Nuclear Engineering and Technology 52 (2020) 2107e2118
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Nuclear Engineering and Technology
journal homepage: www.elsevier .com/locate/net
Original Article
Performance analysis of S-CO2 recompression Brayton cycle based onturbomachinery detailed design
Yuandong Zhang a, Minjun Peng a, Genglei Xia a, *, Ge Wang b, Cheng Zhou b
a Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin, 150001, Chinab Beijing Institute of Control and Engineering, Beijing, 100000, China
a r t i c l e i n f o
Article history:Received 6 November 2019Received in revised form8 February 2020Accepted 24 February 2020Available online 28 February 2020
CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction
The supercritical carbon dioxide (S-CO2) Brayton cycle was firstproposed by Feher [1] in the 1960s, but was not fully developed inview of the limitations of the industrial technology at the time.Recently, the S-CO2 energy conversion system has regained atten-tion due to the recompression Brayton cycle (shown in Fig. 1)proposed by Dostal et al. [2] and the technological breakthroughs ofrelated equipment. The application feasibility of S-CO2 recom-pression Brayton cycle in different fields such as coal-fired [3], solar[4] and nuclear power generation [5] has been widely studied dueto its advantages in simplicity, compactness, security and economy.In the field of nuclear power, the S-CO2 recompression Braytoncycle is one of the promising candidate energy conversion systemsfor Generation IV reactors. The S-CO2 Brayton cycle can reduce thecompression work and the volume-to-power ratio utilizing the
arbin Engineering University,rovince, China.
by Elsevier Korea LLC. This is an
supercritical fluid thermophysical properties at the critical pointshown in Fig. 2, which makes the turbomachinery miniaturizationand meets the demand of special applications such as in aerospaceand ships. Meanwhile, the usage of S-CO2 as working fluid canachieve high energy conversion efficiency at modest reactor outlettemperature (e.g., ~45% at 550 �C) [6], which can reduce the CO2corrosivity to ensure the long-term operational safety of theequipment and system.
The S-CO2 Brayton cycle mainly includes heat source, turbo-machinery (compressor and turbine) and heat exchangers (recu-perator and precooler). Among them, turbomachinery as theimportant work equipment is critical to the efficiency of the cir-culatory system. Up to now, scholars have carried out a series ofstudies on the S-CO2 Brayton cycle system and turbomachinery.Crespi et al. [7] and Ahn et al. [8] summarized the different layout,application object and technology development status of S-CO2Brayton cycle respectively. They believe that the S-CO2 Braytoncycle with different layouts can achieve an average thermal effi-ciency of 40% and even 50e60% under higher design parameters,which makes it stand out in a variety of applications such as fossil,
open access article under the CC BY-NC-ND license (http://creativecommons.org/
Ns specific speedDs specific diameterN revolution speed [rpm]Q volumetric flow rate [m3/s]DH enthalpy rise [J/kg]Dc impeller tip diameter [m]C velocity [m/s]W relative velocity [m/s]u angular velocity [rad/s]r radius [m]d diameter [m]G mass flow rate [kg/s]r density [kg/m3]H mechanical work [J]h enthalpy [J/kg]s entropy [J/K]T temperature [K]P pressure [MPa]
h efficiencyrsplit recompressed fractionQ reactor power [W]Cp specific heat [kJ/(kg$K)]ε recuperator effectivenessg pressure ratio
Subscriptsin inletout outletmin minimum valuemax maximum valuemc main compressorrc recompressing compressort turbineHTR high temperature recuperatorLTR low temperature recuperatorh hot side of recuperatorc cold side of recuperatord minimum temperature difference
Fig. 1. Layout of S-CO2 recompression Brayton cycle.
Fig. 2. S-CO2 thermophysical properties near the pseudocritical temperature at 8 MPa[20].
Y. Zhang et al. / Nuclear Engineering and Technology 52 (2020) 2107e21182108
nuclear or renewable fuels. Wang et al. [9] compared the perfor-mance of the S-CO2 Brayton cycle with different layouts includingsimple recuperation cycle, recompression cycle, precompressioncycle, intercooling cycle, partial-cooling cycle, split expansion cycleand so onwhen integratedwith the solar power tower system. Eachlayout of S-CO2 Brayton cycle demonstrates high efficiency, but stillfaces some challenges. Therefore, Wang thinks a novel S-CO2 cycle
layout with high efficiency, large specific work, and wide temper-ature difference needs to be built to solve the problems of relativelysmall specific work and narrow temperature difference across thesolar receiver. Ma et al. [10], Sarkar and Bhattacharyya [11], andSong et al. [12] analyzed the effects of key system design parame-ters on S-CO2 Brayton cycle performance when given the constantturbomachinery efficiency. Deng et al. [13] and Zhang at al [14].proposed the design optimization of S-CO2 Brayton cycle, whichwere also based on parametric analysis with constant turbine ef-ficiency. In the study of S-CO2 turbomachinery, the thermophysicalproperties near the critical point shown in Fig. 2 pose challenges tothe design and analysis of S-CO2 turbomachinery, especiallycompressor. Turbomachinery design methods based on ideal gasassumption are not applicable for S-CO2 compressor due to thesharp variation of properties. Hence, a revised methodology whichshould be devoid of ideal gas assumption is required for accuratedesign and analysis of S-CO2 compressor. Compared with thecompressor design, the SCO2 turbine design is easier resulting fromthat its operating conditions are far away from the critical point andthe thermophysical properties are almost constant. Lee et al. [15]developed the S-CO2 turbomachine design and analysis code forthe water-cooled small modular reactor application. And a config-uration with multiple shafts was proposed to replace the singleshaft configuration for increasing the design flexibility and system
Y. Zhang et al. / Nuclear Engineering and Technology 52 (2020) 2107e2118 2109
safety. Luo et al. [16], Zhou et al. [17] and Liu et al. [18] realized thegeometry design of S-CO2 turbomachinery by one-dimensionalmethod and utilized CFD to analyze the local flow field character-istics. In addition, Tang et al. [19] completed the optimizationdesign and performance prediction for S-CO2 compressor based onsimulated annealing algorithm.
It can be found that despite several research works on the S-CO2Brayton cycle performance have been already carried out, thesestudies were limited to the premise of given constant equipmentefficiency. However, the efficiency of equipment, especially that ofturbomachinery, will change when matched with different systemdesign parameters and thus affect the performance of the circula-tory system. Moreover, the special thermophysical properties ofsupercritical fluids make the turbomachinery operating character-istics more complex than that of traditional working fluids. Thetraditional design methods and calculation models adopted to datehave great limitations in S-CO2 turbomachinery because of theideal gas assumption. Meanwhile, the one-dimensional design andCFD local flow field analysis of S-CO2 turbomachinerymostly stay atthe equipment level. And there was no in-depth discussion aboutits coupling characteristics with circulatory system, which is notconducive to obtain the turbomachinery performance re-quirements and Brayton cycle design guidance. Therefore, theprevious research needs to be further improved to more accuratelyconsider the effects of turbomachinery performance on the S-CO2
Brayton cycle coupling characteristics under different designconditions.
Based on above description, an in-house code was developed inthis paper to realize the geometric design and performance pre-diction of S-CO2 turbomachinery, and was coupled with systemcode for S-CO2 Brayton cycle characteristics analysis. The calcula-tion results of the developed code were compared with theexperimental data to verify the accuracy of the calculation modelsand process. The influence of different key design parameters onperformance of S-CO2 recompression Brayton cycle was investi-gated based on the detailed design of turbomachinery. Besides, therelevant impact mechanisms are discussed through various defi-nitions and dimensionless parameters.
2. Calculation methods and models
This chapter starts with the description of the 1-D mean linecalculation methods and models for the radial compressor andturbine. After that, the thermodynamic models for each equipmentand the system characteristics analysis process of S-CO2 recom-pression Brayton cycle are delineated. In addition, the thermo-physical properties of S-CO2 required in calculation are derivedfrom NIST Standard Reference Database 23 [20].
Fig. 3. Turbomachinery meridional view.
2.1. Radial compressor
Fig. 3(a) presents the meridional view of radial compressor. Therotating impeller driven by the shaft from turbine imparts kineticenergy to the flow when the S-CO2 enters the compressor. Then indiffuser, the kinetic energy of S-CO2 is converted into the increasein pressure. At last, the high pressure S-CO2 leaves the compressorthough the volute.
The design and analysis process of compressor includes threeparts: 1) preliminary calculation, 2) geometric design and 3) per-formance prediction. The preliminary calculation is based on thedesign objective and the traditional empirical chart method. Thegeometric design completes the detailed design of the impeller andthe calculation of velocity triangle by initial geometric input pa-rameters and models. The loss models are used in performanceprediction to analyze the characteristics of compressor designedpreviously. The detailed 1-D mean line design and analysis meth-odology is illustrated in Fig. 4.
2.1.1. Preliminary calculationThe Balje's Ns-Ds diagram method [21] was applied to the pre-
liminary calculation of radial compressor. The efficiency of radialcompressor was depicted by two dimensionless parameters, i.e.specific speed (Ns) and specific diameter (Ds), in Ns-Ds diagram. TheNs and Ds were defined as
Ns ¼ NffiffiffiffiQ
p
DH0:75 (1)
Ds ¼DcDH0:25ffiffiffiffiQ
p (2)
It is found that Ns and Ds is related to the revolution speed ‘N’,volumetric flow rate ‘Q’, thermodynamic enthalpy rise ‘DH’ andimpeller tip diameter ‘Dc’. Therefore, based on the optimal range ofNs (0.6e0.77 for radial compressor [22]), the appropriate revolutionspeed can be determined by iterative computation, and then Ds canbe calculated by Cordier's equation (3) as
Ds;compressor ¼2:719N�1:092s;compressor (3)
2.1.2. Geometric designGeometric design serves as an important link between the
preliminary calculation and the performance prediction. Perfor-mance prediction can only be carried out after the completion ofgeometric design computed by initial parameters and geometricmodels. Geometric design can be divided into impeller volute,diffuser and impeller in compressor. This paper only gives briefintroduction of this process because of the length.
Velocity triangles should be briefly mentioned when introducingthe 1-D mean line calculation approach for geometric design. Thevelocity trianglesof the impeller inlet andoutlet are calculated for theflow angles and velocities. The relationship and symbols of impellerinlet and outlet velocity triangles are defined in Fig. 5.
The S-CO2 enter the compressor with a velocity C1. The relativevelocity W1 and flow angle b1 at the inlet can be calculated. Theimpeller tangential velocity U1 is computing by
where u, r1h and r1s is angular velocity, hub radius and shroudradius, respectively.
Fig. 4. 1-D mean line design and analysis methodology.
Fig. 5. Impeller velocity triangles.
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In the outlet, the impeller tangential velocity U2 is calculated byimpeller outlet radius r2 and angular velocity u as Eq. (4). The ab-solute velocity C2r is estimated using continuity equation given by
C2r ¼GS�CO2
�ðr2A2Þ (5)
where A2 is the area at impeller outlet.The absolute fluid velocity C2 at impeller outlet is combined
effect of radial velocity C2r and tangential velocity C2u given by
Therefore, the full velocity triangle at impeller outlet can beobtained according to the above parameters.
1-D mean line calculation approach based on the geometricmodels of radial compressor and governing equations is performedin geometric design. The related theoretical calculations aredescribed below.
The mass flow G is constant when flowing through any sectionsof the compressor, so the mass flow satisfies Eq. (8):
C¼GS�CO2
�ðrAsinaÞ (8)
The energy transmitted from rotation to the fluid is calculatedby Euler equation:
H2 �H1 ¼ U2C2w � U1C1w (9)
And the last is energy equation:
Hþ q ¼ H2 � H1 þ�C22 �C1
1
�.2 (10)
where H and q is mechanical work and energy exchange betweenfluid in compressor and the outside, respectively.
2.1.3. Performance predictionThe irreversible losses in the impeller of compressor are calcu-
lated by loss models, which updates the initial assumed efficiencyuntil convergence. Meanwhile, the off-design performance ofcompressor is also predicted. Nine loss models classified into in-ternal and external loss models are considered in this paper forperformance prediction of compressor as shown in Table 1. Spe-cifically, the internal loss models quantify the irreversible losses ofthe fluid when passing through the impeller. And the externallosses quantify the non-isentropic loss occurring outside theimpeller.
2.2. Radial turbine
Fig. 3(b) presents themeridional view of radial turbine. Contraryto the working principle in compressor, S-CO2 enters the radialturbine through the nozzle where the fluid obtains an optimumangle. Then the fluid imparts torque to the rotating shaft and theexpanded gas exits the turbine axially.
Consistent with the design process of radial compressor, threeparts including 1) preliminary calculation, 2) geometric design and3) performance prediction constitute the complete design andanalysis process of the radial turbine. However, the design of tur-bine is easier than that of compressor resulting from that S-CO2working in turbine is far away from the pseudocritical regionwherethe thermophysical properties of S-CO2 change smoothly.
2.2.1. Preliminary calculationThe preliminary calculation is applied to estimate the stages and
rotor diameter (Dt) based on the Balje'sNs-Ds diagram. The revolution
Table 1Loss models for radial compressor.
Loss mechanism Loss correlations Ref. Property
Incidence loss DHinc ¼ fincW1u=2 (11)finc ¼ 0:5e0:7 (12)
Recirculation loss DHrc ¼ 8� 10�5 sinhð3:5a32ÞD2f U
22 (31) Oh [28]
Mixing lossDHmix ¼
C22
2þ 2tan2a2
�1� εwake � b3=b2
1� εwake
�(32)
Johnston [29]
Y. Zhang et al. / Nuclear Engineering and Technology 52 (2020) 2107e2118 2111
speed(N)hasbeendetermined incompressorpreliminarycalculationdue to the coaxial design of turbomachinery. The equations of specificspeed (Ns) and specific diameter (Ds) are calculatedbyEqs. (1) and (2).The difference is that the optimal range of Ns for radial turbine is0.4e0.7 and the specific diameter Ds is computed by
Ds;turbine¼ 2:056N�0:812s;turbine (33)
2.2.2. Geometric designThe geometric design is carried out by 1-D mean line design
method to determine the rotor velocity triangles, the rotor geom-etry and the nozzle geometry. The principle and governing equa-tions adopted in geometric design of turbine are similar to those ofthe compressor design, so no further description is given.
2.2.3. Performance predictionFour loss models are chosen for calculating the enthalpy losses
occurring the turbine. The efficiency of turbine will update the ef-ficiency given initially until convergence. Meanwhile, the off-design performance of turbine can also be obtained if necessary.The loss models used in this paper for turbine design are intro-duced in Table 2.
2.3. S-CO2 recompression cycle
2.3.1. Layout of recompression cycleThe S-CO2 recompression cycle which has potential for high
efficiency and simplicity is chosen for performance analysis. Fig. 1presents the layout of a reactor system coupled with direct S-CO2
recompression cycle. The efficiency of this cycle is improved byintroducing a recompressing compressor which can also avoid thepinch-point problem in the recuperator caused by the varied S-CO2thermophysical properties. As shown in Fig. 1, the working fluidenters the turbine to generate power after heated in the reactor(4 / 5/6). The energy of exhaust gas is recovered via high tem-perature recuperator (HTR) and low temperature recuperator (LTR)(6/ 7/8). The working fluid then splits into two parts before theprecooler. One part of working fluid is cooled through the precoolerand compressed in main compressor (8 / 1/2). The other part iscompressed to a higher temperature and pressure directly inrecompressing compressor (8 / 3) which reduces the heat rejec-tion in precooler. The working fluid at the outlet of maincompressor flows through the LTR and merges with the other partof working flow at the recompressing compressor outlet (2 / 3).The combined working fluid is preheated in the HTR and returns tothe reactor for a complete energy conversion system cycle (3 / 4).
Y. Zhang et al. / Nuclear Engineering and Technology 52 (2020) 2107e21182112
2.3.2. Thermodynamic modeling and calculation methodologyThe computational models andmethodology for performing the
desired cycle analysis are introduced in this part. The description ofthe equipment modeling such as turbomachinery and heat ex-changers is addressed. And the integration of the equipmentmodels and detailed design of turbomachinery discussed aboveinto the cycle calculation is presented.
The modeling principle of turbine is similar to that ofcompressor. Themain input parameters for turbomachinery are theinlet fluid conditions, pressure ratio and an assumed efficiencywhich will be updated in subsequent detailed turbomachinerydesigns. The calculation procedure is the following:
sin¼ sout ¼ f ðTin; PinÞ (49)
hin ¼ f ðTin; PinÞ (50)
Pout ¼ Ping (51)
hout;s ¼ f ðsout ; PoutÞ (52)
ht;out ¼�hout;s �hin
ht þ hin (53)
hc;out ¼�hout;s �hin
�hc þ hin (54)
Tout ¼ f ðhout ; PoutÞ (55)
where s and h is entropy and enthalpy. Subscript in, out, c and tdenotes inlet, outlet, compressor and turbine, respectively.
The heat exchanger calculates the inlet and outlet parametersbased on the energy balance. Meanwhile, the pressure drop of eachprocess in the system is obtained by a series of pressure losscoefficients.
Based on the thermodynamic models descripted above, a codefor S-CO2 recompression cycle analysis was developed followingthe calculation flowchart presented in Fig. 6. The code starts fromevaluating the main and turbine based on input parameters. Thenassuming a minimum temperature difference ‘Td’ which is usuallyset to 10 K in engineering design for preventing the pinch points inrecuperator, occurs in the LTR cold side. And the parameters of LTRand recompressing compressor can be calculated based on mini-mum temperature difference and energy balance. In the next step,the judgment is performed to determine the position of minimumtemperature difference. If it is not in the position assumed above, T8will be updated and calculation is iterated until temperature dif-ference of LTR equals to Td. After that, the parameters of HTR will becomputed and the mass flow rate can be calculated based on theenthalpy difference between inlet and outlet of reactor. Therefore,the necessary input parameters for the turbomachinery detaileddesign are all obtained and the efficiency of turbomachineryassumed previously will be updated by the result of detailed designuntil convergence. At last, the cycle efficiency is calculated based onthe following formulas:
Fig. 6. Flowchart of calculation for S-CO2 recompression cycle.
Table 3Compressor design and operating conditions in SNL.
Shaft speed (rpm) 75000 in design, 55000 in experiment
Inlet temperature (K) 305.30Inlet pressure (MPa) 7.687Mass flow rate (kg/s) 3.53Pressure ratio 1.8
Y. Zhang et al. / Nuclear Engineering and Technology 52 (2020) 2107e2118 2113
h¼Wt �
�1� rsplit
�Wmc � rsplitWrc
Q(56)
where W, Q and rsplit is work, reactor power and recompressedfraction, respectively. Subscriptmc and rc denotesmain compressorand recompressing compressor.
Fig. 7. Comparisons of calculated performance with the experimental data.
3. Model validation
The turbomachinery deigned and experimented by WrightSteven A et al. [34] in Sandia National Laboratory (SNL) wascalculated to verify the accuracy of the turbomachinery detaileddesign code. Meanwhile, the system experiment conducted byIverson Brian D et al. [35] was validated for the integrated code of S-CO2 cycle.
3.1. Compressor
The structural design and performance analysis of the SNLcompressor was completed based on its operating conditionsshown in Table 3. The comparisons between design results calcu-lated by code and actual structure are shown in Table 4. Meanwhile,due to the power limit of the experimental motor, the shaft speedwhich was designed to be 75000 rpm only reaches 55000 rpmduring the experiment in SNL. Hence, the design shaft speed of thecompressor in this paper was 75000 rpm and the performanceprediction was carried out under the experimental shaft speedcondition (55000 rpm). And the results of performance predictionare presented in Fig. 7. It can be seen that the code proposed abovecan implement the compressor geometry design accurately. Be-sides, the trends of off-design conditions performance predictionare consistent with that of experiment.
3.2. Turbine
Due to the lack of experimental data of S-CO2 turbine, only theenthalpy drops calculated based on the loss models were analyzedin the validation of turbine. Table 5 shows the comparisons ofenthalpy drop obtained in SNL experiment and calculated in codeunder different conditions. It can be found that the enthalpy dropcould be calculated by loss models, which is beneficial to perfor-mance prediction for turbine.
Table 6Verification of S-CO2 cycle integrated code.
Experiment Calculation
Compressor A efficiency (%) 36.3 43.9Compressor B efficiency (%) 61.9 62Turbine A efficiency (%) 79.1 84.1Turbine B efficiency (%) 84.6 89.7Outlet temperature of compressor A (K) 319.95 322.76Outlet temperature of compressor B (K) 342.65 342.68Outlet temperature of turbine A (K) 642.05 640.89Outlet temperature of turbine B (K) 642.05 640.94Cycle efficiency (%) 4.9 6.1
Fig. 8. Effects of recompressed fraction on cycle and turbomachinery efficiency.
Fig. 9. Effects of recompressed fraction on main compressor enthalpy loss.
Y. Zhang et al. / Nuclear Engineering and Technology 52 (2020) 2107e21182114
3.3. S-CO2 cycle
The S-CO2 cycle integrated code was validated by IversonBrian D et al.'s experiment. Due to the focus in this paper is S-CO2
recompression cycle performance analysis based on the detaileddesign of turbomachinery, only the efficiency of turbomachineryand part of key system parameters are verified. The experimentaldata are compared with results calculated by integrated code inTable 6. It can be found the error between turbomachinery effi-ciency designed based on the operating conditions and theexperimental data is acceptable. Meanwhile, the calculation re-sults of the key system parameters are very close to the experi-mental data.
4. Result and discussion
A comprehensive performance analysis of S-CO2 recom-pression Brayton cycle coupled with 5MWt reactor was carriedout, which is based on the detailed design of the turbomachinery,by the in-house code mentioned above. The effects of recom-pressed fraction, temperature, pressure and other parameters onthe characteristics of S-CO2 circulatory system were investigatedrespectively. Meanwhile, the reasons why those effects existwere explained by the S-CO2 thermophysical properties, theenthalpy drop and work of turbomachinery, the performance ofheat exchangers, and exergy destruction of each device in thesystem.
4.1. Effects of recompressed fraction
The characteristics of the S-CO2 recompression Brayton cyclewere analyzed under different recompressed fraction conditionsby given the maximum cycle pressure Pmax ¼ 20 MPa, minimumcycle temperature Tmin ¼ 305 K, heat source temperatureTmax ¼ 850 K and pressure ratio g ¼ 2.6. Fig. 8 shows the variationof cycle and turbomachinery efficiency with different recom-pressed fractions. The cycle thermal efficiency increases with therecompressed fraction gradually and reaches a peak when therecompressed fraction is about 0.4. After that, the cycle thermalefficiency decreases rapidly as the recompressed fraction con-tinues to increase. In addition, it can be found in Fig. 8 that the
compressor efficiency is more sensitive to the changes of recom-pressed fraction than that of turbine. The slow reduction of tur-bine efficiency results from the turbine loss increasing with themass flow required for cooling the reactor. Similarly, the efficiencyof compressors will decrease when the mass flow is large due tothe increase of skin and disk friction loss in Fig. 9. When the massflow of compressor is too small due to the unreasonable recom-pressed fraction, the occurrence of surge also reduces thecompressor performance and even jeopardizes its operation.,which is reflected in Fig. 9 as the increase of blade loading loss,recirculation loss and mixing loss. Therefore, the efficiency of thecompressors increases with recompressed fraction firstly and thendecrease. When the recompressed fraction is around 0.4, the ef-ficiencies of all turbomachineries are relatively high and the cyclethermal efficiency peaks.
The recycling heat by recuperators is crucial factor for high cycleefficiency. The recompressed fraction affects the performance ofrecuperators by changing its mass flow rate and fluid temperature.Recuperator effectiveness, defined as the ratio of actual heattransfer capacity to themaximum achievable heat transfer capacity,can explain the effect of the recompressed fraction on the heatexchangers. The recuperator effectiveness is calculated by Eq. (57)and (58) [36] and the results are shown in Fig. 10.
Fig. 10. Effects of recompressed fraction on heat exchangers performance.
Y. Zhang et al. / Nuclear Engineering and Technology 52 (2020) 2107e2118 2115
εHTR¼hCph;HTR �ðT6 � T7Þ
�i.h
min�Cph;HTR;Cpc;HTR
��ðT6 � T3Þ
i(57)
εLTR ¼hCph;LTRðT7 � T7Þ
�i.h
min�Cph;LTR; rsplitCpc;LTR
��ðT7 � T2Þ
i(58)
where ε, Cp and rsplit is recuperator effectiveness, heat capacity rateand recompressed fraction. Subscript LTR, HTR, h and c denotes lowtemperature recuperator, high temperature recuperator, hot andcold tube in recuperator, respectively. The number subscriptscorrespond to the positions in Fig. 5.
When recompressed fraction increases from 0 to about 0.4, theLTR effectiveness has little effect while the HTR effectivenessgradually increases and peaks. When the recompressed fractionexceeds 0.4, the HTR effectiveness slowly decreases. However, theLTR effectiveness decreases rapidly due to the shift of the minimumtemperature difference point from the cold side to the hot side.Therefore, the cycle thermal efficiency drops rapidly after slowlyreaching the peak.
In addition, the recompressed fraction also has a great influenceon the cooling power of the precooler. As increase of recompressedfraction, the mass flow rate through the precooler decreases andthe heat release to the environment is reduced. However, when therecompressed fraction greater than 0.4, the precooler temperaturerises rapidly due to the shift of the minimum temperature differ-ence point. Therefore, although the mass flow rate of the precoolercontinues to decrease, the heat release of the system is increasedand the cycle thermal efficiency is lowered due to the rapid rise ofthe inlet enthalpy.
4.2. Effects of temperature
The effects of temperature on S-CO2 recompression Braytoncycle performance was investigated when given the recompressedfraction rsplit ¼ 0.4, maximum cycle pressure Pmax ¼ 20 MPa andpressure ratio g ¼ 2.6. As the reactor outlet temperature increases,the cycle thermal efficiency is raised obviously in Fig. 11(a). How-ever, the rate of efficiency growth gradually decreases and theexcessively high maximum system temperature increases thecorrosiveness of carbon dioxide. The minimal temperature(304 Ke307 K) was set above critical point to avoid the cavitationconsequence in main compressor. As the compressor inlet
condition is near the critical temperature, the cycle performance isimproved while its growth rate is also gradually reduced. As thecompressor inlet condition is near the critical temperature, thecycle performance is improved whereas its growth rate is alsogradually reduced like the phenomenon that occurs when themaximum temperature increases continuously. However, differentfrom the effect of recompressed fraction, different temperatureshave little influence on turbomachinery efficiency as shown inFig. 11(b). That is because the temperature changes almost have noeffect on the mass flow rate when given the recompressed fraction,which results in no surge or high frictional losses. Fig. 11(c) can alsoprove that the different temperature conditions above mentionedhave little impact on turbomachinery performances. Comparedwith that of Fig. 9, the enthalpy losses, e.g. skin friction loss, diskfriction loss and mixing loss, change little with reactor outlettemperature when given Tmin ¼ 305 K. As a result, the turboma-chinery efficiency in Fig. 11(b) does not change significantly likethat in Fig. 8.
Fig. 11(d) illustrates the variations of turbomachinery powerwith maximum and minimum temperatures. The working fluidnear the critical point has low compressibility factor resulting thatthe main compressor requires less compression work than therecompressing compressor despite a larger mass flow rate in maincompressor, e.g. the main compressor compressionwork at 305 K isabout 75% of that at 306 K and 60% at 307 K. However, the mini-mum temperature dropping from 305 K to 304 K has little effect onthe compression work, which means that the design minimumtemperature does not need to be too close to the critical point forpreventing cavitation and transcritical operation. The increase ofreactor outlet temperature is beneficial to improve the expansionwork of turbine and reduce the compression work of the recom-pressing compressor slightly. At the same time, it can be also foundthat the reduction rate of the recompression work is graduallyslowed down and the compression work of the main compressorhardly changes. Therefore, the net work of the turbomachinery willincrease rapidly at first as the maximum temperature rises and theminimum temperature decreases. Nonetheless, due to the decreasein the rate of change in turbomachineryworkmentioned above, therate of increase in the net work of the turbomachinery also de-creases. And consequently, the trend of the cycle thermal efficiencyin Fig. 11(a) appears.
4.3. Effects of pressure
The effects of system pressure on cycle thermal efficiency wasstudied when recompressed fraction was 0.4, reactor temperaturewas 850 K andmain compressor inlet temperature was 305 K. Sincethe cyclic pressure drop loss is considered, the minimum andmaximum system pressures are located at the main compressorinlet and outlet, respectively. It can be seen in Fig. 12 that as theminimum pressure approaches the critical pressure, the systemefficiency gradually increases due to the sharp increase in density ofthe working fluid and the reduction in the required compressionwork. The increase of main compressor outlet pressure can alsoimprove the Brayton cycle performance while its growth rate isgradually slower, like the effects of maximum temperature.Therefore, excessive system pressure will not further promotesystem efficiency, but also bring risks to economic and operationalsafety. It is worth noting that, unlike trends of the other efficiencycurve, the Brayton cycle performance is poor under the condition ofminimum pressure Pmin ¼ 7.5 MPa, which is caused by the occur-rence of the minimum temperature difference point on the hot sideof the LTR. The transfer of the minimum temperature differencepoint causes the performances of the heat exchanger to drasticallydecrease and eventually affects the cycle efficiency, which is similar
Fig. 11. Effects of temperature on cycle and turbomachinery.
Fig. 12. Effects of pressure on cycle thermal efficiency.
Y. Zhang et al. / Nuclear Engineering and Technology 52 (2020) 2107e21182116
to the case where the recompressed fraction is too large (rsplit > 0.4in Fig. 8). In addition, similar to the effect of temperature, theturbomachinery efficiency does not change much due to the sub-stantially constant mass flow rate.
Exergy analysis can analyze the component irreversibility byquantizing the exergy destruction, which can explain the effects of
pressure on system performance [37,38]. The device level irre-versibility under different pressure conditions is indicated in Fig.13.Generally, the S-CO2 thermophysical property causes the device tohave less irreversibility when the minimum pressure is near thecritical point compared with the condition of Pmin ¼ 8.5 MPa. Sincethe operating conditions shown in Fig. 13 have similar pressureratios at the same Pmax, the irreversibility of turbomachinery varieslittle at two different minimum pressures. The irreversibility of LTRand precooler with smaller heat transfer power resulting from theflow split also changes little, while the irreversibility of the HTR andreactor with higher heat exchange power is more sensitive to thechange of the minimum pressure. With the reduction of the min-imum pressure, the irreversibility of the HTR and reactor decreasesby 13.5% and 28% respectively, in contrast with that of turboma-chinery is only reduced by about 5%. The increase in maximumpressure will slightly aggravate the irreversibility of turboma-chinery and low-power heat exchangers (LTR and precooler).However, the irreversibility of the reactor and HTR which haveLarge heat transfer power decreases with increasing maximumpressure. Therefore, it can be found from the comparison of theordinate values in Fig. 13(a) and (b) that the increase of themaximumpressure is beneficial to improve the irreversibility of thesystem and enhance thermal efficiency eventually. Meanwhile, theirreversibility sensitivity of reactor and HTR decreases with theincrease of the maximum pressure, causing the cycle thermal ef-ficiency to hardly increase in Fig. 13 when Pmax > 20 MPa. Inaddition, the irreversibility trend of heat exchangers under the
Fig. 13. Effects of pressure on device irreversibility.
Y. Zhang et al. / Nuclear Engineering and Technology 52 (2020) 2107e2118 2117
condition with Pmin ¼ 7.5 MPa is different from the other twoconditions. With the increase of the maximum pressure, the irre-versibility of heat exchangers increases rapidly, which is caused bythe transfer of the minimum temperature difference pointmentioned above. Therefore, when Pmin ¼ 7.5 MPa, the perfor-mance of Brayton cycle deteriorates greatly.
5. Conclusion
A comprehensive research on S-CO2 recompression Braytoncycle, a promising energy conversion system candidate for Gener-ation IV reactors, was performed based on the detailed design andanalysis of turbomachinery. An in-house code was developed torealize the turbomachinery geometric design, performance pre-diction and its coupling with system calculation code in this paper.The effects of key operating parameters on S-CO2 circulatory sys-temwere investigated and the corresponding influencemechanismwas discussed from a different perspective. The main conclusionsare listed in the following.
(1) The S-CO2 turbomachinery design and analysis ability ofdeveloped code in this paper was preliminarily validated.The resultant performance curve can be used as device in-puts for the subsequent system-level simulation calculations.
(2) The recompressed fraction affects the turbomachinery per-formance by changing the mass flow rate. The increase offriction loss when the mass flow rate is large and theoccurrence of surge when the mass flow rate is small willboth decrease the turbomachinery efficiency and deterioratethe system performance eventually. By contrast, the turbo-machinery efficiency is insensitive to variation in pressureand temperature due to the almost constant mass flow rate.
(3) The position of minimum temperature difference point iscritical to S-CO2 recompression Brayton cycle efficiency.When the minimum temperature difference point is locatedin cold side of the LTR, the change in system design param-eters will affect the energy conversion capability to a smallextent. However, the cycle performance is greatly degradedwhen the minimum temperature difference point is trans-ferred from the LTR cold side to the hot side.
(4) The thermophysical properties of S-CO2 near the criticalpoint greatly enhance the cycle efficiency. The increase ofdensity and decrease of compressibility factor cause lesscompression work required when the system minimumtemperature and pressure, i.e. the temperature and pressureat the main compressor inlet, are near the critical point. As a
result, the net output work of turbomachinery increases andcirculatory system performance is improved.
(5) The increase of the heat source operating parameters canreduce the irreversibility of the high-power heat exchanger(HTR and reactor) and thereby improve the cycle thermalefficiency. However, the growth rate of cycle efficiencygradually decreases and the excessive heat source parame-ters will introduce operational risks.
Conflict of interest statement
We declare that we do not have any commercial or associativeinterest that represents a conflict of interest in connectionwith thework submitted.
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