execution. For the present study, a value of every 1000 main time steps is used.

= 1000

Location 16. NDELAYNumber of delayed neutron precursor families, -1 < NDELAY < 7, which is used in Block 12.

— 6

Location 17. NDKGRPNumber of delay heat groups, -1 < NDKGRP < 7, which is used in Block 12.

= 6

Location 18. N PR EATNumber of entries in the table of external reactivity, as a function of time.PREATB, Block 12, Loc. 29-48 and Loc. 49-68. This is normally used for transient overpower accidents, otherwise the value is 0.

= 3

- A12-

Location 22, NTOTABNumber of entries in the table of core inlet temperature as a function of time. Since PRIMAR-4 is being used to represent the reactor system, only 1 value is needed, usually the nominal steady-state core inlet temperature. The table TOTAB is in Block 14, starting with Loc. 45.

= 2

Location 23. MULSTRRestart file save option

= 0 Normal restart option, Only one restart file is saved, which is the latest one written.1 All restart files are saved. Restarts are written at multiples of NSTER, Loc.15, Block 1.

Location 24, ICLCMPData for transient plots on logical unit 11 = 0 Data for plots of transient is not saved> 1 Data output for transient information plots are stored on logical unit 11, which must be

created or overwritten during job execution.

= 11

Location 25, IN EDIT!Input edit optionThe detailed description of the input can be written in an edited format, if desired. This is usually not done due to the size of the output.

= 0 No input edit > 0 Input edit

Location 27. IPRIONPRI MAR-4 option used for the reactor system modeling

= 4 For PRIMAR-4 option < 0 For PRIMAR-1 option

- A13 -

Location 31. ICREXPControl rod driveline expansion model option

This integer activates the model for calculating the reactivity feedback from control rod drivelines expansion and controls the printing of the results.= 0 No control rod drive expansion feedback

1 -3 Calculate feedback from single-node model2 Calculates this feedback and prints the result every transient step 4 Calculate feedback from multi-node model

* Use of ICRDDB flag (Block 1, Loc. 71) is recommended.

Location 36. IRADEXRadial expansion model optionThis integer activates the model for calculating the reactivity feedback from radial core expansion and selects the model to be used.

= 0 No radial expansion feedback> 0 Radial expansion feedback using the inlet coolant temperature < 0 Radial expansion feedback using the inlet plenum wall temperature = 1,2,3 Simple radial expansion model with different print option = 4,5,6,7 Detail radial expansion

In this study, the detailed radial core expansion feedback model is used, with normal printout, and the temperature of the inlet plenum wall is used to determine the temperature of the core support, or grid plate.

= -4

Location 39. NFUELDNumber of dollars of fuel reactivity worth which has to be reached to terminate the calculation. Recommended value is -5.

= -5

Location 45. NPOWDKNumber of power curves or sets of decay heat parameters used (< 6)

= 1

In this study, each channel is assumed to have the same decay heat curve.

Location 46. NPDKSTNumber of entries in the POWLVL and POWTIM tables for initializing the decay heat precursors (< 9). See Block 12, Loc. 325-404

= 1

- A14-

Locations 51-54 used only if IRADEX > 3 or < -3

The detailed radial core expansion reactivity feedback model requires additional input data which is not included in the neutronics information. A schematic of the core restraint system model is shown in Fig. 1-1.

Location 51. NPDKSTTotal number of subassemblies in the active core region, including control and internal blanket subassemblies. Used for calculating the core radius in the radial expansion reactivity feedback calculation.

Number of subassembly is listed in the Basic Plant Parameters. Refer to Fig. B

NPDKST := N hot Assy + NdrAssy + NibAssy + NrbAssy + NcrAssy ...+ NgemAssy + NussAssy

NPDKST = 139

Location 52, MTGRDSupport grid material, used for calculating the thermal expansion of the grid during a transient

= 1 316 SS2 HT-9

Location 53. MTACLPAbove-core load pad material, used for calculating the thermal expansion of the above-core load pad during a transient

= 1 316 SS2 HT-9

Location 54, MTTLPTop load pad material, used for calculating the thermal expansion of the top load pad during a transient

= 1 316 SS2 HT-9

- A15-

Location 55, MODEEXAxial expansion option

= 0123

Force balance or free expansion, depending on radial gap Cladding controlled fuel expansion Independent free expansion Force balance all the time

This integer selects the model used for calculating the reactivity feedback from axial expansion of the fuel and cladding. This is not used with DEFORM-4; when DEFORM-4 is not used, the value of 0 is used for the option of a force balance (or free expansion, if there is a fuel-to-cladding gap) between the fuel and the cladding. The model requires additional input on the relative strength and thermal expansion characteristics, which is in Block 63 for each channel.

Location 56. JREXTThis integer includes a correction to the reactivity extrapolation in the code. It should always be used unless comparison with older results is necessary.

= 0 No correction term1 Add correction term to reactivity extrapolation

Location 57, IFT19Not currently used= 0

Location 58. (REACTReactivity model option

= 0 Use detailed reactivity models1 Use FFTF empirical reactivity model2 Use EBR-II empirical reactivity model

-1 Compute, write out but don’t use FFTF model-2 Compute, write out but don't use EBR-II model

Location 59, NSUBTRTotal number of subassemblies in the reactor, including drivers, radial and internal blankets, control assemblies, radial reflectors and shields.

Total number of subassemblies is calculated in the Basic Plant Parameter.Refer to Fig. B

NSUBTR := NsumAssy NSUBTR = 367

- A16 -

Location 60. NRRNGSNumber of restraint rings in core restraint design

= 0 No restraint rings1 Restraint ring at top load pad2 Restraint rings at top and above-core load pads

KALIMER-150 has only one former ring (restraint ring) at the top load pad elevation.

Location 61. MTRRACMaterial of the restraint ring at the above-core load pad elevation

= 1 316 SS2 HT-9

0 Not used since there is only one restraint ring.

Location 62. MTRRTMaterial of the restraint ring at the top load pad elevation

= 1 316 SS2 HT-9

Location 63. MTRFCRadial reflector and/or blanket above-core load pad material

= 1 316 SS2 HT-9

All subassembly load pads are the same as the duct material, HT-9.

Location 64. MTRFTRadial reflector and/or blanket top load pad material

= 1 316 SS2 HT-9

All subassembly load pads are the same as the duct material, HT-9.

- A17 -

Location 65, 1ROPTAssumption for low power-to-flow ratios

= 0 Subassemblies vertical at the grid plate1 Above-core load pads remain compacted (most pessimistic)

The assumption for low normalized power-to-flow ratios is that there is sufficient bending of the assemblies exterior to the active core region to continue to hold the assemblies together, even though the top of the average driver assembly in the outer row does not push against the restraint ring (through the top load pads of the radial blankets and shields). This is likely when B4C shields are used due to the reverse radial temperaturegradient, causing inward bending. Activating this option provides the most conservative estimate of the negative reactivity feedback during almost all accident scenarios.

- A18-

i Core Centerlinei

Top Load Pads

Top Restraint Ring

Above-Core Load Pads

CO o

interiorCore

Subassemblies

OuterAssemblieso 3

CoreBarrel

Grid Plate

NOT TO SCALE

Fig. 1-1 Core Restraint System Model for KALIMER-150 Core Design

- A19 -

BLOCK 3, INPMR4Block 3 contains general integer input data for the PRI MAR-4. All of the input data in this Block are required for modeling the primary and intermediate loops and decay heat removal systems. The model of the KALIMER plant that was developed for this study is shown in Fig. 3-1, in which the various components as listed in Tables 3-1 and 3-2 are represented. Figure 3-2 illustrates the internal structures of KALIMER.

Primary circuitThe primary circuit contains all of the sodium which flows through the core in the reactor vessel. The sodium travels from the core into the hot pool, then through the intermediate heat exchanger (IHX) for the intermediate heat transport system. The sodium flows out of the IHX into the cold pool, then primary pump sucks the sodium through the flow guide surrounding the core. The circuit is completed by the sodium flowing back through the discharge pipe of EM pump into the inlet plenum and up through the core assemblies.

The driver and internal and radial blanket subassemblies are represented by the detailed SAS4A channel model. PRIMAR-4 sets all of the SAS4A channels to be represented by liquid element 1 (E1), connecting compressible volumes CV1 and CV2, which simulates the core inlet plenum and hot pool. The SAS4A channels are set to be always the first liquid segment S1 in PRIMAR-4. The remainder of the core assemblies are represented using more liquid elements between CV1 and CV2. As shown in Fig. 3-1, the KALIMER core includes 6 control rod, 48 reflector, 54 B4C shield, 54 IVS, and 72 radial shield assemblies, which are not represented by the SAS4A core channels.

The control rod assemblies are represented by three liquid elements, E2, E3, and E4, where E2 and E4 are pipe elements with characteristics of the pin section of the assembly below and above E3. E3 is represented as the power producing region, which is designated as a "bypass channel" element in PRIMAR-4. This type of element is designed for simulating the power producing regions of the core which may exist outside of the SAS4A channels. Since all of the control rod assemblies are considered to be identical, the 6 control assemblies are represented with 1 set of these 3 elements duplicated 6 times. This is controlled by the multiplicity factors for the liquid segments. The pipe and "bypass channel" elements in PRIMAR-4 uses the same equation for calculating the liquid flow rate, so that the elements E2, E3, and E4 can be combined into one liquid segment (S2). However, the heat transfer calculations are different, so three temperature groups are required, T1, T2, and T3 for E2, E3, and E4, respectively. These are listed in Table 3-2.

In the same manner as for the control rod assemblies, the reflector and B4C shield assemblies are simulated by one set of three elements. The total flow areas of these assemblies are represented by only one flow segment (S3), consisting of three liquid elements of E5, E6, and E7, and corresponding temperature groups, T4, T5, and T6. Another set of three liquid elements is used to simulate the IVS, radial shield assemblies and the core bypass flow. The core bypass flow is associated with

- A20-

leakage at the grid plate and subassembly connection. This sodium flows up to the hot pool in the gaps between the subassemblies. Since this region does not have a defined geometry, small flow rates just large enough to ensure stability of the heat transfer calculation in PRIMAR-4 are assumed. These three elements E8, E9 and E10 are in liquid segment S4 and in temperature groups T7, T8, and T9.

The hot pool is modeled by one volume, CV2, which contains hot sodium and cover gas. Most of the sodium flow leaves CV2 through the IHX . KALIMER has 2 identical IHTS loops, each with its own steam generator (SG). The current PRIMAR-4 model of KALIMER is developed with one lumped IHX and its associated intermediate loop out to the SG. The elements of E11, E12, and E13 represent the sodium flow on the shell side of the IHX, where E12 covers the active heat transfer section between the primary sodium and the intermediate loop. E11 and E13 are piping elements with characteristics simulating the inlet and outlet sections of the IHX. All three elements are in the same liquid segment, S5, but three temperature groups are required, T10, T11, and T12. The multiplicity factor is 4 to account for 4 IHXs. The sodium leaving E13 flows into the cold pool, CVS.

The sodium is taken from the cold pool through the flow guide by the primary EM pumps as shown in Fig. 3-1. For the present PRIMAR-4 model, the pumps are modeled as two groups. The first group pump contains a flow path from E14 through E17 in liquid segment S6, going from CV3 to CV1. E15 is the upward flow channel within the EM pump body. Pump discharge pipe feeding sodium into the core inlet plenum, CV1, consists of E16 and E17. E16 is associated with the vertical section of the discharge pipe coming down from the pump, and E17 with the horizontal section going into the core inlet plenum. The liquid elements E14 and E15 are in temperature group T13, and E16 and E17 are in T14. This grouping of elements and temperature groups are repeated for E18 and E19 (T15), E20 and E21 (T16) for the second group pump (liquid segment S7).

KALIMER has 4 EM pumps in the reactor vessel and two group pumps are modeled in Fig. 3-1. Each group represents two pump circuits. The first group represents 3 pump loops, while the other group represents one of the pump loops. This would be useful if the effect of the failure of one pump were to be analyzed, or if the effect of the breaking of 1 out of 4 the discharge pipes are to be investigated. In this model, the primary coolant pumps was handled by the characteristics curve of flow rate vs. pump head in normal pump operation. Basically the operating characteristics of the EM pump can be described in terms of a set of parameters used in conjunction with nondimensional or normalized variables. A simple pump option is used because KALIMER doesn't have a detailed EM pump design yet.

KALIMER has the annular boundary region dividing the hot and cold pools as illustrated in Fig. 3-2. Four IHXs and four EM pumps are located in the annular region. The baffle and separation plates on the top and bottom of the annular region allow flow from the hot and cold pools into the annular region, but this is greatly restricted by the close lit of the plates to the vessel components. The annular region is represented by CV4, with

- A21 -

each connected to the larger pool by a short pipe section of E22 and E23, respectively. This allows sodium to enter or leave the buffer region in response to temperature changes in the sodium. This volume is particularly important in long-term transients as it provides a considerable heat sink to moderate the temperature rise of the hot and cold pools. These heat transfer can be represented by the component-to-component heat transfer model specially provided by PRIMAR-4. The liquid element E22 between CV2 and CV4 is in the the temperature group T17, and E23 between CVS to CV4 is in T18.

Passive decay heat removal system

The KALIMER design incorporates the passive safety decay heat removal system (PSDRS), which is modeled by the flow path connecting CV2 and CVS over the reactor baffle. PSDRS is represented by one liquid segment of S10, consisting of two liquid elements of E24 and E25. Each element has individual temperature group T19 and T20. The overflow from the hot pool into the cold pool occurs when the hot pool level rises above the top of reactor baffle. A valve element E25 is additionally modeled at the exit of the overflow path. This allows the PSDRS to be shut off during normal operation of the reactor, and activated when the sodium level in the hot pool rises above the top of reactor baffle. The nominal heat removal capacity of PSDRS is considered to initialize the heat balance of the KALIMER plant. PSDRS begins the transient calculations operating at its full rated capacity for nominal power reactor conditions. Since the nominal power of PSDRS is only 1.3 MW, in comparison to the total reactor power of 392.2 MW, this has a negligible effect on the course of the transients until the SG is lost and power is reduced to decay heat level.

Intermediate loop

KALIMER has two identical intermediate heat transport system. These are modeled as identical loops, represented by the one loop shown in Fig. 3-1. Each IHTS loop contains the shell side of IHX, intermediate loop pump, the sodium side of SG, and all necessary piping. The water side of SG is not modeled, but a simplified treatment is used instead. The pump in the cold return section of the IHTS loop is modeled with EM pump model in PRIMAR-4, which is represented by E27. The sodium flows through a long horizontal pipe from the SG building into the containment building, E28. The sodium then flows vertically down into the reactor vessel through the IHX downcomer, E29. The intermediate sodium is on the tube side of the heat exchanger, E30, and flows vertically upward out of the IHX through E31. Another long horizontal section takes the sodium back to the steam generator, E32. Since the IHX heat transfer section is already included in temperature group T11, the element E30 has the same temperature group, T11.

Steam generator

The SG uses the simple model available in PRIMAR-4. It is assumed that the SG rejects heat at their nominal full power capacity during the steady-state. The normalized temperature drop across the SG, E33, is specified as a function of time. This is easily changed to the other option, which specifies the SG outlet temperature as a function of time, if desired for a particular accident. The sodium flows out of the SG and returns to the pump through the simple pipe, E34. The intermediate loops between CV6 and CV7 are represented by S11 and the loop from E29 to E31 is represented with one liquid segment, S12. The remaining loop between CVS and CVS is represented by S13.

- A22-

E32(SI 3)

SG

E33

CVS <

CV7

E28

(EMP,

E29

E27

E26

CV6

E34 ESC

SI 2)

E31He gas

El 1

®E12

IHX

E13

E22

CV4-r®

r#i

El 5 ®I

E23

El 4E16

Cold Pool

E17

CV2

Hot Pool

S4) (S3) f82] Si

E10 E7 E4

E9 E6 E3

E8 E5 E2

CO

CV1 Inlet Plenum

CV3

E24

PSDRS

CV4

El 9

E20S7)

E1BE25

E21

Fig. 3-1 Schematic of the PRIMAR-4 Model of the KALIMER Plant

- A23-

Fig. 3-2 Reactor Internal Structures of KALIMER

- A24 -

Table 3-1. PRIMAR-4 Model of the KALIMER Plant: Compressible Volumes

Compressible Volume No. Type Description

Primary Loop

1 1 Core Inlet Plenum2 7 Hot Pool, plenum with cover gas3 8 Cold Pool, pool with cover gas4 4 Annulus Volume

Intermediate Loop

5 4 Intermediate Loop Pipe (Hot Side)6 9 Intermediate Loop Pipe (Cold Side)7 4 Intermediate Loop Pipe (Cold Side)

- A25-

Table 3-2. PR!MAR-4 Model of the KALIMER Plant: Elements

Liquid Flow Liquid Flow Liquid Flow TemperatureComponent Element Seament Group

Primary Heat Transport SystemCore 1 1 -

Control Rod Assembly:Lower section 2 2 1Blanket section 3 2 2Upper section 4 2 3

Reflector, B4C Shield Assemblies: Lower section 5 3 4Blanket section 6 3 5Upper section 7 3 6

Radial Shield IVS Assemblies:Lower section 8 4 7Blanket section 9 4 8Upper section 10 4 9

IHX:Inlet section 11 5 10Tube section 12 5 11Outlet section 13 5 12

Pump Group 1Pump inlet pipe 14 6 13Pump 15 6 13Pump outlet pipe 16 6 14Pump outlet pipe 17 6 14

Pump Group 2Pump inlet pipe 18 7 15Pump 19 7 15Pump outlet pipe 20 7 16Pump outlet pipe 21 7 16

Annulus VolumeHot pool side 22 8 17Cold pool side 23 9 18

- A26-

Table 3-2. PRIMAR-4 Model of the KALIMER Plant: Elements (continued)

Liquid Flow Liquid Flow TemperatureComponent Element Seament Grouo

PSDRSInlet section 24 10 19Outlet valve 25 10 20

Intermediate Heat Transport System

Vertical suction pipe 26 11 21Pump 27 11 21Pump discharge pipe 28 11 22IHX downcomer 29 12 23IHX tube side 30 12 11Vertical outlet pipe 31 12 24Horizontal pipe 32 13 25SG shell side 33 13 26Horizontal suction pipe 34 13 27

- A27-

Table 3-3. PRIMAR-4 Model of the KALIMER Plant: Elements: Temperature Elements

LiquidSeq.

Comp.Vol. In Out

Temp. Elem Group No.

. Elem. Type Description

1 1 2 0 1 1 Core subassemblies

2 1 2 1 2 3 Pipe2 3 2 Bypass channel3 4 3 Pipe

3 1 2 4 5 3 Pipe5 6 2 Bypass channel6 7 3 Pipe

4 1 2 7 8 3 Pipe8 9 2 Bypass channel9 10 3 Pipe

5 2 3 10 11 3 Pipe11 12 6 IHX, shell side12 13 3 Pipe

6 3 1 13 14 3 Pipe13 15 5 Pump impeller14 16 3 Pipe14 17 3 Pipe

7 3 1 15 18 3 Pipe15 19 5 Pump impeller16 20 3 Pipe16 21 3 Pipe

8 2 4 17 22 3 Pipe9 3 4 18 23 3 Pipe

10 2 3 19 24 13 Annular element20 25 11 Valve

11 6 7 21 26 3 Pipe21 27 5 Pump impeller22 28 3 Pipe

12 7 5 23 29 3 Pipe11 30 7 IHX, tube side24 31 3 Pipe

13 5 6 25 32 3 Pipe26 33 8 SG (sodium side)27 34 3 Pipe

- A28 -

Location 1, NCVPNumber of compressible volumes in the primary loop.

= 4 As shown in Table 3-1 and Fig. 3-1

Location 2. NCVSNumber of compressible volumes in the secondary or intermediate loop.

= 3 As shown in Table 3-1 and Fig. 3-1

Note that the intermediate loop in the model represents 2 identical loops in the plant. The secondary loops include the intermediate heat transport loop and DRAGS loop. KALIMER has no DRAGS design.

Location 3, NCVPNumber of compressible volumes in the DRAGS loop.

= 0 Not yet operational

Location 4, NSEGLPNumber of liquid segments in the primary loop.

= 10 As shown in Table 3-2 and Fig. 3-1

Location 5, NSEGLSNumber of liquid segments in the secondary loop.

= 3 As shown in Table 3-2 and Fig. 3-1

Location 6, NSEGLPNumber of liquid segments in the DRAGS loop.

= 0 Not yet operational

Location 7, NSEGGPNumber of gas segments in the primary loop.

= 0 No gas segments are used in the primary loop

Location 8, NSEGGSNumber of gas segments in the secondary loop.

- 0 No gas segments are used in the secondary loop

- A29-

Location 9, NSEGGDNumber of gas segments in the DRAGS loop,

= 0 Not yet operational

Location 10, NELEMTTotal number of liquid flow elements, max=140 A bypass channel must not be split into more than one flow element.

= 34 As shown in Table 3-2

Location 11-48. ITYPCV (ICV)Compressible volume type.

TypeNumber Description

1 inlet plenum2 compressible liquid volume, no cover gas3 closed outlet plenum, no cover gas4 almost incompressible liquid junction, no cover gas5 pipe rupture source6 pipe rupture sink, guard vessel7 outlet plenum with cover gas8 pool with cover gas9 pump bowl and cover gas10 expansion tank with cover gas11 compressible gas volume, no liquid

Compressible Volume No.

TypeNumber Description

Primary Loop1 1 Core Inlet Plenum2 7 Hot Pool, with cover gas3 8 Cold Pool, with cover gas4 4 Annulus Volume

Intermediate Loop5 4 Intermediate Loop Pipe (hot side)6 9 Intermediate Loop Pipe (cold side)7 4 Intermediate Loop Pipe (cold side)

.A30-

Location 49-188, ITYPEL (IELL)Liquid flow element type.

Type Number12345678910 11 12 13

Descriptioncore subassemblies, SAS4A channelscore bypass assembliespipecheck valve pump impeller IHX, shell side IHX, tube sidesteam generator, sodium side DRAGS heat exchanger, tube side DRAGS heat exchanger, shell side valveair dump heat exchanger, sodium side annular element

* DRAGS is a direct air cooling system

Liquid Loc. Element ElementSeament No. No. Type Description

Primary Loop1 49 1 1 Core subassemblies2 50 2 3 Pipe

51 3 2 Bypass channel52 4 3 Pipe

3 53 5 3 Pipe54 6 2 Bypass channel55 7 3 Pipe

4 56 8 3 Pipe57 9 2 Bypass channel58 10 3 Pipe

5 59 11 3 Pipe60 12 6 IHX, shell side61 13 3 Pipe

6 62 14 3 Pipe63 15 5 Pump impeller64 16 3 Pipe65 17 3 Pipe

7 66 18 3 Pipe67 19 5 Pump impeller68 20 3 Pipe69 21 3 Pipe

8 70 22 3 Pipe9 71 23 3 Pipe10 72 24 13 Annular element

73 25 11 Valve

- A31 -

Liquid Loc. Element ElementSeament No. No. Type Description

Intermediate11

Loop74 26 3 Pipe75 27 5 Pump impeller76 28 3 Pipe

12 77 29 3 Pipe78 30 7 IHX, tube side79 31 3 Pipe

13 80 32 3 Pipe81 33 8 SG (sodium side)82 34 3 Pipe

Location 189-268. JCVL (M. ISGUCompressible volumes at the ends of the liquid segment

This can be found in Fig. 3-1. The results are as follows:

Loc. Starts with Loc. Ends withSeament No. No. CV No. No.

Primary Loop1 189 1 190 22 191 1 192 23 193 1 194 24 195 1 196 25 197 2 198 36 199 3 200 17 201 3 202 18 203 2 204 49 205 3 206 410 207 2 208 3

Intermediate Loop11 209 6 210 712 211 7 212 513 213 5 214 6

Location 269-324. JCVG (M. ISGG)Compressible volumes at the ends of the gas segment

No gas segment is used for the study.

- A32-

Location 325-364, NELML (ISGUNumber of elements in the liquid segment

The number of elements in each liquid segment can be found by examining Fig. 3-1. The combining of elements into one segment implies that the fluid flow calculations for each element in the segment is the same, with the results as follows.

Segment No. Loc. No. Number of Elements

Primary Loop 1 2345678910

325 1326 3327 3328 3329 3330 4331 4332 1333 1334 2

Intermediate Loop11 335 312 336 313 337 3

Location 365-404. JFSELL (ISGUFirst element number in segment ISGL Segment ISGL contains elements JFSELL(ISGL) through JFSELL(ISGL) + NELML(ISGL)-1

Segment No. Loc. No. Number of First Elements

Primary Loop1 365 12 366 23 367 54 368 a5 369 116 370 147 371 188 372 229 373 2310 374 24

- A33-

Segment No. Loc. No. Number of First Elements

Intermediate Loop11 375 2612 376 2913 377 32

Location 405, NPUMPNumber of sodium pumps, Max. 12

The number of sodium pumps in the model is 2 in the primary loop, with each representing 2 identical pumps, and 1 in the intermediate loop, with 2 identical intermediate loops. Therefore a total number is 3.

= 3

Location 406-417. IELPMP (IPMP)Element number of pump IPMP

The element number corresponding to each pump in the model is:

Pump No. Loc. No. Element No.

1 406 152 407 193 408 27

Primary loop (pump group 1) Primary Loop (pump group 2) Intermediate Loop

Location 418-429. IEMPMP (IPMP)Type of pump

= -2 EM pump-1 Electromagnetic pump0 Use table of pump head vs. time1 Centrifugal pump2 Homologous pump model3 EBR-II pump model

The type of pump being represented by PRIMAR-4 is an EM pump, which uses the characteristic curves of

Pump No. Loc. No. Pump Model

1 418 02 419 03 420 0

Primary loop (1st group) Primary loop (2nd group) Intermediate Loop

A34 -

Location 430-469. ILRPMP (IPMP)Type of pump

= 0 Pump operation according to model selected at Block 3, Loc. 418-429Uses locked rotor model for IEMPMP = 2 according to pump Wb and SB

(See Block 18, Loc. 1983-2222)1 Pump speed set to zero, locks rotor immediately as in a pump seizure

-1 Portable of pump speed vs. time (IEMPMP = 1 or 2)-2 for table of pump head vs. flow

Location 470. NIHXNumber of IHXs, Max. = 4

= 1

Location 473-476. IELIHX (IIHX)Element number of the IHX, primary loop.

= 12 As shown in Table 3-3 and Fig. 3-1

Location 481-484. ILIHXS (IIHX)Element number of the IHX, intermediate loop.

= 30 As shown in Table 3-3 and Fig. 3-1

Location 489-492, IHXCLC (IIHX)IHX model option

= 0 Use detailed IHX> 0 Table No. ITAB for table look-up IHX, in which case NTNODE (Block 3, Loc.

513-612) must equal 2,

Location 497. IPRADJIHX model option

- 0 No pressure adjustments for channel flow estimation errors.1 Adjustments for the outlet plenum only, Recommended value.2 Adjustments for both inlet and outlet plenums.

This input activates different corrections to the mass flow difference between the SAS channels and PRIMAR-4 as a result of the use of extrapolated values for mass flow rate between these two models. The current recommended value is 1 for this input, which applies a correction to the mass of the outlet plenum.

- A35-

Location 510, ISRCRPCompressible volume number of pipe rupture source

= 0 No pipe rupture occurs in this study

Location 511. ISNKRPCompressible volume number of pipe rupture sink.

= 0 No pipe rupture occurs in this study

Location 512, NTGPTNumber of temperature groups. <= 100The liquid flow elements representing a bypass channel must be a separate temperature group. The same is true of IHX.

The combining of elements in the same flow segment into one temperature group implies that the heat transfer calculations for each group is the same.

= 27 As indicated in Table 3-3

- A36-

Location 513-612. NTNODE (ITGP)Number of nodes in the temperature group.Each temperature group must have at least 2 nodes. (For a tabular IHX, it must equal 2).

The number of nodes in each temperature group is a user choice, subject to the restriction given in the input description. As would be expected, more nodes have been placed in elements with potentially large temperature gradients in the flow direction, as follows:

TemperatureGroup No. Loc. No, Number of Nodes

Primary Loop1 513 42 514 73 515 44 516 45 517 76 518 47 519 48 520 79 521 410 522 411 523 2012 524 413 525 1014 526 1015 527 1016 528 1017 529 418 530 419 531 2020 532 4

Intermediate Loop21 533 1022 534 823 535 2024 536 2025 537 2026 538 2027 539 20

- A37-

Location 613-712, IFSTEL (ITGP1First element in the temperature group.

The first element in each temperature group is found from the list of elements in Table 3-2.

TemperatureGroup No. Loc. No. First Element.

Primary Loop1 613 22 614 33 615 44 616 55 617 66 618 77 619 88 620 99 621 1010 622 1111 623 1212 624 1313 625 1414 626 1615 627 1816 628 2017 629 2218 630 2319 631 2420 632 25

Intermediate Loop21 633 2622 634 2823 635 2924 636 3125 637 3226 638 3327 639 34

- A38-

Location 713-812. ILSTEL (ITGP)Last element in the temperature group.

The last element in the temperature group is also found from Table 3-2. TemperatureGroup No. Loc. No. Last Element

Primary Loop1 713 22 714 33 715 44 716 55 717 66 718 77 719 88 720 99 721 1010 722 1111 723 1212 724 1313 725 1514 726 1715 727 1916 728 2117 729 2218 730 2319 731 2420 732 25

Intermediate Loop21 773 2722 734 2823 735 2924 736 3125 737 3226 738 3327 739 34

-A39-

Location 813. NBYPNumber of bypass channels.

The number of bypass channel elements is 3, being element numbers 3, 6, and 9.

3 As listed in Table 3-3

Location 814-821. NTLWBY (IBYP)Number of nodes in walls A and B in bypass channel

The number of nodes in the walls A and B in the bypass channel is set to 7, which gives the maximum number of nodes in each bypass channel. Refer to Fig. 18-6 in Block 18.

Bypass Channel Element No. Loc. No. Number of Nodes

1 3 814 72 6 815 73 9 816 7

Location 822-829. IDKTYP (IBYP)Decay heat curves for bypass channels.

The decay heat curve to be used for each bypass channel has set to 1.

Bypass Channel Element No. Loc. No. Decay Curve No.

1 3 822 12 6 823 13 9 824 1

Location 830-837. IELBYP (IBYP)Element numbers for bypass channels. (Usually opposite active core)

Bypass Channel Loc. No. Element No.

23

830831832

369

- A40-

Location 839, NSGNNumber of steam generators.

= 1 As shown in Fig. 3-1 and Table 3-2.

Location 840-851. IELSGN (ISGN)Element number for steam generator.

= 33 As shown in Fig. 3-1 and Table 3-2.

Location 852-863. ISGCLC (ISGN)Option of steam generator model

= 0 Use detailed steam generator model> 0 Table look-up ITAB for steam generator, temperature drop vs. time< 0 - table number for table of outlet temperature vs. time

(see Block 18, Loc. 2937-3440)

Table look-up option is used for all steam generator modeling. The choice of either normalized temperature drop or steam generator outlet temperature is made based on the accident scenario and the characteristics of the steam generator.

= 1

Location 864-875. IEVAP (ISGN)For all steam generator models,

= 1 Evaporator2 Superheater3 Once-through

The choice of steam generator type needs to be made regardless of the modeling used for the steam generator. In this study, it is appropriate to use a once-through steam generator, type 3.

Location 890, IP4PRTPrint PRIMAR-4 results every IP4PRT PRIMAR step,

= 500

- A41 -

Location 973. NVALVENumber of valves, <= 8

= 1 As shown in Table 3.2 and Fig. 3-1

Location 974-981. IELVLV OVLV)Element number for valve IVLV

= 25 As shown in Table 3.2 and Fig. 3-1

Location 982-989, ITABVV (IVLV)Table number in DTMPTB (Block 18, Loc. 2937-3104) tables for valve pressure drop coefficient vs. time.Note: Enter the initial pressure drop coefficient for the value G2PRDR(IELVLV(IVLV)) (Block 18, Loc. 1002-1141)

The DTMBTP table for the valve loss coefficient is set to table 2, because the steam generator table is table 1. See Loc. 852-863, Block 3.

= 2

Location 1008, NEXPFBOption for control rod drive expansion reactivity feedback

= 0 No contribution to control rod expansion feedback from vessel wall heating> 0 Number of liquid elements and/or compressible volumes contributing to control

rod expansion feedback

The model contains a contribution to the control rod driveline expansion reactivity feedback from the reactor vessel. Since the control rods are suspended from the top of the reactor vessel, a thermal expansion of reactor vessel would move the control rods out of the core.To include this possibility, NEXPFB = 4, which would allow contributions from the walls of CV2 and CV3.

= 2

Location 1009-1018. IEXPFB (K)Option for control rod drive expansion reactivity feedback

> 0 Element number< 0 - Compressible volume number

The compressible volumes contribute to the expansion of the reactor vessel, moving the core with respect to the top of the reactor vessel. Compressible volumes are designated by negative integers. Based on Fig. 3-1, the walls of CV2 and CVS would be involved.

= -2, -3

- A42 -

Location 1052-1081, lELHT (K)

Element number of the K-th element involved in component-to-component heat transfer from IELHT(K) to IELHT2(K). For the second wall of annular element IELL, lELHT = 1000+IELL

The heat transfer between CV2 and CV4, and between CVS and CV4 is considered in this study. This modeling provides a significant heat sink to limit the temperature rise of the hot pool. Including these heat transfer paths also means that the code must execute a steady-state "null-transient" in order to initialize the temperatures. In these locations, the walls of a particular element or volume is listed. The corresponding coolant in another element or volume is listed in Loc. 1082-1111. Given the heat transfer paths described above, the input data in these locations is as follows.

Heat Transfer WallPath No. Temperature Loc. No. Value

1 1052 122 1053 153 1054 194 1055 245 1056 24

Location 1082-1111. lELHT 2(K)Element number- ICV- Temperature of heat sink (If -IELTH2 > max no. of C.V.S.)

These locations contain the corresponding elements for the coolant transferring heat with the wall in Loc. 1052-1081.

Heat Transfer Path No.

CoolantTemperature Loc. No. Value

1 CV4 1082 -42 CV4 1083 -43 CV4 1054 -44 CV2 1055 -25 CV4 1056 -4

Location 1112-1141, NELHTN(K)+N = Use first N nodes -N = Use last N nodes0 = Use all nodes

Heat Transfer CoolantPath No. Temperature Loc. No. Value

1 CV4 1112 02 CV4 1113 03 CV4 1114 04 CV2 1115 85 CV4 1116 -12

- A43-

Location 1153, NCCVNumber of connected compressible volume cover gases with common gas pressures.

There are two compressible volumes which share the same cover gas, the hot pool and the cold pool in the reactor vessel, or CV2 and CV3.

= 2

Location 1154, ICCVFSFirst compressible volume with common gas pressures

The number of the first compressible volume which shares the cover gas space is CV2.

= 2

Location 1155-1158, ISSIHX fllHX)Option to specify the steady-state temperature drop across an IHX

This option specification is required since the code will not initialize correctly for an IHX which has the inlet and outlet in the same compressible volume. For consistency, this option is also applicable to DRCAS heat exchanger.

= 1 If user specifies.= 0

Location 1171, NIHXBYNumber of liquid segments that bypass the IHX

In the present model, 3 flow paths bypass the IHX.

— 3

Location 1172-1181, IHXBYP(K)Liquid segments numbers for the segments that bypass the IHX

= 22 leakage flow path between CV2 and CV423 leakage flow path between CVS and CV424 overflow path for PSDRS

Location 1243, NANELNumber of annular elements.

= 7 As shown in Table 3-3

Location 1244-1273, IELANE (IANL)Element number of annular element.

= 24

- A44 -

= 1

Location 1274, NSCRVCNumber of sections in the RVACS < 7

Location 1275, IELANE OANL)Number of entries in table of h vs. T for simple RVACS model.

= 0 Use detailed RVACS model= 2

Location 1276-1281. IELRVC (IRVC)Element number or -!CV, starting at the bottom and going up.

If lELRVC(IRVC) > 1000, use second wall of element lELVRC(IRVC) - 1000.

= 1024

Location 1282-1287. NANRVC (IRVC)Number of nodes in this section, only applicable if C.V.

= 1 10

Location 1288, ISSCPCNumber of time steps in the null transient to initialize component-component heat transfer

The steady-state "null transient" is required to initialize the system temperatures when component-to-component heat transfer is included. For the present model, a null transient of 4000 sec is sufficient to stabilize all of the temperatures for the accident calculations, and a step size of 20 sec is a typical value (see Loc. 26, Block 11), so 200 time steps are needed.

= 200

Location 1289, ISST15Print PRIMAR-4 results every ISST15 steps during the null transient.

For analysis purpose, a printout every 20 steps during the null transient gives adequate information, so ISST15 = 20.

= 20

A45-

Location 1290, IDBRVDebug parameter for RVACS = 0 No debug= 1 Regular print every time step= 2 Detailed debug prints

- A46 -

BLOCK 11, OPCINGeneral integer input for running the code is contained in Block 11. This input block contains controls for time step size and for convergence criteria for various models. Many of these values have default values, as indicated.

Location 1, EPSTEMSteady-state temperature convergence criterion for fuel-pin temperatures. The recommended value is 0.01 K.

= 0.01

Location 3. EPSPOWNeutron flux amplitude convergence criterion

= 0.00001 Based on typical values for prevails studies

Location 5, DTPThe Initial and maximum main time step length depends on the transient being analyzed

— 0.25 For LOF0.50 For TOR0.50 For LOHS

These values can be increased during stages of the transient when changes are slow.

— 0.10

Location 6. DTMXBThe maximum heat transfer time step length after coolant boiling inception, (sec)

= 0.01 Recommended value 0.02 Maximum value

Location 7. TIMAXThe maximum problem time, (sec)

= 500.0

This value is arbitrary, depending the length of calculation desired. This value is used in conjunction with MAXSTP, Block 1, Loc. 11, to control the length of the calculation. Restart file is saved when time TIMAX is reached if NSTEP (Block 1, Loc. 15) > 0.

- A47-

Location 9, TCOSTPNumber of CPU seconds at the end of the calculation reserved for writing the restart file, when NSTEP > 0, (sec)

= 10.0 Sufficient for operation

Location 10, DTFUELMaximum allowable fuel temperature change per heat transfer time step, (K)

= 50.0 Recommended value

Location 11, OTCLADMaximum allowable clad temperature change per heat transfer time step, (K)

= 30.0 Recommended value

Location 13. DTPOInitial PRIMAR time step size, (s)

-10.0 Recommended value

Location 14, DTP MAXMaximum PRIMAR time step size before boiling starts, (s)

= 10.0 Recommended value

Location 15. DTPBOIMaximum PRIMAR time step size after start of boiling, (s)

= 0.01 Recommended value

Location 26. DTSSCPTime step size for the null transient, which is a calculation to determine the initial temperatures throughout the reactor system modeled by PRIMAR-4 when the component-to-component heat transfer option is used. (See also Block 3, Loc. 1288).

= 10.0 Based on the typical reactor system design

Location 27, EPSSCPConvergence criterion for component temperatures in the null transient, (K)

= 1.0D-12

- A48 -

BLOCK 12, POWINAThis block data support the core modeling. Only nonzero entries are indicated unless a zero value has a particular meaning.

Most of the neutronics information comes from Ref. A2 and those data are for Beginning-of-equilibrium cycle (BOEC) condition.

Location 2, GENTIMPrompt neutron lifetime, (sec)

GENTIM := 2.954 x 10" 7 BOEC value from Table C-20 of Ref. A2

Location 3. POWTOTTotal reactor power, (Watt)

POWTOT := 3.922 x 108 392.2 MWth, from Table C-1 of Ref. A2

Location 4-9, BETADN(L)The effective delayed neutron fraction for the delayed neutron precursor families.For this study, six delayed neutron precursor families are used, with the data obtained from Table C-20 of Ref. A2 for each family with the following delayed neutron fractions;

BETAeffective := 0.0035541

k := 1 . .6

GROUPk := BETAk :=

1 2.3532 17.4993 14.9124 36.0155 21.3386 7.883

BETTADNk := ^BETA^fective^ x BETA|<

BETTADNk =1

1 8.362870-52 6.219370-43 5.299970-44 1.2870-35 7.583770-46 2.801770-4

- A49 -

Location 10-15, DECCON(L)The decay constant for each delayed neutron precursor family, obtained from Table C-20 of Ref. A2, with units of 1/sec.

GROUPk = DECCONk :=

1 0.013462 0.030943 0.11747

4 0.30459

5 0.85965

~6 2.94183

DECCONk=1

1 0.01346

2 0.03094

3 0.11747

4 0.30459

5 0.85965

6 2.94183

Location 29-48. PREATB (L)Transient external reactivity or power table utilized by function PREA for NPREAT > 0 (Block 1, Loc. 18)If reactivity is input, entries are in dollars. If power is input, entries are normalized to nominal power, where L=1, .... NPREAT

= 0.0 0.0 0.0 NPREAT = 3

Location 49-68. PREATM (L)Transient problem times at which values in PREATB table are to be applied, where L=1, ..., NPREAT

= 0.0 60.0 1.0x1(fi

Location 69, FRPRFraction of total reactor power represented by the sum of all SAS4A channels.

This is the fraction of the total power contained in the driver and internal and radial blankets subassemblies. It is noted that the radial blankets is included in SAS4A channels. The data are obtained from page A1 of Ref. A2, which are for BO EC condition.

FRPR := PWRhot+ PWRdr + PWRib + PWRrb

FRPR = 0.97749

- A50 -

Location 70, FRFLOWFraction of the total reactor flow represented by the sum of all SAS4A channels.

This represents the fraction of the total flow that goes through the driver and internal and radial blankets subassemblies. The data are listed in the Basic Plant parameter.

FRFLOW := F_hotassy + F_ DR assy + FJBassy + F_RBassy

FRFLOW = 0.98

Location 71, CRDLENLength of the control rod drivelines washed by sodium leaving the active core region, for ICR EXP =1 (single node model, Block 1, Loc. 31)

CRDLEN is the length measured from the top of the active fuel region to the free surface in the outlet plenum.

For the purpose of calculating the driveline expansion, the total CRDL length subjected to thermal expansion is the sum of the length washed by sodium leaving the core region plus the length from the top of the subassembly to the top of the active fuel. The other input associated with the driveline characteristics are required in the PRIMAR-4 model.

CRDLEN := 15.625-4.513 E3 and E19 in Fig. M-3 of Ref. A2

CRDLEN = 11.112 m

Location 72, CRDEXPThermal expansion coefficient of the control rod drivelines, (1/K)

Assuming the driveline is made of 316SS, the suggested value by SAS4A is 2.0*1 O'5 (1/K)

= 2.0x 10*

Location 73, ACRDEXControl rod driveline expansion reactivity feedback coefficient

Reactivity change = ACRDEX * (change in length) + BCRDEX*(change in length)2BCRDEX is not used in the current model

- -22.71 ($/m)

In the KALIMER design, the worth of total control rods is 22.71 $ at BOEC condition and the length of active fueled region in the core is 1 m. Assuming the worth is uniformly distributed along the span of 1 m, the reactivity coefficient becomes -22.71 $/m. This assumption may insert more negative reactivity into the core during the initial travel of control rods, because the control rods travel along the s-curve shape

- A51 -

Location 74. BCRDEXControl rod driveline expansion reactivity feedback coefficient

= 0 Not used in the current model

Location 75, CRDMCControl rod driver line mass times specific heat, for ICREXP =1 (Block 1, Loc. 31), (J/K)

This value is obtained from the suggested value in SAS4A, 5.6E+4fora control rod driveline 6 (m) in length. Assuming KALIMER has the same mass per unit length as suggested in SAS4A, this value is weighted by the length of driveline, CRDLEN, given in Loc. 71.

CRDMCCRDLEN

6.0x5.6x 10 CRDMC = 103712

where, CRDLEN = 11.112 m

J/K

Location 76, CRDHAControl rod drive surface area times heat transfer coefficient, for ICREXP =1, (W/K)

The suggested value in SAS4A is 2300.0 (W/K) for a 6 (m) long CRDL.

CRDHA := f CRDLEN^ x (2300.0) CRDHA = 4259.6 W/K

Location 77, UIVOLCoolant volume in the upper internal structure region

This input is defined as the coolant volume in the upper internal structure region. The suggested value in SAS4A is 25.0 m3 given fora 6 (m) CRDL.

UIVOL := /CRDLENl 6.0 x(25) UIVOL = 46.3 nv

y

The actual hot pool sodium volume of KALIMER is obtained from Fig. M-3 of Ref. A2

VoLhot := 54.843 + 38.926 + 38.814 Vol_hot = 132.583 m

The fraction of the upper internal structureUIVOL Vol hot

0.34922

- A52-

Location 78, RDEXPCCoefficient in simple radial expansion feedback model ($/K)

Detail model is used in this study

Location 79. XMCXACXMC/XAC in simple radial expansion feedback model

where,XMC = Distance from nozzle support point to core midplane XAC = Distance from nozzle support point to above core load pad

Not used data because the detail model is used in this study.

XMC := 2.08138 m

thus,XMCXAC

0.74591

XAC := 2.79038 m

Location 260-289. BETADK (L. IPW)Decay heat precursor yield group L in decay heat curve IPW (L = 1 to NDKGRP, IPW = 1 to NPOWDK) (Block 1, Loc. 17&45) where, NDKGRP = 1 to 6, NPOWDK = 1 to 5

The decay heat precursor yield for each group used to represent the decay heat curve is taken from previous work on a similar fuel.

L BETADK

1 2.20054*1Ch22 1.90590*10-23 9.93659*10-34 5.25396*10-35 1.93225*10-36 1.67409*10-2

- A53 -

Location 290-319. DKLAM (L IPW)Decay heat group decay constant for group L in decay heat curve IPW

The decay heat group decay constant for each group used to represent the decay heat curve is taken from previous work on a similar fuel.

L DKLAM

123456

6.56251 *10-2 1.7791T10-3 1.37667*1 CM 6.08268*10-^ 2.25624*10-7 1.89684*10-8

Location 320-324. BETAHT (L. IPW)Sum of BETADK (L, IPW), If BETAHT(IPW) > 0, the code renormalizes BETADK. This option is used to shift a decay heat curve up or down without changing its shape. Note that decay power is normalized to initial fission power not total power. This can be dealt here.

This value is obtained by simply summing the values for BETADK, Loc. 260-265

= 6.2250*1*2

Location 325-364, POWLVL (L. IPW)Table of normalized power for initializing the decay heat

The normalized power history for initializing the decay heat is assumed to be constant operation at nominal conditions for one cycle. There is only one entry in the table.

= 1.0000

Location 365-404. POWTIM (L. IPW)Time (s) at level POELVL, Assume a histogram power trace with NPDKST (Block 1, Loc. 46) steps, starting at L =1 and ending at L = NPDKST

The time at power level POWLVL given in Loc. 325-364 is the time for one complete cycle, 80% of 2*365 days, or 292 days. Converting this to seconds,

POWTIM := 2 x 365 x (0.80) x (24) x (3600)

POWTIM = 5.04576 x 10? sec

- A54 -

Locations 408 - 415 used only if IRADEX > 3 or < -3

IRADEX was set to -4, at Block 1, Loc. 36

Location 408, SLLMAXMaximum allowable slope of subassembly at grid plate with respect to vertical based on subassembly nozzle/grid plate clearances; default = 2.0 *10-4 (m/m)

The grid plate design assumes that the subassemblies are free to tilt at the grid plate, so an arbitrary large value is chosen. This would normally be calculated from design information on the grid plate to subassembly connection, but such data for KALIMER-150 are not available at this time.

= 1.000

Location 409, PITCHGSubassembly pitch at the grid plate at the reference temperature TR (Block 13, Loc. 419)

The subassembly pitch at the grid plate under hot condition is 0.16186 m, which isobtained from Table C-5 of Ref. A2. This implies an inlet temperature of 386.2 °C. The reference temperature is 300 K, and the mean thermal expansion coefficient forthe grid plate (316 SS) is 1.7525*1 O'5 per K.

The grid plate pitch at the reference temperature is then calculated as:

Gridpitch := 0.16186 m Ecoeff_ss := 1,7525 x 10"5 m/K

PITCHG := Gridpitch - Gridpitch x Ecoeff_ssx [(Tcorein + 273.15) - 300]

PITCHG = 0.160066 m

Location 410, PITCH AFlat-to-fiat dimension across the above-core load pad at the reference temperature TR (Block 13, Loc. 419).

The flat-to-flat dimension of the subassembly load pad (ACLP) pitch is not given in the KALIMER-150 design information. It is assumed that the design would provide for the pitch at the the load pads to be the same as the pitch at the grid plate at normal full power conditions. This means the ACLP pitch would be 0.16186 m at hot condition, which is obtained from Table C-5 of Ref. A2. Assuming that the load pad experiences only 75% of the coolant temperature rise through the core,

Taclp := Tcorein + 0.75 x (Tcoreout - Tcorein)

Taclp = 767.2 °C

- A55-

The mean thermal expansion coefficient for HT9 between the reference temperature(300 K) and the operating temperature (delTaclp) is 1.215*1O’5 per K,so the load pad dimensions at the reference temperature is calculated as below:

Ecoeff_ht9 := 1.215 x 10™ 5 m/K

PITCH A := Gridpitch - Gridpitch x Ecoeff_ht9 x [(Taclp + 273.15) - 300]

PITCH A = 0.1604 m

Location 411. PITCHTFlat-to-flat dimension across the top load pad at the reference temperature TR (Block 13, Log. 419).

The flat-to-flat dimension at the top of load pad is the same as for the ACLP, Loc. 410. so

PITCHT := PITCHA

PITCHA = 0.1604 m

Location 412, RDEXCPRadial expansion coefficient for uniform core dilation, ($/m)

The uniform radial expansion coefficient, given in Table C-19 of Ref. A2, is in the unit of (dk/k)/(dR/R) (pcm/%). The value is -5*141 (pcm)/% at BOEC condition.

CoeffRad := -141.0x5

-5

CoeffRad2 :=CoeffRad x 10

BETAeffective

BETAeffective = 0.0035541

CoeffRad2 = -1.98362 $/(dR/R)%

The effect of radial expansion on the reactivity feedback is dominant at the boundary between driver and radial blanket assemblies. Therefore the reference core radius for RDEXCP is calculated as:

Number of subassembly within the boundary region

Noassy := NhotAssy + NdrAssy+ NibAssy + NcrAssy + NgemAssy + NussAssy Noassy = 91

Lattice pitch of subassembly is the same for all types. Pitch_Dasy = 0.161 m

\/3 2 2Noassy x -y- x (Pitch_Dasy) := n x (Radius_eff)

-A56-

Radius eff := Noassy x — x (Pitch„Dasy)2 x — 2 71

n0.5

Radius_eff = 0.806375 m

therefore,

RDEXCP := CoeffRad2x-----—----- RDEXCP =-245.993 $/mRadius eff

Location 413, TLRPRCClearance between the top load pads and the restraint ring, Default value is 2.54*10*3 m.

This clearance is set based on the amount of thermal bending of the subassembly at a normalized power-to-flow ratio of 0.7. This is the power-to-flow ratio above which the core geometry should be well-defined to ensure controllability at nominal power throughout all of the operational cycles. Given all of the other values for the input variables for this model, avalue of 1.20*1 O'3 m resulted in the transition to a well-defined geometry occurring at this normalized power-to-flow ratio, so

TLRPRC := 1.2 x 10" 3 m

Location 414, BNDMM1Applied bending moment at the top of the core region, representing the flat-to-fiat temperature difference at the outer edge of the active core. Default value is 1.4*10*3

The applied bending moment at the top of the core is based on the estimated flat-to-flat temperature difference in the radial direction at that elevation. This temperature difference is typically around 10 K, and this was used to estimate the thermal bending of the subassembly. Using the equation that the moment is equal to (alpha)*(delta-T)/D, this yields about 9.6*10‘4, which was rounded-off to 1.0*10-3. As more information becomes available, this estimate can be improved.

BNDMM1 := 1.0x 10" 3

Location 415. BNDMM2Applied bending moment in the region above the core, representing the flat-to-flat temperature difference in this region for subassemblies at the outer edge of the active core. Default value is 1.4*10 3

The applied bending moment for the upper region is assumed to be the same as the one at the top of the core. There is considerable doubt as to the behavior of the flat-to-flat temperature difference in this region of the subassembly. However, the results from the model have proven to be not particularly sensitive to the value as long as the core geometry is well-defined above a power-to-flow ratio of 0.7. If it is believed that a lower value is appropriate, the top load pad and restraint ring clearance must be recalculated to reflect the change in value.

BNDMM2 := 1.0x 10”3

-A57-

Location 419. DFLCTSSubassembly displacement at the ACLP at zero power resulting from creep and irradiation swelling history, positive outward, for subassemblies at the outer edge of active core All subassemblies are assumed to be straight at zero power, so

= 0.0

Location 420. DFLTSSSubassembly displacement at the top load pad at zero power resulting from creep and irradiation swelling history, positive outward, for subassemblies at the outer edge of active core. All subassemblies are assumed to be straight at zero power, so

= 0.0

Locations 421 - 428 used only if IRADEX > 3 or < -3

IRADEX was set to -4, at Block 1, Loc. 36

Location 421, ACLPRCClearance between the compacted ACLP and the restraint ring at the ACLP elevation, if any. If no above-core restraint ring, enter 0.

KALIMER-150 has only one restraint ring at the top of assembly.

= 0.0

Location 422. FCDTR1Nominal steady-state above-core restraint ring temperature, expressed as a fraction of the average coolant temperature rise through the core.

KALIMER-150 has only one restraint ring at the top of assembly.

= 0.0

Location 423, FCDTR2Nominal steady-state top restraint ring temperature, expressed as a fraction of the average coolant temperature rise through the core.

The top restraint ring is assumed to experience only 10% of the coolant temperature rise through the core. While there is not any design information to evaluate the accuracy of this number, it should be stressed that the particular value used is largely unimportant for any transient results due to the long time constant associated with the ring thermal response. However, it is extremely important to have the value be consistent with the other input variables so the core loading behavior with power-to-flow ratio is correct. If this input value is changed, others also need to be changed. For this case,

= 0.10

■ A58-

Location. 424, FCDTRFNominal steady-state reflector load pad temperature, expressed as a fraction of the average coolant temperature rise through the core.

The reflector region of the model is identified as all of the subassemblies exterior to the outermost row of driver assemblies. This includes radial shields in the present case. An estimated of 35% is made for the average assembly in the outer region, but the results are not particularly sensitive to this number and large errors can be tolerated. This input value must be in a consistent set with the other values in the model in order to ensure that the core configuration is well-defined above a power-to-flow rate of 0.7.

0.35

Location. 425, DRCOLLAdditional clearance between the subassembly and its load pad, known as a "floating collar",

0.0 Not used for the present case.

Location 426, CRSACAdditional clearance in the interior of the core, or the difference between the actual core radius and the ideal core radius, Default is 6.35*1 O'4 m

The additional clearance remaining in the interior of the core is due to the non-ideal packing of the subassembly load pads as the subassemblies are pushed together during the ascent to power. As with some other input variables in this model, the particular value is not important, only its relation to several of the other input variables. The value used in this study is based on the measured value in a full-scale simulation test of the FFTF core load pads, and factored based on the relative number of assemblies in the two cores. FFTF has 91 subassemblies in the core.

Since the core size is proportional to the square root of the number of assemblies.

CRSAC = 0.00128 m

Location 427. PR1TCThermal response time constant for the above-core restraint ring

KALI (VIE R-150 has not restraint ring at the ACLP elevation.

- 0.0

-A59-

Location 428, PR2TCThermal response time constant for the top restraint ring

This value does not have any appreciable impact on the near term results for transients, but can be invloved in the details of the long-term response.

— 500.0

- AGO -

BLOCK 13 PMATCM

Block 13 contains the basic input data for the thermophysical properties of the core material. These data are general channel independent fuel and cladding properties. The metallic fuel properties were taken from the Metallic Fuels Handbook. The cladding properties for HT-9 are taken from the Nuclear System Materials Handbook.

Thermophysical properties required as input data for the SAS4A core model are contained in two input data blocks, Block 13 for the basic data, and Block 63 for any additional data specific to each channel and not covered in Block 13. Some of the properties are modified before being used as input data in order to be consistent with the model in SAS4A.

References:

For sodium propertyG. Birgerson et al., The SAS4A LMFBR Accident Analysis Code System, ANL/RAS 83-38, Revision 2 (February 1988)

For metallic fuel propertyG. L. Hof man et al., Metallic Fuels Handbook, ANL-FR-29 (November 1985).

For cladding HT-9 propertyNuclear System Materials Handbook, TID-26666, Hanford Engineering Development Laboratory.

- A61 -

Location 11-70, EXKTB (L. ICLAD)Thermal conductivity of the cladding in table location L (W/m-K), 10 < L<21, If only EXKTB (1) is entered, EXKTB is temperature independent.

Location 71-90. EXKTM (L)Temperature in table location L, (K)

Thermal Conductivity of HT9 Cladding

i := 1 .. 18

EXKTMj := (K_HT9), :=

294.2732337342347352357362367372377382387392397310231073

1088.72

24.524.724.925.225.425.625.926.126.326.526.827.027.227.427.627.828.028.0

123456789

101112131415161718

- A62-

Ther

mal

Con

duct

ivity

(W/m

-K)

Thermal Conductivity of HT9 Cladding

27 -

K HT9. 26 -

24 -

23 -

300 400 500 600 700 800 900 1000 1100

EXKTM.Temperature (K)

-A63-

Location 91-250, RHOTAB (L, IFUEUTheoretical fuel density in table location L, (kg/m3), 1 <= L<= 20, for fuel type FUEL, Used for I METAL = 0,

Location 251-410, RHOTEM (L. IFUEUTemperature in table location L, (K)

Density of U-Pu-Zr Alloy (Fuel Pin)

i := 1 .. 13 100% TD 75% TD

RHOTEMIj := Rho_UPuZrj :=

29340050060070080086893810001100120013001378

15800157201563015550154701539015330151701511015020149301485014780

123456789

10111213

0.75 x Rho_UPuZn =11850117901172311663116031154311498113781133311265111981113811085

100% TD: Theoretical density for U-15Pu-10Zr 75% TD : Fuel pin smear density (75%)

- A64 -

Den

sity

(kg/

m3)

Density of U-Zr Alloy (Blanket Pin)

j := 1 .. 10 100% TD 85% TD

RHOTEM2j := RhoJJZrj :=

1 293 160202 400 159503 500 158904 600 158105 700 157306 800 156407 900 155408 1000 152209 1100 15120

10 1200 15020

0.85 x Rho_UZfj = 13617 13558 13507 13439 13371 13294 13209 12937 12852 12767

100% TD: Theoretical density for U-IOZr 85% TD : Blanket pin smear density (85%)

1.62-10'

1.6-10'

1.58-10'

1.56-10'

RhoJJPuZr.1.54-10

RhoJJZr.U-Pu-Zr

1.52-10

1.5-10

1.48-10

1.46-10 1000RHOTEM1., RHOTEM2.

Temperature (K)

-A65-

Den

sity (

Kg/

m3)

i := 1 .. 10Density of Sodium

RHOTEMSj := RhoJNaj :=

1 550 883.242 650 860.533 750 837.594 850 814.435 950 791.066 1050 767.467 1150 743.648 1250 719.609 1350 695.33

10 1450 670.85

Rho_Na.

1000RHOTEM3.

1200

Temperature (K)

- A66-

Location 419, TRReference design point temperature, (K)

At this temperature, pin dimensions are measured.

= 300.0 K

Location 420-579. XKTAB (L, IFUEL)Fuel conductivity in table location L, (W/m-K), 1 <= L<= 20, for fuel type IFUEL,

Location 580-599, XKTEM (L)Temperature in table location L, (K)

Thermal Conductivity of U-Pu-Zr and U-Zr (100% TD)

U-15Pu-10Zr U-10Zr(Fuel pin) (Blanket pin)

XKTEMj :=

1 2932 3733 4734 5735 6736 7737 8738 9739 1073

10 1173

KIOOJJRuZrj :=

9.811.413.4 15 517.7 20.1 22.6 25.327.830.6

K100_UZrj :=

16.4 18.0 20.122.4 24.9 27.630.533.6 36.8 40.3

-A67-

Thermal Conductivity of U-Pu-Zr (75% TD) and U-Zr (85% TD)

For smeared densities of 75% and 85% the thermal conductivities are adjusted using the following correction for porosity.

Assuming that 25% of the porosity becomes logged with sodium and 75% remains void after irradiation, for typical fuel temperature of 1000 K,

For 25% porosity U-15Pu-10Zr

K = Corrected fuel thermal conductivity Ks = Fuel thermal conductivity, 100% TD

Ks := linterp(XKTEM , K100_UPuZr, 1000) Ks = 25.975 W/m-K

Kna = Sodium thermal conductivity Kna := 58.32 W/m-K

Pv = Gas filled porosity Pna = Sodium filled porosity

Pv := 0.25 x (0.75) Pna := 0.25 x (0.25)

2 2 2

K_Ks25 := 1 - Pv3 - Pna3 +Pna3xr 1

K_Ks25 = 0.7169

For 15% porosity U~10Zr

Ks := linterp(XKTEM , K100_UZr, 1000) Ks = 34.464 W/m-K

Pv := 0.15 x (0.75) Pna := 0.15 x (0.25)

2 2 2

K_Ks 15 := 1 - Pv3 - Pna3 +Pna3x-F - r iyx Pna3 +0 - Pna3J

K Ks15 = 0.7847

- A68 -

Ther

mal

cond

uctiv

ity (W

/m-K

)Thermal Conductivity of U-Pu-Zr (75% TD1 and U-Zr (85% TD)

K75_UPuZrj := (K_Ks25) x K100_UPuZn

K85_UZrj := (K_Ks15) x K100_UZrj

i := 1 .. 10

XKTEMi :=

1 2932 3733 4734 5735 6736 7737 8738 9739 1073

10 1173

75%’TD U-15Pu-10Zr (Fuel pin)

K75 UPuZn =1

1 7.032 8.173 9.614 11.115 12.696 14.417 16.28 18.149 19.9310 21.94

85% TD U-10Zr (Blanket pin)

K85_UZrj =1

1 12.872 14.133 15,774 17.585 19.546 21.667 23.938 26.379 28.8810 31.62

- A69 -

Ther

mal

cond

uctiv

ity (W

/m-K

)

Thermal conductivity of Sodium

XKTEMj := K_Naj :=

1 293 92.632 373 88.183 473 82.844 573 77.745 673 72.876 773 68.207 873 63.738 973 59.449 1073 55.31

10 1173 51.33

K_Na.

60 -

XKTEM.Temperature (K)

Sodium density at 1000 K

linterp(XKTEM, K_Na, 1000) - 58.3249 W/m-K

- A70-

Location 606-765. CPFTAB (L. (FUEL)Fuel specific heat in table location L, (J/kg-K), 1 <= L<= 20, for fuel type (FUEL

Location 766-785, CPFTEM (L)

Temperature in table location L, (K)

Specific Heat of U-Zr-Pu Alloy

Fuel Blanketi := 1 - 20 (U-15Pu-10Zr) (U-10Zr)

CPFTEMj := CpJJPuZrj := CpJJZrj :=

29840050060070080087389092310001100120013001379140014871588160016571700

133.04146.2

158.87172.02185.18197.85207.6191.36159.84169.59182.26194.93208.08217.83217.68217.08216.37216.37216.37216.37

150.7153.14169.72191.18216.05241.90261.29265.8

239.76178.99178.99178.99178.99178.99178.99178.99203.62206.54220.44220.44

123456789

1011121314151617181920

Sodium

Cp_Naj :=

1282.411282.411282.411282.411272.42 1265.75 1263.09 1262.47 1262.40 1263.22 1267.95 1277.21 1291.59 1307.07 1311.86 1335.14 1370.16 1374.99 1400.13 1421.81

Note: Specific heat capacity is not dependent on the smear density,

Spec

ific h

eat (

J/kg

-K)

Specific Heat of U-Pu-Zr and U-Zr

CD

Cp_UPuZr.S e-e

Cp_UZr.£'5 D OI

260

240 "

220

200

180

160

140

280

120200 400 600 800 1000 1200 1400 1600 1800

CRFTEM.Temperature (K)

Specific Heat of Sodium

1400 -

1300 "

800 1000 1200 1400 1600 1800CRFTEM.

Temperature (K)

- A72-

Location 786-791. TFSOL (IFUEL)Fuel solidus temperature (K)

= 1379.0 for U-15Pu-10Zr= 1487.0 for U-10Zr= 370.0 for Sodium

Location 794-799. TFUQ (IFUEL)Fuel liquidius Temperature (K)

= 1588.0 for U-15Pu-10Zr= 1657.0 for U-10Zr= 380.0 for Sodium

Location 802-807. UFMLT(IFUEL)Fuel heat of fusion, (J/kg)

= 91600.0 for U-15Pu-10Zr= 90200.0 for U-10Zr= 113000.0 for Sodium

Location 810, TESOL (ICLAD)Cladding solidus temperature, (K)

= 1690.15 for HT-9

Location 813, TELIQ (ICLAD)Cladding liquidus temperature, (K)

= 1710.15 for HT-9

Location 816, UEMELT(ICLAD)Cladding heat of fusion (J/kg)

= 268300.0 for HT-9

- A73-

Location 819-878, CPCTABCladding specific heat, (J/kg-K),

Location 879-898, CPCTEM (L)Temperature, (K)

Specific Heat of HT-9

i := 1 .. 12

CPCTEMj :=

1 3732 4733 5734 G735 7736 8737 9238 9739 998

10 102311 107312 1088.56

Cp_HT9j :=

482.5521.48563.37615.38684.68784.96866.081021.51210.0868.34747.97762.14

400 ----------- '----------- 1----------- '----------- '----------- '----------- '----------- '-----------1300 400 500 600 700 800 900 1000 1100

CPCTEM.iTemperature (K)

- A74 -

Location 990-1049, CROETB (L, ICLAD)Specific heat * density for cladding in table location L , (J/m3-K), 0 < L< 21 If only CROETB(1) is entered, CROETB is temperature independent.

Location 1050-1069, CROETM (L)Temperature, (K)

CROETMj := (CpRho_HT9)j :=

123456789

101112

373566040237904330850471178052202105958630655969077194809133690654728056269805729620

37347357367377387392397399810231073

1088.56

CpRho„HT9.CC 0-6

1000 1100CROETM.

Temperature (K)

Location 1086. RGASSIIdeal gas constant

= 8.31434 Suggested value in SAS4A

- A75 -

Properties of stainless steel, 304SS and 316 SS, are obtained from Table M-3 of Ref. A2. These data are not required in Block 13 but they will be referred later in other block data.

Tcssj :=

21.1137.7893.33148.89204.44

260315.56371.11426.67482.22537.78593.33648.89704.44

760815.56

Density of Stainless Steel i := 1 .. 16

Tkssj := Tcssj + 273.15

Tkssj =1

1 294.262 310.933 366.484 422.045 477.596 533.157 588.718 644.269 699.8210 755.3711 810.9312 866.4813 922.0414 977.5915 1033.1516 1088.71

Rho_304SSj :=

8024.438024.437996.757971.847946.937922.027894.347869.427844.517819.67791.927767.017742.17717.187689.57664.59

Rho_316SSj :=

7963.547963.547935.867908.187888.87863.897838.987814.067789.157767.017739.337717.187689.57667.367642.457617.54

5 Rho„304SS,7900

Rho_316SS.

7700

Temperature (K)

- A76-

Spec

ific H

eat (

J/kg

-K)

Specific Heat of Stainless Steel (Structure)

Tkssj =1

1 294.262 310.933 366.484 422.045 477.596 533.157 588.718 644.269 699.8210 755.3711 810.9312 866.4813 922.0414 977.5915 1033.1516 1088.71

Cp__304SSj :=

477.42483.79503.00519.40533.32545.11555.11563.67571.13577.83584.13590.36596.87604.00612.09621.50

Cp_316SSj :=

465.65472.33492.50509.71524.31536.68547.18556.16563.99571.03577.64584.18591.01598.50607.01616.90

Cp_304SS.

Cp_316SS.

1000 1100

Temperature (K)

- A77-

BLOCK 14, PRIMIN

This input block contains data on the coolant flow and temperatures in the primary loop. Most of the data is used by the PRIMAR-4 model, while the rest involves the boiling model. Only nonzero values are discussed unless a value of zero has a particular meaning.

Location 1, PXCoolant exit pressure at ZPLENU (Block 14, Loc. 88), (Pa)

PX is calculated based on atmospheric pressure at the surface of the outlet plenum, with the elevation ZPLENU which is at the top of the subassembly. The pressure and elevation ZPLENU must be consistent with the PRIMAR-4 pressure and elevation in Block 18.

Sodium density at hot plenum temperature is calculated using the data of Block 13, Loc. 91-250:

Thot := Tcoreout Thot = 803.15 K

p_hot := linterp(RHOTEM3, Rho_Na ,Thot) p_hot = 825.28046 kg/m3

Elevation ZPLENU is from E11 to E3 of Fig. 18-1, which is a copy of M3 of Ref. A2,

Thus,PX := 1.01325 X (10)5 + p_hotx (9.807) x (15.625 - 6.385)

PX = 1.7611 x 105 Pa at the subassembly exit

It is noted that hot pool level (compressible volume 2) can be determined from this input.

Location 45-64, TOTAB (L)Core inlet temperature as a function of time. L is defined in NTOTAB (Block 1, Loc. 22)

Since PRIMAR-4 calculates the transient coolant temperatures at each time step, only the steady-state value is needed as input data.

TOTAB := Tcorein TOTAB = 659.35 K

Since NTOTOB = 2, TOTAB = 659.35 659.35

-A78-

Location 65-84, TOTME (L)Entry of time for TOTAB, (s)

TOTME = 0.0 1.0x105

Location 85, TNTRYTemperature of the sodium reentering the subassembly from the top. Used only if PRIMAR-4 is not used.

Since PRIMAR-4 is utilized, it is set to the steady-state temperature at the core outlet plenum.

TNTRY := Tcoreout TNTRY = 803.15 K

Location 87, ZPLENLReference elevation for the coolant inlet plenum.Default = bottom of assembly in channel 1

It is set to the elevation of the bottom of the subassembly. Refer to Fig. 51-1.

ZPLENL := -1.5910 m

Location 88, ZPLENUReference elevation for the coolant outlet plenum.Default = top of assembly in channel 1

It is set to the elevation of the top of the subassembly. Refer to Fig. 51-1.

ZPLENU := 3.1647 m

Location 90. DZBCGLMinimum distance above subassembly exit for bubble breakaway

= 0.1 Suggested value

Location 91. DZBCGUMaximum distance above subassembly exit for bubble breakaway

= 0.25 Suggested value

Note: When the top of the bubble is above DZBCGU or the bottom is above DZBCGL, the portion above DZBCGL is broken away.

- A79-

BLOCK 51, INPCHN

Channel Dependent Options (Integer Input)

Block 51 contains the general integer input data for selecting general channel- dependent input options. This includes the number of segments and nodes per axial zone, correspondence of material properties with channel assignment, and selection of appropriate temperature nodes for plotting outputs. Much of the input is generated in connection with the channel geometry, with reference to Fig. 51-1.

Core Channel Modeling

The core is represented by SAS4A model. Four types of assembly are treated in the SAS4A model, which are:

1st. channel

2nd. channel 3rd. channel 4th. channel

Assembly with the highest average power-to-fiow ratio with a respectively high average power (peak power assembly)

All remaining driver assemblies All internal blanket assemblies All radial blanket assemblies

The remaining assemblies are each treated as a bypass channel, as are the control rod assemblies, shield assemblies, reflector assemblies, and etc. The bypass channel consists of 3 channels in PRIMAR-4 model.

SAS4A uses a multi-channel treatment where each channel represents a fuel pin, its associated coolant, and a fraction of the subassembly duct wall. Each channel above represents an average pin in a group of similar subassemblies.

In the metal fuel of KALIMER-150, sodium is filled as bonding above the fuel pin in the active core. The SAS4A fuel model provides axial blanket zones above and below the fuel region. Since there are not any axial blankets in the KALIMER-150 design, the lower blanket region has 0 segments and the upper blanket region is used to represent the sodium bonding with 4 segments. The SASSYS-1 channel axial description is shown in Fig. 51-1. The core has five axial zones (KZ=5):

KZ=1, A lower reflector with 2 axial segments KZ=2, A lower reflector zone with 2 axial segments KZ=3, A lower reflector zone with 3 axial segmentsKZ=4, A fuel pin zone with 20 segments for the active fuel, 4 segments for the

sodium bonding, and 6 segments for the upper fission gas plenum.KZ=5, An upper reflector zone with 4 axial segments

The internal and radial blankets have the same zones and noding as the drivers.

- A80-

Location 4, NPLNNumber of segment in gas plenum, 1 <= NPLN <= 6

= 6

Location 5, NREFBNumber of reflector zones below the pin section, 1 <= NREFB <= 5

= 3

Location 6, NREFTNumber of reflector zones above the pin section, 1 <= NREFT <= 5 NREFB + NREFT <= 6

= 1

Location 7-11, NZNODENumber of segments in Zone KZ, KZ <- 7 Total number of all segments in all zones <= 48 Only one segment per node is necessary.

KZ Segments

12345

2 Lower Reflector zone2 Lower Reflector zone3 Lower Reflector zone30 Upper & lower blankets, fission gas, and fuel region4 Upper Reflector zone

Location 14, NTNumber of radial temperature nodes within the fuel, 3 < NT < 12

= 11 It is usually set to 11.

Location 15. IFUELVTable number of property value to be used for core fuel, 0 < IFUELV <= IFUEL1 IFUEL1 is defined in Block 1, Loc. 3.

Table number of property table to be used from Block 13 for core fuel.

Property Table Channel Number

2244

1 (hot driver assembly)2 (remaining driver assemblies)3 (inner blanket assemblies)4 (radial blanket assemblies)

-A81-

Location 16, IFUELBTable number of property value to be used for axial blanket fuel, 0 < IFUELB <= IFUEL1 IFUEL1 is defined in Block 1, Loc. 3.

The fifth table of the fuel material in Block 13 is for sodium property. The sodium bonding above the fuel pin is modeled by axial blanket fuel.

Property Table Channel Number

5555

1 (hot driver assembly)2 (remaining driver assemblies)3 (inner blanket assemblies)4 (radial blanket assemblies)

Location 17. ICLADVTable number of property value to be used for cladding table.

Table number of property table to be used from Block 13 for cladding. Only one clad table for HT-9 is used in Block 13.

Property Table Channel Number

1111

1 (hot driver assembly)2 (remaining driver assemblies)3 (inner blanket assemblies)4 (radial blanket assemblies)

Location 25. NPINNumber of pins per subassembly

Number of Pins Channel Number

271271127127

1 (hot driver assembly)2 (remaining driver assemblies)3 (inner blanket assemblies)4 (radial blanket assemblies)

N„Dpin = 271 N_Bpin = 127

Location 26, NSUBASNumber of subassemblies in channel

Number of Pins Channel Number

6482448

N hot Assy = 6 NdrAssy = 48

1 (hot driver assemblies)2 (remaining driver assemblies)3 (inner blanket assemblies)4 (radial blanket assemblies)

NibAssy = 24 NrbAssy = 48

- A82-

Location 27, MZUBNumber of segments in upper blanket

= 4

Sodium bonding above the fuel pin is represented by the upper blanket. Since sodium bonding is 20 cm, the length of each segment is 20 cm / 4 = 5 cm.

Location 28. MZLBNumber of segments in lower blanket

= 0

There is no axial blanket in the KALIMER fuel design.

The following input data, from Loc. 90 to Loc. 94. represent the axial nodes for which output is sent to the plotting file for post processing. The values do not have any effect on the calculation, or on the values typically plotted from File 11, the standard plot file.

Location 90, JCLNAxial heat transfer segment, output on the plotting unit for fuel information, 1 <= JCLN <= MZ

= 20

This number is usually taken as the top node in the core fuel region.

Location 91, JNENAxial coolant node, output on the plotting unit for cladding temperature,1 <= JNEN <= MZC

= 27

This node is usually selected as the same node as JCLN, Loc. 90, but the node number is based on the coolant node structure.

Location 92, JHCNAxial coolant node, output on the plotting unit for coolant temperature,1 <= JHCN <= MZC

= 27

This node is usually selected as the same node as JCLN, Loc. 90, but the node number is based on the coolant node structure.

- A83-

Location 93, JNSNAxial coolant node, output on the plotting unit for structure temperature,1 <= JNSN <= MZC

= 27

This node is usually selected as the same node as JOLN, Loc. 90, but the node number is based on the coolant node structure.

Location 94, JRPROAxial heat transfer segment, 1 <= JRPRO <= MZ, output on the plotting unit for total radial profile (written each time the mass averaged fuel temperature, TBAR, increased by DTFUEL degrees)

= 20

This node is usually selected as the same node as JCLN, Loc. 90

Location 118. IEQMASRadial fuel mesh size assumptions

= 0 Equal radial distance between points at which temperatures are calculated> 0 Equal cylindrical areas associated with each radial temperature node

= 1

Location 181, IAXEXPSimple axial expansion reactivity feedback model.

= 0 No simple axial expansion feedback= 1 Calculate feedback= 3 Calculate and print simple axial expansion feedback for each channel

See Block 1, Loc. 55 for model choice.

Location 203. IDKCRVPower or decay heat curve for this channel

= 1 Decay heat curve is set the same for all channels

- A84-

axial elevation (m)

4 segmentsReflector

MZ=30 -

i_____________* ' i Gaso sogmerits .......

! PlenumSodiumbondingX __________4 segments f—........— --------

20segments

MZ=2 I-----------MZ=

3 segments Reflector

segments

segments

MZC=42

MZC=41

Ocy"OcdO c<ts

ooo

MZC=2

MZC=1

CD

=5uzs

CO

3.1647

2.351

1.200

1.000

0.000

-0.5585

-1.1170

-1.591

ii

KZ=5

v

KZ=4

::KZ=3

KZ=2

i k

VKZ=1

Fig. 51-1 SAS4A Axial Zones and Fuel Nodes for KALIMER-150 Core

- A85-

Fig. 51-2 Component names of KALIMER

Note: RV Liner is called Reactor Baffle, alternatively.

- A86 -

BLOCK 61, GEOMIN

This input block contains all of the geometrical data required by the SAS4A channel models. The input data are based on the information provided in Ref. A2. The channel models assume a single pin geometry for the calculation, which extends from the bottom to the top of the subassembly. The single pin is divided into a number of axial zones, where one zone represents the fuel and fission gas plenum as shown in Fig. 51-1. The data defining the zones in the channel is in Block 51.

Location 1-7, ACCZ (KZ)Coolant flow area per fuel pin in zone KZ.

ACCZ is the total flow area within the subassembly divided by the number of fuel pins. The total flow area is the cross-sectional area within the hexcan, minus the cross-sectional area occupied by the fuel pins and the space wire. The number of axial zones KZ is 5, as shown in Fig. 51 -1. The same flow area is used in each zone.

Data are from Tables C-5 and

Number of pins per Assembly

Assembly lattice pitch (m)

Duct inner flat-to-flat (m)

Duct outer flat-to-flat (m)

Pin outer diameter (m)

Wire wrap diameter (m)

-6 of Ref. A2. Dimensions

Driver Fuel

N_Dpin - 271

Pitch_Dasy =0.161

L_Dinflat = 0.1496

L_Doutflat = 0.157

OD_Dptn = 0.0074

DJOwire = 0.0014

the values at cold condition.

Blanket Fuel

N_Bpin = 127

Pitch_Basy = 0.161

L_Binflat = 0.1496

L_Boutflat = 0.157

OD_Bpin = 0.012

D_Bwire = 0.00095

For Driver (Channels 1 and 2)

ACCZi :=-----------xV3x(L Dinflat)2 - n xN_Dpin 2

OD Dpin- 7TX

D DwireV

ACCZ! = 2.69717 x 10-5 nr

For Blanket (Channels 3 and 4)

ACCZ3

ACCZ3

1NJ3pin X

^x(L_Binflat)2 D_BwireV2 J

= 3.88063 x 10 m2

- A87 -

Location 8-31, AXHI (J)Length of axial node in the zone representing the fuel and blankets, 1 <= J <= MZ

According to Block 51, there are 24 axial nodes for the fuel and the axial blankets (sodium bonding). It is noted that there is no lower blanker in KALIMER. Active core consists of fuel slug with 20 nodes, an upper blanket with 4 nodes, and a lower blanket with 0 nodes. The upper 4 nodes are not real axial blankets, but are modeled using sodium to provide heat capacity of sodium bonding.

Dimensions are from Fig. C-4 of Ref. A2.

Fuel region L_slug := 1.00 m

Upper sodium bonding region L_sodium := 0.20 m

Thus, length of axial segment is determined:

k := 1 .. 20 AXHIk := L~Slug AXHh = 0.05 m20

m := 21 .. 24 AXHIm := L~S—1—ID AXHI21 = 0.05 m4

* A88 -

Location 32-38. DHZ (KZ)Hydraulic diameter in each zone KZ

This is calculated using the following equation:

DHZ(KZ) = 4* (coolant flow area1 No. of pin)/(wetted perimeter) where coolant flow area per pin was already calculated in ACCZ(KZ).

For Driver (Channels 1 and 2)

Wetted perimeter per pin

Peri D x+ txx (OD Dpin) + tix (D Dwire)V3 N_Dpin ™

Peri_D = 0.02956 m

Thus, hydraulic diameter

DHZi = 0.00365 m

For Blanket (Channels 3 and 4)

Wetted perimeter per pin

Peri B := -= x6 ^ (L__Binflat) V3 N_Bpin

+ n x (ODJBpin) +jtx (D_Bwire)

PerLB = 0.04476 m

Thus, hydraulic diameter

DHZ3 = 0.00347 m

- A89 -

Location 39-45, DSTIZ (KZ)Thickness of inner structure node (m)See Block 13, Loc. 1214 for consistent input.

The structure in the channel model represents the hexcan duct wall, the sodium in the gaps between the assemblies, and the spacer wire. The structure thickness is set to simulate the correct thermal time response for the structure. This is accomplished by first calculating an equivalent steel wall cross-sectional area representing the steel and sodium, according to the equation:

Effective wall area (assuming HT9 material properties at 400 deg C):

AwaILn = A wall + Agap*(Cp(NA)*p(NA))/(Cp(HT9)*p(HT9))

This areas are calculated as follows, with ID and OD referring to the inside and outside flat-to-flat dimensions, respectively. It is noted that drivers and blanket assemblies have the same duct design. Therefore, DSTIZ’s for all KZ are the same.

Awall :=^x (L_Doutflat2 - L_Dinfiat2)

Agap := — x (pitch_Dasy2 - L_Doutflat2)

where, PitchJDasy = 0.161 m

AwaILn := Awall + Agap x (855) x (1275) (615.4) x (7656.7)

Awall = 0.00196 m2

Agap = 0.0011 m2

AwaILn = 0.00222 m2

The structure thickness is determined by using the equivalent area and the hexcan inside flat-to-flat distance. t_wall can be determined from the equation to calculate Awall, with the relation of L_Doutflat = L_Dinflat + 2 x t_wall.

t wall 2x_(AwaN_n)+L Dinflat2 - L DinflatVi

1X —

2

t wall = 0.00417 m

The structure thickness is divided into two radial nodes, and for the present study, half of the thickness is used for each node.

DSTIZ := ~ x (t_wall) DSTIZ = 0.00208 m

- A90 -

Location 46-52, DSTOZ (KZ)Thickness of outer structure node (m)

The thickness of the outer structure node is the same as the inner structure node, half of the thickness in each node, so that:

DSTOZ := DSTiZ DSTOZ = 0.00208 m

Location 53, PLENLLength of fission gas plenum

Actual length of fission gas plenum is from Fig. C-4, Ref. A2., which is consistent with Fig. 51-1.

L_FGR := 2.351 - 1.2 L_FGP = 1.151 m

Location 54-77, RBR (J)Cladding inner radius for axial segment J, 1<= J <= MZ, (m)If all values are the same, only the first must be input.

Location 78-101. RER (J)Cladding outer radius for axial segment J, 1 <= J <= MZ, (m)If all values are the same, only the first must be input.

The cladding inner radius for each axial segment in the fuel and axial blanket region is the same, as given by the cladding outer diameter and cladding thickness.

For Driver (Channels 1 and 2)

Clad inner diameter ID_Dclad = 0.0063 m

Pin outer diameter OD_Dpin = 0.0074 m

Thus, cladding inner radius

RBR,

cladding outer radius

RER1 := OD^Dpin 2

RBR-j = 0.00315 m

RER-| = 0.0037 m

- A91 -

For Blanket (Channels 3 and 4)

Clad inner diameter ID_Bclad = 0.01092 m

Pin outer diameter OD_Bpin = 0.012 m

Thus, cladding inner radius

RBR3 := 'D-Bclad RBR3 = 0.00546 m

cladding outer radius

RER3 := 0D-Bpirt RER3 = 0.006 m

Location 102. RBRPLCladding inner radius in gas plenum, (m)

Location 103, RERPLCladding outer radius in gas plenum, (m)

The clad inner and outer radius in the gas plenum are the same as for the fuel region,Location 54-77 and 78-101.

For cladding inner radius

RBRPL-i := ID"Dclad RBRPLt = 0.00315 m For Driver

RBRPLs := 'D-Bclad RBRPLs = 0.00546 m For Blanket

For cladding outer radius

RERPL] := OD-Dpin RERPL-i = 0.0037 m For driver

RERPL3 := °D-Bpm RERPLs = 0.006 m For Blanket

- A92 -

Location 104-127, RINFP(J)Fuel inner radius for each axial segment J, (m) 1 <= J <= MZIf all values are the same, only the first must be input.

The fuel inner radius for each axial segment in the fuel region is set to 1.0*10"6 m, to accommodate the use of DEFORM-4.

= 1.0x1 O'6 Suggested value

Location 128-151, ROUTFP(J)Fuel outer radius for axial segment J, (m) 1 <= J <= MZif all values are the same, only the first must be input.

The fuel outer radius for each axial segment in the fuel region is set to the clad inner radius, Loc. 54-77, when DEFORM-4 is not being used.

ROUTFPi := ID-Pclad ROUTFPi = 0.00315 m

ROUTFP3 := '°-^Clad ROUTFP3 = 0.00546 m

Location 152-158. ZONEL (KZ)Length of zone KZ, (m)

The length of each zone KZ in the single pin model is shown in the Fig. 51-1 of Block 51. Starting from the bottom of the assembly ,

i := 1 .5

ZONEL; :=

1 1.591 - 1.11702 1.1170-0.5585

3 0.5585-0

4 2.351 - 0~~5 3.1647-2.351

ZONEL; =1

1 0.47402 0.55853 0.55854 2.35105 0.8137

total length of subassembly ^ ZONEL; 4.7557 mi

-A93-

Location 159-165. SRFSTZ (KZ)Structure perimeter in zone KZ per pin

The structure perimeter is used in conjunction with the structure thickness,Loc. 39-42, to simulate the proper thermal time response of the structure.

Structure perimeter per pin = { Awall_n/No. of pins + 7i/4*(wire OD)2}/ wall thickness where, Awll_n is obtained from Loc. 39-45.

For Driver (Channels 1 and 2)

SRFSTZ-j :=

+ Dwire):N Dpin 4

t wall

SRFSTZ-] = 0.00233 m

For Blanket (Channels 3 and 4)

SRFSTZ3 :=

AwaILn N Bpin

+ ^ x (D_Bwire)2

t_wall

SRFSTZ3 = 0.00436 m

- A94-

Location 166, AREAPCCoolant plus pin area per pin, in the pin section, (m2)

The coolant plus pin area per pin, in the pin section, is determined by total cross-section area per pin and subtracting the cross-sectional area of the space wire:

= {(3)0-5 / (2 * No. of pin)} * (duct ID)2 - n * (wire ID / 2)2

For Driver (Channels 1 and 2)

D Dwire 2

2AREAPC-i :=

2 x (N_Dpin)- 71 x

AREAPC-j = 6.99801x 10-5 m

For Blanket (Channels 3 and 4)

^3x(L Binflat)2

2 x (N_Bpin)D J3wire

2

2AREAPC3

AREAPC3 = 1.51904x10-4 m

- A95-

Location 169-175, DRFO (KZ)Thickness of the outer reflector node in zone KZ, (m)

For KZ not equal to KPIN, DRFO is the thickness of the outer reflector node(two-slab geometry)

For KZ equal to KPIN, DRFO is the cladding thickness in the plenum region(RERPL - RBRPL) (Loc. 103 - Loc. 102, Block 61)

The reflector zones above and below the fuel pin section are treated in a different manner. The thickness of the reflector zones is based on a heat transfer model which represents the reflector zones in a slab geometry. The reflector is assumed to be a solid pin with the same area and perimeter as the driver or blanket fuel pins. A two node slab geometry is used for the heat transfer to the reflector, where the effective reflector thickness can be obtained from:

n * R(radius)2 = P(perimeter) * t(thickness), where P = 2 * n * R

In order to preserve both the perimeter and the cross-sectional area

t_reflector = R / 2 for a slab geometrywhere, R = cladding outer radius (RER, Loc. 78)

Thus,

For driver pins t Dreflector := QP-DPin 2x2

t_Dreflector = 0.00185 m

For blanket pins t Breflector := QP-BPin 2x2

t_Breflector = 0.003 m

These thickness are divided equally between the inner and outer reflector nodes. The clad thickness for the fuel and fission gas plenum region is t_clad (m), which is used for the reflector thickness in this zone.

Clad thickness data are obtained from the Basic Plant Parameter.

t_Dclad = 0.00055 m t_Bclad = 0.00054 m

For Driver (Channels 1 and 2): KZ := 1 „ 5

KZDRFCM KZ DRFOl KZ =

1 (t Dreflector) x 0.5 9.250070-4~~2 (t Dreflector) x 0.5 9.250070*4

(t Dreflector) x 0.5 9.250070-4

4 t Dclad 5.500070-45 (t_Dreflector) x 0.5 9.250070-4

- A96 -

For Blanket (Channels 3 and 4):

KZ z= DRFO_3kz :=DRFO„3kz =

1 (t B reflector) x 0.5 1.500070-32 (t Breflector) x 0.5 1.500070-33 (t Breflector) x 0.5 1.500070-34 LBclad 5.400070-4

~5 (t_Breflector) x 0.5 1.500070-3

Location 180, RBRONominal cladding inner radius, (m)

The same as the cladding inner radius listed in Loc. 54-77.

RBRO-| := ID-Dclad RBROt = 0.00315 m for driver

RBRO3 := ID"BClad RBRO3 = 0.00546 m for blanket

Location 181. RERONominal cladding outer radius, (m)

The same as the cladding outer radius listed in Loc. 78-101.

REROi := PD-DP'n RERO-i = 0.0037 m for driver

RERO3 := P.D-BP'n RERO3 = 0.006 m for blanket

Location 182-188. SER (KZfReflector perimeter per pin wetted by coolant in the reflector zone, (m)

The reflector perimeter per pin in each zone is the nominal pin perimeter, consistent with the cross-sectional area used to determine the reflector thickness in Loc. 169-175 and Loc. 189-195. The pin parameter is also used in the gas plenum region.

= 2 * 7i* R(pin radius = clad outer radius) for both drivers and blanket assemblies

SERi := 2 x 7t x OD—DPin2

SER-| - 0.02325 m for driver

SER3 :=2xnx0D-Bpin2

ser3 = 0.0377 m for blanket

-A97-

Location 189-195, DRFl (KZ)Thickness of the inner reflector node in zone KZ, (m)

KZ:= 1 ..5

For Driver (Channels 1 and 2)

KZDRFUkz DRFUkz =

T (t Dreflector) x 0.5 9.250070-4~2 (t Dreflector) x 0.5 9.250070-4~3 (t Dreflector) x 0.5 9.250070-4

4 0.0 0.00005 (t_Dreflector) x 0.5 9.250070-4

For Blanket (Channels 3 and 4)

KZ DRFI_3kz := DRFI_3kz =~T (t Breflector) x 0.5 1.500070-3

2 (t B ref lector) x 0.5 1.500070-33 (t Breflector) x 0.5 1.500070-34 0.0 0.00005 (t_Breflector) x 0.5 1.500070-3

- A98-

BLOCK 62, ROWING

This input block contains all of the channel dependent neutronics input data. The majority of the data comes from the combination of the subassembly-by -subassembly data for the core. This block also includes other data to account for differences in irradiation between the channels, but for this study, all assemblies are assumed to have an irradiation of one cycle.

The assembly arrangement in a 1/6 symmetry representation of the reactor core is shown in Fig. C. Each core position represents a number of identical subassemblies around the core, which in this case is usually 6.

Location 2, GAMSSFraction of total power in direct heating of structure A representative value is 0.0078.

= 0.0078

Location 4, GAMTNCFraction of total power in direct heating of coolant A representative value is 0.0048.

= 0.0048

Location 5. GAMTNEFraction of total power in direct heating of cladding A representative value is 0.0114.

= 0.0114

Therefore, the fraction of total power deposited into the fuel is:

1 - (0.0078 + 0.0048 + 0.0114) = 0.976

- A99-

Location 6-29. PSHAPE (J)Ratio of pin power at axial segment J to the power ROW in the peak axial fuel pin segment for all nodes in the core, 1 <= J <= MZ, MZ is the number of axial heat transfer segments in the core plus axial blankets (Refer to Fig. 51-1)

Axial power distribution data for the pin length is obtained from Table C-28 and Fig. C-4 of Ref. A2. Normalized axial positions along the reference pin length (3.468 m) are:

i1 := 1 .. 30 i2 := 31 .. 60 i3 := 61 .. 81

Posn := j2 = PoSj2 :=

0.00.007230.021680.036130.050580.065030.079490.093940.108390.122840.137290.151740.166200.180650.195100.209550.224000.238460.252910.267360.281810.296260.310710.323880.335770.347650.359540.371420.383310.39519

0.407070.418960.430840.442730.454610.466500.478380.490270.502150.514040.525920.537800.549690.561570.573460.585340.597230.609110.622180.636440.650690.664940.677930.689640.701350.713060.724770.736490.748200.75991

313233343536373839404142434445464748495051525354555657585960

123456789

101112131415161718192021222324252627282930

Posi3 :=

0.771620.783330.795040.806760.818470.830180.841890.853600.865320.877030.888740.900450.912160.923870.935590.947300.959010.970720.982430.99414

1.0

616263646566676869707172737475767778798081

- A100

For Driver fuel (Channels 1 and 2)

The power density at each axial location for the driver fuel is from Table C-28 of Ref. A2.

0.000.000180.000420.000680.000980.001330.001770.002300.002950.003750.004720.005880.007260.008860.010670.012680.014820.016980.018960.020490.021150.020370.017402.412062.604812.846873.097943.338783.473693.66536

123456789

101112131415161718192021222324252627282930

DFi2 := j3 = DFj3 -

3.829283.962274.062004.097634.127594.122504.082234.007313.946373.801853.624553.416943.182143.012112.724362.422052.118211.837440.004420.004620.004640.004570.004500.004450.004380.004290.004170.004030.003870.00370

616263646566676869707172737475767778798081

0.003520.003330.003140.002940.002750.002550.002360.002170.001990.001810.001630.001460.001300.001130.000970.000820.000660.000510.000360.000200.0000

313233343536373839404142434445464748495051525354555657585960

- A101 -

For Inner blanket (Channel 3)

The power density at each axial location for the inner blanket is from Table C-28 of Ref. A2.

i1 =IBj 1 :=

i2 = \B\2 := i3 = !Bi3 :=

123456789

101112131415161718192021222324252627282930

0.00.000830.001980.003220.004660.006370.008450.011000.014140.017970.022630.028230.034850.042560.051340.061070.071470.081980.091740.099360.102820.099230.084582.178412.403892.646802.886873.115413.601963.80201

313233343536373839404142434445464748495051525354555657585960

3.971164.108214.212124.395714.428254.421424.375274.289103.953813.802173.619243.404903.158912.516992.260011.990911.714941.451380.013880.014570.014790.014660.013810.013790.013740.013580.013310.012950.012510.01201

616263646566676869707172737475767778798081

0.011460.010880.010280.009670.009040.008420.007800.007190.006590.006000.005420.004860.004310.003770.003240.002720.002210.001710.001210.000720.00000

- A102-

For Radial blanket (Channel 4)

The power density at each axial location for the radial blanket is from Table C-28 of Ref. A2.

RBn := j2 = RBj2 :=

0.000.000730.001740.002830.004080.005560.007350.009540.012220.015490.019430.024150.029710.036160.043470.051530.060090.068690.076600.082670.085160.081580.068432.111202.295632.525592.765672.999883.540983.75131

3.928634.072474.182574.393444.431414.429034.386634.303713.971673.823693.645593.437453.199832.595092.352272.110511.887091.722080.016480.018110.018690.018370.016890.016330.015750.015150.014530.013900.013250.01260

313233343536373839404142434445464748495051525354555657585960

123456789

101112131415161718192021222324252627282930

i3 =616263646566676869707172737475767778798081

RBi3 :=

0.011940.011270.010610.009950.009290.008650.008010.007390.006780.006180.005590.005020.004450.003900.003360.002830.002300.001780.001260.000750.00000

- A103-

k:- 1 ..81

NomxSizw) axial pccrlco

i := 1.. 80

PWR DF:=^(PoS|+1 - Posi) % DP, i

PWR DF 1.00215

PWR IB: £ (Posi+1 - Post) x IBi PWRJB = 1.00159

PWR_RB = (Posj+i - Posj) x RBj PWR RB - 1.00192

-AKM-

The SAS4A core model represents the fuel zone (KZ=4) by 24 axial nodes including 4 upper nodes, which represents sodium bonding above the fuel. The reference length of the whole core is 3.468 m, which is represented by the dimension from -1.1170 to 2.351 m in Fig. 51-1.

The elevation of MZ(J=1) is mid-height of the bottom segment of the active core region and MZ(J=24) is mid-height of the top segment of the sodium bonding region. Since SAS4A requires a power shape along the core plus axial blanket regions (from MZ=1 to MZ=24) as the PS HA PE input data, a new power shape need to be generated using the given design data. The new power shape (average value of each segment) is calculated as follows:

Lref := 3.468 m

Lcore := 1.0 m Lnabond := 0.2 m from Fig. 51-1

mesh size . . . LcoreAxsizel :=-------- Axsize2 := Lnabond20 4

i := 1 .. 20

. 1.1170 + Axsizel x[0.5 + (i- 1)]X' ; Lref

Axi = 0.329296 m AX20 - 0.60323 m

j := 21 .. 24

A___ 1.1170 + Lcore + Axsize2 x [0.5 + (j - 21)]AXi 1— ----------------------------------------------------------------

Lref

AX21 = 0.61765 m AX24 = 0.6609 m

Total length of MZ, between MZ(1) and MZ(24)

MZIength := (AX24 - Axi) x Lref MZIength = 1.15 m

Power density at each Ax(i) position is determined using the built-in function of linear interpolation linterp(x,y,z), provided by MathCad.

For driver

For inner blanket

For radial blanket

fD(Ax) := linterp(Pos ;DF,Ax)

fl(Ax) := linterp(Pos .IB ,Ax)

fR(Ax) := linterp(Pos, RB , Ax)

- A105-

Pin power density for subassemblies

k := 1 .. 24

Driver fuel Inner blanket Radial blanket

DFO|< := IBOk := RBOk :=

fl(Axi)fl(Axa)fl(Ax3)fl(Ax4)fl(Axs)fl(Axe)fl(Axy)fl(Axe)fl(Axg)fl(Axio)fl(Axn)

fl(Axi2)fl( Ax13)fl(Ax14)fl(Ax15)fl(Axie)fl(Ax17)fl(Axig)fl(Axig)fl(Ax20)f!(Ax2i)fl(Ax22)fl(Ax23)1I(Ax24)

1

2

3456

78

910

11

12

1314151617181920

21

22

2324

fR(Axi)fR(Ax2)fR(Ax3)fR(Ax4)fR(Ax5)fR(Axe)fR(Ax7)fR(Ax8)

fR(Axg)fR(Ax10)fR(Axn)fR(Ax12)fR(Ax13)fR(Ax14)fR(Ax15)fR(Ax1s)fR(Axi7)fR(Ax18)

fR(Axig)fR(Ax20)fR(Ax2i)fR(Ax22)fR(Ax23)fR(Ax24)

fD(Axi)fD(Ax2)fD(Ax3)fD(Ax4)fD(Axg)fD(Ax6)fD(Ax7)fD(Ax8)fD(Axg) I

fD(Axio)fD(Axn)fD(Axi2)fD(Axi3)fD(Axu)fD(Ax15)fD(Ax16)fD(Ax17)fD(Ax18)fD(Ax19)fD(Ax20)fD(Ax2i)fD(AX22)fD(Ax23)f D( Ax24)

Driver

DFOk =1

1 2.499872 2.766673 3.06824 3.351595 3.532686 3.750837 3.926948 4.056799 4.102441C 4.1256911 4.0988712 4.0223113 3,9444614 3.7617915 3.5332916 3.2637117 3.0349118 2.7005819 2.333332C 1.9764221 0.6401522 0.0045623 0.0046324 0.00459

Inner blanket

IBOk =1

1 2.281132 2.566323 2.858434 3.161615 3.663536 3.89027 4.07188 4.206699 4.400931C 4.425711 4.3943412 4.3063515 3.9518114 3.7608415 3.5250316 3.2443717 2.6030718 2.23884IS 1.910322C 1.5818421 0.5124322 0.0143623 0.0147324 0.0147

Radial blanket

RBOk -

11 2.195222 2.44943 2.73723

4 3.051265 3.60572

6 3.843767 4.03426

8 4.176829 4.39953

1C 4.43052

11 4.4041512 4.32031 12 3.9697214 3.7834515 3.554116 3.28238

17 2.6761818 2.33325 16 2.04527 2C 1.80376 21 0.60802 22 0.01761 28 0.01852

0.01846

- A106 -

Axial location along the core plus blanket regions needs to be redefined based on the length from MZ(1) to MZ(24).

k := 1 .. 24

Lref_new := Axg4 - Axi Lref_new = 0.331603

. Axk - Ax-|Ax1k := -—---------

Lref_new

Mesh sizes for all axial nodes (MZ=1 to 24)

Total power for each channel is calculated.

PWFLDFnew := ^ x DFOkk

PWRJBnew := ^ x IBOk^

k

PWR_RBnew := ^ ^~~e1 x RB0k

are the same. Axsizel = 0.05

k := 1 .24

PWRJDFnew = 0.98768

PWR_IBnew = 0.97462

PWR„RBnew = 0.97692

m

The new power shape for each channel is calculated based on the above total power.

DF1|c :=PWR DFnew

lB1k :=

( Axsizel A l Lref J x IBOk

PWR IBnew

RB1k :=

f A®!?!!) x RBOk. I Lref )

PWR RBnew

- A107-

Actual elevations of MZ(1-24) based on the SAS4A core model are calculated as:

Bx1 k := AxSlze1 + MZIength x (Ax1 k)

Summary of power shape for each channel k := 1

Normalized Actuallocation elevation (m)

Ax1 k = Bx1 k =1

1 0.0252 0.0753 0.1254 0.1755 0.2256 0.2757 0.3258 0.3759 0.4251C 0.47511 0.52512 0.57512 0.62514 0.67515 0.72516 0.77517 0.825IE 0.875IS 0.9252C 0.97521 1.02522 1.07522 1.12524 1.175

11 02 0.043483 0.086964 0.130435 0.173916 0.217397 0.260878 0.304359 0.347831C 0.391311 0.4347812 0.4782613 0.5217414 0.5652215 0.608716 0.6521717 0.6956518 0.73913IS 0.782612C 0.8260921 0.8695722 0.9130422 0.9565224 1

DF1 k = IB1 k =1

1 0.036492 0.040393 0.044794 0.048925 0.051576 0.054757 0.057328 0.059229 0.059881C 0.0602211 0.0598312 0.0587212 0.0575814 0.0549115 0.0515816 0.0476417 0.044316 0.03942IS 0.034062C 0.0288521 0.0093422 0.0000722 0.0000724 0.00007

11 0.033742 0.037963 0.042284 0.046775 0.054196 0.057557 0.060238 0.062239 0.06511C 0.0654711 0.0650112 0.063713 0.0584614 0.0556315 0.0521516 0.0479917 0.0385118 0.03312IS 0.028262C 0.023421 0.0075822 0.00021

22 0.0002224 0.00022

..24

RB1k =I 1

1 0.03242 0.036153 0.04044 0.045035 0.053216 0.056737 0.059548 0.061649 0.06493 1C 0.0653911 0.06512 0.0637615 0.0585914 0.05584 If 0.0524516 0.0484417 0.0395 jjE 0.0344315 0.03018 2t 0.0266221 0.0089722 0.00026 X 0.00027 24 0.00027

- A108-

pc'A

'er d

enar

yk 1 .. 24

DF1keeIB1k00

0.05 -

0.05 -

0.04 -

0.03 -

0.02 -

r>crr>alztd i>la cccnico

To chock the normalized power distribution, k := 1.. 24

PWR DF1 DF1k k

PWR IB1 £lB1k k

PWFLRB1 =^RB1k

k

PWR_DF1 = 1

PWRJB1 = 1

PWR_RB1 = 1

•At 09 -

Pin power averaged over the each channel is calculated as:

The power fractions for subassemblies at BO EC are listed in the Basic Plant Parameters.

Hot driver

Remaining driver

Internal blanket

Radial blanket

PWRhot = 0.10116

PWRdr = 0.68726

PWRib = 0.09926

PWRrb = 0.08981

Power sum PWRsas4 := PWRhot + PWRdr + PWRib + PWRrbfor SAS4A core

PWRsas4 = 0.97749

The numbers of subassemblies and pins per subassembly in channel are listed in Block 51, Loc. 25 (NPIN) and Loc. 26 (NSUBAS).

subassembly

NhotAssy = 6

NdrAssy = 48

NibAssy = 24

NrbAssy - 48

Sum Nsas4Assy := NhotAssy + NdrAssy + NibAssy + NrbAssy

Nsas4Assy = 126

pins per subassembly

N_Dpin = 271

N_Bpin = 127

The power fraction per pin for each channel is calculated as:

Hot driver PWRhotpin := PWRhot PWRhotpin = 6.2214 x 10™ 5NhotAssy x N_Dpin

Remaining driver PWRdrpin := PWRdr PWRdrpin = 5.28336 x 10™ 5NdrAssy x N_Dpin

Inner blanket PWRibpin := PWRib PWRibpin = 3.25656 x 10™ 5NibAssy x N_Bpin

Outer blanket PWRrbpin := PWRrb PWRrbpin = 1.47326 x 10™ 5NrbAssy x N_Bpin

- A110-

From the axial power shape table (DF1 (k)) listed above, the 10 th axial node in the hot driver assembly has a peak power.

k:= 1 ..24

DF1k =1

1 0.036492 0.040393 0.044794 0.048925 0.051576 0.054757 0.057328 0.059229 0.0598810 0.0602211 0.0598312 0.0587213 0.0575814 0.0549115 0.0515816 0.0476417 0.044318 0.0394219 0.0340620 0.0288521 0.0093422 0.0000723 0.0000724 0.00007

According to the definition of SAS4A core model, Loc. 6-29 (PSHAPE), the pin power at axial node needs to be normalized by the power in the peak axial fuel pin segment.

NormPWR := PWRhotpinx (DF110)

NormPWR = 3.7468 x 10" 6

Norhotk :=DF1|<x PWRhotpin

NormPWR

NorDFk :=DF1kx PWRdrpin

NormPWR

NorlBk :=IB1kx PWRibpin

NormPWR

NorRBk :=RB1kx PWRrbpin

NormPWR

- A111 -

Location 6-29. PSHAPE (J)Ratio of pin power at axial segment J to the power ROW in the peak axial fuel pin segment for all nodes in the core, 1 <= J<=MZ, MZ is the number of axial heat transfer segments in the core plus axial blankets (Refer to Fig. 51-1)

Enter only for IPOWRZ = 0. The first entered segment value (J=1) is for the lower-most segment in the lower axial blanket. Values are normalized to ROW or POWTOT using NPIN, NSUBAS, and PRSHAP at the initial steady-state.

As a result, PSHAPE (J) data are listed as follows:

Ax11< —1

1 02 0.043483 0.086964 0.130435 0.173916 0.217397 0.260878 0.304359 0.3478310 0.391311 0.4347812 0.4782613 0.5217414 0.5652215 0.608716 0.6521717 0.6956518 0.7391319 0.7826120 0.8260921 0.8695722 0.9130423 0.9565224 1

Norhotk = NorDFk = NorlBk = NorRBk =1

1 0.605932 0.67063 0.743684 0.812375 0.856276 0.909147 0.951838 0.98339 0.99436

10 1

11 0.993512 0.9749413 0.9560714 0.911815 0.8564116 0.7910717 0.7356118 0.6545819 0.5655620 0.4790521 0.1551622 0.0011

23 0.00112

24 0.00111

1

1 0.127392 0.142143 0.158844 0.177065 0.209246 0.223057 0.234118 0.242389 0.2553110 0.257111 0.2555712 0.2507113 0.2303614 0.2195515 0.2062416 0.1904817 0.155318 0.135419 0.1186920 0.1046721 0.0352822 0.00102

23 0.0010724 0.00107

1

1 0.514572 0.569493 0.631554 0.689895 0.727166 0.772067 0.808318 0.835049 0.8444410 0.8492211 0.843712 0.8279513 0.8119214 0.7743215 0.7272916 0.671817 0.624718 0.5558819 0.4802920 0.4068221 0.1317722 0.0009423 0.0009524 0.00094

1

1 0.29332 0.329963 0.367524 0.40655 0.471046 0.500187 0.523538 0.540879 0.5658510 0.5690311 0.56512 0.5536913 0.508114 0.4835515 0.4532316 0.4171417 0.3346918 0.2878619 0.2456220 0.2033821 0.0658922 0.0018523 0.0018924 0.00189

- A112-

Location 30-40, PSHAPR (I)Normalized radial power shape within the pin by radial node, i, normalized power per unit fuel mass, 1 <= I <= NT (Block 51, Loc. 14)

A flat power profile is assumed for the fuel pin, so a value of 1.0 is used for all radial nodes.

1.0 for all 11 radial nodes

Location 45, PUN (M)Relative power level at the end of the M steady-state division. It is required that PLIN is 1.0 at the end of the steady-state. This input is used by DEFORM-4 to calculate the appropriate conditions in the pin at the start of the transient. Since DEFORM-4 is not used for this study, a single value of 1.0 is sufficient.

1.0

Location 62, ADOPDoppler coefficient when part of core represented by this channel is not voided, (delta k/k)

Doppler coefficients of each assembly for non-voided condition is from Table C-22c of Ref. A2 (BOEC condition). The coefficient of driver assembly is -0.00109, which needs to be divided into for hot and remaining driver assemblies, weighting by number of assembly.

for hot driver (Channel 1)

ADOPhot = -1.2111 x 10,-4

for remaining driver (Channel 2)

ADOPdr := -0.00109 x NdrAssy ADOPdr = -9.6889x10"NhotAssy + NdrAssy

for internal blanket (Channel 3)

ADOPib := -0.00189

for radial blanket (Channel 41

A DO Prd := -0.00080

-A113-

Location 63, BDOPDoppler coefficient when part of core represented by this channel is fully voided, (delta k/k)

Since the present study focuses on the ATWS events without sodium boiling, this input data are not necessary. Therefore the same input data as ADOP (Loc. 62) are used as dummy data.

for hot driver (Channel 1)

ADOPhot := -0.00109 x f--------NhotAssy-------V NhotAssy + NdrAssy) ADOPhot = -1.2111 x 10

for remaining driver (Channel 2)

ADOPdr := -0.00109 x f-------- N--rAss^-------- ] ADOPdr = -9.6889 x 10" 4V NhotAssy + NdrAssy)

for internal blanket (Channel 31

ADOPib := -0.00189

for radial blanket (Channel 4)

ADOPrd := -0.00080

-A114-

Location 64-87, WDOPA (J)Doppler axial weighting factorEnter MZ values for IREACZ = 0 (Block 51, Loc. 365), default value.

Axial power shape is assumed to be similar to Doppler axial weighting factor.

Normalizedlocation

Ax1k =1

1 02 0.043483 0.086964 0.130435 0.173916 0.217397 0.260878 0.304359 0.347831C 0.391311 0.4347812 0.4782612 0.5217414 0.5652215 0.608716 0.6521717 0.6956516 0.7391319 0.78261>0 0.8260921 0.8695722 0.9130422 0.9565224 1

Actualelevation (m)

Bx1 k =1

1 0.0252 0.0753 0.1254 0.1755 0.2256 0.2757 0.3258 0.3759 0.4251C 0.47511 0.52512 0.57512 0.62514 0.67515 0.72516 0.77517 0.82516 0.87519 0.9252C 0.97521 1.02522 1.07522 1.12524 1.175

DF1k = IB1 k - RB1 k -1

1 0.036492 0.040393 0.044794 0.048925 0.051576 0.054757 0.057328 0.059229 0.059881C 0.0602211 0.0598312 0.0587213 0.0575814 0.0549115 0.0515816 0.0476417 0.044316 0.0394219 0.034062C 0.0288521 0.0093422 0.0000723 0.0000724 0.00007

11 0.03242 0.036153 0.04044 0.045035 0.053216 0.056737 0.059548 0.061649 0.064931C 0.0653911 0.06512 0.0637613 0.0585914 0.0558415 0.0524516 0.0484417 0.039516 0.0344319 0.030182C 0.0266221 0.0089722 0.0002623 0.0002724 0.00027

11 0.033742 0.037963 0.042284 0.046775 0.054196 0.057557 0.060238 0.062239 0.06511C 0.0654711 0.0650112 0.063713 0.0584614 0.0556315 0.0521516 0.0479917 0.0385116 0.0331219 0.028262C 0.023421 0.0075822 0.00021

23 0.0002224 0.00022

- A115

Location 112-159, VOIDRA(J)Coolant void reactivity worth per unit coolant mass, per kg, (delta k/k/kg)

The coolant void reactivity coefficients given from core physics team are only 5 data points. Those data are for BOEC condition. Using the cubic spline interpolation, embedded function in the MathCAD, the coefficients at 20 segments are calculated.

i := 1 .. 5

Actualelevation (m)

XLoq :=

0.210.420.630.841.05

XLoc is actual elevation from the bottom of the core.These values are converted to the normalized dimensions consistent with the MZ scale. Using the calculation results in Loc. 6-29, Block 62,

fLoc(x) := linterp(Bx1 ,Ax1 ,x)

Vxj := fLoc(XLoCj)

The independent variable of the function fLoc(x), Bx1, means the actual elevation of the core and the dependent variable, Ax1, means the normalized elevation of Bx1.

Location

Vx; =1

1 0.16092 0.34353 0.52614 0.70875 0.8913

driver fuel

Vy_drj :=

-1.4713x 10~;

7,9475 X 10"'

1.1431x10"'

5.6046 x 10"'

-4.1773x10''

internal blanket

Vyjbj :=

2.1775 x 10~4

4.8958 x 10" 4

5.8826 x 10~4

4.2815x 10~4

1.4280x 10'^

radial blanket

Vy„rbj :=

-7.8083 x 10~5

-1.5425 x 10~4

-1.8025 x 10~4

-1.4010X 10~4

-6.0662 x 10" 5

Vsdr := lsp!ine(Vx, Vy_dr) Vsib := lspline(Vx ,Vy_ib) Vsrb := lspline(Vx ,Vy_rb)

fvoid_dr(x) := interp(Vsdr, Vx ,Vy_dr ,x)

fvoid_ib(x) := interp (Vsib, Vx, Vyjb, x)

fvoid_rb(x) := interp (Vsrb ,Vx, Vy_rb ,x)

where, Vx and Vy are vectors of real data values, and Vs is a vector generated by cubic spline interpolation, x is the value of the independent variable at which you want to interpolate a result.

- A116-

fvoicLdr(x)

-5 10

-1 10

-1.5-10

x. Vx

fvoid_ib(x)

-2-10

x. Vx

-5*10

fvoid_rb(x)

-1.5 10

-2 10

- A117-

SAS4A needs reactivity feedback coefficient data (delta k/k/kg) per subassembly, VOIDRA is calculated by dividing the number of assemblies for each channel.

Coni := 3.997.10621

VOIDRA_hot := fvoid_dr(Ax1) x Coni

VO ID RAJ B := fvoidJb(Ax1)xCon1

Axial location

Ax1 % =1

1 02 0.043483 0.086964 0.130435 0.173916 0.217397 0.260878 0.304359 0.3478310 0.391311 0.4347812 0.4782613 0.5217414 0.5652215 0.608716 0.6521717 0.6956518 0.7391319 0.7826120 0.8260921 0.8695722 0.9130423 0.9565224 1

hot pin driver (Channel 1)

VOIDRA hot =

VOIDRA„DF := fvoid„dr(Ax1) x Coni

VOIDRA_RB := fvoid_rb(Ax1) x Coni

remaining driver (Channel 2)

VOIDRA DF =1

1 -5.595370-52 -4.436770-53 -3.155870-54 -1.798170-55 -4.086470-66 9.672370-67 2.284370-58 3.497270-59 4.560770-510 5.4370-511 6.061270-512 6.410970-513 6.435470-514 6.104570-515 5.4670-516 4.56870-517 3.494470-518 2.30370-519 1.031870-520 -2.963670-621 -1.658670-522 -3.032370-523 -4.394670-524 -5.722770-5

1

1 -5.595370-52 -4.436770-53 -3.155870-54 -1.798170-55 -4.086470-56 9.672370-57 2.284370-58 3.497270-59 4.560770-510 5.4370-511 6.061270-5

12 6.410970-513 6.435470-514 6.104570-515 5.4670-516 4.56870-517 3.494470-518 2.30370-519 1.031870-520 -2.963670-621 -1.658670-522 -3.032370-523 -4.394670-524 -5.722770-5

- A118-

Axial location

Ax1 k1

1 02 0.043483 0.086964 0.130435 0.173916 0.217397 0.260878 0.304359 0.3478310 0.391311 0.4347812 0.4782613 0.5217414 0.5652215 0.608716 0.6521717 0.6956518 0.7391319 0.7826120 0.8260921 0.8695722 0.9130423 0.9565224 1

internal blanket (Channel 3)

VOID RAJ B =1

1 -1.553270-52 1.776470-53 5.475970-54 9.408370-55 1.343770-46 1.742470-47 2.123370-48 2.472770-49 2.776970-410 3.022970-411 3.200270-412 3.298470-413 3.307470-414 3.2270-415 3.046270-416 2.801870-417 2.502270-418 2.162970-419 1.794770-420 1.405870-421 1.004570-422 5.99170-523 1.978370-524 -1.910670-5

radial blanket (Channel 4)

VOIDRA_RB =

1

1 -5.124370-62 -1.435670-53 -2.474370-54 -3.585870-55 -4.727270-56 -5.855970-57 -6.928870-58 -7.903370-59 -8.736670-510 -9.392170-511 -9.852470-512 -1.010370-413 -1.013170-414 -9.925770-515 -9.505470-516 -8.896570-517 -8.125470-518 -7.218770-519 -6.205570-520 -5.116170-521 -3.981270-522 -2.83170-523 -1.69670-524 -6.066570-6

- A119

Location 160-207, CLADRA (J)Cladding reactivity worth per unit clad mass, per kg, (delta k/k/kg)

Cladding coefficients at BOEC condition are given by core physics team. The coefficient data are for the whole core. The subassembly number for each region may be 6 or 12 depending on their locations as shown in Fig. C.

NA := 6 NB := 12

NormalizedLocation Hot driver (Channel 1)

Vxj =1

1 0.16092 0.34353 0.52614 0.70875 0.8913

CCL31 j :=

-9.3609 x 10

-2.5857 x 10

-3.1652x10

-2.2032x10

-4.6956 x 10

Remaining driver (Channel 2)

CCL32| := CCL51j := CCL52j :=

-9.9164 x 10'6 -1.2953X 10" 6

-2.7422 x 10" 5 -7.3859 x 10" 6

-3.3443 x 10" 5 -9.5669 x 10" B

-2.3243 x 10" 5 -5.9245 x 10" 6

-4.9331 x 10" 6 8.9738x10" 7

Internal blanket (Channel 3)

CIB21j := CIB42i :=

-1.1213x 10"5 -1.0626x 10" 5

-2.3600 x 10" 5 -2.5334 x 10" 5

-2.8120 x 10" 5 -3.0692 x 10" 5

-1.9926 x 10" 5 -2.2139 x 10" 5

-6.0454 x 10" 6 -6.9706 x 10" 6

-7.6663 x 10-6

-2.2451 x 10-5

-2.7574 x 10-5

-1.9303 x 10-5

-3.8235 x 10-6

CIB53j :=

-1.1216 x 10-6

-2.6107 x 10

-3.1443x10-5

-2.2972 x 10-5

-7.6562x10-6

CCL62j :=

6.9447x10-6

1.0232 x 10-5

1.1210 x 10-5

9.8500x10-6

6.5798 x 10-6

CCL63; :=

-2.8404 x 10

1.4423 x 10-6

-6

-4.3789 x 10-6

-1.9268 x 10-6

2.3691 x 10-6

- A120-

Radial blanket (Channel 4)

CRB71 j := CRB72j := CRB73j := CRB74j := CRB84j :=

4.3832 x 10“ 6 5.8818X 10"^ 7.2577 x 10" 6 6.7308 x 10" 6 1.5385x10“6

8.8073 x 10"^ 1.1460X 10“5 1.4549 x 10" 5 1.3744 x 10" 5 3.7334 x 10“ 6

1.0446 x 10“ 5 1.3399 x 10“ 5 1.6943X 10" 5 1.6020 x 10" 5 4.5193x10"®

7.9021 x 10" 6 1.0411 x 10~5 1.3264x10" 5 1.2525 x 10" 5 3.3268 x 10“ 6

3.0909 x 10“ 6 4.4851 x 10“ 6 5.6967 x 10“ 6 5.2117x 10“6 1.0602 x 10" 6

Average cladding reactivity worth per subassembly for each channel is calculated as:

Cy_hotj :=CCL31i x NA

x

NhotAssy

Cy_dfj := fCCL32;xNA + CCL51 jx NA + CCL52jx NB + CCL62;x NB ..A [ + CCL63j x NB

Cy ibj := (ClB21jxNA + CIB42j x NB + CIB53]X NA) x------ -------v ; NibAssy

Cy_rbj := (CRB71 j x NA + CRB72j xNB + CRB73;x NB + CRB74; x NA ..A x I + CRB84i x NB

1NdrAssy

1NrbAssy

hot driver

Cy_hotj =1

1 -9.360970-62 -2.585770-53 -3.165270-54 -2.203270-55 -4.695670-6

driver fuel

Cy dfj =1

1 -1.221370-62 -8.115870-63 -1.056270-54 -6.490970-65 7.768870-7

internal blanket

Cyjbj =1

1 -8.396770-62 -2.509470-53 -3.023770-54 -2.179470-55 -6.910770-6

radial blanket

Cy rbj =1

1 5.058770-62 1.025570-53 1.202470-54 9.303870-65 3.848370-6

A121 -

Vschotlspline(Vx ,Cy_hot)

Vscdf := !spline(Vx,Cy_df)

Vscib := lspline(Vx,Cy_ib)

Vscrb := lspline(Vx,Cy_rb)

where, Vx and Vy are vectors of real data values, and Vs is a vector generated by cubic spline interpolation, x is the value of the independent variable at which you want to interpolate a result.

fclad_hot(x) := interp (Vschot, Vx, Cy_hot, x)

fclad_df(x) := interp (Vscdf, Vx , Cy_df, x)

fcladjb(x) := interp(Vscib,Vx,Cy_ib,x)

fclad„rb(x) := interp (Vscrb ,Vx,Cy_rb ,x)

t1 *10fclad_hot(x)Cy„hot

-2 10

-3 10

-4 10

- A122 -

fclad_df(x)

-5-10

-1 10

-1.5 10

fclad_ib(x)

-3 10

-4-10

fclad_rb(x)

5 10

- A123-

CLADRA_hot := fclad_hot(Ax1)

CLADRAJB := fclad_ib(Ax1)

CLADRA_DF := fclad_df (Ax1)

CLADRA_RB := fclad_rb(Ax1)

Axiallocation hot pin driver remaining driver internal blanket radial blanket

Ax1 % = CLADRA_hot = CLADRA_DF = CLADRAJB = CLADRA_RB=1

1 5.00770-62 3.506370-63 1.834470-64 5.469770-85 -1.769470-66 -3.574570-67 -5.297170-68 -6.873970-69 -8.241470-610 -9.340670-611 -1.012670-512 -1.055570-513 -1.058370-514 -1.018170-515 -9.39470-616 -8.289270-617 -6.935370-618 -5.399370-619 -3.729970-620 -1.965370-621 -1.435170-722 1.697370-623 3.51970-624 5.283670-6

1 1

1 0 1 5.546870-62 0.04348 2 1.961670-63 0.08696 3 -2.039870-64 0.13043 4 •6.303270-65 0.17391 5 -1.067470-56 0.21739 6 -1.499970-57 0.26087 7 -1.912470-58 0.30435 8 •2.289470-59 0.34783 9 -2.615670-510 0.3913 10 -2.876870-511 0.43478 11 -3.062670-512 0.47826 12 -3.163670-513 0.52174 13 -3.170170-514 0.56522 14 -3.075670-515 0.6087 15 -2.890170-516 0.65217 16 -2.629270-517 0.69565 17 -2.308770-518 0.73913 18 -1.943770-519 0.78261 19 -1.54670-520 0.82609 20 -1.124870-521 0.86957 21 -6.895270-622 0.91304 22 -2.49670-623 0.95652 23 1.856570-624 1 24 6.068370-6

1

1 6.754570-62 3.181970-63 -8.803670-74 -5.250970-65 -9.748470-66 -1.419270-57 -1.839970-58 -2.218970-59 -2.538170-510 -2.782770-511 -2.947970-512 -3.030870-513 -3.028770-514 -2.940570-515 -2.775970-516 -2.548170-517 -2.270470-518 -1.955870-519 -1.613970-520 -1.252670-521 -8.795370-622 -5.026170-623 -1.295870-624 2.317870-6

1

1 3.540870-72 1.474970-63 2.73770-64 4.088170-65 5.475870-66 6.847870-67 8.151870-68 9.335470-69 1.034670-510 1.11470-511 1.169770-512 1.200170-513 1.203670-614 1.179170-515 1.128670-516 1.055270-517 9.618570-618 8.515170-619 7.277670-620 5.944270-621 4.553370-622 3.143370-623 1.752470-624 4.190770-7

- A124-

Location 208-255. FUELRA U)

Core fuel reactivity worth per unit core mass, per kg, (delta k/k/kg)

Fuel coefficients at BO EC condition are given by core physics team. The coefficient data are for the 1/6 core symmetry as shown in Fig. C. The assembly number for each region may be 6 or 12 depending on their locations.

NA := 6

NormalizedLocation

Vxi =1

1 0.16092 0.34353 0.52614 0.70875 0.8913

NB := 12

Hot driver (Channel 1)

FCL31 j :=

7.2026 x 10-5

1.3050 x 10-4

1.5091 x 10-4

1.1779 x 10-4

5.5544 x 10-5

Remaining driver (Channel 2)

FCL32; := FCL51 j := FCL52i := FCL62j := FCL63i :=

7.2166 x 10“ 5 5.6403 x 10” 5 5.9426x10" 5 4.5864 x 10" 5 4.7555x10" 5

1.3095 x 10“ 4 1.0433 x 10“ 4 1.0884 x 10“ 4 8.6330 x 10“ 5 8.9974 x 10“ 5

1.5142X 10“4 1.2122x 10“ 4 1.2642 x 10“ 4 1.0061 x 10“4 1.0497x 10“ 4

1.1800 x 10“4 9.4850 x 10" 5 9.9108X 10“5 7.8609 x 10“ 5 8.1888x 10'5

5.5189 x 10“ 5 4.4486 x 10“ 5 4.7034 x 10“ 5 3.6094 x 10“ 5 3.7658 x 10“ 6

Internal blanket (Channel 3)

FIB21 j := FIB42j:= FIB53i :=

-1.0094 x 10" 5 -1.0035x 10“ 5 -1.0033x10“ 5

-1.7347 x 10“ 5 -1.9036 x 10“ 5 -1.9173X 10“5

-1.9580 x 10" 5 -2.1958 x 10" 5 -2.2172x10“ 5

-1.5393 x 10“ 5 -1.7206 x 10" 5 -1.7378 x 10“ 5

-6.4662 x 10“ 6 -7.2128 x 10“ 6 -7.4089 x 10“ 6

- A125-

Radial blanket (Channel 4)

FRB71 j := FRB72j := FRB73j := FRB74j := FRB84j :=

1.3210x 10"6 2.0322 x 10" 6 2.6644 x 10™ 6 2.1836X 10“6 3.1925 x 10“ 7

3.3451 x 10" 6 4.7669x10" 6 6.4580 x 10™ 6 5.8896 x 10" 6 1.2836x10“ 6

4.1398X 10"6 5.8147x10"6 7.8625x10“ 6 7.2731 x 10" 6 1.6532x 10“ 6

2.9114X 10"6 4.2073 x 10" 6 5.7242x10“ 6 5.1760x 10"6 1.0955 x 10“ 6

7.2975 x 10" 7 1.3898X 10" 6 1.9214 x 10™ 6 1.4613X 10"6 1.0048 x 10“ 7

Average fuel reactivity worth per subassembly for each channel is calculated as:

FCL31jX NAFy_hotj :=-----------------

NhotAssy

Fy dfj := (FCL32jxNA+ FCL51 jxNA + FCL52jx NB + FCL62;x NB x —1-----(+FCL63ixNB I ^rAssy

Fy ibj ™ (FIB21jX NA+ FIB42jX NB + FIB53jX NA) x----------------y~ v } NibAssy

Fy_rbj := f FRB71 j x NA + FRB72j x NB + FRB73j x NB + FRB74; x NA U FRB84j x NB

1NrbAssy

hot driver

Fy_hotj =1

1 7.202670-52 1.30570-43 1.509170-44 1.177970-45 5.554470-5

driver fuel

'y dfi =1

1 5.428270-52 1.00770-43 1.170870-44 9.150870-55 3.418370-5

internal blanket

-y ibj =1

i -1.004970-52 -1.864870-53 -2.141770-54 -1.679670-55 -7.075270-6

radial blanket

Fy rbj =1

1 1.69270-62 4.281570-63 5.259270-64 3.767770-65 1.126870-6

A126 -

Vsfhot := lspline(Vx, Fy__hot)

Vsfdf := lspline(Vx, Fy_df)

Vsfib := lspline(Vx ,FyJb)

Vsfrb := !spline(Vx, Fy_rb)

where, Vx and Vy are vectors of real data values, and Vs is a vector generated by cubic spline interpolation, x is the value of the independent variable at which you want to interpolate a result.

ffuel_hot(x) := interp(Vsfhot ,Vx, Fy_hot ,x)

ffuel_df(x) := interp('Vsfdf ,Vx, Fy_df,x)

ffueljb(x) := interp (Vsfib ,Vx,Fy_ib,x)

ffuel_rb(x) := interp (Vsfrb , Vx, Fy_rb, x)

1.5 10

Fy„hot

- A127-

ffuel_df(x)

-5 10

-5-10

-1 -10ffueljb(x)

-1.5-10

-2-10

-2.5 -10

ffuel_rb(x)

- A128-

FUELRA_hot := ffuel_hot(Ax1)

FUELRAJB := ffuel_ib(Ax1)

FUELRA_DF := ffuel_df(Ax1)

FUELRA_RB := ffuel_rb(Ax1)

Axiallocation

Ax1 k1

1 02 0.043483 0.086964 0.130435 0.173916 0.217397 0.260878 0.304359 0.3478310 0.391311 0.4347812 0.4782613 0.5217414 0.5652215 0.608716 0.6521717 0.6956518 0.7391319 0.7826120 0.8260921 0.8695722 0.9130423 0.9565224 1

hot pin driver

FUELRA hot =

remaining driver

FUELRA DF=

internal blanket

FUELRA IB -

1

1 1.915470-52 3.183670-53 4.602570-54 6.116470-55 7.669370-56 9.205470-57 1.066970-48 1.200470-49 1.315570-410 1.407270-411 1.472370-412 1.507770-413 1.510770-414 1.479270-415 1.416370-416 1.326670-417 1.21570-418 1.08670-419 9.438570*520 7.922670-521 6.350170-522 4.758770-523 3.186270-524 1.670370-5

1 1

1 1.228770-5 1 -2.252370-62 2.232870-5 2 -4.097370-63 3.359670-5 3 -6.188170-64 4.563770-5 4 -8.433970-65 5.799770-5 5 -1.074370-56 7.02270-5 6 -1.302670-57 8.185270-5 7 -1.518970-58 9.243870-5 8 -1.714470-59 1.015270-4 9 -1.879770-510 1.087270-4 10 -2.007670-511 1.138370-4 11 -2.095370-512 1.16770-4 12 -2.141370-513 1.171770-4 13 -2.143970-514 1.151170-4 14 -2.101970-515 1.105970-4 15 -2.017670-516 1.037370-4 16 -1.893970-517 9.464670-5 17 -1.734170-518 8.349270-5 18 -1.541670-519 7.062870-5 19 -1.322370-520 5.653970-5 20 -1.08470-521 4.171770-5 21 -8.34370-622 2.664970-5 22 -5.807470-623 1.182670-5 23 -3.3170-624 -2.262170-6 24 -9.270270-7

radial blanket

FUELRA RB =

1

1 -6.435470-72 -7.663870-83 5.505870-74 1.215870-65 1.896670-66 2.570770-67 3.215870-68 3.809570*69 4.329570*610 4.754270*611 5.064470-612 5.241270-613 5.265870-614 5.125270-615 4.83770-616 4.429570-617 3.930870-618 3.368370-619 2.760370-620 2.119970-621 1.4670-622 7.93670-723 1.33770-724 -5.067470-7

- A129-

Location 256. PRSHAPRatio of power per subassembly averaged over this channel to the power per subassembly averaged over all channels.

Note that these values are normalized by SAS4A over all assemblies such that the average is 1.0.

The total power fraction was calculated already in Loc. 6-29, Block 62.

Hot driver

Remaining driver

Internal blanket

Radial blanket

Sum of power for SAS4A core model

Sum of assembly number for SAS4A core model

PWRhot = 0.10116

PWRdr = 0.68726

PWRib = 0.09926

PWRrb = 0.08981

PWRsas4 = 0.97749

Nsas4Assy = 126

NhotAssy = 6

NdrAssy = 48

NibAssy = 24

NrbAssy = 48

The power per subassembly averaged over all channels is calculated as:

PWRsas4PWRsas4Assy :=Nsas4Assy

PWRsas4Assy = 0.0077579

Thus the ratio of power per subassembly averaged over each channel to the "PWRsas4Assy" is:

Hot driver

Internal blanket PRSHAP IB :=

Radial blanket

PWRhot 1NhotAssy

= 2.17328

PWRsas4Assy

PWRdr 1NdrAssy

: 1.8456

PWRsas4Assy

PWRib 1NibAssy

0.53312

PWRsas4Assy

PWRrb ^ 1

NrbAssy PWRsas4Assy

PRSHAP RB = 0.24118

- A130 -

BLOCK 63, PMATCH

This input block contains thermophysical properties for the subassemblies represented by each channel that are not already input in Block 13, Usually this data is applied to certain model options, such as the force balance model for calculating the axial expansion of the fuel and cladding. PMATCM. Some of the input also relates to DEFORM-4, and nonzero values are listed herein, unless a value of zero has a special meaning.

Location 2. AHBPARCoefficient in the bond gap conductance correlation, (W/m2-K)

If all three parameters are not equal to 0.0, the bond correlation is of the form:

HB = AHBPAR + 1.0/(BHBPAR + (gap size + CHBPR)/HBPAR)

= 1800 This value is not used in the present calculation.

Location 3, BHBPAR

= 6.1*10-5 This value is not used in the present calculation. (m2-KA/V)

Location 4. CHBPAR

= 1.32*10This value is not used in the present calculation, (m)

Locations. HBMAXMaximum value of bond conductance when a gap exists; minimum value when a gap does not exist. Default when AHBPAR, BHPAR, and CHBPAR > 0.0

HBMAX = AHBPAR + 1.0/( BHBPAR + CHBPR/HBPAR)

The maximum and minimum value of bond conductance at any time is set to 1.0*106 for irradiated metallic fuel. However, the value of 1.324*105 is used for KALIMER fuel.

= 1.324*10* (W/m2-K)

Location 6, HBMIN

= 1.324*105 (W/m2-K)

- A131 -

Location 7, HBPARIf all three parameters in Loc. 2-4 are zero, then the bond conductance equation when a gap exists is of the form: (W/m-K)

Bond conductance = HBPAR/gap

= 0.0286 Based on previous result, but not used in the present calculation

Location 11-17. XKSTIZ (KZ)Inner structure thermal conductivity in zone KZ, (W/m-K)

Structure material is HT9. Based on the the properties of HT-9, Block 13, Loc. 11-90, at the core average temperature (731.25 K). XKSTIZ is calculated using interpolation.KZ is 5 as defined in Fig. 51 -1.

Tcoreavg = 731.25 K

XKSTIZ := linterp(EXKTM, K_HT9Tcoreavg) XKSTIZ = 26.55 W/mK

Location 18-24. XKSTOZ (KZ)Outer structure thermal conductivity in zone KZ, (W/m-K)

XKSTOZ := XKSTIZ XKSTOZ = 26.55 W/mK

Location 25. DEL (KZ)Product of Stefan-Boltzmann's constant and the emissivity of cladding (W/m2-K4)See Block 13, Loc. 1107-1109

Suggested values of Stefan-Boltzmann constant is 5.67*1 O'8 (W/m2-K4) from Block 13, Loc.1107-1109. cladding emissivity (HT-9) is assumed to be 0.85 for this study.

DEL := 5.67x 10”8x(0.85) DEL = 4.8195x 10~8 W/m2-K4

Location 26. DGOInitial grain size, (m)

= 0.0

Location 27, POGASInitial plenum gas pressure at reference temperature TR (Block 13, Loc. 419), (Pa)

= 1.01325*10s atmospheric pressure

- A132-

Location 28-34, XKRF (KZ)Thermal conductivity of reflector for values of KZ not equal to KZPIN, (W/m-K)

Reflector is made of HT-9. The thermal conductivity of HT-9 at the core average temperature (731.25 K). Refer to Block 13, Loc. 11-90.

XKRF := XKSTIZ XKRF = 26.55 W/mK

Location 35, DENSSDensity of solid cladding at the reference temperature TR (Block 13, Loc. 419), (kg/m3)

The density of the HT-9 at TR is calculated using the data of Block. 13, Loc. 819-898 and Loc. 990- 1069. Since property data at 373 (K) are available as lower boundary in the tables, those data are utilized.

CpRho_HT91 = 3.73566 x 106 J/m3-K Cp_HT9i = 482.5 J/kg-K

CpRho HT9i , QDENSS := —----- ------- - DENSS - 7742.3 kg/m3

Cp„HT91

Location 36, COOLDNCoolant density used in the calculation of the coolant void reactivity worth, (kg/m3)

The density of the sodium at the core average temperature (731.25 K) is determined from Block. 13, Loc. 91-410.

Tcoreavg = 731.25 K

COOLDN := linterp(RHOTEM3, Rho_Na,Tcoreavg) COOLDN = 841.89 kg/m3

Location 37-43. RHOCSI (KZ)Product of density and heat capacity for the inner structure, (J/m3'K)

The density * specific heat of HT-9 at the core average temperature (731.25 K) is determined from Block. 13, Loc. 990-1069.

RHOCSI := linterp(CROETM,CpRho_HT9,Tcoreavg)

RHOCSI = 5.0079 x 106 J/m3"K

- A133-

Location 44-50, RHOCSQ (KZ)Product of density and heat capacity for the outer structure, (J/m3'K)

RHOCSO := RHOCSI RHOCSO = 5.0079 x 106 J/m3 K

Location 51-57, RHOCR (KZ)Product of density and heat capacity for the reflector, (J/m3"K)Reflector is made of HT9.

RHOCR := RHOCSI RHOCR = 5.0079 x 106 J/m3"K

Location 58. RHOCGProduct of density and heat capacity for gas in the fission gas plenum, (J/m3K)

= 5.57*1(P Based on previous work

Location 59, RGThermal resistance of the gas in the fission gas plenum, (K-m2/W)

= 0.03 Based on previous work

Location 73, FUELEXFuel axial expansion coefficient, (1/K)Used only with simple axial expansion feedback calculation, See IAXEXP (Block 51, Loc. 181)

= 2.01*10~6 Based on the available data for the metallic fuel compositionat operating temperature. The value is 1.10*1 O'5 for typical oxide fuel.

Location 74, CLAPEXCladding axial expansion coefficient, (1/K)Used only with simple axial expansion feedback calculation

= 1.40*1 O’5 Based on the available data for HT-9 at operating temperature

- A134-

Location 75. YFUELThe Young's modulus of the fuel, (Pa)Used only with simple axial expansion feedback calculation

= 2.80*109 Based on the available data of metallic fuel.The value is 1.5*1011 for typical oxide fuel

Location 76, YCLADThe Young's modulus of the cladding, (Pa)Used only with simple axial expansion feedback calculation

= 1.52056*1011 Based on the available data

Location 77. FULREXFuel linear expansion coefficient for bond gap conductance calculation, (1/K)

= 2.0V10-9 Same as the FUELEX (Loc. 73)

Location 78. CLADREXCladding linear expansion coefficient for bond gap conductance calculation, (1/K)

= 1.40*10-5 Same as the CLAD LEX (Loc. 74)

Location 79. EXPCFFEffective multiplier for axial fuel expansionUsed only for simple axial expansion feedback model only

= 1.0 For nominal fuel expansion

- A135-

BLOCK 64, COOLIN

This input block contains all of the coolant flow information required by each channel.

Location 1-2, APR, BFRLiquid slug friction factor coefficient

AFR = 0.4089 Recommended values in the SAS4A model

BFR = -0.25

Location 3-5. C1. C2. C3Coefficients in the convection heat transfer correlation:

He = Kc * (C1 * (Re * Pr)C2 +C3) / Dh Lyon-Martinelli correlation

Kc : Constant thermal conductivity Re : Reynolds number Pr : Prandtl number Dh : Channel hydraulic diameter

C1 = 0.0144 Recommended values in the SAS4A model

C2 = 0.86

C3 = 4.480

Location 7, RELAMReynolds number for the transition from the laminar friction factor correlation to the turbulent friction factor correlation

= 7509.0 Recommended value

Location 8, AFLAMCoefficient in the laminar friction factor correlation, Laminar friction factor = A FLA M/Re

= 99.0 Recommended value

- A136-

Location 47, WOSteady-state coolant flow rate per fuel-pin in the channel, (kg/s)

The steady-state coolant flow rate per pin in the channel is obtained from the process of grouping the channels, and is the average of the flow rates of the assemblies in each channel, weighted by the number of assemblies in each orifice zone.

The fraction of the flow rate in each assembly is obtained from page A1 of Ref. A2.

Total core flow rate Wcore = 2143.1 kg/sec

F_hotassy = 0.096

F_DRassy = 0.674

FJBassy := 0.11

F_RBassy := 0.1

F_hotassy + F_DRassy + FJBassy + F_RBassy = 0.98

hot driver

remaining driver

internal blanket

radial blanket

Sum of flow fraction

The number of assemblies are:

hot drive assembly NhotAssy = 6

remaining driver assembly (total) NdrAssy = 48

internal blanket assembly NibAssy = 24

radial blanket assembly NrbAssy = 48

The number of fuel pins per subassembly are:

driver fuel assembly N_Dpin = 271

blanket assembly N_Bpin = 127

- A137 -

Flow rate per fuel pin in each channel is calculated as:

For channel #1

For channel #2

For channel #3

For channel #4

WOi := Wcorex (F_hotassy) x 1(NhotAssy) x (N_Dpin)

WOi = 0.12653 kg/sec per pin

WO2 := Wcorex (F_DRassy) x1

(NdrAssy) x (N_Dpin)

W02 = 0.11104 kg/sec per pin

WO3 := Wcorex (FJBassy) x —: 1(NibAssy) x (N_Bpin)

WO3 = 0.07734 kg/sec per pin

WO4 := Wcorex (F_RBassy) x 1(NrbAssy) x (N_Bpin)

WO4 = 0.03516 kg/sec per pin

i := 1 .. 41

1 0.126532 0.111043 0.077344 0.03516

- A138-

Location 48-63, XKORV (K,M)Orifice coefficients

K = 1,2........ . NREFB+NREFT+1 (See Block 51, Loc. 5-6)XKROV(K,M) is the coefficient at the bottom of zone K.

K = NREFB + NREFT + 2XKROV(K,M) is the coefficient at the top of the subassembly

K < 8, M = 1, for upward flow (Loc. 48 - 55)M = 2, for downward flow. (Loc. 56 - 63)

Example [ (K= 1,2,.... ), M=1,2)

The location of orifice coefficients in the SAS4A core model is shown in Fig. 64-1.

4 segments :---------- -----------------■ Reflector

6 segments

r—Sodium bondingX^4 segments

20segments

3 segments

segments

2egmer ts

GasPlenum

Core

Reflector

aooO

axial elevation (m)

3.1647

CD

3o3

w

2.351

1.2001.000

0.000

-0.5585

-1.1170

-1.591

K=6

K=5

K=4

K=3

K^2

K=:

Fig. 64-1 Location of orifice coefficients in SAS4A core model

- A139-

Pressure drop along the subassembly should be the same for all core channels from the design point of view. SAS4A performs the pressure calculation for the hot subassembly (Channel 1) using the given input data. After then SAS4A adjusts automatically the inlet orifice coefficients for other core channels to have the same pressure drop as the hot channel. The core bypass channels modeled by SASSYS-1 are also adjusted automatically to have the same pressure drop as the hot channel.

Pressure loss due to orifice coefficient is calculated as below, where the flow rate and flow area are the values for one rod.

2

2'AP := Kx

2 x p x A

W,2

2

where W = p * v * A

Sodium density is listed in the table of Block 13, Loc. 91-410

pjn := linterp(RHOTEM3,Rho_Na,Tcorein) pjn = 858.39 kg/m3

p_out := iinterp(RHOTEM3,Rho_Na,Tcoreout) p_out = 825.28 kg/m3

where Tcorein = 659.35 K Tcoreout = 803.15 K

Pressure drop at the Assembly Inlet Orifice

Pressure drop data in the core for KALIME-150

pressure loss at the inlet plenum

pressure loss at the outlet plenum

pressure loss at the core including inlet orififce

DelPip := 0.007 MPa

DelPop := 0.004 MPa

DeIPcore := 0.595 MPa

- A140-

Location 53 and 61, XKORV (K.M)Orifice coefficient at the top of the subassembly.

The pressure loss at the outlet plenum is assumed to occur at the top of the subassembly, the location of K=6 in Fig. 64-1. The XKROVs for the upward and downward are assumed the same.

WOi = 0.12653 kg/sec flow rate per rod, Loc. 47, Block 64

ACCZt = 2.69717 x 10 5 m2 flow area per rod, Loc. 1-7, Block 61

K1_6 ;= 2 x (DelPop) x 106x(p_out) x(ACCZj)2

(WOi)2

K1_6 = 0.300001

Location 48 and 56. XKORV (K.M1Orifice coefficient at the bottom of the subassembly.

From the SAS4A edit run, the calculated pressures are:

pressure at the top of subassembly Ptop_ch1 := 0.1761 MPa

pressure at the bottom of subassembly Pbotm_ch1 := 0.5618 MPa

static head of the subassembly Pstatic := 4.7557x 9.81 x (P-in +^P-0Ut) 1

Pstatic = 0.03927 MPa

Then, the Irreversible pressure loss calculated by the SAS4A model is computed.

Ploss := Pbotm_ch1 - Ptop__ch1 - Pstatic Pioss = 0.34643 MPa

The pressure difference between the design data and the SAS4A result is occur at the inlet orifice region in the subassembly (K=1 ocation in Fig. 64-

K1_1 := 2 x (DeIPcore + DelPip - Pioss) x 106x (pjn) x (A^Zl)

(WOi)2

assumed to 1).

K1_1 = 19.93704

- A141 -

Location 67-68. THETA1. THETA2Coefficients in the numerical scheme for determining the degree of implicitness

For fully implicit calculation, THETA1 =0, THETA2 =1.0

THETA1 = 0.5 Recommended valueTHETA2 = 0.5 Recommended value

Location 69, DTLMAXMaximum temperature change of the liquid coolant per time step, (K)

= 15.0 Recommended value

Location 70, D TV MAXMaximum temperature change of the coolant vapor per time step, (K)

= 50.0 Recommended value

Location 71, DZ1MAXMaximum motion of the liquid/vapor interface per time step, (m)

= 0.1 Recommended value

Location 72. HCONDCondensation heat transfer conductance of the coolant, (W/m2-K)

= 63000.0 Recommended value

Location 73. SLMINMinimum initial length of a liquid slug, (m) Recalculated as cladding melting is approached.

= 0.02 Recommended value

Location 75. WFMINMinimum thickness of a coolant film on the cladding, (m) Burnout is assumed for film thickness less than WFMIN

= 1.0*10-7 Recommended value

- A142-

Location 76. WFMINSMinimum thickness of a coolant film on the structure, (m)

= 1.0*10-7 Same as the WFMIN (Loc. 75)

Location 77. WFSOOInitial thickness of liquid film on the structure, (m) Default value is WFO (Loc. 84)

= 1.427*10-4 Recommended value

Location 84, WFOInitial thickness of a coolant film left on the cladding in a voided region, (m)

That thickness corresponding to a total liquid volume fraction of 0.15 (spread between cladding and structure films) in the voided region.

= 1.427*10-* Recommended value

Location 165, DTSDegree of superheat required before any bubble formation, (K)

= 10.0 Recommended value

- A143-

BLOCK 65, FUELIN

The only input data in this block is one entry, Loc. 2, which must be input to the code.

Location 2. FMELTMThe minimum fuel melt fraction that must exit at the failure node before PLUT02 or LEVITATE is allowed to be called, (must be input > 0)

This value is only used for avoiding difficulties in job execution, but the calculation do not use this value.

= 0.2 Suggested value

- A144-

BLOCK 18, PMR4IN

This section contains the development of the model of the KALIMER reactor plant using PRIMAR-4. All of the floating-type input data required for primary and intermediate modeling is described in this section. The integer input data is contained in Block 3, INRMR4.

Since there are 13 liquid segments in the model, ISGL := 13

Location 2-41, FLQSSL (ISGL)Initial flow rate in liquid segments, (kg/s)

The input for these locations is the initial flow through the 13 liquid segments.

Since there is no core bypass flow in KALIMER, the core flow is the total primary flow.

Core flow rate Wcore = 2143.1 kg/sec

The flow distribution data in the core are from page A1 of Ref. A2.

For hot driver assembly,

For remaining driver assembly

For Internal blanket assembly

For radial blanket assembly

For control rod assembly

F_hotassy = 0.096

F_DRassy = 0.674

FJBassy := 0.11

F_RBassy := 0.1

F_CRassy := 0.005

FLOSS(1) Flow through the first liquid segment (S1), modeled by SAS4A

The value for the core region is not used by the code. FLOSS(1) was already specified in SAS4A model, Loc. 70, Block 12. Therfore the input of FLOSS(1) IS SET TO 0.0.

FLOSS 1 := 0.0

FRFLOW = 0.98 From Loc. 70, Block 12

SAS4fiow := Wcore x FRFLOW SAS4flow = 2100.238 kg/sec

- A145-

FL0SS(2) Flowthrough the control rod assemblies (S2)

FLOSS2 := Wcore x F_CRassy

FLOSS2 = 10.7155 kg/sec

FLOSS(3) Flow through the reflector and B4C shield assemblies (S3)

Since the flow fractions for these assemblies in core are not provided, the fractios are determined based on the power. Power fractions of these assemblies are obtained from page A1 of Ref. A2.

Reflector assembly

B4C assembly

IVS assembly

Radial shield assembly

PWRrf = 0.00288

PWRbcs = 0.00362

PWRivs = 0.00563

PWRrs = 0.000153

Then, the flow fraction of S3 is calculated as:

^00 PWRrf + PWRbcsFS3 :=-----------------------------------------------------

PWRrf + PWRbcs + PWRivs + PWRrs

FS3 = 0.52919

Therefore, the flow rate through S3 is

FLOSS3 := [Wcore - (SAS4flow + FLOSS2)] x FS3

FLOSS3 = 17.0115 kg/sec

FLOSS(4) Flow through the IVS and radial shield assemblies (S4)

FLOSS4 := [Wcore - (SAS4flow + FLOSS2)] x (1 - FS3)

FLOSS4 = 15.135 kg/sec

- A146-

FL0SS(5) Flowthrough the IHX shell side from the hot pool (S5)

There are four IHXs in KALIMER. The flow through the RSDRS overflow path into the annulus of the cold pool is in parallel with the IHXs, and must be subtracted from the total flow through the IHXs. The steady-state overflow is set to the minimum value, but enough high to overcome numerical instability.

FWover := 1.0 kg/sec

FLOSS5 := (Wcore ~ FWover) FLOSS5 = 535.525 kg/sec4

FLOSS(6),(7) Flow through the flow guide and pump (S6 and S7)

floss6Wcore

4FLOSS6 = 535.775 kg/sec

FLOSS7 := FLOSS6 FLOSSy = 535.775 kg/sec

FLOSS<8),(9) Flow between CV2 and CV4 (S8) and between CVS and CV4 (S9)

There is nominally no flow between CV2 and CV4, between CVS and CV4 at steady-state.

FLOSSs := o kg/sec FLOSS9 := 0 kg/sec

FLOSS(10) Flowthrough the RSDRS overflow path (S10)

There is nominally no flow through the RSDRS overflow path; however, an FWover is assumed to flow through the path

FLOSS 10 := FWover FLOSS 10 - 1 kg/sec

FLOSS(11) Flow through the cold intermediate loop to the common header (S11)

KALIMER has two identical intermediate loops. SAS4A/SASSYS-1 models only one loop. The liquid segment S11 represents the flow path from node 22 to node 5 in Fig. 18-2. The flow rate through each intermediate loop is 901.8 kg/s.

FLOSS 11 := 901.8 kg/sec

- A147 -

FL0SS(12) Flow through the IHX seconday side including the common heads (S12)

There are two identical IHXs in each IHTS loop. The liquid segment S12 represents one IHX and associated piping, from node 5 to node 11 in Fig. 18-2.

FLOSS12 := 0.5x(FLOSS-t 1)

FLOSS-] 2 = 450.9 kg/sec

FLOSS(13) Flow through the hot intermediate loop including the SG (S13)

The liquid segment S13 represents the flow path from the steam commom header of two IHXs (node 11) to node 22 of fig. 18-2.

FLOSS 13 := FLOSS11

FLOSS13 = 901.8 kg/sec

Summary of the flow rate through the liquid segment

i := 1 .. ISGL LOCj := i + 1

Location No.

LOCj =2345678

91011

12

1314

FLOSS] =1

1 02 10.71553 17.01154 15.1355 535.5256 535.7757 535.7758 0

9 0

10 1

11 901.812 450.913 901.8

Total core flow

FLOSS] + SAS4flow = 2143.1 kg/sec

Note:

multiplier of S5 = 4 IHX primarymultiplier of SG = 3 3 pumpsmultiplier of S12=2 IHX secondary

These multipliers are input data (Loc. 82-161, Block 18)

- A148 -

Location 42-81. ZjNLflSGL)Elevation of the inlet of the liquid segment, (m)

It is noted that the zero level of the core is the end of the bottom of axial blanket to be consistent with SAS4A channel model. Since there is no axial blanket in the KALIMER fuel design, the zero level of the KALIMER core is at the end of the bottom of the fuel region. The assembly elevation of the KALIMER core is shown in Fig. 51-1. The elevation of the remainder of the reactor system is estimated from Figs. 18-1 and 18-2, which are copies of Fig. M-3 and F-8 of Ref. A2.

The difference between the top of core (E11) in Fig. 18-1 and the top of assembly model in Fig. 51-1 is set to be

Zref := 6.385-3.1647 Zref = 3.2203 m

ZINL(1): Elevation of the inlet of the core element

ZINL-i := -1.5910 ZINL-j = -1.591 m From Fig. 51-1

ZINL(2): Elevation of the inlet of the control rod assembly

ZINL2 := ZINL1 ZINL2 = -1.591 m

ZINL(3): Elevation of the inlet of the reflector and B4C shield assemblies

ZINL3 := ZINL1 ZINL3 = -1.591 m

ZINL(4): Elevation of the inlet of the radial shield and IVS assemblies including the core bypass

ZINL4 := ZINL-| ZINL4 = -1.591 m

ZINL(5): Elevation of the inlet of the IHX

ZINL5 := 13.725-0.35-Zref ZINL5 = 10.1547 m

where 13.725 (m) is the elevations of E5 in Fig. 18-1 and 0.35 (m) is the length between the top of the IHX shell and the top of the tube bundle in Fig. 18-3.

• A149-

ZINL(6): Elevation of the inlet of the flow guide in the first primary pump group (3 pumps)

ZINL6 := 1.85 - Zref ZINL6 = -1.3703 m

where 1.85 (m) is the elevation of E21 in Fig. 18-1.

Z!NL(7): Elevation of the inlet of the flow guide in the second primary pump group (1 pump)

ZINLy := ZINL6 ZINLy = -1.3703 m

ZINL(8): Elevation of the inlet of the pipe connecting CV2 to CV4

ZINL8 := 12.675-Zref ZINLg = 9.4547 m

where 12.675 (m) is the elevation of E8 in Fig. 18-1.

ZINL(9); Elevation of the inlet of the pipe connecting CV3 to CV4

ZINLg := 6.725 - Zref ZINLg = 3.5047 m

where 6.725 (m) is the elevation of E23 in Fig. 18-1.

ZINL(10): Elevation of the inlet of the overflow path of PSDRS

Assume the inlet of the overflow path is at the top of the hot pool. The elevation of E3 in Fig. 18-1 is 15.625 (m).

ZINL-io := 15.625-Zref ZINL10 - 12.4047 m

ZINL(11): Elevation of the inlet of the cold return pipe including the intermediate pump

Assume the inlet of S11 is at the node 22 of Fig. 18-2. The elevations of E0 in Fig. 18-1 and node 22 in Fig. 18-2 are 18.725 and -8.0 (m), respectively.

ZINLn := 18.725-8.0-Zref ZINLn = 7.5047 m

ZINL(12): Elevation of the inlet of the intermediate pipe including the IHX tube side

Assume the inlet of S12 is at the node 5 of Fig. 18-2. The elevation of node 5 is 3.0 (m).

ZINL12 := 18.725+ 3.0-Zref ZINL12 = 18.5047 m

- A150-

ZINL(13): Elevation of the inlet of the intermediate pipe including SG

Assume the inlet of S13 is at the node 11 of Fig. 18-2. The elevation of node 11 is 1.20 (m).

ZINL13 := 18.725 + 1.20-Zref ZINL13 = 16.7047 m

i := 1 .. ISGL LOG; := 41 + i

Summary of the inlet elevation of the liquid segment

Location No.ZINLj =

1

1 -1.5912 -1.5913 -1.5914 -1.5915 10.15476 -1.37037 -1.37038 9.45479 3.504710 12.404711 7.504712 18.504713 16.7047

42434445464748495051525354

- A151 -

Fig. 18-1 Elevation and Volume of KALIMER

unit: E (m), V (m3)

EC 15 725F1 17.0751E2 15.375t5 . 1hC25E- 1.0.625E5 13720til I 3.375E7 : 12.821E5 12.575'E 9 7.5!E10 5 fllE11 6.385.:E1 2 r _ _5.,925El 3 .2.04E.14 1.14!C15 O'F16 _ -0 25C17(=18E19 4 2203E20 : . 3.2203E21 ........1,85.S222. ____ 154523 8.725.

VI _ __ 34.402V? 8.23V3 _ .. .62.964V4 58,9.91.V5 34#_______V7 . 95.2 IJV8 22.727y§_ j . 54,643yio . ,36.626

hvi • . .38,814V1_2. 25.78V13 19,72VH . .7 7.803

V _ ..._ 55,0.36/

. ..VcoldVhol

.212,9,1 32,58'

Vavo 151.94!Vsodu 407.42'

- A152-

: 14'SCI-20

: ?0'$CHtt

"W 0-t"iJCI120>= - 5F.*£ cm, f - 0:7925eni, p-53 34 os»

qyg “is w$chk>: Uv = 90.3 cm. t - O.^tovir.. i>-7K.^n

* y : z1 0 0 02 0 0 1203 0 3C04 BO 5 0 3005 BO 5 186 7 3006 80S 373.6 3C07 0 373.6 3003 0 373.6 1205 0 373.6 010 aor> 0 120

11 605 180.7 12012 805 373.6 12013 960 186 7 12014 960 16.7 120in llf>0 16.7 1201G 1150 136.7 12017 1150 ISO. 7 106016 115-0 420.7 100019 1150 426.7 91020 1150 426.7 -650

21 1150 426.7 -BOO22 1150 -49.3 -BOO23 1150 -49.3 -2002-1 1150 -2-19.3 -20025 1150 -2-19.3 17620 1150 -249.3 72027 1160 249.3 37023 960 -245.3 87029 960 -245.3 30030 960 136.7 300

Node 22: S11 inlet, S13 outlet

Node 5 : S12 inlet, S11 outlet

Node! 1: S13 inlet. S12 outlet

Fig. 18-2 IHTS Elevation of KALIMER

41 S3-

Location 82-161. CVLMLTOVL ISGL)Multiplicity factors at liquid segment ends. M=1 at inlet, M=2 at outlet. i := 1 .. ISGL

Multiplicity factors at all liquid segments except those mentioned below are set to 1 as initial values.

CVLMLTIj := 1 at inlet CVLMLT2j := 1 at outlet

4 IHXs are represented by one segment, with the flow rate duplicated for the total through all IHXs. All IHXs are assumed to be identical. Therefore, the multiplicity factor of liquid segment S5 is 4.

CVLMLTI5 := 4 at inlet CVLMLT25 := 4 at outlet

There are 4 pump loops in the KALIMER design. For flexibility, these four loops are represented by 2 pump loops in the model, with the first loop representing 3 pumps and the second loop representing 1 pump. Therefore, the multiplicity factors of liquid segment S6 at the inlet and at the outlet are 3. The second pump loop has actually 1 pump in the model and the multiplicity factors of S7 is 1.

CVLMLT16 := 3 at inlet CVLMLT26 := 3 at outlet

Each IHTS loop contains two IHXs and associated piping.

CVLMLT112 := 2 at inlet CVLMLT212 := 2 at outlet

LOC1 j := 2x i + 80 LOC2j 2 x i + 81

Multiplicity factor at inletLocationNo.

LOC1 j828486

88

9092949698

100

102

104106

CVLMLTIj =1

1 1

2 1

3 1

4 1

5 46 37 1

8 1

9 1

10 1

11 1

12 2

13 1

Multiplicity factor at outletLocationNo.

LOC2j838587899193959799

101

103105107

CVLMLT2j =1

1 1

2 1

3 1

4 1

5 46 37 1

8 1

9 1

10 1

11 1

12 2

13 1

- A154 -

Location 162-301. ZOUTEL (IELL)Height at the outlet of each liquid element.Note: ZOUTEL(IELL) is also the height at the inlet of element (IELL+1) if (IELL+1) is in

the same segment

Since there are 34 liquid elements in the model, IELL := 34

The assembly elevation of the KALIMER core is shown in Fig. 51-1. The elevation of the remainder of the reactor system is estimated from Figs. 18-1 and 18-2, which are copies of Fig. M-3 and F-8 of Ref. A2. The reference elevation is the same as described for the segment inlet, Loc. 42-81, Block 18

Zref = 3.2203 m

ZOUTEL(1): Elevation of the top of the core subassemblies

ZOUTEL-j := 3.1647 m

ZOUTEL(2): Elevation of the top of the pipe representing the part of the control rod assembly below the active fuel region

This is assumed to be the end of the bottom of the axial mesh in the core region.

ZOUTEL2 := 0.00 m

ZOUTEL(3): Elevation of the top of the fuel region in the control rod assemblies This is assumed to be the top of the axial mesh in the core region.

ZOUTEL3 := 2.351 m

ZOUTEL(4): Elevation of the top of the control rod assemblies.

ZOUTEL4 := ZOUTEL1 ZOUTEL4 = 3.1647 m

ZOUTEL(5): Same as for the liquid element 2.

ZOUTEL5 := ZOUTEL2 ZOUTEL5 = 0 m

- A155-

Z0UTEL(6): Same as forth© liquid element 3.

ZOUTELg := ZOUTEL3 ZOUTEL6 = 2.351 m

Z0UTEL(7): Same as forth© liquid element 4.

ZOUTEL7 := ZOUTEL4 ZOUTELy = 3.1647 m

Z0UTEL(8): Same as forth© liquid element 2.

ZOUTELg := ZOUTELg ZOUTELg = 0 m

ZOUTEL(9): Same as forth© liquid element 3

ZOUTELg := ZOUTELg ZOUTELg = 2.351 m

ZOUTEL(10): Same as for the liquid element 4

ZOUTEL10 := ZOUTEL4 ZOUTEL10 = 3.1647 m

ZOUTEL(11): Elevation of the top of the heat transfer region in the IHX

ZOUTELn := ZINL5 ZOUTELg = 10.1547 m

ZOUTEL(12): Elevation of the bottom of the heat transfer region in the IHX

The elevation of the IHX outlet nozzle, E10 in Fig. 18-1, is 6.8 (m). Dimension of the IHX internal 0.575 (m) is obtained from Fig. 18-3.

ZOUTEL12 := 6.8 + 0.575 - Zref ZOUTEL12 = 4.1547 m

ZOUTEL(13): Elevation of the exit of the IHX outlet nozzle

The elevation of E10 in Fig. 18-1 is 6.8 (m).

ZOUTEL13 := 6.8-Zref ZOUTEL13 = 3.5797 m

- A15G-

Z0UTEL(14): Elevation of the bottom of the primary EM pump body

The elevation of E23 in Fig. 18-1 is 6.725 (m).

ZOUTEL14 := 6.725-Zref ZOUTEL# = 3.5047 m

ZOUTEL(15): Elevation of the top of the primary EM pump

The elevation of E17 in Fig. 18-1 is 6.725 (m). Dimensions of the primary EM pump are obtained from Fig. 18-5, which is a copy of Fig. F-1 of Ref. A2

ZOUTEL15 := 6.725 + (0.5 + 5.0 +1.5)- Zref

ZOUTEL15 = 10.5047 m

ZOUTEL(16): Elevation of the exit of the vertical section of the pump discharge pipe

The elevation of E22 in Fig. 18-1 is 1.54 (m).

ZOUTEL16 := 1.54-Zref ZOUTEL16 = -1.6803 m

ZOUTEL(17): Elevation of the exit of the horizontal section of the pump discharge pipe

ZOUTEL17 := ZOUTEL16 ZOUTEL17 = -1.6803 m

ZOUTEL(18): Same as the liquid element E14

ZOUTELig := ZOUTELm ZOUTEL18 = 3.5047 m

ZOUTEL(19): Same as the liquid element E15

ZOUTELig := ZOUTEL15 ZOUTELig = 10.5047 m

ZOUTEL(20): Same as the liquid element E16

ZOUTEL20 := ZOUTELig ZOUTEL20 = -1.6803 m

ZOUTEL(21): Same as the liquid element E17

ZOUTEL21 := ZOUTEL17 ZOUTEL21 = -1.6803 m

- A157-

ZOUTEL(22): Elevation of the exit of the pipe connecting the hot pool to the annular volume (CV4)

The elevation of E8 in Fig. 18-1 is 12.675 (m). Assuming of 0.1 (m) length of pipe E22,

ZOUTEL22 := (12.675-0.1) - Zref ZOUTEL22 = 9.3547 m

ZOUTEL(23): Elevation of the exit of the pipe connecting the cold pool to the annular volume (CV4)

The elevation of E23 in Fig. 18-1 is 6.725 (m). Assuming of 0.1 m length of pipe E23,

ZOUTEL23 := (6.725-0.1)-Zref ZOUTEL23 = 3.4047 m

ZOUTEL(24): Elevation of the exit of the overflow path of PSDRS, equivalent to the elevation of the separation plate

The elevation of E23 in Fig. 18-1 is 6.725 (m).

ZOUTEL24 := 6.725 - Zref ZOUTEL24 = 3.5047 m

ZOUTEL(25): Elevation of the exit of the overflow path of PSDRS

Assuming of 0.1 m length of valve E26,

ZOUTEL25 := ZOUTEL24 - 0.1 ZOUTEL25 = 3.4047 m

ZOUTEL(26): Elevation of the bottom of the intermediate EM pump

The elevation of node 25 of Fig. 18-2, the bottom of the IHTS pump, is 1.76 (m).The elevation of E0 in Fig. 18-1, top of reactor vessel, is 18.725 (m), which is assumed to be the same elevation of node 0 of Fig. 18-2.

ZOUTEL26 := 18.725 +1.76- Zref ZOUTEL26 = 17.2647 m

ZOUTEL(27); Elevation of the exit of the intermediate EM pump

The elevation of node 26 of Fig. 18-2, the top of the IHTS pump, is 7.20 (m).

ZOUTEL27 ;= 18.725 + 7.20- Zref ZOUTEL27 = 22.7047 m

- A158 -

ZOUTEL(28): Elevation of the branch pipe of the IHX inlet

The elevation of node 5 of Fig. 18-2 is 3.0 (m).

ZOUTEL28 := 18.725 + 3.0 - Zref ZOUTEL28 = 18.5047 m

ZOUTEL(29): Elevation of the bottom of the heat transfer section of the IHX tube side

The elevation of the bottom of the heat transfer section of IHX is the same as for liquid element E12.

ZOUTEL29 := ZOUTEL12 ZOUTEL29 = 4.1547 m

ZOUTEL(30): Elevation of the top of the heat transfer section of the IHX tube side

The elevation of the top of the heat transfer section in the IHX tube side is the same as for liquid element E11.

ZOUTEL30 := ZOUTEL11 ZOUTEL30 = 10.1547 m

ZOUTEL(31): Elevation of the exit of the intermediate loop pipe

The elevation of node 11 of Fig. 18-2 is 1.2 (m), which is equivalent to the inlet of liquid segment S13.

ZOUTEL31 := ZINL13 ZOUTEL31 = 16.7047 m

ZOUTEL(32): Elevation of the top of the steam generator

The elevation of the top ofSG, node 19 of Fig. 18-2, is 9.1 (m).

ZOUTEL32 := 18.725 + 9.1 - Zref ZOUTEL32 = 24.6047 m

ZOUTEL(33): Elevation of the bottom of the heat transfer section of SG

The elevation of the bottom of SG, node 20 of Fig. 18-2, is -6.5 (m),

ZOUTEL33 := 18.725 - 6.5 - Zref ZOUTEL33 = 9.0047 m

ZOUTEL(34): Elevation of the exit of the intermediate loop pipe

The elevation of node 22 of Fig. 18-2 is -8.0 (m), which is equivalent to the inlet of liquid segment S11.

ZOUTEL34 := 18.725-8.0-Zref ZOUTEL34 = 7.5047 m

This data is consistent with the inlet of S11, ZINL-| 1 = 7.5047 m

- A159-

Summary of the outlet elevation of the liquid element

i := 1 .. IELL LOCj := 161 +i

LocationNo.

LOCi =162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195

ZOUTELj =1

1 3.16472 03 2.3514 3.16475 06 2.3517 3.16478 09 2.35110 3.164711 10.154712 4.154713 3.579714 3.504715 10.504716 -1.680317 -1.680318 3.504719 10.504720 -1.680321 -1.680322 9.354723 3.404724 3.504725 3.404726 17.264727 22.704728 18.504729 4.154730 10.154731 16.704732 24.604733 9.004734 7.5047

- A160 -

Fig. 18-3 IH

X Shell Side D

esign of KALIMER

inlet region medium region outlet regionspacing spacing spacing

0.6923 0.5796 0.6923,

.0993

0.9993

1.0005

0 350

0.575

.6.925

IHX Shell side design data

- A162

-

0.6923

T1CO

CD&

XX5(D3£DO<D<Ji(O'30

1mx

U----------- ►

lotal'nozzle"

0.4154

middle section

Inlet nozzle data

o sia.213: 0.0127 FBO.OOOS, .3t!4=: 1702 p/d : 1.6

o ^Sf0| °5(baffle flow hole) .^1^:0.0088 .93^/2124:2

o 42410

0 02 wzzzzzzzzzzzzzz0.9993/20.0136

.0065/2

0.578/20.9793/2

0.3272/20.33/20.35/2

center line

B?|:m

Data of baffles, shell and inner piping configuration

0 9SW[MW]:98.75 o [KPa]

.# 38 Cf^:19.2

.aiS:3xr2 : 56.8 QW:42.7 4: *1: 149S0IIA|g4kS 092XI 4: *2: IHXLH2I 14^52011 AI96i#9 elbowsXI

o S^[Kg/s].S : 535.35, 2: 450.88

o!429[C].# : 529.9, S: 339.7

Location 302-441. XLENEL WELL)Length of each liquid element, (m)

The assembly elevation of the KALI MER core is shown in Fig. 51-1. The elevation of the remainder of the reactor system is estimated from Figs. 18-1, 18-2, and 18-3.

XLENEL(1): The distance between the subassembly inlet and outletThe core channels have a length of 4.7557 m, so to be consistent with the core modeling.

XLENELy := 4.7557 m

XLENEL(2): The length of the lowest region in liquid segment 2

XLENEL2 := ZOUTEL2 - ZINL2 XLENEL2 = 1.591 m

XLENEL(3): The length of the central region in liquid segment 2

XLENEL3 := ZOUTEL3 - ZOUTEL2 XLENEL3 = 2.351 m

XLENEL(4): The length of the highest region in liquid segment 2

XLENEL4 := ZOUTEL4 - ZOUTEL3 XLENEL4 = 0.8137 m

XLENEL(5): Same as the liquid element 2

XLENEL5 := XLENEL2 XLENELy = 1.591 m

XLENEL(6): Same as the liquid element 3

XLENELg := XLENEL3 XLENELe = 2.351 m

XLENEL(7): Same as the liquid element 4

XLENELy := XLENEL4 XLENELy = 0.8137 m

XLENEL(8): Same as the liquid element 2

XLENELs := XLENEL2 XLENELy = 1.591 m

- A163-

XLENEL(9): Same as the liquid element 3

XLENELg := XLENEL3 XLENELg = 2.351 m

XLENEL(10): Same as the liquid element 4

XLENEL10 := XLENEL4 XLENELg = 0.8137 m

XLENEL(11): The length of the inlet section of the IHX

The length is estimated from Fig. 18-3 as half 1.15 (m).

XLENEL11 := -1^5 XLENELn = 0.575

XLENEL(12); The length of the heat transfer region of the IHX, given by the distance between the tube sheet faces

XLENEL12 := ZOUTELn -ZOUTEL12 XLENEL12 = 6

XLENEL(13): The length of the outlet section of the IHX

XLENEL13 := ZOUTEL12-ZOUTEL13 XLENEL13 = 0.575

XLENEL(14): The length of the flow guide to the primary EM pump inlet

XLENEL14 := Z0UTEL14-ZINL6 XLENEL14 = 4.875

XLENEL(15); The length of the primary EM pump region

XLENEL15 := ZOUTEL15 - ZOUTEL14 XLENEL15 = 7

XLENEL(16): The length of the vertical section of the pump discharge pipe of the first primary pump group

XLENEL16 := ZOUTEL15-ZOUTEL16 XLENEL16 = 12.185

-A164-

The length of the horizontal discharge pipe is assumed to be a distance between flow guide wall and support barrel (Refer to Fig. 51-2). 6.60 and 3.74 (m) are the diameters of the flow guide and the support barrel, respectively. These data are from Table M-1 of Ref. A2

XLENEL17 := (6-60-3.74) XLENEL17 = 1.43 m

XLENEL(17): The length of the horizontal section of the the pump discharge pipeof the first primary pump group

XLENEL(18): Same as the liquid element 14

XLENEL18 := XLENEL14 XLENELis = 4.875 m

XLENEL(19): Same as the liquid element 15

XLENEL-I9 := XLENEL15 XLENEL19 = 7 m

XLENEL(20): Same as the liquid element 16

XLENELao := XLENEL16 XLENEL20 - 12.185 m

XLENEL(21): Same as the liquid element 17

XLENEL21 := XLENEL17 XLENEL21 =1.43 m

XLENEL(22): The length of a fictitious pipe E22

The length of the pipe is assumed to be 0.1 (m), which is an arbitrary number.

XLENEL-22 := 0.1 XLENEL22 = 0.1 m

XLENEL(23): The length of a fictitious pipe E23

The length of the pipe is assumed to be 0.1 (m), which is an arbitrary number.

XLENEL23 := 0.1 XLENEL23 = 0.1 m

- A165-

XLENEL(24): The length of the overflow path of PSDRS

XLENEL24 := ZINL10 - ZOUTEL24 XLENEL24 = 8.9 m

XLENEL(25): The length of the fictitious valve

Assuming arbitrarily the length to be 0.1 (m)

XLENEL25 := 0.1 XLENEL-25 = 0.1 m

XLENEL(26): The length of the cold return pipe of the intermediate loop

The length from node 22 to node 25 in Fig. 18-2.

XLENEL26 := (8.0 - 2.0) + (2.493 - 0.493) + (2.0 - 1.76)

XLENEL26 = 8.24 m

XLENEL(27): The length of the intermediate EM pump body

The length from node 25 to node 26 in Fig. 18-2.

XLENEL27 := ZOUTEL27 - ZOUTEL26 XLENEL27 = 5.44 m

XLENEL(28): The length of the cold intermediate loop pipe to top of reactor head

The length from node 26 to node 5 in Fig. 18-2.

XLENEL28 := (8.7 - 7.2) + (11.5- 9.6) + (8.7 - 3.0) + (2.493 + 1.867) + (9.6 - 8.05)

XLENEL28 - 15.01 m

XLENEL(29): The length of the central downcomer of the IHX

The length from node 5 of Fig. 18-2 to bottom of IHX tube

XLENEL29 := [(1.867 - 0) + (8.05 - 0) + (3.0 - 0)] + [(18.725 - Zref) - ZOUTEL2g]

XLENEL.29 = 24.267 m

- A166 -

XLENEL(30): The length of the heat transfer section of the IHX tube sideThis length is the same for the primary side (liquid element 12)

XLENEL30 := XLENEL12 XLENEL30 = 6 m

XLENEL(31): The length of the hot pipe of the intermediate loop to common header

It is set to the length from node 1 to node 11 in Fig. 18-2 plus the elevation change the reactor vessel.

XLENEL31 := [(1.2-0) + (8.05 - 0) + (1.867 - 0)] + [(18.725 - Zref) - ZOUTEL30]

XLENEL31 = 16.467 m

XLENEL(32): The length of the hot pipe of the intermediate loop to SG

The length from node 11 to node 19 in Fig. 18-2.

XLENEL32 := (9.6 - 8.05) + (1.867-0.167) + (11.5-9.6) + (1.867 - 0.167) ...+ (10.6- 1.2) +(4.267- 1.867) + (10.6-9.1)

XLENEL32 = 20.15 m

XLENEL(33): The length of the heat transfer section of the SG shell side

The length from node 19 to node 20 in Fig. 18-2.

XLENEL33 := ZOUTEL32 - ZOUTEL33 XLENEL33 = 15.6 m

XLENEL(34): The length of the cold return pipe of the intermediate loop

The length from node 20 to node 22 in Fig. 18-2.

XLENEL34 := (8.0 - 6.5) + (4.267 + 0.493)

XLENEL34 = 6.26 m

- A167-

Summary of the length of the liquid element

i := 1 .. I ELL LOCj := 301 + i

LocationNo.

LOCj =302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335

XLENELj =1

1 4.75572 1.5913 2.3514 0.81375 1.5916 2.3517 0.81378 1.5919 2.35110 0.813711 0.57512 613 0.57514 4.87515 716 12.18517 1.4318 4.87519 720 12.18521 1.4322 0.123 0.124 8.925 0.126 8.2427 5.4428 15.0129 24.26730 631 16.46732 20.1533 15.634 6.26

- A168-

AREAEL(1): The flow area for the core region is not used, a nonzero value is input.

AREAEL-i := 1.0 m2

Location 442-581. AREAEL HELL)Cross-sectional flow area of the liquid element, (m2)

AREAEL(2): The flow area of the lower region of bypass channel 1

The flow area of a control rod assembly. Design data of control rods are from Table C-7 of Ref. A2. Following the calculation procedure of Loc. 1-4, Block 61,

Control rod assembly

Pin per assembly

Duct inner flat to flat

Pin outer diameter

Wire diameter

Number of control rod assembly

N_Cpin - 61

L_Cinflat - 0.1496

OD_Cpin = 0.016

D_Cwire = 0.001

NcrAssy = 6

AREAELg :=^ X (L_Cinflat)2 - - x (OD_Cpin)2x (N_Cpin)2 4

+ — x (D_Cwire)2 x (N_Cpin)4

x NcrAssy

AREAEL2 = 0.04241 m2

AREAEL(3)-(4): The flow areas of the central and the upper regions of bypass channel 1

These flow areas are the same as for the lower region, AREAEL(2).

AREAEL3 := AREAELg AREAEL3 = 0.04241

AREAEL4 := AREAEL2 AREAEL4 = 0.04241

m2

m2

- A169-

AREAEL(5): The flow area of the lower region of bypass channel 2

Bypass channel 2 consists of reflector and B4C assemblies. Design data of reflector and B4C are from Table C-8 and C-9 of Ref. A2, respectively. These pins don't have a wire wrap.

Reflector B/iC shield

Pin per assembly N_Rpin = 61 N_BSpin = 7

Duct inner flat to flat L_R inflat = 0.1496 LBS inflat = 0.1496

Pin outer diameter OD_Rpin = 0.0188 OD_BSpin = 0.0546

Number of reflector assembly NrfAssy = 48 NbcsAssy = 54

AREAELg :=^5 x (L_Rinflat)2 - - x (OD_Rpin)2 x (N_Rpin)

2 4

+^ X (LJ3Sinflat)2 - - x (OD_BSpin)2 x (N.BSpin)

2 4

x NrfAssy ...

x NbcsAssy

AREAEI.5 = 0.27911 m2

AREAEL(6)-(7): The flow areas of the central and the upper regions of bypass channel 2

These flow areas are the same as for the lower region, AREAEL(5).

AREAELg := AREAEL5 AREAELg = 0.27911 m1

AREAEL7 := AREAELg AREAELy = 0.27911 nr

- A170 -

Bypass channel 3 consists of radial shield and IVS assemblies. Design data of radial shield are from Table C-10 of Ref. A2. It is assumed that the IVS assembly is the same as the driver fuel assembly. The pin of radial shield don't have a wire wrap.

AREAEL(8): The flow area of the lower region of bypass channel 3

Radial shield IVS

Pin per assembly

Duct inner flat to flat

Pin outer diameter

Wire diameter

N_RSpin - 61

L_RSinflat = 0.1496

OD_RSpin = 0.0188

N/A

Number of shield assembly NrsAssy = 72

N_Dpin = 271

L_Dinflat = 0.1496

OD_Dpin - 0.0074

D_Dwire = 0.0014

NivsAssy = 54

AREAELg :=^ x (L_RSinflat)2

^ x (L_Dinflat)2

+ — x (D_Dwire) 4

- - x (OD_RSpin)2 x (N_RSpin) 4

- ^ x (OD_Dpin)2 x (N_Dpin) ...

2x (N_Dpin)

x NrsAssy ...

x NivsAssy

AREAELg - 0.57101 m2

AREAEL(9)-(10): The flow areas of the central and the upper regions of bypass channel 3

These flow areas are the same as for the lower region, AREAEL(8).

AREAELg := AREAELg AREAELg = 0.57101 m2

AREAEL10 := AREAELg AREAEL-|o - 0.57101 m2

- A171 -

The area of the baffle flow hole of the IHX inlet, Design data are from Fig. 18-4.

Diameter of flow hole D_hole := 0.0088 m

Number of flow hole No_hole := 2 x (1702)

AREAELt 1 := - x (D_hole)2 x (No_hole) AREAEM1 = 0.20704 m24

AREAEL(11): The flow area of the entrance of the primary side of the IHX

AREAEL(12): The flow area of the primary side sodium

Design data are from Fig. 18-4.

Outer diameter of IHX tube ODJHXtube := 0.0127 m

Inner diameter of IHX tube IDJHXtube := 0.0111 m

Number of tube NoJHXtube := 1702

Inside diameter of IHX shell: IDJHXshell := 1.0065 m

Outside diameter of central pipe ODJHXpipe ~ 0.35 m

AREAEL12 := - x (IDJHXshell)2 - - x (ODJHXtube)2 x (NoJHXtube) 4 4

-71x (ODJHXpipe)'

AREAEL12 = 0.48383 nr

AREAEL(13): The outlet flow area on the primary side of the IHX.

Design data are form Fig. 18-3.

Outlet nozzle of IHX IDJHXnozzle := 0.4 m

AREAEL13 : J x (IDJHXnozzle)2 AREAEL13 = 0.12566 m2

- A172-

AREAEL(14): The flow area for the inlet of flow guide

Design data arc taken from Table M-1 and Fig. M-4 of Ref. A2

Flow guide outer diameter FOOD := 6.6 m

Flov/ guide wall thickness FGWT := 0.025 m

Support barrel outer diameter SBOD = 3.74 m

1 St layer inner diameter

layer thickness

gap distance between layers

L1 ID := 3.943 m

LAYRT := 0.15 m

LGAP := 0.025 m

2 nd layer inner diameter L2ID : LI ID i 2 x (LAYRT + LGAP) L2ID = 4.293 m

3 rd layer inner diameter L3ID := L2ID i 2x (LAYRT 4 LGAP) L3ID = 4.643 m

The flow area surrounding the pump discharge pipe is approximated to be 10% total area.

Since there are four primary pumps in the reactor vessel, the flow area of El 4 is divided by 4.

moo

AREA_FG := x (FGOD - 2 x FGWT)2 - - x (SBOD)2 - - x [ (LI ID 4 LAYRT)2 - (L1 ID)2 4 44

+ ^x[(L2lD- LAYRT)2 - (L2ID)2] - ^ x[ (L3ID i LAYRT)2 - (L3ID)2

AREA FAAREAEL14 -------- —x(1.1) AREAEL14 = 5.39609 ir*4

A1?3

Estimated from Fig. 18-5, the outer annulus flow area is assumed to be 20% total area subtracted by the central flow area.

Inside diameter of pump shell ID_psheli := 1.13 m

Diameter of central channel OD_pchannel := 0.4 m

AREAELi5 := — x (ID^pshell2 - OD_pchannel2) x (0.2)4

AREAEL15 - 0.17544 m2

AREAEL(16): The flow area of the vertical section of the pump discharge pipe (1st group)

The flow area of the discharge pipe is estimated from Fig. 18-5 and Table M-1 of Ref. A2.

Inside diameter of EMP discharge pipe D_ppipe := 0.4 m

AREAEL16 := - x (D_ppipe)2 AREAEL16 = 0.12566 m2

4

AREAEL(17): The flow area of the horizontal section of the pump discharge pipe (1st group)

This flow area is the same as for liquid element 16

AREAEL-I7 AREAELie AREAEL17 = 0.12566 m2

AREAEL(18)-(21): The flow area of the second primary pump (2nd group)Since the two primary pump groups are identical, the flow areas of the corresponding components are the same.

AREAEL(15): The flow area of the vertical annular region of the primary pump (1st group)

AREAEL18 := AREAEL14 AREAEL18 - 5.39609 m:

AREAEL19 := AREAEL-15 AREAEL19 = 0.17544 m:

AREAEL20 AREAEL-I6 AREAEL20 = 0.12566 m;

AREAEL21 AREAEL17 AREAEL21 = 0.12566

- A174-

C V. rr ■H I h1.1 3m

Fig. 18-5 Layout of KALIMER Primary EM Rump

-A175-

AREAEL(22): The flow area of E22

The flow area is arbitrarily assumed to be 0.1 m2.

AREAEL22 •= 0.1 AREAEL22 = 0.1 m2

AREAEL(23): The flow area of E23

The flow area is arbitrarily assumed to be 0.1 m2.

AREAEL23 := 0.1 AREAEL23 = 0.1 m2

AREAEL(24): The flow area of the overflow path of PSDRS

The flow area of annulus between reactor baffle and reactor vessel, Design data are from Table M-1 of Ref. A2

Inside diameter of reactor vessel ID_rv := 6.92 m

Outside diameter of reactor baffle OD_rb := 6.87 m

AREAEL24 := -x[(ID_rv)2- (OD_rb)2]4

AREAEL24 = 0.54153 m2

AREAEL(25): The flow area of the fictitious valve E25

The flow area is the same as the liquid element 24.

AREAEL25 := AREAEL24 AREAEL25 - 0.54153 m2

AREAEL(26): The flow area of the cold return pipe of the intermediate loop

Outside diameter and wall thickness of the intermediate loop pipe with larger diameter are from Fig. 18-2. It should be noted that only one IHTS loop is modeled by SASSYS-1A .

Outer diameter of pipe OD_ihtspipe1 0.508 m

Thickness of pipe Tw_ihtspipe1 := 0.009525 m

AREAEL26 := — x (OD_ihtspipe1 - 2 x Twjhtspipel )2 4

AREAEL26 = 0.18777 m2

- A176-

The flow area is assumed to be the same as the liquid element 26.

AREAEL27 := AREAEL26 AREAEL27 = 0.18777 m2

AREAEL(28): The flow area of the intermediate loop pipe to top of the reactor head

The flow area is the same as the liquid element 26.

AREAEL28 := AREAEL26 AREAEL28 = 0.18777 m2

AREAEL(27): The flow area of the intermediate EM pump body

AREAEL(29): The flow area of the central downcomer of the IHX

The inside diameter of the central downcomer is 0.33 (m) from Fig. 18-3.

AREAEL29 := - x (0.33)2 AREAEL29 = 0.08553 m2

4

AREAEL(30): The flow area of the heat transfer section of the IHX tube side

The flow area of the IHX tube side is calculated using the design data from Fig. 18-4 and AREAEL(12). It should be noted that only one IHX is modeled by SASSYS-1.

Tube outside diameter OD IHXtube = 0.0127 m

Tube wall thickness TwJHXtube := 0.0008 m

Tube inside diameter IDJHXtube := ODJHXtube - TwJHXtubex (2)

IDJHXtube - 0.0111 m

Number of tube NoJHXtube = 1702

AREAEL30 := — x (ID_IHXtube)2x (No_IHXtube) 4

AREAEL30 = 0.1647 m2

- A177-

AREAEL(31): The flow area of the hot pipe of the intermediate loop to common header

Outer diameter and wall thickness of the intermediate loop pipe with smaller diameter are from Fig. 18-2.

Outside diameter of pipe OD_ihtspipe2 := 0.3556 m

Thickness of pipe Tw_ihtspipe2 := 0.007925 m

AREAEL31 := — x (OD_jhtspipe2 - 2x Tw_ihtspipe2)2 4

AREAEL31 - 0.09066 m2

AREAEL(32): The flow area of the hot pipe of the intermediate loop to SG

The flow area is the same as the liquid element 26.

AREAEL32 := AREAEL26 AREAEL32 = 0.18777 m2

AREAEL(33): The flow area of the heat transfer section of the SG shell side

The flow area of SG tube side is calculated using the design data from page A22 of Ref. A2. Multiplicity factor 0.9 is applied to account of flow-blockage due to SG internals.

Number of tubes without plugging NCLSGtube := 224

Outer diameter of tube OD_SGtube := 0.023 m

SG shell inner diameter ID_SGshell := 2.7 m

AREAEL33 := - x (ID.SGshell)2 - - x (OD_SGtube)2 x (NO_SGtube) 4 4

x (0.9)

AREAEL33 - 5.06924 nr

AREAEL(34): The flow area of the cold return pipe of the intermediate loop

The flow area is the same as the liquid element 26.

AREAEL34 := AREAEL26 AREAEL34 = 0.18777 m2

- A178-

Summary of the flow area of the liquid element

i := 1 .. IELL

LocationNo.

LOCj442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475

LOCj := 441 + i

AREAELj =1

1 12 0.042413 0.042414 0.042415 0.279116 0.279117 0.279118 0.571019 0.5710110 0.5710111 0.2070412 0.4838313 0.1256614 5.3960915 0.1754416 0.1256617 0.1256618 5.3960919 0.1754420 0.1256621 0.1256622 0.123 0.124 0.5415325 0.5415326 0.1877727 0.1877728 0.1877729 0.0855330 0.164731 0.0906632 0.1877733 5.0692434 0.18777

A179-

Location 582-721. DHELEM (IELUHydraulic diameter of the liquid element, (m)

DHELEM(1): The hydraulic diameter in the core model is not used in the calculation, so a nonzero number is input.

DHELEM! := 1.0 m

DHELEM(2)-(4): The hydraulic diameter of control rods (bypass channel 1)

The flow area of liquid element E2 calculated in Loc. 442-581, Block 18 is a total flow area of 6 control rod assemblies.

AREAEL2 = 0.04241 m2

Wetted perimeter is

Peri_bp1 := x (L_Cinflat) +7tx (OD_Cpin) x (N_Cpin) ...V3

_+ 7tx (D_Cwire) x (N_Cpin)

x NcrAssy

Peri_bp1 = 22.656 m

Thus, hydraulic diameter of the lower region of bypass channel 1 is

DHELEM2 := 4x(areael2)

Peri_bp1DHELEM2 = 7.4883 x 10 m

The hydraulic diameters of the central and upper regions of bypass channel 1 are the same as for the lower region, respectively.

DHELEM3 := DHELEM2

DHELEM4 := DHELEM2

DHELEM3 = 7.4883 x 10 3 m

DHELEM4 = 7.4883 x 10™ 3 m

- A180-

The flow area of liquid element E5 calculated in Loc. 442-581, Block 18 is a total flow area of the reflector and B4C assemblies.

AREAEL5 = 0.27911 m2

DHELEM(5)-(7): The hydraulic diameter of reflector and B4C assemblies (bypass channel 2)

Wetted perimeter is

Peri_bp2 := — x (LJRinflat) + nx (OD_Rpin) x (N_Rpin)LVs+ x (L_BSinflat) titx (OD_BSpin) x (N.BSpin)

LVS

x NrfAssy ...

x NbcsAssy

Peri_bp2 = 290.631 m

Thus, hydraulic diameter of the lower region of bypass channel 2 is

DHELEM5 := 4 x(AREAELs)

Peri_bp2DHELEM5 = 3.8414 x 10 m

The hydraulic diameters of the central and upper regions of bypass channel 2 are the same as for the lower region, respectively.

DHELEMe := DHELEMs DHELEM6 = 3.8414x 10 3 m

DHELEM? := DHELEM5 DHELEM; = 3.8414x 10“ 3 m

- A181 -

The flow area of liquid element E8 calculated in Loc. 442-581, Block 18 is total flow area of the radial shield and I VS assemblies.

AREAELg = 0.57101 m2

DHELEM(8)-(10): The hydraulic diameter of radial shield assembly (bypass channel 3)

Wetted perimeter is

Peri_bp3 := -?= x (L_RSinflat) + kx (OD_RSpin) x (N_RSpin)Lys+ ~L x (L_Dinf!at) + n x (OD_Dpin) x (N_Dpin) ...

V3_+ 7t x (D_Dwire) x (NJOpin)

Peri_bp3 = 729.269 m

x NrsAssy ...

x NivsAssy

Thus, hydraulic diameter of the lower region of bypass channel 3 is

DHELEMg := 4x(AREAELs)

Peri_bp3DHELEMg = 3.132x 10 m

The hydraulic diameters of the central and upper regions of bypass channel 3 are the same as for the lower region, respectively.

DHELEMg := DHELEMs DHELEMg = 3.132x 10~3 m

DHELEMio := DHELEMs DHELEM10 = 3.132x 10~3 m

DHELEM(11): The hydraulic diameter of the inlet section of the IHX

The flow area of liquid element E11 calculated in Loc. 442-581, Block 18 is

AREAELn = 0.20704 m2

Wetted perimeter is

Peri_11 := 7ix (D_ho!e) x (No_hole) Peri_11 = 94.10704 m

Thus, hydraulic diameter is

(AREAELn) _ 3DHELEMn := 4x--------------DHELEMn = 8.8x 10 d m

Peri_11

-A182-

DHELEM(12): The hydraulic diameter of the shell side of the IHX

The flow area of liquid element E12 calculated in Loc. 442-581, Block 18 is

AREAEL12 = 0.4838 m2

Wetted perimeter is

Peri_12 := ttx (IDJHXshell) +jcx (OD_IHXtube) x (NoJHXtube) ...+ 7i x (ODJHXpipe)

Peri_12 = 72.16835 m

Thus, hydraulic diameter is

(AREAEL12}DHELEM12 := 4x^------------- \=L DHELEM12 = 0.0268 m

Peri_12

DHELEM(13): The hydraulic diameter of the outlet section of the IHX

The inside diameter of the IHX outlet nozzle is 0.4 m from Fig. 18-3.

DHELEM13 := 0.4 m

DHELEM(14): The hydraulic diameter of the inlet section of the primary pump

The flow area of liquid element E14 calculated in Loc. 442-581, Block 18 is

AREAEL14 = 5.39609 m2

Wetted perimeter includes the four discharge pipes and their shrouds. The inside diameter of the discharge pipe shroud is approximated to be 1.2 times diameter of pipe.

PerLFL := n x (FOOD - 2 x FGWT) + n x (SBOD) + n x (L3ID + LAYRT) ...+ 7t x (L3ID) + 7U x (L2ID + LAYRT) + nx (L2ID) + 71 x (L1 ID + LAYRT) ... + tc x (L1 ID) + 4 x [ttx (D_ppipe)] + 4 x [71 x (1.2 x D_ppipe)]

Since there are 4 primary pumps, the perimeter per pump is divided by 4.

Peri FIPeri_14 := ~ Peri_14 = 31.43006 m

4

-A183-

Thus, hydraulic diameter is

DHELEMm := 4 x (AREAEL^) DHELEM14 = 0.6867 m

RerM 4

DHELEM(15): The hydraulic diameter of the vertical annular region of the primary pump (1st group)

Since the detailed configuration of KALI ME R EM pump is not determined yet, the hydraulic diameter is calculated based on a general formula.

The flow area of liquid element E15 calculated in Loc. 442-581, Block 18 is

AREAEL15 = 0.17544 m2

Thus, hydraulic diameter is

DHELEM-I5 := /4x (AREAfj-1s) DHELEM15 = 0.4726 m

V n

DHELEM(16): The hydraulic diameter of the vertical section of the pump discharge pipe (1st group)

Insdie diameter of the discharge pipe E16 in Loc. 442-581, Block 18 is

D_ppipe - 0.4 m

Hydraulic diameter is

DHELEM16 := D_ppipe DHELEM16 = 0.4 m

DHELEM(17): The hydraulic diameter of the horizontal section of pump discharge pipe (1st group)

DHELEM17 := DHELEM16 DHELEM17 = 0.4 m

- A184-

Since the two primary pump groups are identical, the hydraulic diameters of the corresponding components are the same.

DHELEM(18)-(21): The hydraulic diameter of the 2nd group pump

DHELEM18 DHELEM14

DHELEM19 := DHELEM15

DHELEM20 := DHELEMie

DHELEM21 := DHELEM17

DHELEM18 = 0.6867 m

DHELEM19 = 0.4726 m

DHELEM20 = 0.4 m

DHELEM21 = 0.4 m

DHELEM(22): The hydraulic diameter of the pipe connecting CV2 and CV4 This input is based on the assumed flow area of 0.1 m2.

AREAEL-22 = 0.1

Hydraulic diameter is

DHELEM22:.j355EaDHELEM22 = 0.3568

DHELEM(23): The hydraulic diameter of the pipe connecting CV3 and CV4

The hydraulic diameter of this flow path is the same as for liquid element 22,

DHELEM23 := DHELEM22 DHELEM23 = 0.3568 m

DHELEM(24): The hydraulic diameter of the overflow path of PSDRS

The hydraulic diameter is calculated using the design data of AREAEL(24) in Loc. 442-581, Block 18,

DHELEM24 := ID_rv - OD„rb DHELEM24 = 0.05 m

- A185-

DHELEM(25): The hydraulic diameter of the annulus between reactor baffle and reactor vessel

The hydraulic diameter is assumed to be the same as for liquid element 24.

DHELEM25 := DHELEM24 DHELEM25 = 0.05 m

DHELEM(26): The hydraulic diameter of the cold return pipe of the intermediate loop

The hydraulic diameter is calculated using the data of AREAEL(26) calculation in Loc. 442-581, Block 18,

DHELEM26 := OD_ihtspipe1 -2x (Twjhtspipel)

DHELEM26 = 0.48895 m

DHELEM(27): The hydraulic diameter of the intermediate EM pump

The hydraulic diameter is assumed to be the same as the liquid element 26.

DHELEM27 := DHELEM26 DHELEM27 = 0.48895 m

D HE LEM (28): The hydraulic diameter of the intermediate loop pipe to top ofreactor head

The hydraulic diameter is the same as the liquid element 26.

DHELEM28 := DHELEM26 DHELEM28 = 0.48895 m

DHELEM(29): The hydraulic diameter of the central downcomer of the IHX

The hydraulic diameter is the inside diameter of the central downcomer of IHX from Fig. 18-3

DHELEM29 := 0.33 m

DHELEM(30): The hydraulic diameter of the heat transfer section of the IHX tube side

Using the design data of AREAEL(30) in Loc. 442-581, Block 18,

DHELEM30 := IDJHXtube DHELEM30 = 0.0111 m

- A186 -

The hydraulic diameter is calculated using the design data of AREAEL(31) in Loc. 442-581, Block 18,

DHELEM31 := OD_ihtspipe2 - 2x (Tw_ihtspipe2)

DHELEM31 = 0.33975 m

DHELEM(32): The hydraulic diameter of the intermediate loop to SG

The hydraulic diameter is the same as the liquid element 26.

DHELEM32 := DHELEM26 DHELEM32 = 0.48895 m

DHELEM(31): The hydraulic diameter of the intermediate loop to the common header

DHELEM(33): The hydraulic diameter of the heat transfer section of the SG shell side

The flow area of liquid element E33 calculated in Loc. 442-581, Block 18 is

AREAEL33 = 5.0692 m2

Wetted perimeter is calculated using the data in AREAEL(33) calculation.

Peri_33 := [nx (ID_SGshell) +nx (OD„SGtube) x (NO_SGtube)]

Peri_33 = 24.66779 m

Thus, hydraulic diameter is

DHELEM33:-4«|A^3)DHELEM33 = 0.822 m

DHELEM(34): The hydraulic diameter of the cold return pipe of the intermediate loop

The hydraulic diameter is the same as the liquid element 26.

DHELEM34 := DHELEM26 DHELEM34 = 0.48895 m

- A187-

Summary of the hydraulic diameter of the liquid element

i := 1 .. IELL LOCj := 581 +i

LocationNo.

DHELEMj =1

1 12 0.007493 0.007494 0.007495 0.003846 0.003847 0.003848 0.003139 0.0031310 0.0031311 0.008812 0.0268213 0.414 0.6867415 0.4726316 0.417 0.418 0.6867419 0.4726320 0.421 0.422 0.3568223 0.3568224 0.0525 0.0526 0.4889527 0.4889528 0.4889529 0.3330 0.011131 0.3397532 0.4889533 0.82234 0.48895

582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615

- A188-

Location 722-861. ROUGHL (IELL)Pipe surface roughness for friction factor, (m)

This date is used in the pipe pressure drop calculation.

Assume 0.00001 relative roughness for a relatively smooth surface in all pipes.

= 0.00001 for all liquid elements (Loc. No: 722 - 755)

Location 862-1001, BENDNM (IELL)Number of bends in each liquid element

This data is input to account for the additional pressure drop associated with each bend. Only those elements containing bends are reviewed.

BENDNM(16) = 1.0 for vertical discharge pipe of pump group 1 BENDNM(20) = 1.0 for vertical discharge pipe of pump group 2

BENDNM (26) = 2.0 BENDNM(28) = 4.0 BENDNM(29) = 2.0 BENDNM(31) = 3.0 BENDNM(32) = 6.0 BENDNM(34) = 1.0

for IHTS, Refer to Fig. 18-2 and Fig. 18-3.

- A189-

Location 1002-1141, G2FRDR (IELL)Initial orifice coefficient

Delta P = G2PRDR*G*ABS(G)/(2*RHO)

Orifice coefficients which are added to the elements to provide additional pressure drop.

These are normally zero as input, with PRiMAR-4 calculating these coefficients during the steady-state to initialize the model. Some values need to be set to provide the correct free surface levels in the volumes. These values are determined by trial-and-error using the PRIMAR-4 steady-state calculation.

Orifice coefficient equation is

G2PRDR :=2x p x AP’

GxG

Using the relation of FLOSS = pxGx AREAEL

.21G2PRDR :=

2 x p x AREAELx AP

FLOSS2

G2PRDR(11) - (13): Orifice coefficients of the IHX shell side (Liquid Segment 5)

The total pressure loss through the shell side of the IHX is 0.038 MPa, which includes the pressure loss of the tube bundle region, 0.0192 MPa. Refer to Fig. 18-4.

APJHX := 38000 Pa

AP 12:= 19200 Pa

for IHX shell side

for tube bundle region (shell side)

The pressure losses of Elements 11 and 13 are assumed to be

AP__11 := 0.5 x (APJHX — AP_12) AP_11 = 9400 Pa

AP 13 := AP 11 AP_13 = 9400 Pa

Sodium density is listed at Loc. 91-250, Block 13.

Rho_hot := linterp (RHOTEM3, Rho_Na, Tcoreout)

Rho__avg := linterp(RHOTEM3,Rho_Na,Tcoreavg)

Rho_cold := linterp (RHOTEM3, Rho_Na, Tcorein)

Rho_hot = 825.28 kg/m3

Rho_avg = 841.89 kg/m3

Rho_coid = 858.39 kg/m3

-A190-

Then

G2PRDFM 1 :=2 x Rho hot x (AREAELi )2 x AP 11

(FLOSSg)2

G2PRDR_11 = 2.31894

G2PRDR_12 :=2 x Rho avg x (AREAELi 2)2 x AP 12

(FLOSSs)2

G2PRDR_12 = 26.388

G2PRDR.13 :=2 x Rho cold x (AREAEL13)2 x AP 13

(FLOSS5)2

G2PRDR_13 = 0.88859

G2PRDR(22) and (23): Orifice coefficients of the E(22) and E(23)

There are no intentional flow between the buffer region(CV4) and pools (CV2 and CVS).

G2PRDR_22 := 1.0x 1010 G2PRDR_23 := 1.0x 101°

G2PRDR(25): Orifice coefficients of the fictitious PSDRS valve

G2PRDR_25 := 1.0x 1010

G2PRDR(30): Orifice coefficients of the IHX tube (Liquid Segment 12)

The pressure loss through the tube side of the IHX is 0.0568 MPa, from Fig. 18-3.

AP_30 := 56800 Pa

G2PRDFL30 :=2 x Rho avg x (AREAEL30)2 x AP 30

G2PRDRJ30 = 12.76041(floss12)2

- A191 -

Pressure balance with pump head in the primary system

The primary system pressure loss should be matched with the prump head.

The rated head of the primary pump Phead_1 := 0.8086 MPa

The system pressure loss calculated by SAS4A/SASSYS-1 during the edit check run

DelPsys_1 := 0.65667 MPa

The difference between the system pressure loss and the pump head

DelPdifM Phead_1 - DelPsys_1 DelPdiff_1 = 0.15193 MPa

The pressure difference between the pump rated head and the system pressure calculated by the code is assumed to occur in the pump inlet and outlet paths, because the geometry of these flow pathes is relatively complicated.

G2PRDFM4 :=2 x Rho_cold x (AREAEL14f x | j x DelPdifM x 1 o'

(FLOSSe)2

G2PRDR_14 = 13228,7706

G2PRDR_16 :=

2 x Rho_cold x (AREAEL1S)2 x f-1 x DelPdiff_1 x 106

(FLOSSe)2

G2PRDR_16 = 3.58716

G2PRDR_17 :=

2x Rho coldx (AREAEL17)2x^x DelPdiff 1 x 106

(FLOSSe)2

G2PRDR_17 = 7,17432

-A192-

Pressure balance with pump head in the intermediate system

The intermediate system pressure loss should be matched with the pump head.

The rated head of the intermediate pump Phead_2 := 0.4 MPa

The system pressure loss calculated by SAS4A/SASSYS-1 during the edit check run

DelPsys_2 := 0.16924 MPa

The difference between the system pressure loss and the pump head

DelPdiff_2 := Phead_2 - DelPsys_2 DelPdiff_2 = 0.23076 MPa

Sodium temperatures in the intermediate system are obtained from the code result for the edit check run.

sodium temperature in the hot side Tihtshot := 787.20 K

sodium temperature in the cold side Tihtscold := 617.885 K

Sodium density is listed at Loc. 91-250, Block 13.

Rho_cold2 := linterp (RHOTEM3, Rho_Na, Tihtscold) Rho_cold2 = 867.82 kg/m3

Rho_hot2 := linterp(RHOTEM3.Rho_Na.Tihtshot) Rho_hot2 = 828.97 kg/m3

G2PRDR 29 :=

2 x Rho cold2 x (AREAEL29)2 x Q x DelPdiff 2x 10*

(FLOSS! 2)2

G2PRDR 29 = 3.60277

G2PRDR_33 :=

Rho_hot2 + Rho_cold2j x (AREAE|_33)2 x^|x De|Pc|iff_2 x 106j

(FLOSS13)2

G2PRDR_33 = 9279.3316

- A193-

Location 1142, BNDLODEffective LVD per band

The equivalent length of pipe, in diameters, which provides the same pressure drop as a smooth 90 degree bend.

BNDLOD= 12

- A194 -

Location 1143-1282, WALLMC WELL)Pipe wall mass * heat capacity per unit length, (J/rn/K)

The following values are used for (density * specific heat capacity) calculated at the core average temperature

Tcoreavg = 731.25 K

HT-9 pCp_HT9 := 4.9460 x 106 J/m3-K

316-SS pCp_316SS := 4.4970 x 10® J/m3-K

304-SS pCp_304SS := 4.4190 x 10® J/m3-K

9Cr-1Mo pCp_9CR1Mo := 4.5800 x 10® J/m3-K

WALLMC(1): The value for the core region is not used by the code. It is set to a nonzero value.

WALLMCi := 1.0 J/m-K

- A195-

WALLMC(2): The lower region of bypass channel 1

WALLMC(2) represents the lower region of the control rod assembly. Design data are from Table C-7 of Ref. A2. The value is estimated as follows:

Assembly lattice pitch of control rod assembly, Pitch_CA := 0.161 m

Average area per subassembly

Area.CA :=^x (Pitch_CA)2 Area_CA = 0.02245 m2

Area fraction of pin and structure in control rod assembly, from Table C-7 of Ref. A2.

AFR_CA := 0.3607 + 0.2732 AFRICA = 0.6339

Then, area of pin and structure per subassembly is

Area_CAw := (Area_CA) x (AFR_CA) Area_CAw = 0.01423 m2

Assume that this area all has the properties of FIT-9,

(density) * (specific heat) of HT9 at Tcoreavg is obtained from Loc. 1050-1069, Block 13 Tcoreavg = 731.25 K

CpRho_ht9 := linterp(CROETM,CpRho_HT9,Tcoreavg)

CpRho_ht9 = 5.00794 x 106 J/m3-K

There are 6 assemblies in the core, NcrAssy = 6

WALLMCa := (NcrAssy) x (Area_CAw) x (CpRho_ht9)

WALLMC2 = 4.276 x 105 J/m-K

WALLMC(3)-(4): The central and upper regions of bypass channel 1

The values for the central and upper regions of bypass channel 1 are the same as for the lower region.

WALLMCs := WALLMC2 WALLMC3 = 4.27576 x 105 J/m-K

WALLMC4 := WALLMC2 WALLMC4 = 4.27576 x 105 J/m-K

- A196-

WALLMC(5): The lower region of bypass channel 2

WALLMC(5) represents the lower region of the reflector and B4C shield assemblies.Design data are from Tables C-8 and C-9, of Ref. A2.Using the same method for WALLMC(2),

Assembly lattice pitch of the reflector and B4C shield assemblies,

Pitch_RA := 0.161 m Pitch_BSA := 0.161 m

Average area per subassembly

Area.RA := ^ x (Pitch. RA)2 Area.BSA = ^ z (Pitch.BSA)2

Area fraction of pin and structure in control rod assembly

AFR_RA := 0.7543 + 0.0875 AFR_BSA := 0.5810 + 0.2366

Then, area of pin and structure per each subassembly is

Area_RAw := (Area_RA)x (AFR_RA) Area_RAw = 0.0189 m2

Area_BSAw := (Area_BSA) x (AFR_BSA) Area_BSAw = 0.01835 m2

Numbers of the reflector and B4C shield assemblies,

NrfAssy = 48 NbcsAssy = 54

Thus,

WALLMC5 := [ (NrfAssy) x (Area_RAw) + (NbcsAssy) x (Area_BSAw) ] x (CpRho_ht9)

WALLMGs = 9.506 x 106 J/m-K

WALLMC(6)-(7): The central and upper regions of bypass channel 2

The values for the central and upper regions of bypass channel 2 are the same as for the lower region.

WALUMCe := WALLMGs WALLMC6 = 9.506 x 106 J/m-K

WALLMC7 := WALLMGs WALLMC7 = 9.506 x 106 J/m-K

A197-

WALLMC(8): The lower region of bypass channel 3

WALLMC(8) represents the lower region of the radial shield and I VS assemblies.Design data are from Tables C-10 and C-5 of Ref. A2. The I VS assembly design is identical to the driver assembly. Using the same method for WALLMC(2),

Assembly lattice pitch of the radial shield and I VS assemblies,

Pitch_RSA := 0.161 m Pitch_DA := 0.161 m

Average area per subassembly

Area_RSA := ^ x (Pitch.RA)2 AreaJVSA

Area fraction of pin and structure in each assembly

AFR_RSA := 0.7543 + 0.0875 AFRJVSA :

Then, area of pin and structure per each subassembly is

Area_RSAw ~ (Area_RSA) x (AFR_RSA) Area_RSAw = 0.0189 m2

Area_lVSAw := (Area_IVSA) x (AFRJVSA) AreaJVSAw = 0.01404 m2

Numbers of radial shield and I VS assemblies,

NrsAssy = 72 NivsAssy = 54

Thus,

WALLMCg := [ (NrsAssy) x (Area_RSAw) + (NivsAssy) x (AreaJVSAw) ] x (CpRho_ht9)

WALLMCg = 1.061 x 107 J/m-K

WALLMC(9)-(10): The central and upper regions of bypass channel 3

The values for the central and upper regions of bypass channel 3 are the same as for the lower region.

WALLMCg := WALLMCg WALLMCg = 1.061 x 107 J/m-K

WALLMC10 := WALLMCg WALLMC10 = 1.061 x 107 J/m-K

:= ^ x (Pitch_DA)2

= 0.3763 + 0.2490

- A198-

WALLMC(11): Inlet section of the IHX shell side

Material of IHX shell and internals is SS304. Design data are from Figs. 18-3 and 18-4. Using the data in AREAEL(11) of Loc. 442-581, Block 18,

IHX shell inside diameter IDJHXshell = 1.0065 m

IHX shell outside diameter ODJHXshell := 1.05 m

IHX shell thickness TwJHXshell := 0.02175 m

Inner diameter of the central downcomer ID_ctube := 0.33 m

Outer diameter of the central downcomer OD_ctube := 0.35 m

Diameter of flow hole DJiole = 0.0088 m

Height of flow hole region HJiole := 0.554 m

Number of flow hole No_hole = 3404

Total volume of steel in the inlet section of IHX:

Vol_w11 := - x (oDJHXshell2 - IDJHXshell2) x (H_hole) ... 4+ fyjx (D_hole)2X (TwJHXshell) x (No_hole)

Vol_w11 = 0.03442 m3

WALLMC(11) is calculated based on (steel volume * pCp_304SS ) / Length,

WALLMCi 1 := Vol_w11 x pCp„304SS x------------H_hoie

WALLMCi, = 2.746 x 105 J/m-K

- A199 -

Using the data in the WALLMC(11) calculation, the cross-sectional area of the IHX shell is calculated as follows:

Area_w12 := - x (oDJHXshell2 - IDJHXshell2)4

Area_w12 = 0.07026 m3

WALLMC(12) is calculated based on (steel area * pCp_304SS),

WALLMC12 := Area_w12 x pCp_304SS

WALLMC12 = 3.105 x 105 J/m-K

WALLMC(13): Outlet section of the IHX shell side

The dimensions of Fig. 18-3 is used. The outlet nozzle thickness is assumed to be the same as the IHX shell thickness.

Inside diameter of outlet nozzle IDJHXnozzle = 0.4 m

Area_w13 := - x[[ IDJHXnozzle + 2x (TwJHXshell) f - (IDJHXnozzle)2]4

Area_w13 = 0.02882 m3

WALLMC(13) is calculated based on (steel area * pCp_304SS ),

WALLMC13 := Area_w13 x pCp_304SS

WALLMC13 = 1.273 x 105 J/m-K

WALLMC(12): Heat transfer section of the IHX shell side

-A200-

WALLMC(14): Flow guide of the 1 si group pump

The steel volume ts calculated using the data in AREAELI14) of Loc. 442-581, Block 18 and Fig. 18-1. Note that the steel volume within the liquid element E14 is approximated based on simple geometry. The outer diameter of pump inlet shroud is assumed to be 1.5 times discharge pipe diameter. Material of structure is listed in Table M-1 of Ref. A2.

(volume of steel)1 (density ' specific heat) in the liquid element E14 .

Mvol_w14 := — x[ (FGOD)2 - (FGOD - 2x FGWT)2 ]x (5.825- 1.85) xpCp 304SS ... 44 ^ x [ (FGOD)2 - (SBOD)2] x (FGWT) x pCp 304SS ...

+ - x [ <L1 ID 4 LAYRT)2 - (L1 ID)2 J x (5.825 - 2.04) x pCp_316SS ...4

4- - x [ (L2ID 4 LAYRT)2 - (L2ID)2] x (5.825 - 2.04) x pCp_316SS ...4

i ^x[(L3ID i LAYRT)2 <L3ID)2"| x (5.825 - 2.04)x pCp_316SS ...

4 itx (D_pplpe) x FGWTx (6.725-1.85) x (4) x pCp_316SS ...* k x (1.5 x D_ppipe) x FGWT x (6.725 - 1.85) x (4) x pCp_316SS

Mvol. w14 = 7.108x 107 m3

where.E(12)=5.825 mE(21)=1.85 mE(13)=2.04 mE(23)=6.725 mE(18)=6.385 m

L3ID

WALLMC(14) is calculated based on (steel volume) *(pCp ) / (Length), where the length of E14 is obtained from Loc. 302-441. Block 18.

XLENEL-,4 = 4.875 m

WALLMCmMvol w14 ^ ,/1'j XLENEL14 X (,4 j Divided by 4 because a single pump

is modeled.

WALLMCk = 3.645 x 106 J/m-K

-A201-

WALLMC(15): The vertical annular region of the primary pump (1st group)

Detailed information on the KALI MER EM pump is not available, so the following approximation is made. The metal mass of one EM Pump is 19.31 ton from page A16 of Ref. A2.

WALLMC(15) is calculated based on (mass / density) * (pCp_304SS ) / (Length), where the length of E15 is obtained from Loc. 302-441, Block 18. Density of 304SS at 725 K is 7832 kg/m3, from Table M-3b of Ref. A2,

XLENEL15 = 7 m

XLENEL15

WALLMC15 = 1.556 x 106 J/m-K

WALLMC(16): The vertical section of pump discharge pipe (1st group)

Pump discharge pipe (Core inlet pipe) outer diameter, from Table M-1 of Ref. A2 OD_ppipe := 0.4508 m

Inside diameter of pump discharge pipe D_ppipe = 0.4 m

WALLMC(16) is calculated based on (Area) * (pCp_304SS)

WALLMC-I6 := - x[ (OD_ppipe)2 - (D_ppipe)2] x pCp_304SS4

WALLMCie = 1.5x 105 J/m-K

WALLMC(17): The horizontal section of pump discharge pipe (1st group)

Same as for the WALLMC(16),

WALLMC17 := WALLMC16 WALLMC17 = 1.5x 10,5 J/m-K

-A202-

WALLMC(18)-(21): The primary EM pump (2nd group)

Since the two primary pump groups are identical, WALLMC(18)-(21) are the same as the corresponding components of WALLMC(14)-(17).

WALLMC18 := WALLMC14 WALLMC-is = 3.645 x 106 J/m-K

wallmc19 := WALLMC15 WALLMC19 = 1 556 x 10® J/m-K

WALLMC20 := WALLMCie WALLMC20 = 1.5x 105 J/m-K

WALLMC21 := WALLMC17 WALLMC21 = 1.5x 105 J/m-K

WALLMC(22): The fictitious pipe connecting the hot pool and the annular region.

A nominal value is input which is compatible with the heat transfer calculation.

WALLMC22 := 1.0 J/m-K

WALLMC(23): The fictitious pipe connecting the cold pool and the annular region

A nominal value is input which is compatible with the heat transfer calculation.

WALLMC23 := 1.0 J/m-K

WALLMC(24): The flow path over the reactor baffle for PSDRS

This is the first wall of the annular element model to simulate PSDRS.

Design data are from Table M-1 of Ref. A2.

Reactor vessel outer diameter

QO

_rv := 7.02 m

Reactor vessel thickness Tw_ rv := 0.05 m

Reactor baffle outer diameter

QO

_rb = 6.87 m

Reactor baffle thickness Tw_„rb := 0.025 m

A203-

WALLMC(24) is calculated based on (Area) * (pCp_316SS )

Area_w24 := - x [ (OD_rb)2 - (OD_rb - 2 x Tw_rb)2]4

WALLMC24 := Area_w24x(pCp_316SS)

WALLMC24 = 2.418x 106 J/m-K

WALLMC(25): The fictitious valve for PSDRS model

A nominal value is input which is compatible with the heat transfer calculation.

WALLMC25 := 1.0 J/m-K

WALLMC(26): The cold return pipe of the intermediate loop

Using the dimensions for calculating the flow area AREAEL(26), Loo. 442-581, Block 18,

Outer diameter of IHTS pipe ODJhtspipel = 0.508 mwith larger diameter

Thickness of IHTS pipe Twjhtspipel = 0.00953 m

WALLMC(26) is calculated based on (Area) * (pCp_304SS).

Area_w26 := — x[ (ODJhtspipel)2 - [ ODJhtspipel - 2x (Twjhtspipel) ]2]4

WALLMC26 := Area_w26x (pCp_304SS)

WALLMC26 = 6.591 x 104 J/m-K

- A204-

WALLMC(27): The intermediate EM pump body

It is assumed to have the same characteristics as the primary EM pump (E15). Using the same method to calculate WALLMC(15),

XLENEL27 = 5.44 m From Loc. 302-441, Block 18

WBLLMC" - (w)'<»»>-”4SS) X 3iugL!-

WALLMC27 = 2.003 x 10' J/m-K

WALLMC(28): The intermediate loop pipe to the branch pipe

WALLMC(28) is the same as for WALLMC(26).

WALLMC28 := WALLMC26 WALLMC28 = 6.591 x 104 J/m-K

WALLMC(29): The central downcomer of the IHX

Using the data in WALLMC(11),

Area_w29 := — x [ (OD_ctube)2 - (ID_ctube)2] 4

WALLMC29 := Area_w29 x (pCp_304SS)

WALLMC29 = 4.72 x 104 J/m-K

- A205-

WALLMC(30): The heal transfer section of the IHX tube side

Using the data in the AREAEL(12) calculation, Loc. 442-581, Block 18,

Outer diameter of IHX tube ODJHXtube = 0.0127 m

Inner diameter of IHX tube IDJHXtube = 0.0111 m

Number of IHX tube NoJHXtube = 1702

WALLMC(30) is calculated based on (Area) * (pCp_304SS).

Area_w30 := -x[ (ODJHXtube)2-(IDJHXtube)2] x (NoJHXtube)4

WALLMC30 := Area_w30x (pCp_304SS)

WALLMC30 = 2.249 x 105 J/m-K

WALLMC(31): The hot pipe of the intermediate loop to common header

Using the dimensions for calculating the flow area AREAEL(31), Loc.

Outer diameter of IHTS pipe OD_ihtspipe2 = 0.3556with smaller diameter

Thickness of IHTS pipe Tw_ihtspipe2 = 0.00792

WALLMC(31) is calculated based on (Area) * (pCp_304SS ).

Area_w31 := — x [ (OD_ihtspipe2)2 - [ ODJhtspipe2 - 2 x (Tw_ihtspipe2) ]2] 4

WALLMC31 := Area_w31 x (pCp_304SS)

WALLMC31 = 3.825 x 104 J/m-K

442-581, Block 18,

m

m

- A206-

WALLMC(32): The hot pipe of the intermediate loop to SG

Same as for the WALLMC(26).

WALLMC32 := WALLMC26 WALLMC32 = 6.591 x 104 J/m-K

WALLMC(33): The heat transfer section of the SG shell side

Using the data in the AREAEL(33) calculation, Loc. 442-581, Block 18,

Inner diameter of SG shell ID_SGshell = 2.7 m

Assuming the wall thickness 2 inch, Tw_SGshell := 0.0508 m

WALLMC(33) is calculated based on (Area) * (pCp_304SS).

Area_w33 := - x [ (ID.SGshell + 2 x Tw_SGshell)2 - (ID_SGshell)2]4

WALLMC33 := Area_w33x (pCp_304SS)

WALLMC33 = 1.94 X 106 J/m-K

WALLMC(34): The cold return pipe of the intermediate loop

Same as for the WALLMC(26).

WALLMC34 := WALLMC26 WALLMC34 = 6.591 x104 J/m-K

- A207-

Summary of the wall mass * Specific heat of the liquid element

i := 1 .. IELL

LocationNo

LOCj =114311441145114611471148114911501151115211531154115511561157115811591160 1161 116211631164116511661167116811691170117111721173117411751176

LOCj := 1142 + i

WALLMCj =1

1 12 4.2767053 4.2767054 4.2767055 9.5067066 9.5067067 9.5067068 1.0617079 1.06170710 1.06170711 2.74670512 3.10570513 1.27370514 3.64570615 1.55670616 1.570517 1.570518 3.64570619 1.55670620 1.570521 1.570522 123 124 2.41870625 126 6.59170427 2.00370628 6.59170429 4.7270430 2.24970531 3.82570432 6.59170433 1.9470634 6.591704

- A208 -

Location 1283-1339. WALLH (IELUPipe wall conduction heat transfer coefficient, (W/m2-K)

WALLH is calculated using the following formula:

WALLH = (Thermal conductivity of steel) / (Representative thickness)

Thermal conductivity of HT-9 as a function of temperature is listed in Loc. 71-90, Block 13.

Core average temperature Tcoreavg = 731,25 K

K_wHT9 := linterp(EXKTM ,K_HT9, Tcoreavg) K_wHT9 = 26.5495 W/m-K

Thermal conductivities of 304SS and 316SS are from Table M-3 of Ref. A2

K_w304SS := 21.55 W/m-K

K_w316SS := 20.31 W/m-K

WALLH(1): The heat transfer coefficient for the core region is not used by the code.It is set to a non zero value.

WALLH-i := 1.0 W/m2-K

WALLH(2): The lower region of bypass channel 1

Using the data for calculating AREAEL(2), Loc. 442-581, Block 18,

Outer diameter of the control rod pin OD_Cpin = 0.016 m

WALLH2 •=K wHT9

WALLH2 = 3318.69 W/m2-K

WALLH(3)-(4): The central and upper regions of bypass channel

Same as for the lower region of bypass channel 1

WALLH3 := WALLH2 WALLH3 = 3318.69 W/m2-K

WALLH4 := WALLH2 WALLH4 = 3318.69 W/m2-K

- A209-

WALLH(5): The lower region of bypass channels 2

This element represents the lower section of the reflector and B4C shield assemblies. Using the data for calculating AREAEL(5), Loc. 442-581, Block 18,

Outer diameter

Number of assembly

Area of pin and structure per each subassembly, (Loc. 1143-1282, Block 18)

Reflector

OD_Rpin = 0.0188

NrfAssy = 48

Area_RAw = 0.0189

B4C shield

OD_BSpin = 0.0546

NbcsAssy = 54

Area_BSAw = 0.01835

m

Representative diameter of WALLH(5) for heat conduction is approximated as follows:

w5 (OD Rpin x NrfAssy x A rea RAw) + (OD BSpin x NbcsAssy x Area BSAw)(NrfAssy x Area_RAw) + (NbcsAssy x Area_BSAw)

Tr_w5 = 0.03749 m

Thus,

WALLH5 := K wHT9T r_w5^i WALLH5 = 1416.254 W/m2-K

WALLH(6)-(7): The central and upper regions of bypass channel 2

Same as for the lower region of bypass channel 2,

WALLH6 := WALLHg WALLH6 = 1416.254 W/m2-K

WALLHy := WALLH5 WALLHy = 1416.254 W/m2-K

-A210-

WALLH(8): The lower region of bypass channels 3

This element represents the lower section of the radial shield and I VS (driver fuel) assemblies, Using the data for calculating AREAEL(8), Loc. 442-581, Block 18 and for calculating WALLMC(8), Loc. 1143-1282, Block 18.

Radial shield IVS

Outer diameter OD_RSpin = 0.0188 OD_Dpin = 0.0074 m

Number of assembly NrsAssy = 72 NivsAssy = 54

Area of pin and structure Area_RSAw = 0.0189 AreaJVSAw = 0.01404per each subassembly

Representative diameter of WALLH(8) is approximated as follows:

Tr wg (OD_RSpinx NrsAssy x Area_RSAw) + (QD_Dpinx NivsAssy x AreaJVSAw)(NrsAssy x Area_RSAw) + (NivsAssyx AreaJVSAw)

Tr_w8 = 0.01472 m

Thus,

\A/AI i u - KjwHT9WALLHa zTr^w8x WALLHg = 3606.961 W/m2-K

WALLH(9)-(10): The central and upper regions of bypass channel 3

Same as for the lower region of bypass channel 3,

WALLHg := WALLHg WALLHg = 3606.961 W/m2-K

WALLH10 := WALLHg WALLH10 = 3606.961 W/m2-K

- A211 -

WALLH(11): Tne inlet section of the IHX shell

Using the data for calculating WALLMC(t 1), Loc. 1143-1282, Block 18.

IHX shell thickness TwJHXshell = 0.02175 m

wAiiu K_w304SS11 ' (TwJHXshell) WALLHn = 990.805 W/m2-K

WALLH(12): The heat transfer section of the IHX shell side

Same as for the WALLH(11)

WALLH-I2 := WALLHn WALLH12 = 990.805 W/m2-K

WALLH(13): The outlet section of the IHX

Same as for the WALLH(11)

WALLH13 := WALLHn WALLH13 = 990.805 W/m2-K

WALLH(14): Flow guide of the primary pump (1st group)

Using the data for calculating AREAEL(14), Loc. 442-581, Block 18

Core shield thickness LAYRT = 0.15 m

K w316SSWALLH14 = 270.8 W/m2-KVVMLLrl•]4 :=

WALLH(15); The main part of a primary pump

No specific geometry for the EM pump is available. Representative thickness of WALLH(15) is assumed to be the thickness of discharge pipe.

Representative thickness Tw_ppipe := 0.5 x (OD_ppipe - D_ppipe)

Tw_ppipe = 0.0254 m

WALLH15K w316SS (Tw_ppipe) WALLH15 = 799.606 W/m2-K

- A212-

Using the data for calculating WALLMC(16), Loc. 1143-1282, Block 18.

Thickness of discharge pipe Tw_ppipe = 0.0254 m

WALLH16 := K-w316SS WALLH16 = 799.606 W/m2-K(Tw_ppipe)

WALLH(17): The horizontal section of pump discharge pipe (1st group)

Same as for the W ALLH(16)

WALLH17 := WALLH16 WALLH17 = 799.606 W/m2-K

WALLH(18)-(21): The primary EM pump (2nd group)

Since the two primary pump groups are identical, WALLH(18)-(21) are the same as the corresponding components of WALLH(14)-(17)

WALLH(16): The vertical section of pump discharge pipe (1st group)

WALLH18 := WALLH14 WALLH18 = 270.8 W/m2-K

WALLH19 := WALLH15 WALLH19 = 799.606 W/m2-K

WALLH20 := WALLH16 WALLH20 = 799.606 W/m2-K

WALLH21 := WALLH17 WALLH21 = 799.606 W/m2-K

WALLH(22): The fictitious pipe connecting the hot pool and the annular region

It is set to an arbitrary large value.

WALLH22 := (1.0) x 105 W/m2-K

WALLH(23): The fictitious pipe connecting the cold pool and the buffer region

It is set to an arbitrary large value.

WALLH23 := (1.0) x 105 W/m2-K

- A213-

The first wall of the annular element model. Using the data for calculating WALLMC(24), Loc. 1143-1282, Block 18.

Thickness of reactor baffle Tw_rb = 0.025 m

WALLH24 := K-W316SS WALLH24 = 1624-8 W/m2-Kf TW-rb |l 2 J

WALLH(25): The fictitious valve for PSDRS model

Same as for the WALLMC(24),

WALLH25 := WALLH24 WALLH25 = 1624.8 W/m2-K

WALLH(24): The flow path over the reactor baffle for PSDRS

WALLH(26): The cold return pipe of the intermediate loop

Using the data for calculating WALLMC(26), Loc. 1143-1282, Block 18.

Thickness of IHTS loop pipe Tw_ihtspipe1 = 0.00953 mwith larger diameter

WALLHae := K-w304SS WALLH26 = 2262.467 W/m2-K(Twjhtspipel)

WALLH(27): The intermediate EM pump

No specific geometry for the EM pump is available. Same as for the WALLMC(26),

WALLH27 := WALLH26 WALLH27 = 2262.467 W/m2-K

WALLH(28): The intermediate loop pipe to the top of reactor head

Same as for the WALLMC(26),

WALLH28 := WALLHae WALLH28 = 2262.467 W/m2-K

- A214-

WALLH(29): The central downcomer of the IHX

Using the data in WALLMC(11) and Fig. 18-3,

K W304SSWALLH29 := OD ctube-ID ctube^

WALLH29 = 2155 W/rrf-K

WALLH(30): The heat transfer section of the IHX tube side

Using the data for calculating WALLMC(30), Loc. 1143-1282, Block 18,

Outer diameter of IHX tube ODJHXtube = 0.0127 m

Inner diameter of IHX tube IDJHXtube = 0.0111 m

WALLH30 :=K w304SS

ODJHXtube - IDJHXtube^

WALLH30 = 26937.5 W/m2-K

WALLH(31): The hot side pipe of the intermediate loop to the common header

Using the data for calculating WALLMC(31), Loc. 1143-1282, Block 18.

Thickness of IHTS loop pipe Tw_ihtspipe2 = 0.00792 mwith smaller diameter

WALLH31 := K-w304SS WALLH31 = 2719.243 W/m2-K(Tw_ihtspipe2)

WALLH(32): The hot side pipe of the intermediate loop to the top of the SG

Same as for the WALLMC(26).

WALLH32 := WALLH26 WALLH32 = 2262.467 W/m2-K

- A215-

Using the data for calculating WALLMC(33), Loc. 1143-1282, Block 18.

Thickness of SG shell Tw_SGshe!l = 0.0508 m

WALLH33 := K-w304SS WALLH33 = 424.213 W/m2-K(Tw_SGshell)

WALLH(34): The cold return pipe of the intermediate loop

Same as for the WALLMC{27).

WALLH34 := WALLH27 WALLH34 = 2262.467 W/m2-K

WALLH(33): The heat transfer section of the SG shell sido

- A216-

Summary of the wail heat-transfer coefficient for the liquid element

i 1 .. IELL LOCj := 1282 + i

LocationNo.

WALLHj =1

1 12 3318.693 3318.694 3318.695 1416.256 1416.257 1416.258 3606.969 3606.9610 3606.9611 990.812 990.813 990.814 270.815 799.6116 799.6117 799.6118 270.819 799.6120 799.6121 799.6122 10000023 10000024 1624.825 1624.826 2262.4727 2262.4728 2262.4729 215530 26937.531 2719.2432 2262.4733 424.2134 2262.47

1283128412851286128712881289129012911292129312941295129612971298129913001301130213031304130513061307130813091310131113121313131413151316

- A217-

Location 1423-1460, VOLLGC (ICV)Total volume of each compressible volume, liquid+gas, (m3)

7 compressible volumes are defined in Table 3-1 (Refer to Loc. 1, Block 1), ICV := 7

This input data includes both volumes of the liquid and gas regions.All design data are from Fig. 18-1.

VOLLGC(1): The volume of the core inlet plenum

VOLLGC(1) corresponds to V2 of Fig. 18-1.

VOLLGCi := 8.230 m3

VOLLGC(2): The volume of the hot pool

VOLLGC(2) is sum of V9 +V10 +V11+ 0,5*V8 + V14 + V15_hot of Fig. 18-1.

Vo!. 15 of Fig. 18-1 is divided into the cold and hot pool regions.A partial volume of V15 is included into the cold pool region.

Using the data for calculating AREAEL(24), Loc. 442-581, Block 18

Inner diameter of reactor vessel ID_rv = 6.92 m

Outer diameter of reactor baffle OD_rb = 6.87 m

From Fig. 18-1, E(1) = 17.075 m, E(4) = 10.625 m

V15_co!d := - x (I D_rv2 - OD_rb2) x (17.075 - 10.625)4

V15_co!d = 3.49288 m3

VOLLGCa := 54.843 + 38.926 + 38.814 + 0.5 x (22.727) + 17.603 + (55.036 - V15„cold)

VOLLGCa = 213.093 m3

- A218-

V0LLGC(3): The volume of the cold pool

VOLLGC(3) is sum of V1 + V3 + V4 + V12 + V13 + 0.5*V8 + V15_cold of Fig. 18-1.

VOLLGC3 := 34.402 + 62.964 + 58.991 + 25.78 + 19.72 +0.5 x (22.727) + V15_cold

VOLLGC3 = 216.713 m3

VOLLGC(4): The volume of the annular region dividing the cold and hot pools

VOLLGC(4) corresponds to V7 of Fig. 18-1.

VOLLGC4 := 95.211 m3

VOLLGC(5): The fictitious volume of the hot IHTS loop

VOLLGC5 := 1 m3

VOLLGC(6): The fictitious volume of the cold IHTS loop

The fictitious volume CV6 is arbitrary assumed to be 10.0 (m3). Cover gas inventory of CV6 is necessary to absorb the volume change in the IHTS loop due to thermal expansion.

VOLLGCs := 10.0 m3

VOLLGC(7); The fictitious volume of the cold IHTS loop

VOLLGCy := 1.0 m3

- A219-

Summary of total volume of the compressible volume, liquid +gas

1 .. ICV LOCj := 1422 + i

LocationNo.

VOLLGCj =LOCj = 1

1423 1 8.231424 2 213.0931425 3 216.7131426 4 95.2111427 5 1

1428 6 10

1429 7 1

- A220 -

Location 1461-1498, PRESGO (ICV)Initial gas pressure in the compressible volumes which contains cover gas, (Pa)

Atmospheric pressure is assumed for the reactor vessel, CV2 and CV3. The input for the initial pressure of other compressible volumes are set to 0, because they don't contain cover gas.

Palm := (1.01325) x 105 Pa

PRESGOi := 0

PRESGO2 := Patm PRESGOa = 1.01325 X 105 Pa

PRESGO3 := Patm PRESGO3 = 1.01325 x 105 Pa

PRESGO4 := 0

PRESGO5 := 0

PRESGOe := Patm PRESG06 = 1.01325 x 105 Pa

PRESGO7 := 0

i := 1 .. ICV LOCi := 1460 + i

LocationNo.

PRESGOj -LOC| = 1

1461 1 01462 2 1013251463 3 1013251464 4 01465 5 01466 6 1013251467 7 0

- A221 -

Location 1499-1536, ALPHAP (ICV)Volume pressure expansion coefficient, (1/Pa)(1/V)dV/dP, for the compressible volume

The value is set to 1.0E-9 for all compressible volumes based on previous work,

i := 1 .. ICV ALPHAPi := 1.0x 10~9 1/Pa

Location 1537-1574. ALPHAT (ICV)Volume thermal expansion coefficient, (1/K)(1/V)dV/dT, for the compressible volume

The value is based on the thermal expansion of steel. A typical value is 6.0E-5, and this is used for all compressible volumes.

i := 1 .. ICV ALPHATj := 6.0x10 5 1/K

LOCtj := 1498 +I LOC2j := 1536 + i

LocationNo.

LOC1 j ■-1499150015011502150315041505

ALPHAPj =1

1 170-92 170-93 170-94 1?0-95 170-96 1?0-97 170-9

LocationNo.

LOC2i =1537153815391540154115421543

ALPHATj =1

1 670-52 670-53 670-54 670-55 670-56 670-57 670-5

- A222 -

Location 1575-1612, ZCVL (ICV)Reference height for liquid pressure in the compressible volume, (m)

This data is for printout of liquid pressure in each compressible volume. The reference height is estimated from Fig. 3-1 with Loc. 42-81 and Loc. 162-301 of Block 18.

ZCVL-i := ZINLi ZCVL1 = -1.591 m

ZCVL2 := ZOUTEL4 ZCVL2 = 3.1647 m

ZCVL3 := ZINL6 ZCVL3 = -1.3703 m

ZCVL4 := ZOUTEL23 ZCVL4 = 3.4047 m

ZCVL5 := ZOUTEL31 ZCVL5 = 16.7047 m

zcvl6 := ZOUTEL34 ZCVL6 = 7.5047 m

ZCVL7 := ZOUTEL28 ZCVLy = 18.5047 m

LOCj := 1574 + i LocationNo.

LOC; =1575157615771578157915801581

ZCVL; =1

1 -1.5912 3.16473 -1.37034 3.40475 16.70476 7.50477 18.5047

Refer to Fig. 18-1

- A223 -

Location 1613-165. AREAIN (ICV)Area of liquid-gas interface in the compressible volume which contains cover gas.For those volumes without cover gas, AREAIN is set to 1.0.

The volumes containing cover gas are CV2, CVS, and CV6 in the model, as shown in Fig. 3-1.

AREAlNi := 1.0 m2

AREAIN(2): The interfacial area of hot pool and cover gas

All dimensions are from Table M-1 of Ref. A2,

Inside diameter of reactor vessel ID_rv = 6.92 m

Outside diameter of reactor baffle OD_rb - 6.87 m

Inside diameter of reactor baffle ID_rb := 6.82 m

Outside diameter of UIS OD_uis := 1.4 m

Outside diameter of IVTM ODJvtm := 0.5 m

Outside diameter of downcomer of the I FIX from Fig. 18-3.

OD_ctube - 0.35 m

EMP support cylinder OD OD_emp := 1.2 m

There are 4 IHXs, 4 EMPs, 1 UIS, and 1 IVTM in the reactor vessel as shown in Fig. 18-1.

AREAIN2 := - x (ID_rb)2 - (4) x - x [ (OD_ctube)2 + (OD_emp)2] ...4 4+ — x [ (OD_uis)2 + (ODJvtm)2]

4

AREAIN2 = 29.886 m2

AREAIN(3): The interfacial area of cold pool and cover gas

AREAIN3 := - x (lD_rv2 - OD_rb2) AREAIN3 = 0.542 m2

-A224-

AREAIN4 := 1.0 m2

AREAIN5 := 1.0 m2

AREAIN(6): The interfacial area of CV6

Cover gas is necessary to absorb the thermal expansion of the IHTS sodium. The interfacial area is assumed arbitrary to be 0.5 m2.

AREAlNe := 0.5 m2

AREAlNy := 1.0 m2

Summary of the liquid-gas interfacial area

i := 1 .. ICV LOCj := 1612 +i

LocationNo.

LOCj =161316141615161616171618 1619

AREAlNi =1

1 12 29.8863 0.5424 15 16 0.57 1

- A225-

Location 1651-1688. TREFCV (ICV1Initial steady-state gas temperature if gas is present, (K)If input as 0, steady-state gas temperature = liquid temperature Not used for a liquid-only compressible volumes.

These input data are omitted. Therefore the gas temperature will be calculated by code.

Location 1689. GAMGSCRatio of the specific heats, Cp/Cv, for cover gasP * V * GAMGCS = constant. Used for all compressible volumes containing cover gas.

The cover gas of KALIMER is helium.

= 1.667

Location 1690, RGASCGas constant for cover gas, (Pa m3/kg-K)P * V = M * RGASC * TUsed for all compressible volumes containing cover gas

R = 8314/molecular1 weight R = 2078 for HeR = 208.1 for Argon

The gas constant for the cover gas is set to the recommended value for helium,

= 2078.0 Pa-m3/kg-K

Location 1691. UOCVGSViscosity of cover gas at reference temperature TRFU (see Loc. 1692), (Pa-s) Suggested value:

= 1.94* 10-5 at 293 K for He= 2.22 * 10'5 at 293 K for Argon

The viscosity of the cover gas at the reference temperature, TRFU, is set to the recommended value for helium

- 1.94x10-5 Pa-s

Location 1692, TRFUReference temperature for the cover gas viscosity, (K)

= 293.0 K

- A226 -

Location 1693-1720, XLENGG {j$GG)Length of gas segment

Location 1721-1749. AREASG (ISGG)Flow area of gas segment

Location 1805-1832, DHSEGG (ISGG)Hydraulic diameter of gas segment

Location 1833-1860. ROUGHG (ISGG)Surface roughness of gas segmentFor the present study, no gas segment is used.

Location 1861-1898. TAUGAS (ICV)Heat transfer temperature time constant for cover gas, (sec)

For compressible volumes with cover gas, the time constant is set to 100.0 sec based on the previous calculation. If TAUGAS is set to a large value (1 .OE+8 sec), the cover gas temperature maintains essentially constant. This is intended to simulate the continued operation of the cover gas recirculating system, presuming that some kind of temperature control is available in this system.

Only CV2, CVS, and CV6 contain cover gas. TAUGAS for other volumes is set to 0.

i := 1 .. ICV TAUGAS] := 0.0

TAUGAS2 := 100.0 TAUGAS3 := 100.0 TAUGAS6 := 100.0

LOCj := 1860 + i LocationNo.

TAUGAS] =LOG; =

1861 18621863186418651866 1867

1

1 02 100

3 1004 0

5 0

6 100

7 0

- A227-

PUMP OPTIONS

See Loc. 418-469, Block 3 for IEMPMP and TLRPMP

IEMPMP ILRPMP OPTION

Any -2 User-specified normalized pump head vs. normalized flow-1 Any.NE.-2 EM pump0 Any.NE.-2 Table look-up, User-specified normalized pump head vs. time1 -1 Centrifugal pump option 1,

User-specified normalized pump speed vs. time1 0 Centrifugal pump option 1,

User-specified normalized mortar torque vs. time1 1 Centrifugal pump option 1,

Locked rotor (pump speed = 0)2 -1 Centrifugal pump option 2, ANL pump model

User-specified normalized pump speed vs. time2 0 Centrifugal pump option 2, ANL pump model

User-specified normalized mortar torque vs. time2 1 Centrifugal pump option 2, ANL pump model

Locked rotor (pump speed = 0)3 Any,NE.-2 EBR-II pump model

Since IEMPMP is specified as 0in Loc. 430-469, Block 3, Normalized pump head vs time are needed as input data. Number of pump modeled in Fig. 3-1 is 3. therefore, IPMP = 3.

User-specified pump head vs time (IEMPMPQPMP) - 0)

Location 1911-1922. HEADR (IPMP)Pump head at t = 0, computed by the code unless steady-state flow = 0.

Rated heads for the primary and intermediate pumps, from Table F-3 and page A7 of Ref. A2, are 8.086328 x 105 and 4.0 x 105 (Pa), respectively.

System pressure losses need to be balanced against the pump head by adjusting G2PRDR, Loc. 1002-1141, Block 18.

Location 1983-2222. APMPHD (JJPMP)Table of relative pump head, Dimension (20,12), (sec.)

= 1.0 1.0 for IPMP = 1,2, and 3

Location 2223-2462, AMOTTK (JJPMP)Times for pump head table, Dimension (20,12)

= 0.0 1000000.0 for IPMP = 1,2, and 3

-A228-

Nor

mal

ized

Flo

wra

te a

nd H

ead

For steady state run, the relative heads for all three pumps maintain 1.0 throughout the entire calculation time. For the loss of flow event, the coastdown data of KALI ME Ft-150 are obtained from Table F-3b and Fig.F-4 of Ref. A2.

flowratehead

Time, seconds

normalizedtimefs) flow head

0 1 11 0.925 0.85583 0.8616 0.751895 0.804 0.6640810 0.6796 0.4909515 0.578 0.3685220 0.4849 0.2708325 0.4109 0.2052830 0.3398 0.1496435 0.2758 0.1056140 0.2283 0.0782850 0.1602 0.0468760 0.12135 0.0299370 0.09197 0.0199180 0.07014 0.0136100 0.04093 0.00616120 0.02584 0.00319150 0.01477 0.00137180 0.00979 7.01118E-4200 0.00787 4.7611E-4

- A229

Location 2463. GRAVTYAcceleration of gravity, (m/s2)

= 9.807 m/s2

Location 2464-2501. BTAPNA (ICV1Sodium isothermal compressibility for the compressible volumes, (1/Pa) = (1/RHO) (d RHO/ dP) at the reference temperature TREFCV. Suggested value is 2.13E-10 at 720 K

i := 1 .. ICV BTAPNA-2.13x10™ 10 1/Pa

LOCi := 2463 + i LocationNo.

LOCj “2464246524662467246824692470

BTAPNAj =1

1 2.1370-102 2.1370-10

3 2.1370-104 2.1370-105 2.1370-106 2.1370-107 2.1370-10

Location 2502-2539. BTATNA (ICV)Sodium thermal expansion coefficient, (1/K)= (1/RHO) (d RHO/ dT) at the reference temperature TREFCV. Deafult value is -2.8E-4, corresponding to 720 K

i :=1. ICV BTATNA, :=-2.8x10™4 1/K

LOCi := 2501 + i LocationNo.

LOCj =2502250325042505250625072508

BTATNA)=1

;:1 -0.000282 -0.000283 -0.000284 -0.000285 -0.000286 -0.000287 -0.00028

A230 -

Location 2578-2615. HWALL (ICV)Wall-coolant heat transfer coefficient for the compressible volumes, (W/m2/K)

Thermal conductivity of 304-SS K_304SS := 21.5 W/m-K

HWALL(1): Wall heat-transfer coefficient for the inlet plenum

Wall thickness of inlet plenum, from Table M-1 of Ref. A2

twalH := 0.15 m

HWALLt := *-304SS HWALLi = 143.333 W/m2-K(twalh)

HWALL(2): Wall heat-transfer coefficient for the hot pool

Sodium in the hot pool contacts with several walls such as reactor baffle (2.5 cm), support barrel (5.0 cm), baffle plate (2.5 cm) and other thick internal structures as shown in Fig. 3-2. The minimum dimension of 2.5 cm is selected for the calculation of HWALL(2).

twallg := 0.025 m

HWALL2 :=K 304SS (twalla) HWALL2 = 860 W/m2-K

HWALL(3): Wall heat-transfer coefficient for the cold pool

The representative wall thickness of the cold pool is assumed to be the same as the hot pool

twallg := twalla

HWALL3 := K 304SS (twall3)

twalla := 0.025 m

HWALL3 = 860 W/m2-K

HWALL(4): Wall heat-transfer coefficient for the annular region

twalU := 0.025 m

HWALL-4 := K-304SS HWALL4 = 860 W/m2-K(twall4)

- A231 -

HWALL(5): Wal! heat-transfer coefficient for the IHTS loop (hot side)

The wall thickness of IHTS pipe with smaller diameter is from WALLMC(31) on Log. 1143-1282, Block 18.

Tw_ihtspipe2 = 0.007925 m twalls := Tw_ihtspipe2

HWALL5 :=K 304SS (twall5)

HWALL5 = 2712.934 W/m2-K

HWALL(6): Wall heat-transfer coefficient for the IHTS loop (cold side)

The wall thickness of IHTS pipe with larger diameter is from WALLMC(37) on Loc. 1143-1282, Block 18.

Tw_ihtspipe1 = 0.009525 m twalle := Tw_ihtspipe1

HWALL6 := *V304S~ HWALLg = 2257.218 W/m2-K(twalle)

HWALL(7): Wall heat-transfer coefficient for the IHTS loop (cold side)

twally := twalls

HWALLy := HWALL6 HWALLy - 2257.218 W/m2-K

i := 1 .. ICV

LOG} := 2577 + i

LocationNo.

LOCj2578257925802581258225832584

HWALLj =1

1 143.332 8603 8604 8605 2712.936 2257.227 2257.22

- A232 -

Location 2616-2653, AWALL (ICV)Wall surface area for each compressible volume, (m2)

Wall surface area is calculated by dividing wall mass by wall thickness to preserve the heat capacity of wall. Two kinds of material, 316 SS and 304 SS, are used for reactor internals. The wall mass is obtained from Table M-2 of Ref. A2 and the wall thickness is from HWALL (Loc. 2578-2615, Block 18)

Density of core metal at the core average temperature rho_steel := 7805.0 kg/m3

AWALL(1): Wall surface area for the inlet plenum

Massw_1 := 38720.0 kg

AWALLi :=------MaSSW~1------ AWALL1 = 33.07282 m2twalh x rho_steel

AWALL(2): Wall surface area for the hot pool

reactor baffle mass_rb := 39100.0 kg

support barrel mass_sb := 48640 kg

UIS mass_uis := 20000 kg

rotating plug mass_rp := 35610.0 kg

Since reactor baffle and support barrel are partially contacted with hot pool, the portion of metal for CV2 is assumed to be proportional to height, as shown in Fig. 18-1.

Massw_2 mass_rb x 15.875- 12.67515.875- 6.725

+ mass_sbx

+ (mass_uis + mass_rp) x 15.625-6.38518.725-6.385

12.675- 6.385^12.675- 2.04 J

Massw_2 = 84082.024 kg

AWALL-2 :=----- Massw-2----- AWALL2 = 430.914 m2twallg x rho_steel

- A233 -

AWALL(3): Wall surface area for the cold pool

reactor vessel mass_rv := 165890.0 kg

core support mass_cs := 10310.0 kg

Massw 3 := mass rvx

+ mass cs

10.62518.725

+ mass sb x 6.8-2.0412.675-2.04

Massw 3 = 1.2621 x 10" kg

AWALLs :=Massw 3

twallg x rho_steelAWALLs = 646.817 nr

AWALL(4): Wall surface area for the annular region

baffle plate mass_bp ;= 3020.0 kg

separation plate mass_sp := 17570.0 kg

f a 2 _6 725 \Massw 4 := mass rb x —:--------- :------ + mass bp + mass spV 5.875- 6.725)

Massw_4 = 4.60157 x 104 kg

AWALL4 :=----- Massw_4----- AWALL4 = 235.82669 m2twall4 x rho_steel

-A234-

AWALL(5)-(7): Wall surface area for the IHTS loop pipe

Surface area of the IHTS pipe is set to 1.0 m2.

AWALL5 := 1.0 m2

AWALLq := 1.0 m2

AWALL7 := 1.0 m2

LOCj := 2615 +i LocationNo.

LOG; = 26162617261826192620 2621 2622

AWALLj =1

1 33.0732 430.9143 646.8174 235.8275 16 17 1

- A235 -

Location 2654-2691. CMWALL (ICV)Mass times specific heat of the wall of the compressible volume, (J/K)

CMWALL(i) = AWALL(i) * thick(i) * PCp

mass * specific heat of core steel pCp_steel := 4.419 x 106

i := 1 .. ICV

CMWALL; := (AW ALL;) x (twallj) x (pCp_steel)

LOCj := 2653 + i LocationNo.

LOCj =

2654265526562657265826592660

CMWALL; =1

1 2.19227072 4.76057073 7.14577074 2.60537075 3.50217046 4.20917047 3.5021704

J/m3-K

-A236-

BYPASS CHANNEL MODEL

The purpose of the bypass channel is to model components, like control rods and radial shields, that do not need the detailed treatment of a SAS4A channel. The bypass channel is then considered a part of the primary loop and is not included in the SAS4A channel core treatment.

The bypass channel is shown schematically in Fig. 18-6. It is modeled as two reflectors, A and B, a coolant channel, C, and a duct wall, D. The bypass channel is divided into from 1 to 7 vertical sections, with temperatures of the two reflectors and duct wall taken at the centers of each vertical section and the coolant temperatures taken at the interface of each vertical section. The outside surface of reflector A is taken as adiabatic, and heat conduction in the axial direction is neglected. The outside surface of the duct wall can be in contact with a heat sink that represents neighboring subassemblies.

Heat sources are included in each of the two regions of reflectors A and B and also in the duct wall, taken as region 3. A vertical power shape for the heat source can be assigned to the sections in three regions. Two heat sources are included, a neutron heat source and a decay heat source. The neutron heat source arises from fission caused by neutrons, and is a fraction of the reactor power. The decay heat source arises from fission product decay which produces no neutrons.

Material of Bvoass Channelduct wall pin

Bypass channel 1Control rod HT9 b4c

Bypass channel 2Reflector shield HT9 lnconnel-600B4C shield HT9 B4C

Bypass channel 3Radial shield HT9 HT9IVS HT9 U-Pu-10%Zr

- A237-

Fig. 18-6 Bypass Channel Schematics in PRIMAR-4 Model

- A238-

DU

CT W

ALL

Location 2694. C1 BYCoefficient in Lyon-Martinelli convective heat-transfer correlation for bypass channel First coefficient set. C1 (See Loc. 3-5 of Block 64, Loc. 4300-4308 of Block 18, and Loc. 1193-1208 of Block 3).Nu = C1 * (Re * Pr)C2 +C3 Lyon-Martinelli correlation

= 0.025

Location 2695, C2BYC2, See Loc. 2694

= 0.8

Location 2696, C3BYC3, See Loc. 2694

= 7.0

Location 2697-2704. XKALBY (IBYP1Thermal conductivity of bypass wall A, Lower part, (W/m-K)1 <= IBYP <= NBYP (NBYP is input in Loc. 813, Block 3) IBYP := 3

Location 2705-2712, XKAUBY (IBYP1Thermal conductivity of bypass wall A, Upper part, (W/m-K)

Location 2713-2720. XKBLBY (IBYP)Thermal conductivity of bypass wall B, Lower part, (W/m-K)

Location 2721-2728. XKBUBY (IBYP)Thermal conductivity of bypass wall B, Upper part, (W/m-K)

Location 2729-2736. XKDBY (IBYP1Thermal conductivity of bypass wall D, (W/m-K)

This input is according to the material in the bypass wall.For the metallic core, 26.2 (W/m-K) is used for all regions of all bypass channels.

Bvoass ch. Loc. No XKALBY Loc. No XKAUBY

1 2697 26.2 2705 26.22 2698 26.2 2706 26.23 2699 26.2 2707 26.2

Bypass ch. Loc. No XKBLBY Loc. No XKBUBY Loc. No XKBUBY

1 2713 26.2 2721 26.2 2729 26.22 2714 26.2 2722 26.2 2730 26.23 2715 26.2 2723 26.2 2731 26.2

- A239

Location 2737-2744. DABY flBYP)Thickness of bypass wall A in the bypass channel, (m)

Location 2745-2752. DBBY (1BYP)Thickness of bypass wall B in the bypass channel, (m)

Location 2753-2760. DDBY (1BYP1Thickness of bypass wall D in the bypass channel, (m)

The thickness is calculated to preserve the thickness and mass of the contents of the pins in the control rods, in the reflector & B4C shields, and in the radial shield & I VS in the core bypass region. All data are from Loc. 442-581 and Loc. 587-721, Block 18.

For bypass channel 1 (control rod assembly)

Control rod hydraulic diameter

1 st bypass channel flow area

Control rod perimeter

Control rod duct outer flat-to-flat distance taken from Table C-7 of Ref. A2

DHELEM2 = 7.488 x 10

AREAEL2 = 0.04241

PerLbpI = 22.65637

L Coutflat := 0.1570

-3 m

nr

m

m

Number of control rod assembly NcrAssy = 6

Steel area of bypass channel 1 is calculated as:

Ast_bp1 := ^ x (L_Coutfiat)2x (NcrAssy) - AREAELg

Ast_bp1 = 0.08567 m2

DABY and DBBY for wall A and B (Fig. 18-6) are determined by equally dividing the steel thickness. Steel thickness is determined by (steel area) divided by (perimeter).

DABYi := Ast~bp1 xfl ) DABY1 = 0.00189 mPeri_bp1 \2)

DBBY1 := DABYi DBBYi = 0.00189 m

DDBY for wall D in the bypass channel 1 is the hexcan thickness of control rod assembly.

DDBY-i = ~ x (L_Coutflat - L_Cinflat) DDBY-, = 0.0037 m

- A240-

For bypass channel 2 (reflector and B4C assemblies)

Bypass channel hydraulic diameter

2nd bypass channel flow area

Bypass channel perimeter

Duct outer flat-to-flat distance taken from Table C-7 of Ref. A2

Number of reflector assembly

Number of B4C assembly

DHELEM5 = 3.841x10" 3 m

AREAEL5 = 0.27911 m;

Peri_bp2 = 290.63149 m

L_Routflat := 0.1570 m

NrfAssy = 48

NbcsAssy = 54

Steel area of bypass channel 2 is calculated

Ast_bp2 := x (L_Routflat)2 x (NrfAssy + NbcsAssy) - AREAEL5

Ast_bp2 = 1.89825 m2

DABY and DBBY for wall A and B (Fig. 18-6) are determined by equally dividing the steel thickness. Steel thickness is determined by (steel area) divided by (perimeter)

DABY2 := Ast~bp2 x fl) DABY2 = 0.00327 mPeri_bp2 \2)

DBBY2 := DABY2 DBBY2 = 0.00327 m

DDBY for wall D in the bypass channel 2 is the hexcan thickness.

DDBY2 := -1X (L_Routflat - L_Rinflat) DDBY2 = 0.0037 m

- A241 -

For bypass channel 3 (radial shield and IVS assemblies)

Bypass channel hydraulic diameter

3rd bypass channel flow area

Bypass channel perimeter

Duct outer flat-to-fiat distance taken from Table C-7 of Ref. A2

Number of radial shield assembly

Number of IVS assembly

DHELEMg = 3.132x 10"3 m

AREAELg = 0.57101 m;

Reri_bp3 = 729.26877 m

L_RSoutflat := 0.1570 m

NrsAssy = 72

NivsAssy = 54

Steel area of bypass channel 3 is calculated

Ast_bp3 ;= ^ x (L_RSoutflat)2 x (NrsAssy + NivsAssy) - AREAELg

Ast_bp3 - 2.11867 m2

DABY and DBBY for wall A and B (Fig. 18-6) are determined by equally dividing the steel thickness. Steel thickness is determined by (steel area) divided by (perimeter)

DABY3 := Astj3p3 x(l) DABY3 = 0.00145 mPeri_bp3 \2)

DBBY3 := DABYg DBBY3 = 0.00145 m

DDBY for wall D in the bypass channel 3 is the hexcan thickness.

DDBY3 := -1 x (L_RSoutflat - L_RSinflat) DDBY3 = 0.0037 m

- A242 -

Summary of the wall thickness of the bypass channel

i := 1 .. IBYR

LOCAj := 2736 + i LocationNo.

LOCAj =273727382739

DABYj =1

1 0.001892 0.003273 0.00145

LOCBj := 2744 + i LocationNo.

LOCBj =274527462747

DBBY; =1

1 0.001892 0.003273 0.00145

LOCCj := 2752 + iLocationNo.

LOCCj =275327542755

DDBY; =1

1 0.00372 0.00373 0.0037

- A243 -

Location 2761-2768. RCALBY (IBYP)Density * specific heat of bypass wall A, lower part, (J/m3-K)

Location 2769-2776, RCAUBY (IBYP)Density * specific heat of bypass wall A, upper part, (J/m3-K)

Location 2777-2784, RCBLBY (IBYP)Density * specific heat of bypass wall B, lower part, (J/m3-K)

Location 2785-2792. RCBUBY (IBYP)Density * specific heat of bypass wall B, upper part, (J/m3-K)

Location 2793-2800, RCDBY (IBYP)Density * specific heat of bypass wall D, (J/m3-K)

Assume that all bypass path is made of HT-9.

(density) * (specific heat) of HT9 at the core average temperature was calculated for WALLMC(2) of Loc. 1143-1282, Block 18.

CpRho_ht9 = 5.00794 x 106 J/m3-K

Bvoass ch. Loc. No RCALBY Loc. No RCAUBY1 2761 5.008*10* 2769 5.008*10*2 2762 5.008*10-6 2770 5.008*10*3 2763 5.008*10* 2771 5.008*10*

Bvoass ch. Loc. No RCBLBY Loc. No RCBUBY1 2777 5.008*10* 2785 5.008*10*2 2778 5.008*10* 2786 5.008*10*3 2779 5.008*10* 2787 5.008*10*

Bvoass ch. Loc. No RCDBY1 2793 5.008*10*2 2794 5.008*10s3 2795 5.008*1Os

A244 -

Location 2801-2856. PSHPBY (J.IBYP)Power shape by nodes for each bypass channel. Maximum dimension (7,8).Code normalizes distribution. For the number of nodes, see Loc. 513-612, Block 3.

The bypass channel has 7 nodes in the axial direction as shown in Fig. 18-6.The power shape by node for each bypass channel is assumed to be uniform.

i := 1 .. (IBYP x 7)

LOC; := 2800 + i

LocationNo.

LOC; =280128022803280428052806280728082809281028112812281328142815281628172818281928202821

PSHPBY; := 1

PSHPBY; =1

1 12 1

3 1

4 1

5 1

6 1

7 1

8 1

9 1

10 1

11 1

12 1

13 114 1

15 1

16 117 1

18 119 1

20 121 1

- A245 -

Location 2857-2880. GAMNBY (JJBYP)Fraction of total reactor power by region for each bypass channel. Maximum dimension (3,8). If there are no nodes in region 2, then set GAMNBY (2, IBYP) to 0.

Note: See Loc. 69, Block 12, Sum over all of the three regions of all the NBYP bypass channels of the array elements of GAMNBY = 1 - FRPR

Power fraction for each bypass channel, from page A2 of Ref. A2

Control rod assembly

Reflector assembly

B4C assembly

IVS assembly

Radial shield assembly

PWRcr = 0.000975

PWRrf = 0.00288

PWRbcs = 0.00362

PWRivs = 0.00563

PWRrs = 0.000153

Assume power is generated only in reflector wall A of bypass channel. GAMNBY for other nodes are set to 0.

i := 1 .. (3 x IBYP) GAMNBYj := 0.0

GAMNBY1 := PWRcr GAMNBY! = 0.000975

GAMNBY4 := PWRrf + PWRbcs GAMNBY4 = 0.0065

GAMNBY? := PWRrs + PWRivs GAMNBY? = 0.005783

LOCCj := 2856 + i LocationNo,

LOCCj —2857285828592860 2861 2862286328642865

GAMNBYj =1

1 0.0009752 0

3 04 0.00655 06 0

7 0.0057838 0

9 0

- A246 -

Location 2905-2912. PRFRA1 (IBYPlFraction of reactor power distributed in reflector A in region 1 of bypass channel.

Location 2913-2920. PRFRA2 (IBYP)Fraction of reactor power distributed in reflector A in region 2 of bypass channel.

The power is assumed to be uniformly distributed in axial direction. Therefore the power fraction is 0.5 for region 1 and region 2.

i := 1 .. IBYP PRFRAIj := 0.5 PRFRA2j := 0.5

LOC1i := 2904 + i

Location No.

LOC1 j =

LOC2j := 2912 + i

Location No.

LOC2j =290529062907

291329142915

PRFRAIj1

1 0.52 0.53 0.5

PRFRA2;1

1 0.52 0.53 0.5

Location 2921-2928. PERABY (IBYP)Perimeter of wall B in bypass channel, (m)

The pin perimeters were determined as part of DABY and DDBY, Loc. 2737-2744, Block 18.

i := 1 .. IBYP

PERABYj :=

1 Peri bp12 Peri bp2

3 Peri_bp3

LOOj := 2920 + i

LocationNo.

LOC; =292129222923

PERABYj =1

1 22.65642 290.63153 729.2688

- A247 -

Location 2929-2936. PERDBY (IBYP)Perimeter of wall D in bypass channel, (m)

For bypass channel 1

For bypass channel 2

For bypass channel 3

LOCj

PERDBY-j

PERDBY!

perdby2

perdby2

perdby3

PERDBY3

2928 + i

V3x (L_Cinflat) x (NcrAssy)

= 3.109 m

— x (L_Rinflat) x (NrfAssy + NbcsAssy)V3

= 52.859 m

— x (L_RSinflat) x (NrsAssy + NivsAssy) V3

= 65.297 m

LocationNo.

LOG; =292929302931

PERDBYj =1

1 3.10942 52.85943 65.2969

- A248 -

Location 2937-3104. DTTVIPTB (K. ITAB)Table of normalized temperature drop for TABLE (ITAB) for an IHX or steam generator.Table of pressure drop coefficients vs time, Dimension (14,12), See Loc. 852-863 and Loc, 982-989 of Block 3

Set to 1.0 for normal temperature drop in the SG. Set to 0.0 for the loss of heat sink at the SG. Set 1.0E10 for pressure drop coefficient for the fictitious valve (E25)

SG valveLoc. No DTMPTB Loc. No DTMPTB2937 1.0 2951 1.0x1052938 1.0 2952 1.0x1052938 1.0 2953 1.0x105

Location 3105-3272. ZCENTER (K. ITAB)Height of thermal center for TABLE (ITAB) for an IHX or steam generator, (m)

The height of SG thermal center is ZOUTEL(33) + 0.5 * XLENEL(33).

ZCENTER := ZOUTEL33 + 0.5 x XLENEL33

ZCENTER = 16.8047 m

Location 3273-3440, TMPMTB (K. ITAB)Times for DTMPTB and ZCENTER, (s)

SG valveLoc. No TMPMTB Loc. No TMPMTB3273 0.0 3287 0.03274 60.0 3288 60.03275 10000.0 3299 100000.0

Location 3441-3444. DTEVPF MHX)Fraction of total steam generator Na temperature drop in evaporator for the intermediate loop connected to IHX (IIHX). Will be reset to 0.7 if equal to 0.0 or 1.0. Suggested value: 0.9999 for table lookup option

= 0.9999

Location 3445-3448. PRSIHX (IIHX)Steady-state intermediate side IHX inlet pressure, (Pa)

This value is adjusted using SASSYS-1 calculations to give the proper interface elevations in the intermediate loops. This is used in conjunction with PRESGO, Loc. 1461-1498, Block 18. From Table F-7 of Ref. A2, the pressure at the IHX tube side (node 1) is 0.22483 MPa.

= 0.22483 * 106 Pa

- A249 -

Location 3455-3515, DZSHPX (IDZIHX)Fractional axial node heights in IHX.

The node number of IHX in the axial direction is 20. Usually 20 full size nodes are used, but for numerical reasons, a half-size node is placed at each end of each IHX,

Location No345534563457

DZSHPX0.050.050.05

3473 0.053474 0.05

Location 3516-3519. PERSPX (IIHX1Perimeter between the shell and the shell side coolant in the IHX, (m)

IHX dimensions are from Fig. 18-3.

Inside diameter of IHX shell IDJHXshell = 1.0065 m

Outside diameter of central downcomer ODJHXpipe = 0.35 m

PERSPXi := n x (IDJHXshell + ODJHXpipe)

PERSPX! = 4.262 m

Location 3524-3527. PERPTX (IIHX)Perimeter between the tubes and the shell side coolant in the IHX, (m)

IHX dimensions are from Fig. 18-3.

Outside diameter of IHX tube

Number of IHX tube

ODJHXtube = 0.0127 m

NoJHXtube = 1702

PERPTX! :=jix (ODJHXtube) x (NoJHXtube)

PERPTX! = 67.907 m

- A250-

Location 3532-3535, PERT1X (IIHX)Perimeter between the tubes and the tube side coolant in the IHX, (m)

Inside diameter of IHX tube ID IHXtube = 0.0111

PERTIXi := 7t x (IDJHXtube) x (NoJHXtube)

PERTIX-i = 59.352 m

m

Location 3540-3543. DSHIHX (IIHX)Shell thickness of the IHX, (m)

From Fig. 18-4, the thickness of IHX shell is 0.02 (m).

DSHIHX := 0.02 m

Location 3548-3551. DTUIHX (IIHX)Tube thickness of the IHX, (m)

DTUIHX, := i x (ODJHXtube - IDJHXtube)

DTUIHX, = 0.0008 m

Location 3556-3559. RCSHHX (IIHX)Density * specific heat of shell in IHX, (J/m3-K)

The IHX shell is fabricated of 304SS of which the density * specific heat is listed in Loc. 1143-1282, Block 18

pCp_304SS = 4.419 x 106 kg/m3

RCSHHX := pCp_304SS RCSHHX = 4.419x 106 kg/m3

Location 3564-3567, RCTUHX (IIHX1Density * specific heat of tube in IHX, (J/m3-K)

The material of IHX tube is 304SS too.

RCTUHX = 4.419 x 106 kg/m3RCTUHX := pCp_304SS

Location 3572-3575. XKSHHX (IIHX)Thermal conductance of shell in IHX, (W/m-K)

The shell of the IHX is 304SS steel. The thermal conductivity of 304 SS listed in Table M-3 of Ref. A2. is 21.55 (W/m-K) at the core average temperature (731.25 K).

XKSHHX := 21.55 W/m-K

Location 3580-3583. XKTUHX (IIHX)Thermal conductance of tube in IHX, (W/m-K)

The material of IHX tube is 304SS too.

XKTUHX := 21.55 W/m-K

Location 3588-3591. HFPIHX (IIHX)Fouling heat transfer coefficient for shell side flow in IHX, (W/m2-K)

Based on the experience of SAS4A/SASSYS-1, this is set to 1.0*109 (W/m2-K)

HFPIHX := 1.0x 109 W/m2-K

Location 3596-3599. H FI IHX (IIHX)Fouling heat transfer coefficient for tube side flow in IHX, (W/m2-K)

Based on the experience of SAS4A/SASSYS-1, this is set to 1.0*109 (W/m2-K)

HFIIHX := 1.0x109 W/m2-K

Location 3604-3607. SLANTX (IIHX)Slant-height factor for IHX, tube side

The slant-height factor of an IHX to account for non-vertical orientation is set to 1.0.

SLANTX := 1.0

- A252 -

Location 3612 - 3649, VOLGSO (ICV)Initial gas volume, (m3) Used only for ITYPCV(ICV) = 6,7,8,9,10

CV2, CVS, and Cv6 contain cover gas, and other compressible volumes don't contain gas.

i := 1 .. ICV VOLGSOj := 0.0 m3

VOLGS(2) : Gas volume of the hot pool

Total cover gas volume is the sum of V14 and V15 in Fig. 18-1.

VoLcgas := 17.603 + 55.036 Vol_cgas = 72.639 m3

The partial volume of V15, which is the cold pool region was determined at VOLLGC(2) in Loc. 1423-1460, Block 18.

V15_cold = 3.49288 m3

VOLGS02 := VoLcgas - V15_cold VOLGSO2 = 69.1461 m3

VOLGS(3) : Gas volume of the cold pool

VOLGSO3 := V15_coid VOLGSO3 = 3.4929 m3

VOLGS(6) : Gas volume of the CV6

VOLGSOe := 8.0 m3

LOCj := 3611 + i

LocationNo.

LOCj =3612361336143615361636173618

VOLGSOj =1

1 02 69.14613 3.49294 05 0

6 8

7 0

- A253 -

Location 3650. 01 PIPECoefficient in Lyon-Martinelli convective heat-transfer correlation for pipe elements First coefficient, C1Nu= C1 * (Re * Pr)C2 +C3 Lyon-Martinelli correlation

= 0.016

Location 3651. C2PIPEC2, See Loc. 2694 C1, C2, and C3 are suggested values.

= 0.86

Location 3652. C3P1PEC3, See Loc. 2694

= 4.55

Location 3653. CHHXCoefficient in Lyon-Martinelli convective heat-transfer correlation for IHX shell side First coefficient, C1Nu = C1 * (Re * Pr)C2 +C3 Lyon-Martinelli correlation

= 0.016

Location 3654. C2IHXC2, See Loc. 2694 C1, C2, and C3 are suggested values.

= 0.86

Location 3655. C3IHXC3, See Loc. 2694

= 4.55

If Coefficients in Lyon-Martinelli convective heat-transfer correlation for IHX tube side are different from those for IHX shell side , enter tube side values in Location 4310 - 4311.

- A254 -

Location 4174 - 4183. VSLEXP 0QLength times thermal coefficient for the compressible volume walls used for calculating the motion of the core with respect to the control rod driveline due to reactor vessel expansion.

According to Location 1009 -1018 of Block 3, 2 volumes are considered for calculating the motion of the core with respect to the control rod drive line due to reactor vessel expansion. Those are the annulaus element (E24) and the cold pool (CV3). In KALIMER design, the reactor vessel wall contacts with the cover gas and the cold pool. The cover gas is assumed to have the hot pool temperature. The reactor vessel is fabricated with 316 SS and the thermal expansion coefficient at the core average temperature (731.25 K) is listed in Table M-3 of Ref. A2.

Thermal expansion coefficient of 316SS a_316SS := 1.803 x 10 5 per K

Length of the wall of the compressible volume related to VSLEXP

E(23) - E(22) - ( E(19) - E(22)) in Fig. 18-1

For CV3: Len_CV3 := 6.725 - 1.54 - (4.513 - 1.54)

Len_CV3 - 2.212 m

For E24: Len_E24 ;= 15.625 - 6.725 E(3) - E(23), Fig. 18-1

Len_E24 = 8.9 m

Therefore,

VSLEXP2 := Len_CV3x (oo_316SS) VSLEXP2 = 3.988x10 ^ m/K

VSLEXP3 := Len_E24x (a_316SS) VSLEXP3 = 1.605x 10-4 m/K

- A255 -

Location 4216 - 4245. HAELHT (K)

Heat transfer coefficient times area per unit length for heat transfer from wall of liquid element IELHT(K), Loc. 1052 in Block 3, to liquid in compressible volume IELHT2(K), Loc. 1082 in Block 3, (W/m-K)

HAELHT is (h * area) and is used for the component-to-component heat transfer model.

1st wall: IHX primary shell(E12) to CV4

Outside diameter of IHX shell ODJHXshell = 1.05 m

Thickness of IHX shell tJHXshell := 0.02 m

IHX shell height XLENEL12 = 6 m

Heat transfer area Area_1 := nx ODJHXshellx XLENEL12

Area_1 = 19.79203 m2

Assuming the heat transfer coefficient by convection is infinitive,

HAELHT(1) HAELHT_1 := Area_1 x K w3Q4SS tJHXshell

HAELHT_1 = 21325.916 W/m-K

2nd and 3rd walsl: Pump shell(E15 & E19) to CV4

Outside diameter of pump shell ID_pshel! = 1.13 m

Thickness of pump shell t_pshell := 0.0254 m

Pump shell height XLENEL15 = 7 m

Heat transfer area Area_2 -nx ID_pshell x XLENEL15

Area_2 = 24.85 m2

Assuming the heat transfer coefficient by convection is infinitive,

HAELHT<2> HAELHT 2 := Area 2 x K-w316SSt_pshell

HAELHT_2 = 19870.215 W/m-K

HAELHT(3) HAELHT_3 := HAELHT_2

* A256 -

4th wall: Annulus region(E24) to CV2

Ail data are from Table M-1 of Ref. A2,

Outer diameter of reactor baffle OD_rb = 6.87 m

Thickness of reactor baffle t_rb := 0.025 m

Elevation of the top of reactor baffle E(3) = 15.625 mElevation of baffle plate E(8) = 12.675

mElevation of separation plate E(23) = 6.725

m

Heat transfer area Area_4 := nx OD_rb x (15.625 - 12.675)

Area_4 = 63.669 m2

Assuming the heat transfer coefficient by convection is infinitive,

HAELHT(4) HAELHT_4 := Area_4 x K w316SS t_rb

HAELHT_4 = 51724.77 W/K

5th wall: Annulus reaion (E24) to CV4

Heat transfer area Area_5 :=nx OD_rb x (12.675 - 6.725)

Area_5 = 128.41731 m2

Assuming the heat transfer coefficient by convection is infinitive,

HAELHT(5) HAELHT_5 := Area_5 x K-w316SSt_rb

HAELHT_5 = 104326.22 W/K

- A257-

Location 4288 - 4299. DHPMP (IIHX)Steady-state pump head, Used only if ISSPMP > 0, Location 1159-1170 of Block 3

These data are not used.

Primary pump head is 0.8086328 MPa from Table F-3 of Ref. A2. IHTS pump head is 0.4 MPa from page A7 of Ref. A2.

- A258 -

Detailed RVACS Model

The following dimensions are from the configulation of RSDRS in Fig. 18-7.

inside diameter (ID) outer diameter (OD)

Reactor vessel ID_rv = 6.92 m OD_rv = 7.02 m

Containment vessel (Guard vessel)

ID_cont := 7.32 m OD_cont := 7.37 m

Outer shell ID_air := 7.77 m OD_air := 7.93 m

Outer wall ID_silo 8.73 m OD_silo := 10.73 m

Location 4246-4251. XLRVC (IRVC)Length of RVACS section, (m)Used only if section K is a compressible volume.

The top elevation is approximated to E(2) in Fig. 18-1. E(2) is 15.875 and which is consistent with the RSDRS length in Table F-10 of Ref. A2

XLRVC := 15.875 m

Location 4252-4257. PERVAC (IRVC1RV perimeter, (m)

PERVAC := 7ix (OD_rv) PERVAC = 22.054 m

Location 4258-4263. EPSRV(IRVC)Emissivity of reactor vessel

EPSRV := 0.85

Location 4264-4269. EPSGVdRVCtEmissivity of guard vessel inner surface

EPSGV := 0.85

- A259 -

Location 4270-4275. PERGVPerimeter of guard vessel - air

PERGV := TCX (OD_cont) PERGV = 23.1535 m

Location 4276-4281, PERFSPerimeter of finned shell inner surface - air

PERFS := 7TX (ID_air) PERFS = 24.4102 m

Location 4313-4342. WALMC2 (IAEL)Second wall mass * heat capacity per length for annular element IAEL

The material of reactor vessel is 316 SS. All data are from Table m-2 of Ref. A2.

specific heat of 316SS at the core average temperature

Cp_316SSTavg := linterp(Tkss, Cp_316SS ,293)

Cp_316SSTavg = 465.145 J/kg-K

mass of reactor vessel Mass_rv := 165890 kg

length of the second wall of annulus Len_ann2 ::= 18.725 m

..... moo . (Cp_316SSTavg)x (Mass_rv) 6 J/m-KLen_ann2 WALMC2 == 4.121 x 10°

Location 4343-4372. WALLH2 (IAEL)Second wall heat transfer coefficient

Thickness of reactor vessel t_rv := 0.05 m

Conductivity of steel Ksteel := 21.55 W/m-K

WALLH2 := Kst6el (t—rv) WALLH2 = 431 W/m2-K

Location 4373-4402, PERWL2 (IAEL)Second wall perimeter

PERWL2 := n x (ID_rv) PERWL2 = 21.7398 m

- A260 -

Location 4403, TA1RVCAir inlet temperature

TAIRVC ~ 273.15 + 20 TAIRVC = 293.15 K

Location 4404. ZBRVCZ at bottom of RVACS

The location is the bottom of reactor vessel, E15 of Fig. 18-1.

ZBRVC := 0.0 - Zref ZBRVC = -3.2203 m

Location 4405-4407, C1RV. C2RV. C3RVHeat transfer correlation coefficient for air in the RVACS

The recommended values in the code manual are 0.23, 0.8, 3.0-8.0 for C1 RV, C2RV, and C3RV, respectively. Nu = C1 RV * (Re*Pr)C2RV + C3RV

C1 RV := 0.023 C2RV := 0.8 C3RV := 5.0

Location 4408. XLAIRVLength of air inlet section, (m)

The chimney height of PSDRS is 30 m from Table F-10 of Ref. A2,

XLAIRV := 30.0 m

Location 4409, DHAIRVHydraulic diameter of air inlet section, (m)

The total flow area of the air inlet is 8 m2 from Table F-10 of Ref. A2.

Area_airinlet := 8.0 m2

DHAIRV := ^4 x Area_airmjet DHAIRV = 3.19154 m

Location 4410, AARIRVArea of air inlet section, (m2)To be consistent with the SSC-K input

AARIRV := Area_airinlet AARIRV = 8 m2

- A261 -

Location 4411. XLAORVLength of air outlet stack, (m)

The length of outlet stack is the same as the air inlet section.

XLAORV := XLAIRV XLAORV = 30 m

Location 4412. DHAORVHydraulic diameter of air outlet stack, (m)

The air flow area of the outlet stack is the same as the air inlet section.

DHAORV := DHAIRV DHAORV = 3.19154 m

Location 4413. AARORVArea of air outlet stack, (m2)

The same as the air inlet section.

AARORV := AARIRV AARORV = 8 m2

Location 4414-4419. AIRARV (IRVC)Air flow area, guard vessel - finned shell, (m2)

AIRARV := - x (lD_air2 - OD_cont2) AIRARV = 4.75637 m2

Location 4420-4425. AIRAR2 (IRVC)Air flow area, finned shell - concrete wall, (m2)

AIRAR2 := - x (lD_silo2 - OD_air2) AIRAR2 = 10.4678 m2

Location 4426-4431. PERGVO (IRVC)Perimeter for radiation from guard vessel outer surface to outer shell inner surface, (m)

PERGVO := 7i x (OD_cont) PERGVO = 23.1535 m

-A262 -

Location 4438-4443, PERSFO (IRVC)Perimeter for radiation from finned shell outer surface to outer wall, also finned shell outer surface to air, (m)

PERSFO := 71X (OD_air) PERSFO = 24.9128 m

Location 4444-4449, HGASRV (IRVC)Gas h, reactor vessel - guard vessel, (W/m2-K)

To be consistent with the SSC-K input

HGASRV := 2.0 HGASRV = 2 W/m2 -K

Location 4450-4455, SLRVC (IRVC)Slope

= 0 vertical= 1 horizontal

Location 4456-4461. HFSRV(IRVC)Heat transfer coefficient across finned shell, (W/m2 -K)

Assuming no heat transfer across the finned shell.

HFSRV := 0.5 HFSRV = 0.5 W/m2 -K

Location 4462-4467. HCONRV (IRVC)Heat transfer coefficient between concrete nodes, (W/m2 -K)

The thickness of the concrete wall is 1.0 m and the wall is divided into two nodes as shown in Fig. 18-8. Assuming K=1.0 W/m-K, L=0.5 m

HCONRV := — HCONRV = 2 W/m2-K0.5

Location 4468-4497. CPCPMP (K)Multiplicity for component-component heat transfer, default=1.0

5 heat ransfer pathes are specified through Locs. 1052-1081 and 1082-1111, Block 3.

IELHT IELHT2 CPCPMP

12 -4 4.015 -4 3.019 -4 1.024 -2 1.024 -4 1.0

- A263 -

Location 4498-4503. GVMC (IRVC)Mass * specific heat/length of guard vessel, (J/m-K)

The guard vessel (containment wall) of KALIMER is made of 2-1/4 Cr-1Mo material. Mass and Cp data are from Tables M-2 and M-3 of Ref. A2.

mass of guard vessel (containment wall) Mass_gv := 88510 kg

specific heat of 2-1/4 Cr-1 Mo Cp_gv := 640.2 J/kg-K

length of the second wall of annulus Len_ann2 := 18.725 m

Cvmc • (CP-9V)x (Mass_gv)Len_ann2 GVMC = 3.026 x 106 J/m-K

Location 4504-4509. FSMCI (IRVC)Mass * specific heat/length of finned shell inner node, (J/m-K)

mass of finned shell inner node/length M_finin := 7852.0 kg

specific heat of 316SS at 293 K

Cp_awall := linterp(Tkss,Cp_316SS , 293) Cp_awall = 465.145 J/kg-K

FSMCI := (MJinin) x (Cp_awall) FSMCI = 3.65232 x 106 J/m -K

Location 4510-4515. FSMCO (IRVC)Mass * specific heat/length of finned shell outer node, (J/m-K)

The same value as for FSMCI is set.

FSMCO := FSMCI FSMCO = 3.65232x 10® J/m-K

Location 4516-4521, CRMCI (IRVC)Mass * specific heat/length of concrete inner node, (J/m-K)

mass of concrete inner node/length M_conin := 16728.0 kg

specific heat of concrete Cp_con := 0.88 J/kg-K

CRMCI := M_conin x Cp_con CRMCI = 1.472X 104 J/m-K

- A264-

Location 4522-4527, CRMC1 (IRVC1Mass * specific heat/length of concrete outer node, (J/m-K)

mass of concrete outer node/length is assumed to be 1.0 kg/m, because no heat transfer is assumed across the concrete and outside environment.

M_conout := 1.0 kg

CRMCO := (M_conout) x (Cp_con) CRMCO = 0.88 J/m -K

Location 4528-4533. TW6RV (IRVC)Temperature of outer wall node, (K)

TW6RV := 273.15 + 20 TW6RV = 293.15 K

Location 4534, ERSFSEmissivity of finned shell outer surface

ERSFS := 0.85 ERSFS = 0.85

Location 4535. SIFSTBStefan-Boltzman constant, (W/m2 -K)

SIGSTB := 5.672x 10'8 W/m2 -K

Location 4536. RW5RVThermal resistance between surface of outer wall and inner node (node 5), (m2 -K/W)

No heat transfer between inner node and outer node in the concrete is assumed. Therefore, largethermal resistance is used as input data.

RW5RV := 1,0x 1099 RW5RV = 1 x 1099 m2 -K/W

Location 4537. REYTRVReynolds number for transition from laminar to turbulent in air

To be consistent with the SSC-K PSDRS model,.

REYTRV := 40000.0 REYTRV = 4x104

- A265 -

Location 4538. AFRTRVTurbulent friction factor, AFRTRV* Re** BFRTRV

AFRTRV := 0.1875

Location 4539. AFRLRVLaminar friction factor, AFRLRV/Re

AFRLRV := 70.0

Location 4540. ORPINInlet orifice coefficient

Flow loss coefficient is from from Table F-9 of Ref. A2.

ORFIN := 0.014606

Location 4541. XLUNRVLength of upper node between liquid level and top of vessel, (m)

E(1) and E(3) in Fig. 18-1 are 17.075 and 15.625 m, respectively.

XLUNRV := 17.075- 15.625 XLUNRV = 1.45 m

Location 4542. BFRTRVTurbulent friction factor, AFRTRV* Re** BFRTRV

BFRTRV := -0.2 BFRTRV - -0.2

Location 4543. USGVMCMass * specific heat/length of guard vessel in upper node, (J/m -K)

USGVMC := GVMC USGVMC = 3.02612x 106

Location 4544. UNFSMCMass * specific heat/length of air divider in upper node, (J/m -K)

UNFSMC := FSMCI UNFSMC = 3.65232 x 106

J/m-K

J/m-K

-A266-

Location 4545. AIRAUNAir flow area of upper node, (m2)

AIRAUN := Area_airinlet AIRAUN = 8 m2

Location 4546, EPSOWEmissivity of outer wall

EPSOW := 0.6 EPSOW = 0.6

Location 4547-4552. EPSGVO MRVC)Emissivity of guard vessel outer wall

EPSGVO := 0.85 EPSGVO = 0.85

Location 4553-4558, EPSFSI MRVC)Emissivity of finned shell inner surface

EPSFSI := 0.85 EPSFSI = 0.85

- A267 -

Fig. 18-7 Configuration and air flow path of PSDRS

- A255 -

Stack Inlot

Fig. 18*3 PSDRS model

A269 -

Heat transfer correlation by Lyon-Martinelli is employed into SAS4A.

Nu := 4.55 + 0.016x (Rex Pr)0'86"

sodium properties at 731 K (core avergae temp.) thermal conductivity

Kna := linterp(XKTEM,K_Na,Tcoreavg) Kna = 70.15 W/m-K

Prandtl umber at 731 K Pr := 0.0051

viscosity p := 0.000255

Annulus element E(24)

The first wall in the annulus element is reactor barrel and the second wall is reactor vessel.

hydraulic diameter DHELEM24 = 0.05 m

wall thickness of RB Tw_rb = 0.025 m

wall thickness of RV Tw_rv = 0.05 m

metal conductivity K_w316SS = 20.31 W/m-K

flow area AREAEL24 = 0.54153 m2

(a) The first wall in the case of no oveflow through segment S(10),

Re := 0.0 inside of CV2 and CV4

Nu_a := 4.55 + 0.016x (Rex Pr)0"86 Nu_a = 4.55

h_a :=Kna

DHELEM24x Nu_a h_a = 6383.625

h a1 := 10.0

then, overall heat transfer coefficient is

HTC a := I — + Tw~rb . + 1ha K W316SS h a1

-1HTC_a = 9.86

(b) The first wall in the case of full oveflow through segment S(10)

Assume main flow path through S(10), bypassing IHX Wcore = 2143.1

DHELEM24 x Wcore

kg/s

Re :=p x AREAEL24

Nu. b 4.55 + 0.016x (Rex Pr) 0.86

Re = 7.75976 x 10'

Nu h - 24.41

- A270 -

h_b = 34241.993h b :=----- ---------- xNu bDHELEM24

h_b1 := h_b

then, overall heat transfer coefficient is

HTC b := I — + Tw-rb + 1h_b K_w316SS h_b1 J

HTC b = 775.6

(c) The second wall in the case of no oveflow through segment S(10),

HTC of the cover gas (He) h_c := 10.0

then, overall heat transfer coefficient is

HTC C := I —t— + Twrv X"1

he K W304SSHTC c - 9.77

(d) The second wall in the case of full oveflow through segment S(10),

ReDHELEM24 x Wcore

\i x AREAEL24

Nu_d := 4.55 + 0.016x (Rex Pr)

Kna

0.86

h d :=DHELEM24

x Nu d

then, overall heat transfer coefficient is

HTC d := | — + -Tw-rV 1 h_d K„w304SS)

Re = 7.75976 x 10'

Nu_d - 24.41

h d = 34241.993

HTC d - 425.64

Cold pool wall CV(3)

hydraulic diameter = ID of RV - CD of flow guide

Dcv3 := ID_rv - FGOD Dcv3 = 0.32

metal conductivity

flow area Acv3 := —(lD_rv2- FGOD2) 4

m

K_w304SS = 21.55 W/m-K

Acv3 = 3.39795

(a) In the case of no oveflow through segment S(10), Re := 0.0,0.86Nu_a := 4.55+ 0.016x (Rex Pr)' Nu a = 4.55

m^

- A271 -

h_a := Kna x Nu_a h_a - 997.441Dcv3

then, overall heat transfer coefficient is

HTC_a :=(—+ lOLH- 1 HTC_a = 300.96Lh_a K_w304SS)

(b) In the case of full oveflow through segment S(10),

Assume main flow path through S(10), bypassing IHX Wcore = 2143.1 kg/s

Dcv3 x Wcore \x X Acv3

Re = 7.91472 x 10.5

Nu_b := 4.55 +0.016x (Rex Pr) 0.86 Nu_b = 24.75

h_b = 5424.966

then, overall heat transfer coefficient is

HTC_b = 399.28

Appendix.!? Input of SAS4A/SAS SYS-1 for KALIMER Steady State Run

KALIMER STEADY STATE, BOEC, YM KWON, 2004 3.14 CHANNELS CORE

4 0 0 0 0 0 0 0 1 1INPCOM 1 0 0

1 1 4 number of core channel2 1 0 no debugging print option3 2 5 1 number of (fuel) & (clad) type5 1 0 gas plenum above fuel type7 1 0 Temp, in Kelvins8 1 0 use of external reactivity vs time table9 1 0 s-s power in peak axial segment

11 1100000 max. no. main time step12 2 0 20 no. main time step (before/after) #1414 1 0 switch time of main printout15 1 1000 no. main time step for restart16 2 6 6 no. (delayed neutron precursor)&(group)18 1 3 no. entries (external reactivity table)22 1 2 no. entries (Tcorein vs time) table23 1 0 only one restart file is saved24 1 11 plot file unit no.25 1 0 no input edit, 1=input edit27 1 4 PRIMAR-4 option31 1 2 CRDL expansion model option36 1 -4 detail radial expansion model option39 1 -5 dollar of fuel reactivity for stop41 1 100 print frequency for channel-wise reactivity45 1 1 no. decay heat curve46 1 1 no. entries initializing decay heat51 1 139 total no. assemblies in active core52 3 1 2 2 material(grid/ACLP/TLP) 1=316SS,2=HT955 1 3 axial expansion option(force balance always)56 1 1 use of correction term to reactivity58 1 0 use of detailed reactivity model59 1 367 total no. assemblies in reactor core60 1 1 restraint ring at top load pad62 1 1 restraint ring of TLP, 1=316SS63 2 2 2 (ACLP/TLP) of reflector, 2=HT965 1 1 ACLP remains compacted at low PWR/flow

INPMR4 3 1 01 3 4 3 0 no of CV (primary/secondary/DRACS)4 3 10 3 0 no. of liq. segmt (pri./second./DRAGS)7 3 0 0 0 no. of gas segmt (pri./second./DRAGS)

10 1 34 total no. of liq. element11 7 1 7 8 4 494 type of CV49 10 1 3 2 3 3 2 3 3 2 359 10 3 6 3 3 5 3 3 3 5 369 10 3 3 3 13 11 3 5 3 3 779 4 3 3 8 3 type of element

189 10 1 2 1 2 12 12 2 3199 10 3 1 3 1 2 4 3 4 2 3209 6 6 7 7 5 5 6 (start/end)CV of segmt269 2 0 0 (start/end)CV of gas segmt325 10 1 3 3 3 3 4 4 1 1 2335 3 3 3 3 no. of element in segmt365 10 1 2 5 8 11 14 18 22 23 24375 3 26 29 32 1st element number of segmt405 1 3 no. of pump406 3 15 19 27 element number of pump418 3 0 0 0 type of pump (0=head vs time)430 3 0 0 0 tpe of pump (0=dummy,~2=head vs flow)470 1 1 no. of IHX473 1 12 element number of IHX (primary)481 1 30 element number of IHX (intermediate)489 1 0 detailed IHX model497 1 0 no pressure adjustment for IHX model512 1 29 No. of temp, group513 10 4 7 4 4 7 4 4 7 4 4523 10 20 4 5 5 10 5 5 10 4 4533 9 20 4 10 8 20 20 20 20 20 temp, node no.613 10 2 3 4 5 6 7 8 9 10 11623 10 12 13 14 15 16 18 19 20 22 23633 9 24 25 26 28 29 31 32 33 34 1st elemt T-group713 10 2 3 4 5 6 7 8 9 10 11

- B1

723 10 12 13 14 15 17 18 19 21 22 23733 9 24 25 27 28 29 31 32 33 34 last elemt T-813 1 3 no. of bypass(bp) channel814 3 7 7 7 of nodes in wall A & B bp channel822 3 1 1 1 decay curve number for bp channel830 3 3 6 9 element number of bp channel839 2 1 33 (no./element number) of SG852 1 1 SG model (1= Temp. drop vs time, Table number)864 1 3 SG model (3= once-through SG)890 1 500 print frequency of PRIMAR4 result973 2 1 25 (no./element number) of valve982 1 2 Table number of pressure drop coeff. vs time

1008 3 2 24 -3 (no./CV or elemt number) CRDL expan option1052 5 12 15 19 24 24 from elemt number(comp-to-comp HT)1082 5 -4 -4 -4 -2 -4 to elemt number(comp-to-comp HT)1112 5 0 0 0 8 -12 node number, + (first), -(last)1153 2 2 2 (no./1st 'CV number) having common cover gas1171 4 3 8 9 10 (no./liq. segmnt number) bypassing IHX1243 2 1 24 (no./element number) of annular1274 1 2 no. of sections in PSDRS1275 1 0 use of detailed RVACS model1276 2 -3 1024 second wall of element (PSDRS)1282 2 15 7 number of nodes in section1288 1 40000 no. time step to initialize comp-to-comp HT1289 1 10000 print frequency during null transient1290 1 0 no debug print (PSDRS)

OPCIN 11 0 01 1 0.01 s-s Temp, converg. criteion for fuel pin3 1 0.00001 neutron flux amplitude converg. criterion5 1 0.1 initial max del-t length6 1 0.01 max. HT del-t after boiling7 1 500.0 max. problem time (sec)9 1 10.0 CPU seconds reserved at calculation end

10 2 50.0 30.0 max allow Temp, change(fuel/clad)13 1 10.0 initial PRIMAR del-t14 2 10.0 0.01 max. PRIMAR del-t (before/after) boiling26 1 10.0 del-t size for null transt (comp-to-comp HT)27 1 1.00000D-12 convergence criterion for null transient

POWINA 12 0 02 2 2.954 0 0D-07 3.92200D+08 prompt neutron lifetime/power4 5 8.36280D-05 6.2193 0D-04 5.29990D-04 1.28000D-03 7.58370D-049 1 2.80170D-04 effective delayed neutron tract.

10 5 0.01346 0.03094 0.11747 0.30459 0.8596515 1 2.94183 decay constant29 3 0 . 0 0.0 0 . 0 external reactivity (Table)49 3 0.0 60.0 1.000 00D+05 time (Table)69 2 0.97749 0.9800 (power/flow)tract.for SAS4A71 2 11.112 2.00000D-05 CRDL length/alpha of 316SS73 2--22.71 0 . 0 (cl/c2) CRDL expan. rho coeff.75 2 86240.0 3542.0 (mass*Cp)/(area*HTC) of CRDL77 1 38.5 coolant volume contacting CRDL

260 5 2.20054D-02 1.90590D-02 9.93659D -03 5.25396D-03 1.93225D-03265 1 1.67409D-03 decay heat precursor yield290 5 6.56251D-02 1.77 911D-03 1.37667D -04 6.08268D-06 2.25624D-07295 1 1.89684D-08 decay heat group decay constant320 1 0.06225 sum of decay heat precursor yield325 1 1.0 normalized power history (Table)365 1 5.045 76D+07 time (s) at above Table408 2 1.0 0.16 0 0 66 (max.slope)/(assy pitch) gridplate410 2 0.1604 0.1604 flat-to-flat length of (ACLP/TLP)412 1--245.994 radial expansion coeff($/m)413 1 1.20000D-03 clearance between TLP and restraint ring414 2 1.00000D-03 1.00000D-03 bending moment at (TLP/ACLP)423 1 0.10 tract.of core T-rise at top restraint ring424 1 0.35 tract.of core T-rise at reflector load pad426 1 0.00128 core radius of (actual - ideal)428 1 500.0 T -response time const, of top restraint ring

PM AT CM 13 0 011 5 24.5 24.7 24.9 25.2 25.416 5 25.6 25.9 26.1 26.3 26.521 5 26.8 27.0 27.2 27.4 27.626 3 27.8 28.0 28.0 clad conductivity71 5 294.27 323.0 373 . 423.0 473.076 5 523.0 573.0 623.0 673.0 723.081 5 773.0 823.0 873.0 923.0 973.086 3 1023.0 1073.0 1088.72 clad temp.91 5 1.58000D+04 1.57200D+04 1.563 00D+04 1.55500D+04 1.54700D + 04

grup

-B2-

96101111116121131136140151156160171176180251256261271276281291296300311316320331336340419420425429440445449460465469480485489500505509580585589606611616621625626631636641645646651656661665666671676681685686691696701705766771776781785786790

5 1.53900D+04 1.53300D+04 1.517000+04 1.511000+04 1.502000+043 1.49300D+04 1.48500D + 04 1.478000+04 fuel-1 rho (U15PulOZr)5 1.18500D+04 1.17 9 0 0D + 04 1.172300+04 1.166300+04 1.160300+045 1.15430D+04 1.14980D + 04 1.137800+04 1.133300+04 1.126500+043 1.11980D+04 1.113 8 0D + 04 1.108500+04 fuel -2 rho (75% fuel-1)5 1.60200D+04 1.59500D + 04 1.589000+04 1.581000+04 1.573000+044 1.56400D+04 1.55400D + 04 1.522000+04 1.512000+041 1.50200D+04 fuel-3 rho (UlOZr)5 1.36170D+04 1.35580D + 04 1.350700+04 1.343900+04 1.337100+044 1.32940D+04 1.32090D+04 1.293700+04 1.285200+041 1.27670D+04 fuel -4 rho (85% fuel-3)5 8.83240D+02 8.60530D+02 8.375900+02 8.144300+02 7.91060D+024 7.67460D+02 7.43640D+02 7.196000+02 6.953300+021 6.70850D+02 fuel-5 rho (sodium)5 2.93000D+02 4.00000D+02 5.000000+02 6.000000+02 7.00000D+025 8.00000D+02 8.68000D+02 9.380000+02 1.000000+03 1.100000+033 1.20000D+03 1.30000D+03 1.378000+03 1st Temp5 2.93000D+02 4.00000D+02 5.000000+02 6.000000+02 7.00000D+025 8.00000D+02 8.68000D+02 9.380000+02 1.000000+03 1.100000+033 1.20000D+03 1.30000D+03 1.378000+03 2nd Temp5 2.93000D+02 4.00000D+02 5.000000+02 6.000000+02 7.00000D+024 8.00000D+02 9.00000D+02 1.000000+03 1.100000+031 1.20000D+03 3rd Temp5 2.93000D+02 4.00000D+02 5.000000+02 6.000000+02 7.00000D+024 8.00000D+02 9.00000D+02 1.000000+03 1.100000+031 1.20000D+03 4th Temp5 5.50000D+02 6.50000D+02 7.500000+02 8.500000+02 9.50000D+024 1.050000+03 1.15 0 0 0D + 03 1.250000+03 1.350000+031 1.45000D+03 5th Temp1 300.0 reference design Temp5 9.8 11.4 13.4 15.5 17.74 20.1 22.6 25.3 27.81 30.6 fuel-1 conductivity5 7.03 8.17 9.61 11.11 12.694 14.41 16.20 18.14 19.931 21.94 fuel-2 conductivity5 16.4 18.0 20.1 22.4 24.94 27.6 30.5 33.6 36.81 40.3 fuel-3 conductivity5 12.87 14.13 15.77 17.58 19.544 21.66 23.93 26.37 28.881 31.62 fuel-4 conductivity5 92.63 88.18 82.84 77.74 72.874 68.20 63.73 59.44 55.311 51.33 fuel-5 conductivity5 293.0 373.0 473.0 573.0 673.04 773.0 873.0 973.0 1073.01 1173.0 conductivity temp5 1.33040D+02 1.462000+02 1.588700+02 1.720200+02 1.851800+025 1.97850D+02 2.07600D+02 1.913600+02 1.59840D+02 1.695900+025 1.82260D+02 1.949300+02 2.080800+02 2.178300+02 2.176800+024 2.17080D+02 2.163700+02 2.163700+02 2.16370D+021 2.163 7 0D+02 fuel-1 Cp5 1.33040D+02 1.462000+02 1.588700+02 1.72020D+02 1.851800+025 1.97850D+02 2.076000+02 1.913600+02 1.598400+02 1.695900+025 1.82260D+02 1.949300+02 2.080800+02 2.17830D+02 2.176800+024 2.17080D+02 2.163700+02 2.163700+02 2.16370D+021 2.16370D+02 fuel-2 Cp5 1.50700D+02 1.531400+02 1.697200+02 1.911800+02 2.160500+025 2.41900D+02 2.612900+02 2.658000+02 2.39760D+02 1.789900+025 1.78990D+02 1.789900+02 1.789900+02 1.78990D+02 1.789900+024 1.78990D+02 2.036200+02 2.065400+02 2.20440D+021 2.20440D+02 fuel-3 Cp5 1.50700D+02 1.531400+02 1.697200+02 1.911800+02 2.160500+025 2.41900D+02 2.612900+02 2.658000+02 2.39760D+02 1.789900+025 1.78990D+02 1.789900+02 1.789900+02 1.78990D+02 1.789900+024 1.78990D+02 2.036200+02 2.065400+02 2.20440D+021 2.20440D+02 fuel-4 Cp5 1.28241D+ 03 1.282410+03 1.282410+03 1.282410+03 1.27242D+035 1.26575D+03 1.263090+03 1.262470+03 1.26240D+03 1.26322D+035 1.26795D+03 1.277210+03 1.291590+03 1.307070+03 1.311860+034 1.33514D+03 1.370160+03 1.374990+03 1.400130+031 1.42181D+03 fuel-5 Cp5 298.0 400.0 500.0 600.0 700.05 800.0 873.0 890.0 923.0 1000.05 1100.0 1200.0 1300.0 1379.0 1400.04 1487.0 1588.0 1600.0 1657.01 1700. 0 Cptemp4 1379.0 1379.0 1487.0 1487.01 370. fuel sol idus temp (type 1-5]

B3 -

794798802806810813816819824829879884889990995000050055060086

-1:min

i4565858790-1

*4 IN27

1242475282879297

102107162167172177182187192302307312317322327332442447452457462467472582587592597602607612722727732737742747752862867872

1588.0 1657.04 1588.0 1 380.04 91600.0 1 113000.0 1 1690.15 1 1710.151 268300.05 4.82500D+02 5 7.84960D+022 7.47970D+02 5 3.73000D+02 5 8.73000D+02 2 1.07300D+03 5 3.73566D+06 5 5.95863D+06 2 5.626 98D+ 06 5 3.73000D+02 5 8.73000D+02 2 1.07300D+03 1 8.31434

91600.0

5.21480D+02 8.66080D+02 7.62140D+02 4.73000D+02 9.23000D+02 1.08856D+03 4.02379D+06 6.55 96 9D+06 5.72962D+06 4.73000D+02 9.23000D+02 1.08856D+03

90200.0

5.63370D+02 1.02150D+03

5.73000D+02 9.73000D+02

4.33085D+06 7.71948D+06

5.73000D+02 9.73000D+02

1657.0fuel liquidus temp (type 1-5)

90200.0fuel fusion heat (type 1-5)

clad solidus temp. clad liquidus temp,

clad fusion heat6.15380D+02 1.21000D+03

6.73000D+029.98000D+02

4.71178D+06 9.13369D+06

6.73000D+029.98000D+02

6.8468 0D + 02 8.68340D+02

clad Cp (HT9) 7.73000D+02 1.02300D+03

clad temp. 5.22021D+06 6.5472 8D + 06

clad rho*Cp 7.73000D+02 1.02300D+03

clad temp, ideal gas const.

14 0 01 1.76110D+05 Pressure at top of assy1 659.35 659.35 Tcorein (Table)1 0.0 1.00000D+05 time (Table)1 803.15 s -s Tcoreout2 -1.5910 3.1647 (bottom/top) elevation of assembly2 0.1 0.25 (min/max) distance bubble breakaway

18 1 05 0.0 10.7155 17.0115 15.135 535.7755 535.775 535.775 0.0 0.0 0.003 901.8 450.9 901.8 flowrate5 -1.5910 -1.5910 -1.5910 -1.5910 10.15475 -1.3703 -1.3703 9.4547 3.5047 12.40473 7.5047 18.5047 16.7047 ZINL5 1 . 1 . 1 . 1 . 1 .5 1 . 1 . 1 . 4 . 4 .5 3 . 3 . 1 . 1 . 1 .3 1 . 1 . 1 . 1 . 1 .5 1 . 1 . 2 . 2 . 1 .1 1 . multiplicity factor (inlet/outlet)5 3.1647 0.000 2.351 3.1647 0.0005 2.351 3.1647 0.000 2.351 3.16475 10.1547 4.1547 3.5797 3.5047 10.50475 -1.6803 -1.6803 3.5047 10.5047 -1.68035 -1.6803 9.3547 3.4047 3.5047 3.40475 17.2647 22.7047 18.5047 4.1547 10.15474 16.7047 24.6047 9.0047 7.5047 ZOUTEL5 4.7557 1.591 2.351 0.8137 1.5915 2.351 0.8137 1.591 2.351 0.81375 0.575 6.000 0.575 4.875 7.0005 12.185 1.430 4.875 7.000 12.1855 1.430 0.1 0.1 8.900 0.15 8.24 5.44 15.01 24.267 6.0004 16.467 20.150 15.60 6.260 XLENEL5 1.0 0.04241 0.04241 0.04241 0.279115 0.27911 0.27911 0.57101 0.57101 0.571015 0.20704 0.48383 0.12566 5.39609 0.175445 0.12566 0.12566 5.39609 0.17544 0.125665 0.12566 0.1 0.1 0.54153 0.541535 0.18777 0.18777 0.18777 0.08553 0.164704 0.09066 0.18777 5.06924 0.18777 AREAEL5 1.0 0.00749 0.00749 0.00749 0.003845 0.00384 0.00384 0.00313 0.00313 0.003135 0.0088 0.02682 0.4000 0.68674 0.472635 0.4000 0.4000 0.68674 0.47263 0.40005 0.4000 0.35682 0.35682 0.0500 0.05005 0.48895 0.48895 0.48895 0.3300 0.01114 0.33975 0.48895 0.8220 0.48895 DHELEM5 0.00001 0.00001 0.00001 0.00001 0.000015 0.00001 0.00001 0.00001 0.00001 0.000015 0.00001 0.00001 0.00001 0.00001 0.000015 0.00001 0.00001 0.00001 0.00001 0.000015 0.00001 0.00001 0.00001 0.00001 0.000015 0.00001 0.00001 0.00001 0.00001 0.000014 0.00001 0.00001 0.00001 0.00001 ROUGHL5 0.0 0.0 0.0 0.0 0.05 0.0 0.0 0.0 0.0 0.05 0.0 0.0 0.0 0.0 0.0

-B4-

877882887892

1012101510191023103010311034114211431148115311581163116811731283128812931298130313031308131314231428146114661499150415371542157515801613161816891691169317211805183318611866198320032023222322432263246324642469250225072578258326162621265426592694269727052713272127292737274527532761276927772785279328012806

5 1.0 5 0.0 5 2.0 4 3.03 2.318944 13228.7706 4 13228.77064 1.00000D+10 1 3.602771 12.760411 9285.1 12.05 1 .5 9.50600D+06 5 2.74600D+05 5 1.500 0 0D+ 05 5 1.500 0 0D+ 05 5 6.59100D+044 3.82500D+045 1 .5 1416.25 5 990.81 5 799.61 5 799.61 5 799.61 5 2262.474 2719.245 8.2302 10.0 5 0.02 2.15540D+05 5 1.00000D-09 2 1.00000D-09 5 6.00000D-05 2 6.00000D-05 5-1.591 2 7.5047 5 1.0 2 0.5 2 1.667 2 1.94000D-05 1 0.0 1 0.0 1 0.0 1 0.0 5 0.2 100.

2 1.0 2 1.0 2 1.0 2 0.0 2 0.0 2 0.01 9.8075 2.13000D-102 2.13000D-10 5-0.00028 2-0.000285 143.333 2 2257.22 5 33.073 2 1.05 2.19220D+072 4.20910D+043 0.025 3 26.2 3 26.2 3 26.2 3 26.2 3 26.23 0.00189 3 0.00189 3 0.00370 3 5.00800D+06 3 5.00800D+06 3 5.00800D+06 3 5.00800D+06 3 5.00800D+06 5 1 .5 1 .

0

0.0 0.0 1.00

0.0 0.0 0.00.0 4.0 2.0 0.06.0 0.0 1.0 BENDNM26.388 0.88859 K of IHX shell side3.58716 0.0 7.17432 K of pump (1st group)3.58716 0.0 7.17432 K of pump (2nd group)1.00000D+10 0.0 1.000000+10 K of E22-E25

K of IHTS loopK of IHX tube sideK of SG shell side

effective L/D of bend4.27600D+05 4.27600D+05 4.276000+05 9.506000+069.50600D+06 1.06100D+07 1.061000+07 1.061000+073.10500D + 05 1.2 73 00D+05 3.645000+06 1.5560 00+061.50000D + 05 3.64500D+06 1.55 6 0 00+06 1.500000+051.0 1.0 2.418000+06 1.02.00300D+06 6.59100D+04 4.720000+04 2.249000+056.59100D+04 1.94000D+06 6.591000+04 WALLMC3318.69 3318.69 3318.69 1416.251416.25 3606.96 3606.96 3606.96990.8 990.8 270.8 799.61799.61 270.8 799.61 799.61100000. 100000. 720.68 720.68100000. 100000. 793.57 793.572262.47 2262.47 2155.0 26937.52262.47 424.21 2262.47 WALLH213.093 216.713 95.211 1.01.0 (liquid+gas) volume of CV1.01325D+05 1.01325D+05 0.0 0.00.0 initial gas pressure of CV1.00000D-09 1.000000-09 1.000000-09 1.000000-091.00000D-09 vol. P-expansion coeff. of CV6.00000D-05 6.000000-05 6.00000D-05 6.000000-056.00000D-05 vol. T-expansion coeff. of CV3.1647 -1.3703 3.4047 16.704718.5047 reference height of CV29.886 0.542 1.0 1.01.0 (liquid+gas) interface area of CV2078.0 (Cp/Cv) & (gas constant) of He293.0 (viscosity) & (ref. Temp) of He

length of flow area of

hydraulic diameter of surface roughness of

gas segment gas segment gas segment gas segment

100. 100. 0 . 0 .0 . HT time c>onst . of CV1.0 relative head table (1st pump)1.0 relative head table (2nd pump)1.0 relative head table (3rd pump)1000000. time table (1st pump)1000000. time table (2nd pump)1000000. time table (3rd pump)

accelerat.ion gravity2 . 13000D-10 2.13000D-10 2 . 13000D-10 2.13000D-102 . 13000D-10 Na compressibility of CV0 . 00028 -0.00028 -0 . 00028 -0.000280 . 00028 Na thermal expan. coeff.86

o

300.96 86

°

2712.9322 57.22 wall HT coeff.of CV43 0.914 646.817 23 5.827 1.01 . 0 wall surface area of CV4 . 76050D+07 7.14570D+07 2 . 60530D+07 3.50210D+043 . 50210D+04 (mass*Cp) of CV0 . 80 7.00 Coeff. Lyon-Mart ine Hi26 .2 26.2 Thermal conductivity, lower-A26 .2 26.2 of bypass channel(3), upper-A26 .2 26.2 lower-B26 .2 26.2 upper-B26 .2 26.2 D-wall0 . 00327 0.00145 thickness of wall A0 . 00327 0.00145 thickness of wall B0 . 00370 0.00370 thickness of wall D5 . 00800D+06 5.00800D+06 (rho*Cp) lower-A wall5 . 00800D+06 5.00800D+06 upper-A wall5 . 00800D+06 5.00800D+06 lower-B wall5 . 00800D+06 5.00800D+06 upper-B wall5 . 00800D+06 5.00800D+06 D-wall1 . 1 . 1. 1 .1 . 1 . 1. 1 .

B5 -

28112816282128572860286328572860286328812886290529132921292929372951310532733287344134453455346034653470347435163524353235403548355635643572358035883596360436123617365036534174417541744175421642204246425242584264427042764313434343434373440344044405440844094410441144124413441444204426443844444456446244684498450445104516

5 1 .5 1 .1 1 .3 0.000975 3 0.00650 3 0.005783 3 0.005601 3 0.0088133 0.008096 5 0 .4 0 .3 0.5 3 0.5 3 22.6564 3 3.1094 3 1.03 1.00000D+10 3 16.8047 3 0.03 0.01 0.9999 1 0.22483D+065 0.05 5 0.05 5 0.054 0.05 1 0.051 4.262 1 67.907 1 59.352 1 0.0200 1 0.0008 1 4.41900D+06 1 4.41900D+06 1 21.55 1 21.55 1 1.00000D+091 1.00000D+09 1 1.05 0.02 8.03 0.0163 0.0161 1.916 0 0D-04 1 0.90200D-04 1 0.4424 OD-04 1 0.78000D-044 21325.91 104326.22 10.625 2 22.054 2 0.702 0.70 2 23.15352 24.41021 4.12100D+06 1 14.0 1 65.00 1 21.7398 1 293.15 1-3.22033 0.023 1 30.01 3.19154 1 8.0 1 30.01 3.19154 1 8.02 4.75637 2 10.4678 2 23.1535 2 24.9128 2 2.02 0.5 2 2.05 4 .2 3.02600D+06 2 3.65232D+06 2 3.65232D+06 2 14720.0

1. 1 . 1 . 1 .1. 1 . 1 . 1 .

power' shape of bypass channel(3,7)0.0 0.0 power fract . (ch.1)0.0 0.0 power fract .(ch.2)0.0 0.0 power fract .(ch.3)0.0 0.0 power fract . (ch.1)0.0 0.0 power fract .(ch.2)0.0 0.0 power fract .(ch.3)0 . 0 . 0 . 0 .0 . 0 . 0 .0.5 0.5 pwr fract. of region-Al0.5 0.5 pwr fract. of region-A2290.6315 729.2688 perimeter of wall-B52.8594 65.2969 perimeter of wall-D1.0 1.0 normalized Temp drop (SG)1.00000D+10 1.00000D + 10 pressure drop coeff. (valve)16.8047 16.8047 height of thermal center (SG)60.0 100000. t ime (sec) for SG60.0 100000. time (sec) for valve

fract . of Temp . drop in evaporatorsteady -state IHX inlet pressure

0.05 0.05 0.05 0.050.05 0.05 0.05 0.050.05 0.05 0.05 0.050.05 0.05 0.05

69.1461 0.0 0.86 0.86

19870.2

5.022.054 0.70 0.70 23.1535 24.4102

4.75637 10.4678 23.1535 24.9128 2.0

. 5

. 002600D465232D465232D4

fract. of axial node height in IHX perimeter of IHX shell side

perimeter of IHX tube outside perimeter of IHX tube inside

thickness of IHX shell thickness of IHX tube (rho*Cp) of IHX shell

(rho*Cp) of IHX tube thermal conductance of IHX shell thermal conductance of IHX tube

fouling HT coeff. of IHX shell side fouling HT coeff. of IHX tube side

slant-height factor of IHX tube 3.4929 0.0 0.0

initial gas vol. of CV 4.55 coeff. L-M(pipe)4.55 coeff. L-M(IHX shell)length*thermal expan coeff.(cold pool RV)

length*thermal expan coeff.(annulus element) length*thermal expan coeff.(cold pool RV)

length*thermal expan coeff.(annulus element) 19870.2 51724.8

(HT coeff*area) comp-to-comp HT length of RVACS section

RV perimeter emissivity of RV

emissivity of guard vessel(GV) in-surfaceGV-air perimeter

air divider inner perimeter 2nd wall MCp/L for annualr element

2nd wall HTC 2nd wall HTC

2nd wall perimeter air inlet temp,

bottom elevation of RVACS 4.36 HTC1s of air in RVACS

length of air inlet sectionDh of air inlet section

flow area of air inlet sectionlength of air outlet stack

Dh of air outlet stackflow area of air outlet stack

air flow area of GV-divider air flow area of divider-silo

perimeter from GV-outer to divider-inner perimeter from divider-outer to silo

gas h for RV-GV HTC across air divider

HTC between concrete nodes 1. 1. 1. multiplier

06 MCp/L of GV06 MCp/L of air divider inner node06 MCp/L of air divider outer node

MCp/L of concrete inner node

-B6-

452245284534453545364537453845394540454045414542454345444545454645474553

-1fPCHN

47

141521252790

118181183203

-1fPCHN

25-1

fPCHN1525-1

fPCHN25-1

IOMIN158

13182328323639434650535478

102104128152155159162166169173180182186189193

-1IOMIN

-1IOMIN

1

22111111111 1 1-0 1 31 3 1 8 12 2

14720.0 293.150.705.67200D-081.03000.0 0.187564.020.00 20.01.45

. 2

.02612D+06 3.65232D+06 8.0 0.6 0.70

14720.0 MCp/L of concrete outer node293.15 temp. of outer concrete node

emissivity of divider outer surface Stefan-Boltzman const

themal resistance between outer wall nodes Re for transition from Tur. to Lam.

turbulent frict. factor(A) laminar frict. factor (*/Re)

inlet orifice coeff. inlet orifice coeff.

upper node length between Na-level & vesel top turbulent frict. factor(B) A*ReAB

MCp/L of GV in upper node MCp/L of divider inner node in upper node

air flow area of upper node emissivity of concrete wall

0.70 emissivity of GV outer surface0.70 emissivity of divider inner surface

5135134 2 25 1 1 1 1

162

1121

2714

1401

311

032

5 06 0

14

node no.(gas segmt/reflect zone(lower/up)) 4 segmt number (KZ= 1-5)

ra dial node numberproperty number(fuel/axial blank/clad)

(no. pin per assy)/(no. of assy) segmt no. of (upper/lower) blanket

21 node number for plottingradial node(0=equal distance, l=equal mass)

simple axial expansion feedback axial node number for ACLP

number of decay heat curve used

512

2271

148 (no. pin per assy)/(no. of assy)

5122

34

127

25

24property number(fuel/axial blank/clad) (no. pin per assy)/(no. of assy)

512

4127

348 (no. pin per assy)/(no. of assy)

4 2.69717D-05 2.69717D-05 2.697170-05 2 .697170-051 2.69717D-05 flow area (KZ= 1-5)5 0.05 0.05 0.05 0 .05 0.055 0.05 0.05 0.05 0 .05 0.055 0.05 0.05 0.05 0 .05 0.055 0.05 0.05 0.05 0 .05 0.054 0.05 0.05 0.05 0 .05 node length4 0.00365 0.00365 0.00365 0 .003651 0.00365 hydraulic dia.4 0.00208 0.00208 0.00208 0 .002081 0.00208 thickness inner structure4 0.00208 0.00208 0.00208 0 .002081 0.00208 thickness outer structure1 1.151 length of fission gas plenum1 0.00315 clad inner radius (fuel)1 0.00370 clad outer radius (fuel)2 0.00315 0.00370 (inner/outer)clad radi.(gas plenum)1 1.00000D-06 fuel inner radius1 0.00315 fuel outer radius3 0.4740 0.5585 0.55852 2.3510 0.8137 zone length (KZ=l-5)3 0.00233 0.00233 0.002332 0.00233 0.00233 structure perimeter (KZ=1-5)1 6.99801D-05 area of (coolant+pin)4 9.25000D-04 9.25000D-04 9.250000-04 5 .50000D-041 9.25000D-04 thickness of outer reflector2 0.00315 0.0037 nominal clad (inner/outer) radius4 0.02325 0.02325 0.02325 0 .023251 0.02325 reflector perimeter per pin4 9.25000D-04 9.25000D-04 9.250000-04 0 .00000D+001 9.25000D-04 thickness of inner reflector

;i 2 1

;i 3 25 3.88063D-05 3.88063D-05 3.880630-05 3 .88063D-05 3.88063D-05

-B7 -

325478

102128159166169180182189

-1’MIN

-1(INC

246

111621263035404562636469747984

112117122127132160165170175180208213218223228256

-1(INC

61116212662636469747984

112117122127132160165170175180208213218223228256

-1

5 0.003471 0.00546 1 0.006002 0.00546 1 0.00546 5 0.004361 1.519 04D-04 5 1.50000D-032 0.00546 5 0.03775 1.50000D-03

0.00347 0.00347 0.00347 0.00347

0.00600

0.00436 0.00436 0.00436 0.00436

1.50000D-03 1.50000D-03 5.40000D-04 1.50000D-03 0.006000.0377 0.0377 0.0377 0.03771.50000D-03 1.50000D-03 0.00000D+00 1.50000D-03

621

1. 0078 pwr fract. heating structure

2 0.0048 0.0114 pwr fract. heating (coolant/clad)5 0.60593 0.67060 0.74368 0.81237 0.856275 0.90914 0.95183 0.98330 0.99436 1.000005 0.99350 0.97494 0.95607 0.91180 0.856415 0.79107 0.73561 0.65458 0.56556 0.479054 0.15516 0.00110 0.00112 0.00111 PSHAPE5 1.0 1.0 1.0 1.0 1.05 1.0 1.0 1.0 1.0 1.0

1-1.

1-1.

5-5 5 9 5 6 5 44- 1 5 55- 1 5-3 5-2 4-6 5 1

0021110D-21110D-036490547505983047640093459530D-67230D-06120D-56800D-658 6 0D-54680D-49990D-06260D-62920D-89520D-9154 0D-20540D-47230D-32660D-35010D-17328

0404

0 . 0 . 0 . 0 . 0 .

05-4 . 06 2,05 6,05 3 , 05-3 ,06 1. 05-1 . 05-3 ,05- 2 ,06- 2,

04039 05732 05872 04430 00007 43670D- 28430D- 40190D- 49440D- 03230D- 9616 OD- 9124 0D- 16360D- 30870D- 4960 0D- 183 6 OD- 0669OD- 5077 OD- 2150 OD- 7587 OD-

00000

05-3 05 3 05 6 05 205- 406- 2 05-2 05-3 05-1

04479 05922 05758 03942 00007 155 8 OD-0 5 - 49720D-05 43 54 OD-0 5 30300D-05 39460D-05- 03980D-06- 28940D-05- 17 01OD-0 5 - 94370D-05- 85650D-06 60250D-05 2 0040D-04 510 7 OD-04 08600D-04 18620D-05

radial power shape relative power level

flooded Doppler coeff. voided Doppler coeff.

0.05157 0.06022 0.05158 0.02885

weight factor 79810D-05-4.08640D-06 56 07 0D-05 5.43 00 0D-05 1045 0D-05 5.4600 0D-05 03180D-05-2.96360D-06

void coeff.

0.04892 0.05988 0.05491 0.03406 0.00007

-1 4 6 1

-5 -6 -2 -3 -1

6 6 1 1 9 1

72270D-05 30320D-06-1.06740D-05 61560D-05-2.8768 0D-0 5 07560D-05-2.89010D-05 5460OD-05-1.1248OD-05 0683OD-06 1164 OD-05 7 3155 OD-04 1.4 072 0D-04 47 92 OD-04 1.41630D-04 43850D-05 7.92260D-05

clad coeff. 6 6 93 OD-05

67 03 OD-05 fuel coeff. PSHAPE

62555541-91-9

5-5 5 9 5 6 5 44- 1 5 55- 3 5-1 5-8 4-1 5 1

2. 51457 . 77206 .84370 .67180 . 13177 .68890D- .68890D- .03649 . 05475 .05983 .04764 .00934 .59530D- .67230D- .06120D- .56800D- 65860D- .00700D- .57450D- .01260D- 28920D- .43510D- 22870D- .02200D- .13830D- .03730D- .1717 0D- .84560

0 . 0 . 0 . 0 . 0 .

0404

0 . 0 . 0 . 0 . 0 .

05-4 . 06 2,05 6,05 3 ,05- 3 ,06 3 ,06- 5 ,05- 1 .06- 6 ,

5694980831827956247000094

040390573205872044300000743670D-28430D-40190D-4944 0D-03230D-50630D-29710D-0555 0D-93530D-69730D-23280D-18520D-16700D-4646OD-6649OD-

00000

05-3 05 3 05 605 205- 406 106- 605- 106- 5

6315583504811925558800095

0447905922057580394200007155 8 OD49720D43 54 OD30300D39460D8344 OD87390D05830D39930D51900D35960D24380D1717 OD34920D18260D

0.68989 0.84444 0.77432 0.48029 0.00094

0 . 0 . 0 . 0 . 0 .

05-1 . 05 4 . 05 6.05 1 .05- 5 .06 5.06- 8.05- 1 .06- 3.0605050405

-05-2

048920598805491034060000779810D-56070D-10450D-03180D-72270D-46970D-2414 0D-01810D-72990D-28360D-56370D-0152 0D-15110D-06280D-26210D-

0.72716 0.84922 0.72729 0.40682

0.05157 0.06022 0.05158 0.02885

weight factor 05-4.08640D-06 05 5.43000D-05 05 5.4600OD-0505- 2.9 63 6 OD- 0 605 void coeff. 08-1.76940D-0606- 9.3406 OD- 0 605- 9.39400D-0606- 1.9 653 OD-0606 clad coeff.

5.79970D-05 1.08720D-04 1.10590D-04 5.6539OD-05

fuel coeff.

-B8-

POWINC 626 5 0.29330 0.32996 0.36752 0.40650 0.47104

11 5 0.50018 0.52353 0.54087 0.56585 0.5690316 5 0.56500 0.55369 0.50810 0.48355 0.4532321 5 0.41714 0.33469 0.28786 0.24562 0.2033826 4 0.06589 0.00185 0.00189 0.00189 PSHAPE62 1- 0.0018963 1- 0.0018964 5 0.03374 0.03796 0.04228 0.04677 0.0541969 5 0.05755 0.06023 0.06223 0.06510 0.0654774 5 0.06501 0.06370 0.05846 0.05563 0.0521579 5 0.04799 0.03851 0.03312 0.02826 0.0234084 4 0.00758 0.00021 0.00022 0.00022 weight fetor

112 5- 1.553 2 0D-05 1.7764OD-05 5.47590D-05 9.40830D-05 1.3437 0D-04117 5 1.7424 0D-04 2.12330D-04 2.47270D-04 2.77690D-04 3.02290D-04122 5 3.20020D-04 3.29840D-04 3.30740D-04 3.22000D-04 3.04620D-04127 5 2.80180D-04 2.50220D-04 2.16290D-04 1.79470D-04 1.40580D-04132160165170175180208213218223228256

-1POWINC

611162126626364 69 74 79 84

112117122127132160165170175180208213218223228256

-1PMATCH

257

11151822252728 32 35 37

455-5-5-4-5- 5- 5- 5-4- 1

6255554 1- 1-5 5 5 545- 5- 5- 5-4-5 5 5 545-5 5 5 4 1

633 2 14 1 4 1 2 1 4 1 2

00450D-04 75450D-06

99100D-05 1 18190D-06-8

41920D-05-1.83990D-05-2 94790D-05-3.03080D-05-3 54810D-05-2.27040D-05-1 79530D-06-5.02610D-06-1 25230D-06-4.09730D-06-6 30260D-05-1.5189OD-05-1 0953OD-05-2.1413OD-05-2 8939OD-05-1.7341OD-05-1

97830D-80360D-21890D-02870D-95580D-29580D-

05-1 . 07-5 . 05-2 . 05-2 . 05-1 . 06 2,

8.34300D-06-5.80740D-06-3 0.53312

18810D-06-8 7144 OD-0 5-1 14390D-05-2 5416 OD-0 5-1 31000D-06-9

91060D- 25090D- 53 81OD- 94 05 OD- 61390D- 31780D- 43390D- 87 97 OD- 10190D- 32230D- 27020D-

0506-9 05-2 . 05-2 .05- 1 .0606- 1 . 05-2 . 05-2 . 05-1 .

74840D-06 78270D-05 7759OD-05 25260D-05

07430D-05 0076OD-05 01760D-05 08400D-05

0.12739 0.22305 0.25557 0.19048 0.03528 0.00080 0.00080 0.03240 0.05673 0.06500 0.04844 0.00897 5 5

0.14214 0.23411 0.25071 0.15530 0.00102

0.03615 0.05954 0.06376 0.03950 0.00026

12430D-06-1.43560D-05-2 85590D-05-6.92880D-05-7 8524OD-05-1.0103OD-04-1 89650D-05-8.12540D-05-7 98120D-05-2.8310OD-05-154080D-07 84780D-06 16970D-05 05520D-05 5533 OD-06

.47490D-06

.1518OD-06

.20010D-05 ,6185OD-06 ,1433 OD- 0 6

43540D-07-7.6638OD-08 57070D-06 3.21580D-06 06440D-06 5.24120D-06

4 . 42950D- 06 3 . 9308'1 . 46000D- 06 7 . 9360'0 . 24118

1 018 00.0 6 . 1000'1 . 324 D + 05 1 . 3240 . 028626 . 55 26 .5526 . 5526 . 55 26 .5526 . 554 . 81950D- 08 0 . 01 . 01325D+ 0526 . 55 26 .5526 . 557742.3 84 1.89

■ 5;.00790D+0 6 5.007

1588424238230361354000107

04040 06164 05859 03443 00027 4743 OD 9 033 OD 0131OD 21870D 696 0 OD 73 7 OOD 3 3 54 OD 20360D 5151OD 7 524 OD 50580D 80950D 26580D 36830D 33700D

0.17706 0.25531 0.21955 0.11869 0.00107

00000

05-305-804- 905- 6 05-606 4 060506 0607 06 06 06

-07-5

.04503

.06493

. 05584

.03018

.00027

.58580D-

. 73 66 OD-

.92570D- 20550D-

.0665 OD-

. 08 81OD-

.03460D-

.17 91OD-

.27760D-

.19070D-

.2158 OD- 32950D-

.1252 OD-

.76030D-

.06740D-

0.20924 0.25710 0.20624 0.10467

0.05321 0.06539 0.05245 0.02662

weight fetor 05-4.7272 0D-05 05-9.3 9210D-05 05-9.5054OD-05 05-5.11610D-05

5.4758 OD-06 1.11400D-05 1.12860D-05 5.94420D-06

1.89660D-06 4.75420D-06 4.83700D-06 2.11990D-06

Inner struct 44 5 5.00790D+06Outer struct 51 5 5.00790D+06Reflector58 1 5.57000D+05

)D-05 1.320OOD-06 bond gap conductanceD+05 (max/min) gap conductance

k= HBPAR/gap26.55 26.55

inner struct. conductivity (KZ=1-5) 26.55 26.55

outer struct. conductivity (KZ=1-5) Stefan-Boltzman Const/grain size

init. gas press (ref. Temp.) 26.55 26.55

reflector conductivity (KZ=1-5) density of (clad/coolant)

90D+06 5.0079 0D + 06 5.00790D+ 06 5.00790D+06

5.0079 0D+ 0 6 5.0079 0D+ 0 6 5.0079 0D+ 0 6 5.0079 0D+ 0 6

5.0079 0D+ 0 6 5.0079 0D+ 0 6 5.0079 0D+ 0 6 5.0079 0D+ 0 6

rho*Cp of fission gas

rho*Cp

rho*Cp

rho*Cp

-B9-

59 1 0.03 thermal resistance of fission gas73 1 2.01000D- 05 fuel axial expansion coeff.74 1 1.40000D- 05 clad axial expansion coeff.75 2 2.80000D+09 1.52056D+11 Young's modulus (fuel/clad)77 2 2.01000D- 05 1.40000D-05 linear expan. coeff. (fuel/clad)79 1 1.0 multiplier for axial fuel expan.

PMATCH 63 2 179 1 1.0 EXPCFF

PMATCH 63 3 279 1 1.0 EXPCFF

PMATCH 63 4 379 1 1.0 EXPCFF

COOLIN 64 1 01 2 0.1875 -0.20 friction factor coeff.3 3 0.025 0.80 7.0 convective HTC coeff.7 2 2000.0 64.0 Transient Re/coeff. laminar friot.

47 1 0.12653 flow rate per rod48 5 19.93704 0 . 0 . 0 . 0 .53 1 0.300001 forw ard orifice coeff.(K=l-6)56 5 19.93704 0 . 0 . 0 . 0 .61 1 0.300001 rev erse orifice coeff.(K=l-6)67 2 0.5 0.5 numerical scheme(0.5=semi-implicit)69 2 15.0 50.0 max. Temp change (liq/vap)in del-t71 1 0.1 max. motion of liq-vap interface72 2 63000.0 0.02 conden. HTC/initial liq. slug length75 2 1.00000D- 07 1.00000D-07 min. liq. film thick.(clad/struct)77 2 1.42700D- 04 initial liq. film thick. (struct)84 1 1.42700D- 04 initial liq. film thick, (clad)

165 1 10.0 superheat degr for bubble formingCOOLIN 64 2 1

47 1 0.11104

COOLIN 64 3 247 1 0.07734

COOLIN 64 4 347 1 0.03516

FUELIN 65 1 02 1 0.2 min. fuel melt fraction

FUELIN 65 2 1

FUELIN 65 3 2

FUELIN 65 4 3

XNOTES 0 0 0

Input required for null transient calculation.

***********************************************************-1

INPCOM 1 112 2 1014 1 10041 1 10000-1

INPMR4 3 1890 1 200

1288 1 100001289 1 40000

-1OPCIN 11 1

5 1 0.17 12000.0

-1ENDJOB -1

1250 no. main time step for print (before/after) #14

main time step no. for switching printout print frequency for channel-wise reactivity

PRIMAR-4 print frequency(time step)no. time step to initialize comp-to-comp HTprint frequency during null transient

initial max del-t length max. problem time (sec)

-BIO-