Thorium Energy Conference 2015 (ThEC15) October 12-15, 2015, Mumbai, India

DESIGN AND DEVELOPMENT OF HIGH TEMPERATURE HEAT PIPES AND THERMOSIPHONS FOR PASSIVE HEAT REMOVAL FROM COMPACT HIGH

TEMPERATURE REACTOR

K. K. Panda a,*, A. Basak a, I.V. Dulera a a Reactor Engineering Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085,India

E-mail: kkpanda@barc.gov.in, abasak@barc.gov.in, dulera@barc.gov.in *Email of corresponding author: kkpanda@barc.gov.in

ABSTRACT

Compact High Temperature Reactor (CHTR) is 100 kWth, lead-bismuth eutectic (LBE) cooled reactor having several advanced passive safety features to enable its operation as compact power pack. It will also facilitate demonstration of technologies for high temperature process heat applications. In CHTR heat is transferred from primary to secondary side by means of high temperature heat pipes. Heat pipes are also employed to remove heat under postulated accident scenarios. Thus, reliable operation of heat pipes is essential for the safe working of the reactor. In this respect, computer codes have been developed for design and simulation of high temperature heat pipes. This includes design codes using empirical correlations as well as simplified FEM models for system level analysis. To verify the operation of these heat pipes under various steady state and transient conditions full CFD analysis is essential. This has been done by using a commercial CFD code by incorporating user defined functions (UDFs) which address the saturated nature of the vapour phase and the vapour wick interface conditions. A three dimensional transient numerical model has been developed to predict the vapor core, wall temperatures, vapor pressure, and vapor velocity in the screen mesh wick of sodium heat pipe. This thesis will give an outline of all the developed models and compared the predicted results against the experimental data. Keywords: Sodium Heat pipe, Vapour-Liquid Interface, CFD, CHTR 1. INTRODUCTION

CHTR is 233U-Th fuelled, lead-bismuth eutectic (LBE) cooled and beryllium oxide moderated reactor. This reactor with 100 kWth power is being designed to operate at 1000°C to facilitate demonstration of technologies for high temperature process heat applications (I. V. Dulera, 2005). The reactor design incorporates several passive features. This includes primary heat transport by natural circulation of coolant. The heat from the primary to the secondary side is transferred by means of a set of high temperature heat pipes using sodium as working fluid. The design also incorporates heat pipes for heat removal under postulated accident scenarios. High temperature heat pipe would also find an application in achieving a high degree of uniformity in furnaces which may be used for annealing of refractory metal tubes, for application in CHTR. It is important to design and demonstrate reliable and long term operation of these heat pipes. Technologies for design, manufacture and testing of high temperature heat pipes and thermo siphons have been developed and the required facilities have been setup. This paper provides an outline of these developmental activities. The heat pipe is similar in some respects to the thermosyphon .The basic heat pipe differs from the thermosyphon in that a wick. Heat pipes (as shown in Figure 1) are hollow metal enclosures partly filled with a liquid coolant that moves heat from one end to another continuously by evaporation and condensation of the liquid due to capillary pressure. Due to its high conductivity and almost no heat loss, more and more theoretical and experimental researches have been carried out on the performance of heat pipe in recent years. Cotter (1965) developed the general basic theory for calculating heat pipe behavior quantitatively. Tolubinskii et al. (1978) investigated transient performance of sodium and potassium heat pipes. Colwell et al. (1987) and Jang (1988)

Thorium Energy Conference 2015 (ThEC15) October 12-15, 2015, Mumbai, India

developed a simple mathematical model to calculate transient behavior of sodium heat pipe with finite element method (FEM), and the result are in agreement with the experimental results given by Camarda (1977). A transient analysis model was developed by Y. Cao and A. Faghri (1991) using 1D modeling of the vapour flow and 2D modeling of the wick and the heat pipe envelope. Empirical correlations were used to model the pressure drop of the vapour flow, which was assumed to obey Clausius-Clapeyron equation. Faghri and Buchko (1991) developed a 2D axi-symmetric model of the heat pipe, with the input heat flux and a convective and radiative boundary conditions being specified at the evaporator and condenser ends. Faghri and Harley (1994) have presented a transient lumped model of heat pipe which determines the average temperature of the heat pipe as a function of time. Tournier and El-Genk (1996) built a two-dimensional transient model to predict vapor flow in heat pipe and developed a code named HPTAM to investigate the startup of a radiatively cooled sodium heat pipe from a frozen state, and the model predictions are compared with experimental data given by Faghri et al. (1991).Zuo and Faghri (1998) have presented a simplified model wherein the flow of vapour was not modeled; rather the heat pipe was examined from a thermodynamic cycle point of view. Tournier and El-Genk (2003) used HPTAM to simulate the startup transient of the lithium–molybdenum heat pipe and compared the model’s results with experimental measurements given by Reidet al. (1999). Legierski et al. (2006) conducted a study on the modeling and measurements of heat and mass transfer in heat pipes using the FLUENT commercial code for micro heat pipe. Carbajal et al. (2006) have presented the analysis of a flat heat pipe with a concentrated heat source, relevant for use in reentry vehicles. Alizadehdakhel et al. (2010) studied a gas/liquid two-phase flow and the simultaneous evaporation and condensation phenomena by using the volume of the fluid model (VOF) technique in a thermosyphon using FLUENT code.

Figure 1: Schematic of a conventional heat pipe with principle of operation [16]

From the investigations above, due to the rapid development of heat pipe technology and its remarkable advantages, the application of heat pipe to nuclear engineering becomes more and more achievable. Also it is clearly observed that most of the investigations (numerical analysis) have been reported in the literature developed the code for the whole for predicting the liquid and vapor velocities and temperature profile in the evaporator and condenser sections. However no numerical analysis has been made to predict the liquid and vapor velocities in the evaporator and condenser sections and temperature profile by providing the appropriate boundary condition by source term as well as in the form of user defined functions (UDFs) in the commercially available software, so

Thorium Energy Conference 2015 (ThEC15) October 12-15, 2015, Mumbai, India

that parametric study of different geometry as well as different process parameter can be study. Also the effect of heat input on the axial wall temperature distribution, axial velocity profile, system pressure variation and pressure drop in the liquid/vapor interface are studied.

2.1. BASIC DESIGN CALCULATION FOR THERMOSIPHONS

The initial design of the heat pipe is carried out by means of a user friendly in-house computer code HPDATA. The code has two modules, a computational backend and a GUI (Graphical User Interface) front end. The user can carry out various types of analysis, like one point calculation, parametric analysis to optimise the design by changing various parameters of heat pipe, wick, evaporator and condenser. A similar code TSDATA was developed for design of thermo siphons. Both heat pipe and thermosyphon are subject to some operating limits. These are viscous limit, sonic limit, entrainment limit, capillary limit, and boiling limit. An outline of each limit is presented below, for details please refer to (Dunn & Reay, 2006). The viscous limit arises when the vapour pressure of the working fluid at the evaporator region is very low and thus very less pressure differential between the evaporator region and the condenser region to overcome the viscous and gravitational forces. The sonic limit occurs at high heat fluxes, when the velocity of the vapour may approach the sonic velocity. Under this condition, the compressibility of the vapour flow become important, and limits the flow velocity for the vapour. The entrainment limit arises when droplets of the liquid phase get entrained in the vapour phase, thus preventing their return to the evaporator end and hence limiting the heat transfer. In heat pipes, the capillary limit arises when the capillary force generated in the wick is unable to return the liquid phase to the evaporator section. In case of thermosiphons, this effect will not apply, but the gravitational head has to overcome the pressure drops in the vapour and liquid phases. Additional limit arises when the critical heat flux values for boiling heat transfer are approached which leads to the boiling limit. The flooding limit is based on the Kutateladze number. Correlations from Tien and Chang, 1979; Imura et. al., 1983 and Groll and Rosler, 1989 have been used in the program. These have been listed below.

[1] Tien and Chang, 1979 For ≥ 30

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)/(),(32)(1 eeBoBo ldfffKu ϕ= (4)

1f is a function of the Bond number and is presented in the form of a graph in Dunn and Reay,

2006 and Groll, 2006. 2f is a function of dimensionless pressure and expressed by the following correlation:

17.02

−= PKf for 4104×<PK

165.02 =f for 4104×≥PK (5)

Where:

Thorium Energy Conference 2015 (ThEC15) October 12-15, 2015, Mumbai, India

5.0)( σρρ vl

VP g

PK−

= (6)

is a function of inclination angle, the values of which are presented graphically in Dunn and Reay, 2006 and Groll, 2006. Its value is unity when the thermosiphon is operated vertically.

For estimating the sonic limit correlation provided in Dunn & Reay, 2006 was utilized. 5.0)(474.0 vvPLq ρ×=& (7)

The correlations given by Gorbis & Savchenkov, 1972 for the boiling limit were used.

The predictions from the code using these correlations were compared against some experimental data as shown in Figure 2 & 3.

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10

20

30

40

50

60

70

Lim

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10

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Internal diameter (mm)

Flooding (Tien and Chang, 1979) Flooding (Imura et. al., 1983) Flooding (Groll and Rosler, 1989)

Sonic limits and boiling limitsare very high

Figure 2: Parametric output from TSDATA with variation of evaporator side temperature. Experimental data (solid squares) by Nakano et. al.,1998

Figure 3: Parametric output from TSDATA with variation of internal diameter of thermosiphon. Experimental data (solid squares) by Nakano et. al.,1998

The effect of variation of the internal diameter of the thermosiphon at the reference temperature on the limiting heat flow is shown in Figure 2. As compared to the flooding limit, the sonic and boiling limits are very high and thus not performance limiting. As expected, for the flooding limit, there is a wide variation in results. For the reference diameter of 50 mm, this ranges from 30 kW to 65 kW. This is well above the required capacity of 6 kW. The results seems to suggest for the present purpose, the internal diameter of the thermosiphon may be reduced to 25 mm, although the implications on pressure drop vis-à-vis gravity head needs to be checked. Reducing the operating temperature will have a direct implication on the reliability of the thermosiphon, as it reduces the severity of material related issues like corrosion and creep resistance. However, the operating performance of a heat pipe or a thermosiphon with sodium as a working fluid is expected to decrease. To asses this, a parametric case was studied considering change of the evaporator temperature, keeping the inner diameter at its reference value. The results are shown in Figure 3. 2.2. BASIC DESIGN CALCULATION FOR HEAT PIPES For heat pipe limitation various correlations is used as given in (Dunn & Reay, 2006). The minimum axial heat flux due to the sonic limitation will occur at the minimum operating temperature, 6000 C. The entrainment limit is evaluated at the highest operating temperature, 8000 C. Boiling in the wick may result in the vapour blocking the supply of liquid to all parts of the evaporator. It is therefore desirable to have a working fluid with a high superheat T to reduce the chance of nucleation. For that for boiling point limitation degree of super heat is calculated. The requirement of this heat pipe necessitates the ability to dissipate the heat through condenser by

Thorium Energy Conference 2015 (ThEC15) October 12-15, 2015, Mumbai, India

convection and radiation. The heat pipe may reach 900 0C at condenser and therefore vapour pressure is important in determining the wall thickness. For different inclination the mass rate is different due to gravitational effect. For vertical direction (case 1) with evaporator is below the condenser (at 00 C) like in thermosyphon. But in other case gravity is either neglected or opposing the capillary pressure. So limitation is less than case 1. For various limitations and the correlation used are shown in the table given below.

Limiting Value Correlation used

Sonic Limit 50.169653 KW/cm2 = 2( + 1)

Entrainment Limit 54.285184 KW = 2

Boiling Limit(0 super heat) 136.8046194 K ∆ = 3.06

Wall Thickness 0.16196507 mm t = Pr /S

Capillary Limit (case 1) 10.85645239 KW = 2 cos − sin

(case 2) 7.836716 KW (case 3) 4.816980175 KW

Table 1: Heat transfer limitation of heat pipe 3. SIMPLIFIED MODEL OF HEAT PIPE A simplified model was developed, which makes use of finite element method to model the normal operation of the heat pipes. This model can be readily incorporated into existing FEM codes and can therefore be readily utilised to model entire system. From [Dunn & Reay, 2006], it is evident that the most important contribution of the resistances for heat transfer is due to the conduction through the walls and wick of the heat pipe (at the evaporator and condenser regions). The resistances (and hence temperature drops) attributable to heat flow due to transport of either vapour or liquid phase, or phase change from liquid to vapour phase is minor in comparison. Since, modeling of the conduction behavior is relatively straight forward; it provides an easy and computationally inexpensive way to carry out detailed thermal analysis at a system level. Based on the above discussion, a 3D conduction heat transfer model was created using a general purpose FEM (Finite Element Method) code. The model is schematically shown in Figure 7. As the heat pipe is symmetric in both XZ as well as YZ plane, quarter symmetric model is taken for analysis. The wick is modeled using conduction heat transfer only using an effective heat transfer considering the porosity of the wick as described in [Faghri, 1995].The effective thermal conductivity of the wick is calculated as per equation 8. k = k (k + k ) − (1 − ε)(k − k )(k + k ) + (1 − ε)(k − k )

(8)

A temperature dependent model was used, for which the variation of effective conductivity of the wick with temperature was calculated beforehand. The thermal resistance attributable to the liquid-vapour interface is negligible compared to other resistance, hence the nodes on the vapour side are assumed to be at the vapour temperature. Further, the temperature drop due to drop in pressure due to vapour flow will be negligible, hence the temperature degree of freedom of all nodes in the vapour sides are coupled together i.e. all the nodal temperature of vapour nodes are uniform. Adiabatic boundary conditions are given to the bottom surface and symmetric surfaces of the quarter model. In the condenser region along with top surface of the heat pipe wall convective boundary condition is given with 69.67 W/m2K effective heat transfer coefficient (including radiation heat transfer). In the adiabatic region of heat pipe loss of heat transfer through insulation is also accounted by giving heat loss through convection with effective heat transfer coefficient. In the evaporative region heat flux input boundary condition is given. For this model ambient temperature is assumed as 35 0 C. The steady state solution to this model using open-source and commercial FEM codes is straight forward.

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Thorium Energy Conference 2015 (ThEC15) October 12-15, 2015, Mumbai, India

Sodium Vapour

Specific heat Linear with respect to temperature Density 0.05998 kg/m3

Viscosity 2211× 10 N-s/m2

Sodium Liquid(Wick)

Latent Heat 4026× 10 J/kg Thermal conductivity of

the wick User Defined Function as per equation

Specific heat Linear with respect to temperature Density 784.56 kg/m3

Table 2: Thermo physical properties of heat pipe 4.2. Assumptions for heat pipe simulation

The following assumptions have been made before writing the governing equations 1. The vapour flows are considered to be laminar. 2. The vapor is considered to be saturated at t = 0 (time). 3. All thermo physical properties are assumed constant except for the vapor density, which is

computed from the operating pressure and specific heat which is linear with respect to temperature.

4. Wick is assumed as a solid with effective thermal conductivity of sodium liquid and steel, because conductivity is high for molten metal (sodium) and by maintaining the capillary limitation during calculation.

5. Three dimensional quarter symmetry heat pipe is taken because of similar BCs on both side and model in parallelepiped geometry.

6. The initial temperature and pressure is assumed as follows: T(x, y, 0) = Ti (973 K) and Pop (t=0) = PSAT (Ti) =15000 Pa

4.3. Computational domain In the present study the computational domain (Figure 10) is meshed using commercial software. As heat pipe is symmetry both in x direction as well as in z direction at centre plane, so only quarter of the heat pipe is modeled. In the y direction, 800 cells are used in the wall, wick and vapor region of the model. In the x and z direction, 3 and 2 cells are used in the wall and wick respectively for both side of the vapor. In the vapor region 20 cells are used in the x and z direction as in vertically the length of one cell is 0.0005 m and in other directions lengths are 0.0002 m. 4.4. Governing equations

Laminar, incompressible three dimensional equations are solved in the vapour region of the heat pipe. The computational domain consists of vapour core, the wick and the walls of the heat pipe as shown in Figure 9. Based on the above assumptions, the following governing equations are formulated and given below. The continuity equation for the vapour core is ( ) + ( ) + ( ) + ( ) = Г (11)

Flow continuity nearest cell of the liquid vapour interface volumetric mass source term added by user defined function (UDF) , which will be compiled along with each iteration. Mass source term, Г = = (12)

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+ + + = − + + + + (14)

+ + + = − + + + + + Г (15)

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Thorium Energy Conference 2015 (ThEC15) October 12-15, 2015, Mumbai, India

At the end caps (y=0 and y=Lt (400 mm)), the vapour velocity is zero due to the no-slip condition, and the temperature gradient is zero since he end caps are adiabatic. = = = = 0 (23)

The heat pipe is symmetric about center plane both in x as well as in z direction, so the axial velocity along x and z direction, and the axial velocity gradients and temperature gradients are zero at the symmetry plane. = = = = 0 (24)

4.6. Wick-vapour interface boundary conditions Change of phase from liquid to vapour is assumed to occur at the wick-vapour core interface(x = xv, z = zv) (Figure 9). The interface temperature Ti is obtained from an energy balance at the interface − = − + ℎ (25)

= + + ℎ / + (26)

Here, mi < 0 denotes evaporation and mi > 0 denotes condensation. The interface pressure Pi is obtained from the Clausius-Clapeyron equation, with P0 and T0 being reference values: = (27)

The interface mass flux is calculated using kinetic theory of gases: = 22 − 2 − (28)

The above expression has been obtained with the assumption that the mean evaporation coefficient is equal to the mean condensation coefficient, where their variation with temperature and pressure may be assumed to be small [16]. The value of accommodation coefficient in the above expression for evaporation mass transfer rate has been observed to vary over four orders of magnitude[24]. however as per various literature experimental value of accommodation coefficient have been taken in between 0.02-0.04, so for this case the value of is taken as 0.03.

4.7. Computation of operating pressure in the vapor core To allow the system pressurization under steady state assumption, the system pressure term is split into two components.

P = + (29) Here is the hydrodynamic pressure component. The system pressure with respect to time is computed using the ideal gas law and overall mass balance in the vapor core as given below: = + ∆ ∑ / −∑ (30)

,where is the volume of computational cell and TP is the temperature at the center of the computational cell. in the above equation is interfacial evaporation/condensation mass flow rate and can be written as: = 22 − √2 + − (31)

, where and are the hydrodynamic pressure and temperature in the vapor cell adjacent to the wick–vapor interface. 4.8. Computation of vapor densities

Thorium Energy Conference 2015 (ThEC15) October 12-15, 2015, Mumbai, India

The vapor density at a cell is computed from the system pressure as with the incompressible flow assumption: = (32)

A doubled precision code was used in commercial CFD software to perform numerical computation. A fully implicit finite volume method was used to discretize the governing equations and the boundary conditions with staggered mesh. The SIMPLE algorithm was used for pressure and velocity coupling. Under-relaxation method was also applied to damp the sharp gradient and improve the convergence process. Under-relaxation method was applied to temperature variables(0.7), velocity variables(0.35), pressure variables(0.3) and mass transfer at the interface(0.001) respectively. A time delay method was used to calculate the density in the vapour core correspondingly apply the source term. Relative errors are considered as the convergence criteria − ∗ ≤ 10 (33)

,where mj and mj* are interface mass flow rate at current and previous time step. 5. RESULTS AND DISCUSSION The 3-D formulation of the problem was described in Section 5.Numerical analysis is performed by solving the governing Equation (11)-(19) with the boundary conditions (Equation (20)-(24)). Mass and momentum source is given at the wick-vapour interface by calculating mass flow rate(Equation (25)-(28)). The operating pressure of the heat pipe is calculated using Equation (30). Computations are carried out for the heat pipe with the input heat flux of 40 KW/m2. As the computational domain described, one can be seen that the aspect ratio of the entire domain is 31.9 (40 cm/12.535 mm), which is large. Therefore, in order to be able to see the results in 3d, the figures are magnified 10 times larger in the x & z directions and the same method has been followed for the rest of the figures. 5.1. Temperature distribution along the vapour region In CFD simulation the heat pipe is simulated in steady state. After 25 second with time step 0.05 sec the heat pipe is in constant temperature difference of about 22 0C at the surface of heat pipe. Temperature distribution along heat pipe in the surface wall where temperature has measured in experimental setup in evaporator region, adiabatic region, and condenser region respectively is shown in Figure 11. Further the simulation can be optimised by modifying parameters which are assumed as constant and taken from literatures. In Figure 12 radial temperature distributions at the centre line of mid adiabatic plane, mid condenser plane, mid evaporator plane is shown, in which at the interface region the temperature drop clearly indicates the evaporation and condensation phenomena.

Figure 11: Comparison between experimental results & CFD analysis after 14 hrs of operation

Figure 12: Lateral temperature distribution at mid planes of various regions

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2 0 2 4 6 8

10 12 16

ic

Thorium Energy Conference 2015 (ThEC15) October 12-15, 2015, Mumbai, India

the evaporator region vapour pressure drop is due to acceleration of inflow vapour velocity and viscous loss at interface and in condenser region pressure recovery is due to deceleration of vapour velocity. Density variation in the vapour region which is calculated in user defined function as Pop/RT, which is reversely proportional to vapour temperature. 6. CONCLUSION The initial design of high temperature thermosiphons and heat pipe based on estimation of operational limits as predicted by correlations available in open literature has been presented. It is noted that these correlations have not been validated against liquid metals for use in high temperature thermosiphons. Simplified FEM analysis of heat pipe was carried out neglecting heat loss in the vapour region as well as vapour liquid interface, and the result shows the similar temperature pattern with little accuracy. Detailed numerical analysis was carried out for estimating the performance of heat pipe. For simulation of vaporization and condensation phenomena at the vapour-liquid interface user defined functions were incorporated in the commercial CFD software. Further by modeling liquid porous wick of heat pipe which can be used to predict liquid flow behavior. NOMENCLATURE

u x directional velocity (m/s) Symbols:v y directional velocity(m/s) porosity P pressure (Pa) density (kg/m3) K permeability (m2) viscosity (Nm-s)

CE Ergun coefficient wire C specific heat (J/kg K) accommodation coefficient k thermal conductivity (W/m-K) T temperature (K) N number of layers Subscriptsd diameter (m) eff effective q heat flux (W/m2) s solid L length (m) l liquid h heat transfer coefficient (W/m2-K) m mean x axial distance (m) i interface A area (m2) e evaporator

mass flow rate (kg/s) a adiabatic mass flux (kg/m2s) c condenser, capillary

molecular weight (g/mol) w wick, wall M mass (kg) v vapor R gas constant (J/kg-K) o stagnation R Resistance (oC/W) op operating hfg heat of vaporization (J/kg) sat saturation

velocity vector (m/s) P center of the computational cell Vcell volume of the cell (m3) Superscripts:

t time (s) 0 Old value r wire radius (m) * Previous iteration value

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Thorium Energy Conference 2015 (ThEC15) October 12-15, 2015, Mumbai, India

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