Hindawi

Science and Technology of Nuclear Installations

Volume 2020, Article ID 5945718, 16 pages
https://doi.org/10.1155/2020/5945718

Research Article
Supercritical CO2 Brayton Cycle Design for Small Modular
Reactor with a Thermodynamic Analysis Solver

Pan Wu ,1 Chuntian Gao,1 Yanping Huang,2 Dan Zhang,3 and Jianqiang Shan 1,4

1
School of Nuclear Science and Technology, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an, Shaanxi, China
2
CNNC Key Laboratory on Nuclear Reactor Thermal Hydraulics Technology, Nuclear Power Institute of China,
Chengdu 610041, China
3
Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China,
Chengdu 610041, China
4
The State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Correspondence should be addressed to Pan Wu; wupan2015@mail.xjtu.edu.cn and Jianqiang Shan; jqshan@mail.xjtu.edu.cn

Received 13 September 2019; Revised 25 November 2019; Accepted 26 December 2019; Published 24 January 2020

Academic Editor: Arkady Serikov

Copyright © 2020 Pan Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Coupling supercritical carbon dioxide (S-CO2) Brayton cycle with Gen-IV reactor concepts could bring advantages of high
compactness and efficiency. This study aims to design proper simple and recompression S-CO2 Brayton cycles working as the
indirect cooling system for a mediate-temperature lead fast reactor and quantify the Brayton cycle performance with different heat
rejection temperatures (from 32°C to 55°C) to investigate its potential use in different scenarios, like arid desert areas or areas with
abundant water supply. High-efficiency S-CO2 Brayton cycle could offset the power conversion efficiency decrease caused by low
core outlet temperature (which is 480°C in this study) and high compressor inlet temperature (which varies from 32°C to 55°C in
this study). A thermodynamic analysis solver is developed to provide the analysis tool. The solver includes turbomachinery models
for compressor and turbine and heat exchanger models for recuperator and precooler. The optimal design of simple Brayton cycle
and recompression Brayton cycle for the lead fast reactor under water-cooled and dry-cooled conditions are carried out with
consideration of recuperator temperature difference constraints and cycle efficiency. Optimal cycle efficiencies of 40.48% and
35.9% can be achieved for the recompression Brayton cycle and simple Brayton cycle under water-cooled condition. Optimal cycle
efficiencies of 34.36% and 32.6% can be achieved for the recompression Brayton cycle and simple Brayton cycle under dry-cooled
condition (compressor inlet temperature equals to 55°C). Increasing the dry cooling flow rate will be helpful to decrease the
compressor inlet temperature. Every 5°C decrease in the compressor inlet temperature will bring 1.2% cycle efficiency increase for
the recompression Brayton cycle and 0.7% cycle efficiency increase for the simple Brayton cycle. Helpful conclusions and advises
are proposed for designing the Brayton cycle for mediate-temperature nuclear applications in this paper.

1. Introduction widely carried out for the 2400 MWth fast reactor [5],
200 MWth gas fast reactor (SC-GFR) [6], and 36.2 MWth
The study of supercritical carbon dioxide (S-CO2) Brayton micro modular reactor [7, 8] and also as an indirect cooling
cycle becomes popular in engineering area because of its system of small modular sodium-cooled fast reactor [9, 10]
merits of high cycle efficiency, configuration compactness, and lead fast reactor [11]. All these studies are preliminary
and lower purification system requirements compared with feasibility analyses of Brayton cycle working with nuclear
the steam Rankine cycle [1]. Its application area has ex- application, which is summarized in the paper of Pan Wu
tended to the industries of nuclear [2], fossil fuel, waster [12].
heat, solar energy [3, 4], etc. In the role of power conversion A small modular reactor (SMR) can help meet clean
system for nuclear energy, the conceptual studies of S-CO2 energy goals and make electricity more accessible for all.
Brayton cycle working as direct cooling system have been SMR using the S-CO2 Brayton cycle as its indirect power
2 Science and Technology of Nuclear Installations

cooling system owns the advantage of high cycle efficiency intermediate cooling circuit, which is needed in the sodium
and high system compactness. High compactness indicates fast reactor system. That is the reason why the lead fast
that the nuclear power system has the possibility to be reactor is selected as the power source for the S-CO2 Brayton
transported through trucks or ships, which means con- cycle.
struction schedule reduction and lower cost for overall
construction. SMR coupling with the S-CO2 Brayton cycle
2.1. Description of Lead Fast Reactor. The heat source of our
could be used to bring electricity to remote communities and
Brayton cycle design comes from a typical pool-type lead fast
mining or military bases. Additionally, the S-CO2 Brayton
reactor SNCLFR-100 [13], which is a 100 MWth lead-cooled
cycle has a less efficiency decrease when using dry air to
small modular reactor with a passive cooling feature under
discharge the system waste heat, compared with the cases
both normal and abnormal operations proposed by Uni-
using water as the heat sink. China has a large area which
versity of Science and Technology of China (USTC).
needs electricity and lack of adequate water resources in
SNCLFR-100 incorporates some innovative ideas such as
northwest district. SMR coupling with the S-CO2 Brayton
integral arrangement, modular design, and natural coolant
cycle is a perfect solution to this problem.
circulation, which will help simplify the system design and
In this paper, a naturally circulated 100 MWth lead-
improve the reactor safety performance and engineering
cooled small modular reactor (SNCLFR-100) which has a
feasibility. The original design parameters of SNCLFR are
mediate core-outlet-temperature is selected as the target
listed in Table 1.
analysis object [13]. Higher core-outlet-temperature is al-
Another big feature of SNCLFR-100 is its designed core
ways attractive to researchers because it can bring higher
outlet temperature of 480°C. As we all know, higher core
cycle efficiency. However, higher core-outlet-temperature
outlet temperature means higher turbine inlet temperature,
will also bring problems of structural material corrosion,
which could help produce very high power conversion ef-
which is still a tricky problem for lead fast reactors. Lowering
ficiency. However, coolant lead at high temperature will
the core-outlet-temperature is helpful to mitigate this
bring corrosion problems for the core materials, which is still
problem, and the application of S-CO2 Brayton cycle is
not solved for LFR development. Thus, a mediate core outlet
helpful to offset the cycle efficiency decrease caused by low
temperature is benefit for material selection during the core
core-outlet temperature. In this paper, design of the simple
design and improves the engineering feasibility of LFR.
and recompression S-CO2 Brayton cycle is carried out to
The feature of fully natural coolant circulation increases
study if the S-CO2 Brayton cycle could achieve high thermal
the inherent safety performance of SNCLFR-100 under both
efficiency under mediate-core-outlet-temperature, which
normal and abnormal operation scenarios. Calculation re-
makes this nuclear system own the characteristics of high
sults [13] show that SNCLFR-100 is able to guarantee a
compactness and high efficiency. An in-house steady ther-
sufficient safety margin for fuel melting and other constrains
modynamic analysis solver named SASCOB is developed to
considered under accidents of unprotected transient over-
evaluate and optimize the simple and recompression
power and unprotected loss of heat sink [14].
Brayton cycle configuration for the lead fast reactor under
different cooling conditions (including water-cooled and
dry-cooled conditions). The cycle parameter effects, such as 2.2. Description of Typical S-CO2 Brayton Cycle Configuration.
compressor inlet pressure and temperature, turbine inlet The S-CO2 Brayton cycle applies supercritical carbon di-
pressure, recuperator conductance, and recompression oxide as coolant, instead of steam, to transport thermal
compressor flow ratio, are studied to optimize the best energy produced by heat source to the gas turbine, which
Brayton cycle configuration for the 100 MWth LFR. The converts the thermal energy to mechanical energy. So why
model developed in this paper is a powerful tool for con- do we use S-CO2 as the transport medium? As can be seen in
ceptual design and thermodynamic analysis of the nuclear Figure 1, S-CO2 has a very high density and compressibility
reactor system coupled with the S-CO2 Brayton cycle. The near its critical point. Using the compressor driven by the
cycle parameter effects on thermal efficiency are helpful for turbine to compress the high-density CO2 could save the
the S-CO2 Brayton cycle design for nuclear applications. consumed power and increase the cycle efficiency. Evidence
shows that the S-CO2 Brayton cycle has higher cycle effi-
2. Description of Lead Fast Reactor and Typical ciency than that of the steam Rankine cycle and other
S-CO2 Brayton Cycle Configuration Brayton cycles using gases like He and nitrogen, when the
turbine inlet temperature is higher, 550°C (Figure 2).
Corrosion of structural material caused by high-temperature Figure 3 shows the two typical S-CO2 Brayton cycle
lead makes mediate-outlet-temperature core design easy to configurations, which are simple Brayton cycle (SBC) and
be realized. Due to the low hydraulic friction inside the core recompression Brayton cycle (RBC), respectively. For SBC
and the thermodynamic properties of lead, the lead fast which is shown in Figure 3(a), the coolant near CO2 critical
reactor (LFR) owns the potential to transport the reactor point (7.4 MPa and 31°C) at point 5 is circulated and
power totally via effective natural circulation. LFR has great pressurized by the compressor first. Then, the coolant at
safety performance under steady and transient conditions point 6 flows through the recuperator and is heated by the
[13]. At the same time, the coolant of LFR has stable hot side flow of the recuperator. The coolant at point 7
chemical characteristics and does not react with water or air. absorbs the heat through directly heating or indirectly
This feature makes the LFR system possible to eliminate the heating by the heat source and the temperature rise to a high
Science and Technology of Nuclear Installations 3

Table 1: Main design parameters of SNCLFR-100 [13]. level. Then coolant of high pressure and high temperature at
Design parameter Values or characteristics
point 1 enters the gas turbine and drives the shaft to rotate.
The compressor, generator, and turbine share the same
Reactor thermal power 100 MWth
Refueling interval 10 years
rotating shaft, which is also a way to improve the cycle
Coolant/heat transport system Lead/compact pool-type efficiency. Coolant leaving the turbine then enters the low-
Reactor inlet temperature 400°C pressure high-temperature side of the recuperator, and the
Reactor outlet temperature 480°C heat is recuperated to heat the cold side flow at high pressure.
Cooling mode Fully natural circulation After leaving the recuperator, the coolant is further cooled
Mass flow rate through the core 8528 kg/s by the precooler (heat sink) to be close to the CO2 critical
Fuel MOX point. This is the coolant flow path in SBC. However, in SBC,
Cladding T91 there is only one recuperator and the pinch point in the
Core height 3400 mm recuperator restricts the further efficiency improvement of
Active zone height 1000 mm SBC. Based on SBC, MIT proposed the RBC configuration,
Equivalent core diameter 3460 mm
which adds a recompression compressor and splits the
original recuperator into a high-temperature recuperator
(HTR) and a low-temperature recuperator (LTR), to solve
1000 the pinch point problem [15], (Figure 3(b)). Calculation
900 results show that RBC could effectively increase the cycle
800 efficiency than SBC [15].
700 Besides the advantage of high efficiency compared with
Density (kg/m3)

helium Brayton cycle and steam Rankine cycle at the

600
reference temperature considered for this study, the
500 S-CO2 Brayton cycle has the advantage of high com-
400 pactness. CO2 has a higher heat transfer capacity com-
300 pared with other gases, which can help reduce the size of
200 the heat exchanger. The high-density property of CO2
100
makes the CO2 turbine much smaller than that of helium
or steam turbomachinery. Take the turbine size as an
0
20 40 60 80 100
example, CO2, helium, and steam turbine size is about 1 :
Temperature (°C) 6 : 30 under same turbine output power [16]. Additionally,
the S-CO2 Brayton cycle keeps single phase all the time
8 MPa 13 MPa
during the operation, which makes the system quickly
9 MPa 15 MPa
11 MPa
respond to the load change or system disturbance, and has
less risk of flow instability.
Figure 1: CO2 density variation with temperature under super- There are also other Brayton cycle configurations, for
critical pressures. example, intercooling, double recompression or reheating
S-CO2 Brayton cycle [17]. The benefits of these Brayton cycle
is still under investigation. However, all of these mentioned
60 Brayton cycles will result in more complex configuration,
which complicates the control system. That is the reason why
only SBC and RBC are studied in our paper.
50
Cycle thermal efficiency (%)

3. Code Development and Validation of

40 Integrated Thermodynamic Analysis Code
3.1. Mathematical Modeling for Brayton Cycle. The main
30
physical models of SASCOB include turbomachinery model
and heat exchanger model. Gas compressor and turbine are
20 the main turbomachinery model in the S-CO2 Brayton cycle.
The compressor is a machinery which pressurizes low-
pressure gas to high-pressure gas through consuming me-
10
300 400 500 600 700 800 900 1000 chanical energy. In this paper, a lumped parameter method
Turbine inlet temperature (°C) will be applied to evaluate the steady state performance of
compressor. Parameters of pressure ratio and efficiency are
Supercritical steam Nitrogen Brayton cycle used to describe the compressor thermal performance.
Rankine cycle Helium Brayton cycle Figure 4 shows the fluid enthalpy and entropy variation
S-CO2 Brayton cycle
during ideal and realistic compression process. The ideal
Figure 2: Power cycle efficiency comparison between different compression process is regarded as an isentropic process,
power conversion systems. and the realistic compression process need a factor of
4 Science and Technology of Nuclear Installations

5
Precooler

Compressor Turbine Generator

5
2

Re-
Compressor Turbine Generator
compressor

6
Heater 10 1

6 7
Heater
Recuperator 7 8 9
LT recuperator HT recuperator
Precooler
2
4 3
4 3

(a) (b)

Figure 3: Schematic of typical Brayton cycle used in nuclear application. (a) Simple Brayton cycle; (b) recompression Brayton cycle.

h P02
Tc2 � T pc2 , hc2 􏼁. (5)
P2
The power consumed by compressor can be calculated as
follows:
h02 Wmc � m_ hc2 − hc1 􏼁, (6)
P01
h2s With the pressure ratio and efficiency of the compressor, the
P1 compressor outlet condition can be derived from the inlet
condition through equations (1) to (6).
A turbine is used to convert the thermal energy of
h01 coolant to mechanical energy. The lumped parameter
method which is similar to that of the compressor model is
applied here to solve the turbine model with the aid of
parameters of pressure ratio and efficiency.
S There are three heat exchangers in the recompression
Figure 4: Ideal and realistic compression processes inside the supercritical CO2 Brayton cycle, which are low-temperature
compressor. recuperator, high-temperature recuperator, and precooler.
As the heat exchanger may be the largest component in the
compressor adiabatic efficiency to account for the additional Brayton cycle under such a large heat exchange demand, the
enthalpy increase compared with that of the ideal process. compactness of the heat exchanger is very important. The
By knowing the pressure ratio rc and the inlet pressure of printed circuit heat exchanger developed by HEATRIC
compressor Pc1, the outlet pressure pc2 of the compressor can Company has the advantage of high compactness, high-
be calculated by pressure bearing capacity, and wide application scope, which
satisfy the heat exchange requirement of the S-CO2 Brayton
pc2 � pc1 rmc , (1) cycle. Figure 5 shows cross section of the PCHE heat ex-
With the inlet temperature Tc1 and pressure Pc1 and the changer, whose flow channel is made by semicircle hori-
principle that ideal thermal process through the compressor zontal flow tubes, with hot and cold fluid flow channels
is an isentropic process, the ideal outlet entropy sc2s and alternatively configured.
enthalpy hc2s are The conductance is selected to express the heat transfer
capacity and size of the heat exchange instead of effec-
sc2s � sc1 pc1 , Tc1 􏼁, (2) tiveness. The concept of effectiveness is not applied due to
the fact that it will cause dramatical variation of the con-
hc2s � h pc2 , sc2s 􏼁. (3) ductance value for a given heat load under different design
conditions. For example, designing recuperator using the
The actual outlet enthalpy hc2 can be derived from inlet same heat transfer effectiveness results in very large dif-
enthalpy hc1, ideal outlet enthalpy hc2s, and the compressor ference in the recuperator heat transfer conductance, which
efficiency ηmc: can be easily found in Table 3 of [18].
hc1 + hc2s − hc1 􏼁 In order to reduce the calculation error, the heat ex-
hc2 � . (4) changer is divided into N parts through the channel. The UA
ηmc
value of the total heat exchanger can be obtained through
Thus, the temperature of coolant at the outlet of com- equation (7), which is closely related to the inlet and outlet
pressor Tc2 can be obtained by the following equation: temperature at hot and cold sides of the recuperator. The UA
Science and Technology of Nuclear Installations 5

Cold fluid

Hot fluid
t

tf

Figure 5: Cross section of the printed circuit heat exchanger.

calculation method refers to Dyreby’s paper [19] and the through the pressure and enthalpy. The in-house package
reader could find the detailed methodology of calculating predicted the CO2 property very well in most property range
NTU and Cmin in Appendix A: with a relative error lower than 0.5%. Detailed information
N could be found in [12].
UA � 􏽘􏼐NTUi ∗ Cmin,i 􏼑. (7)
i�1
3.2. Validation of SASCOB. Pope [20] proposed a
In the integrated model of SASCOB, the input pa- 2400 MWth reactor concept which is directly cooled by the
rameters include inlet temperature, inlet pressure, effi- S-CO2 recompression Brayton cycle. The main parameters
ciency and pressure ratio of compressor and turbine, of its S-CO2 Brayton cycle are listed in Table 2. Inlet tem-
efficiency and pressure ratio of recompression compressor, perature and pressure of the turbine are 650°C and 20 MPa,
required UA values of each recuperator, fraction of the flow and the inlet temperature and pressure of the main com-
rate flowing into recompressor, and total heat added to the pressor are 32°C and 7.69 MPa, which make the cycle achieve
Brayton cycle. The outlet condition of the compressor and a high cycle efficiency of 50%.
turbine can be obtained by using the turbomachinery Using the detailed parameters (power, heat exchanger
model. By knowing the temperature at state points 2 and 6, size, mass flow rate, turbomachinery pressure ratio, and
a random value between value of T2 and T6 can be assigned efficiency) described in Pope’s paper [20], SASCOB is able to
to T3 and further a random value between value of T3 and get the overall cycle conditions. Figures 6 and 7 show the
T6 can be assigned to T4. By knowing the temperature at comparison of pressure-specific volume map and temper-
state point 3, state point 4, and state point 6, the con- ature and entropy map between values calculated by SAS-
ductance of the low recuperator can be achieved with COB and from the MIT designed cycle. From the figure, we
equation (7). The value of T4 is adjusted to make the can see that the property values at different point calculated
conductance of the low recuperator satisfy the required by SASCOB is very close to those MIT design values.
value set by the user. After the iteration calculation for the The maximum relative error and average relative error
low recuperator, the model proceeds to the calculation for for pressure are 0.33% and 0.17%, while the maximum
the high-temperature recuperator by adjusting the value of relative error and average relative error for temperature are
T3. When the conductance of the low recuperator and high 0.85% and 0.25%. The results indicate that the developed
recuperator both meet the user requirement, the temper- code SASCOB is able to predict the Brayton cycle parameters
ature value at point 3, point 4, point 7, and point 9 is with a very small relative error. Table 3 lists the comparison
confirmed. The mass flow rate of the Brayton cycle will be of some important parameters for the recompression
calculated by Brayton cycle. The loop mass flow rate is 11931 kg s− 1, the
Q recompression compressor flow ratio is 40.7%, while the
m_ � heat . (8) cycle efficiency is 49.7%. When compared with the MIT
h1 − h9
design value, the relative errors of these three key parameters
The Brayton cycle efficiency can be achieved through are 1.9%, 3.1%, and 0.6%, which also demonstrates SAS-
W − Wmc − Wrc COB’s ability in predicting the overall cycle parameters.
ηbrayton � t . (9)
Qheat
4. Brayton Cycle Design for Lead Fast Reactor
The detailed calculation process is found in Appendix B.
In the calculation process, the thermal property of S-CO2 As mentioned in the previous section, SNCLFR-100 owns a
is calculated by the in-house property package [12]. The in- thermal power of 100 MW and inlet and outlet temperatures
house property package is made up of polynomial corre- of 400°C and 480°C. In this paper, the design of the CO2/lead
lation fitted based on CO2 property data from NIST intermediate heat exchanger is not included. Olumayegun
REFPROP. The thermal property package covers pressure et al. assume the turbine inlet temperature as 530°C when its
range of 0.1–20 MPa and temperature range of 0–991°C. core outlet temperature is 545°C [21]. ABR-1000 coupled
Parameters including entropy, temperature, specific volume, with S-CO2 cycle owns an outlet core temperature of 488°C
conductivity, and dynamic viscosity have been obtained and turbine inlet temperature of 472°C [22]. The lead fast
6 Science and Technology of Nuclear Installations

Table 2: Cycle design parameters of MIT 2400 MWth recom- assumed to be 20°C lower than core outlet temperature,
pression Brayton cycle. which is conservative compared with the design of the
Main parameters Value abovementioned reference. The detailed design of the in-
Inlet pressure of main compressor (MPa) 7.69
termediate heat exchanger should be done in the future to
Inlet temperature of main compressor (°C) 32 accomplish this goal. The thermal input for the S-CO2
Main compressor efficiency (%) 90.6 Brayton cycle equals to the core thermal power of 100 MW.
Main compressor pressure ratio 2.61 Under water-cooled condition, the cooling capacity of the
Recompression compressor efficiency (%) 90.0 secondary system is considered to be efficient and the
Turbine efficiency (%) 94.1 compressor inlet temperature should be confirmed through
Turbine inlet temperature (°C) 650 sensitivity analyses. Under dry-cooled condition, the coolant
capacity of the secondary system is assumed to be weak.
Thus, the minimum of compressor inlet temperature varies
22 from 35°C to 55°C, which finally depends on the air dry
20 6 8 9 cooling system design.
1 The cycle efficiency mainly depends on cycle operation
18 conditions, such as maximum pressure and temperature,
minimum pressure and temperature, recuperator conduc-
Pressure (MPa)

16
tance, recompression fraction (only for recompression cy-
14 cle), and turbomachinery efficiency. As the maximum
temperature has already been set to 460°C, other cycle pa-
12
rameters should be optimized. The cycle parameters are
10 initially set referred to existing literature [24], as shown in
Table 4. The effects of compressor and turbine operation
8 condition is first investigated to get the optimal SBC design
5 4 3 2 under water-cooled condition and dry-cooled condition.
6
0.000 0.004 0.008 0.012 0.016 0.020 After that, the effects of the recompression flow ratio and the
Specific volume (m3·kg–1) heat exchanger conductance are investigated under water-
SASCOB
cooled condition and dry-cooled condition.
MIT
Figure 6: Specific volume comparison between calculated and MIT
design values. 4.1. Optimal Design for Simple Brayton Cycle
4.1.1. Effects of Compressor Parameters. In order to study the
700 effects of compressor parameters, the heat exchanger con-
ductance and the turbine inlet pressure for SBC included in
1
600 Table 4 are kept constant. The compressor inlet temperature
varies from 30°C to 55°C at different compressor inlet
500 9
pressures. From Figure 8, we can see that the compressor
Temperature (°C)

2
400
working close to the critical point or pseudocritical point can
achieve the peak cycle efficiency at a certain CIP value. For
300 the working area of CIP around 7.4 to 8.0 MPa, the highest
cycle thermal efficiency is reached when the CIP equals to
200 7.4 MPa and CIT is about 32°C, which is around 34.13%. This
8
3 phenomenon indicates that the compressor inlet condition
100
6 should stay closer to the critical or pseudocritical point to get
0 5 4 high thermal efficiency. However, the CO2 properties, like
3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 density, specific heat, and conductance, vary sharply around
Entropy (kJ·(kg·K–1)) the critical or pseudocritical point, which will bring huge
SASCOB difficulty in controlling the secondary water flow of the
MIT precooler. Staying away from the critical point helps elim-
inate this problem. When CIP equals to 7.4 MPa, 1°C away
Figure 7: Temperature-entropy comparison between calculated
from the critical or pseudopoint, it brings around 0.3% cycle
and MIT design values.
efficiency reduction. The optimal compressor inlet tem-
perature needs to be determined also by evaluating the
reactor system coupled with the S-CO2 Brayton cycle controllability of the compressor inlet temperature. On the
mentioned in paper of Moisseytsev et al. has a core outlet other hand, the CIP temperature is determined by the
temperature of 578°C and an inlet turbine temperature of precooler condition. When the precooler is set to be cooled
560°C [23]. In this paper, the outlet temperature of the by air, CIT at the compressor will increase. When air cooling
secondary side of the intermediate heat exchanger is is considered and the CIT is assumed as 55°C, the cycle
Science and Technology of Nuclear Installations 7

Table 3: Comparison of cycle parameters between SASCOB result and MIT design value.
Parameters SASCOB MIT design point Relative error (%)
Loop mass flow rate (kg·s− 1) 11,931 11,708 1.9
Recompression compressor flow ratio (%) 40.7 42.0 3.1
Cycle efficiency (%) 49.7 50.0 0.6

considered in this part. In this section, the parameters for

Table 4: Initial cycle parameter for simple and recompression
SBC in Table 4 are kept constant excluding TIP. Figure 9
Brayton cycles.
shows the variation of cycle thermal efficiency and turbo-
Parameter Simple Brayton cycle Recompression Brayton cycle machinery work with the turbine inlet pressure change.
Pmin (MPa) 7.4 7.4 With higher TIP, the turbine will produce more work and
Pmax (MPa) 20 20 the compressor also consumed more work due to large
Tmin (°C) 32 32 pressure rise. The balance between turbine produced work
Tmax (°C) 460 460 and compressor consumed work results in the increase of
UA/MW/K 2 LTR/HTR 2.911/2.089 thermal efficiency with increase of TIP. Higher TIP helps
φ — 0.3
increase the cycle thermal efficiency. However, it is also
εcom 0.89 0.89
εrecom — 0.89
interesting to see that the efficiency increase rate decreases
εtur 0.93 0.93 with further rise in TIP. For the cases where TIP is lower
than 20 MPa, TIP increase of 1 MPa brings around thermal
efficiency increase of 0.93%. For the cases where TIP is
35 higher than 25 MPa, TIP increase of 1 MPa only brings
around thermal efficiency increase of 0.13%. At the same
34 time, higher system pressure raises a stricter requirement on
the manufacture of pipe and heat exchangers. For these two
Cycle thermal efficiency

33 considerations, 20 MPa is set as the optimal turbine inlet

pressure.
32

31 4.1.3. Effects of Heat Exchanger. Increasing the heat ex-

changer conductance is helpful to recycle more heat through
30 recuperator and reduce the heat discharged into the heat
sink, which further increase the cycle thermal efficiency. In
29 this section, the parameters for SBC in Table 4 are all kept
constant excluding the heat exchanger conductance. Fig-
30.0 32.5 35.0 37.5 40.0 42.5 45.0 47.5 50.0 52.5 55.0 ure 10 shows the effects of heat exchanger UA on the cycle
Compressor inlet temperature (°C) thermal efficiency for SBC when the values of CIP and CIT,
CIP = 7.4 MPa CIP = 7.8 MPa as well as TIP and TIT, are set as 7.4 MPa/32°C and 20 MPa/
CIP = 7.5 MPa CIP = 7.9 MPa 460°C. From the figure we can see that, when heat exchanger
CIP = 7.6 MPa CIP = 8.0 MPa UA rises, the outlet temperature of recuperator’s high-
CIP = 7.7 MPa pressure side (HP) increases and the outlet temperature of
Figure 8: Effects of compressor inlet temperature (CIT) and the recuperator’s low-pressure side (LP) decreases, which
compressor inlet pressure (CIP) on the cycle thermal efficiency for indicate that more power is recovered by the recuperator. As
SBC. the HP outlet temperature of the recuperator equals to the
inlet temperature at the heat exchanger (HX), more cycle
mass flow rate is needed to accomplish the set HX outlet
efficiency is 4.7% lower than that of simple Brayton cycle
temperature of 460°C. High cycle mass flow rate makes the
configuration whose CIT is close to the critical point at CIP
turbine to produce more work and the compressor to
of 7.4 MPa.
consume more power. It is obvious that the rise of turbine
Another interesting phenomenon is that, when the CIT
produced power is higher than that of the compressor
increases to certain value, for example, 35°C, CIP plays a less
consumed power, which indicates that more net power is
important role in determining the cycle efficiency. In the
produced by SBC and cycle thermal efficiency increases.
working condition area of CIT larger than 35°C, 1 MPa CIP
However, there is a limit in designing recuperator UA
increase brings 0.47% cycle efficiency reduction.
that the minimum temperature difference (min_dt) between
hot and cold sides of the recuperator should be over 10°C to
4.1.2. Effects of TIP. As the turbine inlet temperature (TIT) avoid the pinch point [25]. When the minimum temperature
is constrained by the lead fast reactor outlet temperature, difference is less than 10°C, very large HX volume is needed
which is set as 460°C in this paper, only effects of turbine to increase the recuperator power by a little bit, which is not
inlet pressure (TIP) on cycle thermal efficiency are economical. The dash line in Figure 10 represents the
8 Science and Technology of Nuclear Installations

40.0 80

37.5 70

Turbomachinery work (MW)

Cycle thermal efficiency (%)
35.0 60
32.5 50
Turbine produced work
30.0
40
27.5
30
25.0
20
22.5
Compressor consumed work 10
20.0
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Turbine inlet pressure (MPa)
Figure 9: Effects of TIP on the cycle thermal efficiency for SBC.

55 Turbine produced power 700

450
Thermal efficiency (%) turbomahcinery work (MW)

LP inlet temperature 400

50
350 650
45 300
250

Cycle mass flowrate (kg∗s–1)

HP outlet temperature 600
40 Cycle thermal efficiency 200

Temperature (°C)
LP outlet temperature 150
35 550
100

30 HP inlet temperature
35 500
Minimum temperature difference for recuperator 30
25
Cycle mass flowrate 25
450
20
20
15
Compressor consumed power 400
15 10
5
10 0 350
1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500
Recuperator UA (kW∗K–1)
Figure 10: Effects of the heat exchanger UA on the cycle thermal efficiency for water-cooled SBC.

minimum temperature difference of 10°C. It is worth noting respectively. Every 5°C decrease on the compressor inlet
that the maximum recuperator conductance of 3 MW/K temperature will bring around 0.7% efficiency increase for
satisfies the requirement of the recuperator pinch point. the simple Brayton cycle. However, lower compressor inlet
Therefore, for SBC, the optimal cycle efficiency of 35.9% is temperature needs the air cooling system to consume more
obtained when the recuperator conductance equals to power. The selection of proper compressor inlet temperature
3 MW/K. for dry-cooled SBC should be made by considering the
power consumption of the air cooling system and the overall
For dry-cooled SBC, the compressor inlet temperature
cycle thermal efficiency. The design and analysis for the air
could vary from 40–60°C depending on the weather and air
cooling system will not be expanded in this paper.
cooling tower design [26]. The calculation result of dry-
The detailed cycle configuration of optimized SBC for
cooled SBC at various compresses inlet temperatures be-
water-cooled (CIT of 32°C) and dry-cooled conditions
tween 40°C and 60°C is shown in Figure 11. It is clearly
(regard CIT value as 55°C) is listed in Table 5.
shown that, for a given compressor inlet temperature, the
cycle efficiency increases with the increase of the recuperator
UA. When considering the limit value for recuperator 4.2. Optimal Design for Recompression Brayton Cycle
min_dt to be 10°C, there is a maximum cycle efficiency for
each case. The maximum cycle efficiencies for conditions 4.2.1. Effects of Compressor Parameters. In the effect study of
whose compressor inlet temperature equals to 40°C, 45°C, compressor parameters, the parameters for RBC excluding
50°C, and 55°C are 34.8%, 34.1%, 33.3%, and 32.6%, compressor inlet temperature and inlet pressure in Table 4
Science and Technology of Nuclear Installations 9

39 40

38
CIT = 32°C 35
CIT = 35°C
37
CIT = 40°C
36 30
Cycle thermal efficiency (%) CIT = 45°C
35

Recuperator min_dt (°C)

CIT = 50°C 25
34
CIT = 55°C
20
33

32 CIT = 32°C 15
CIT = 35°C
31
CIT = 40°C
10
30 CIT = 45°C
CIT = 50°C
29 CIT = 55°C 5

28
0
27
1000 2000 3000 4000 5000 6000 7000
Recuperator UA (kW∗k–1)
Figure 11: Effects of the recuperator UA on the cycle thermal efficiency for dry-cooled SBC.

Table 5: Optimal design for the water-cooled simple Brayton cycle.

Cooling type Water cooled Dry cooled
Produced net power 35.9 MW 32.6 MW
Cycle thermal efficiency 35.9% 32.6%
Turbine mass flow rate 426.3 kg/s 515.0 kg/s
TIP/TIT 20 MPa/460°C 20 MPa/460°C
CIP/CIT 7.4 MPa/32°C 7.4 MPa/55°C
Recuperator UA 3000 kW/K 4200 kW/K
Inlet and outlet temperatures of high-pressure side of recuperator 94.0°C/269.8°C 142.9°C/301.96°C
Inlet and outlet temperatures of low-pressure side of recuperator 346.5°C/103.7°C 346.5°C/152.9°C
Minimum temperature difference of recuperator 10.1°C 10.0°C
Turbine produced power 49.8 MW 60.4 MW
Compressor consumed power 13.9 MW 27.8 MW

are kept constant. The effects of compressor parameters on cycle efficiency. This phenomenon indicates that increasing
RBC cycle efficiency shown in Figure 12 are similar to what the CIP is helpful to increase overall cycle efficiency for dry-
are shown in Figure 8 for SBC. The compressor working cooled RBC.
close to the critical point or pseudocritical point can achieve
the peak cycle efficiency at each CIP value. For CIP ranging
from 7.4 to 8.0 MPa, the highest cycle thermal efficiency for 4.2.2. Effects of TIP. In order to investigate the effects of TIP
RBC is 39.80% when the CIP equals to 7.4 MPa and CIT is on the overall cycle efficiency, other parameters for RBC in
about 32°C. At different CIP pressure level, 1°C away from Table 4 are kept constant during this sensitivity analysis.
the critical or pseudopoint, brings around 0.3% cycle effi- Figure 13 shows the variation of cycle efficiency and tur-
ciency reduction. For the conditions whose CIT temperature bomachinery work with different TIPs. It is easy to see that
is away from the critical point, 0.1 MPa CIP increase will the cycle efficiency variation with TIP for RBC is different
result in around 0.2% efficiency increase. This phenomenon from what is shown in Figure 9 for SBC. For RBC, the cycle
is on the contrary to what is found in Figure 8 for SBC. For efficiency increases with the TIP increase firstly, then reaches
RBC, the recompression compressor consumed power is the efficiency peak at around TIP of 23 MPa, and after that
more than the power consumed by main compressor be- starts to decrease although the TIP keep increasing. When
cause its inlet working condition is far from the critical area. TIP is lower than 23 MPa, 1 MPa increase in TIP will bring
Increasing CIP is helpful to decrease the compressor pres- around 1% cycle efficiency increase. When TIP is higher
sure ratio, which will help decrease the power consumed by than 23 MPa, 1 MPa increase in TIP will result in 0.2% cycle
recompression compressor and further increase the overall efficiency decrease. The difference between SBC and RBC is
10 Science and Technology of Nuclear Installations

42
41
40
39

Cycle thermal efficiency

38
37
36
35
34
33
32
31
30
29
30.0 32.5 35.0 37.5 40.0 42.5 45.0 47.5 50.0 52.5 55.0
Compressor inlet temperature (°C)
CIP = 7.4MPa CIP = 7.8 MPa
CIP = 7.5MPa CIP = 7.9 MPa
CIP = 7.6MPa CIP = 8.0 MPa
CIP = 7.7MPa
Figure 12: Effects of recuperator UA on the cycle thermal efficiency for RBC.

39 120
110
100

Turbomachinery work (MW)

Cycle thermal efficiency (%)

38
Thermal efficiency 90
80
Turbine produced work
37 70
60
50
36
40
Compressor consumed work
30
Main compressor consumed work 20
35
Recompressor consumed work 10
16 18 20 22 24 26 28 30
Turbine inlet pressure (MPa)
Figure 13: Effects of TIP on the cycle thermal efficiency for RBC.

mainly caused by the introduction of the recompression capacitance rates of hot and cold CO2 flow. This is helpful to
compressor to the RBC system. The coolant flowing through increase the effectiveness of the low-temperature recuper-
the recompression compressor works far away from the ator. The CO2 bypassed from the main compressor will be
critical point, which means that the recompression com- compressed by another compressor and meet with the
pressor needs more power than the main compressor to coolant flowing out of the low-temperature recuperator at a
compress the same amount of coolant. Increasing TIP not point between the low- and high-temperature recuperators.
only makes the turbine to produce more power but also The system diagram can be found in Figure 3(b).
consumes more work to drive the compressor. The com- In the design for the recompression Brayton cycle, there
bined effect of turbine and compressor makes the cycle are four factors we need to take into consideration, which are
efficiency decrease with TIP after a certain point. the total recuperator UA, the UA distribution between HTR
and LTR, the fraction of coolant flowing through the
recompressor, and the working conditions of two recu-
4.2.3. Effects of Heat Exchanger. A single recuperator has the perators whose min_dt should be less than 10°C. In our
problem of pinch point, which constraints the cycle effi- calculation, for each total recuperator UA value, the fraction
ciency improvement. The cold CO2 of the low-temperature of coolant flowing through the recompressor and the UA
recuperator has higher specific heat capacity than the hot distribution between HTR and LTR varies. Under the
CO2 of the low-temperature recuperator. A bypass loop is condition of certain total recuperator UA and certain
needed to reduce the cold CO2 flow rate and balance the recompression compressor flow fraction, the UA
Science and Technology of Nuclear Installations 11

50

45

40
Highest efficiency
Cycle thermal efficiency (%)

35

30

25

20

15

10
0 10 20 30 40 50 60
Recompressor flowrate fraction (%)
UAT = 1000kW/K UAT = 2000kW/K UAT = 3000kW/K
UAT = 4000kW/K UAT = 5000kW/K UAT = 6000kW/K
UAT = 7000kW/K UAT = 8000kW/K UAT = 9000kW/K
Figure 14: Effects of recuperator UA and recompressor flow rate fraction on the cycle thermal efficiency for water-cooled RBC.

41 (Recompression flow ratio,

(30%, 8000 kW/K, 42%) total recuperator UA,
40 HTR UA ratio)

39 (25%, 8000 kW/K, 56%)

Cycle efficiency (%)

38
(25%, 9000 kW/K, 42%)
37
(20%, 8000 kW/K, 36%)
36
(20%, 9000 kW/K, 36%)
35
(20%, 9000 kW/K, 36%)
34

30 35 40 45 50 55
Compressor inlet temperature (°C)
Figure 15: Effects of compressor inlet temperature on the cycle thermal efficiency for dry-cooled RBC.

distribution between HTR and LTR is automatically opti- because the power consumed by the recompression
mized to achieve the highest cycle efficiency and satisfy the compressor is higher than the power recovered by the
minimum temperature difference for recuperators at the recuperators. When total recuperator UA is higher, RBC
same time. Thus, the cycle thermal efficiency performance at starts to show its advantage over SBC. The optimal
different total recuperator UAs and different recompression recompressor flow rate fraction varies at different total
compressor flow fractions is obtained, which is shown in recuperator UAs. For the case of total UA equaling to
Figure 14. 3000 kW/K, the optimal recompressor flow rate fraction is
From Figure 14, we can first find that, when total about 15%, while for case of total UA equaling to
recuperator UA is less than 2000 kW/K, the simple 6000 kW/K, it is around 25%. Larger UA value will result
Brayton cycle has a higher cycle thermal efficiency than in recuperator minimum temperature to be less than 10°C,
that of the recompression Brayton cycle. This is mainly which is excluded from Figure 14. That is the reason why
12 Science and Technology of Nuclear Installations

Table 6: Optimal design for the water-cooled recompression Brayton cycle.

Cooling type Water cooled Dry cooled
Produced net power 40.38 MW 34.36 MW
Cycle thermal efficiency 40.38% 34.36%
Turbine mass flow rate 563.92 kg/s 616.22 kg/s
Recompression flow ratio 30% 20%
TIP/TIT 20 MPa/460°C 20 MPa/460°C
CIP/CIT 7.4 MPa/32°C 7.4 MPa/55°C
HTR UA 3360 kW/K 3240 kW/K
LTR UA 4640 kW/K 5760 kW/K
Inlet and outlet temperatures of high-pressure side of HTR 206.3°C/315.5°C 263.0°C/327.7°C
Inlet and outlet temperature of low-pressure side of HTR 346.5°C/222.1°C 346.5°C/275.0°C
HTR min_dt 15.7°C 12.0°C
Inlet and outlet temperatures of high-pressure side of LTR 94.0 C/207.0°C
° 142.9°C/262.8°C
Inlet and outlet temperatures of low-pressure side of LTR 222.1°C/104.1°C 275.0°C/154.8°C
LTR min_dt 10.1°C 11.9°C
Turbine produced power 66.11 MW 72.24 MW
Compressor consumed power 42.19 MW 26.6 MW
Recompression compressor consumed power 18.68 MW 11.28 MW

500 42
1, 1, 1, 1

400
2 40
2, 2, 2
Temperature (°C)

7 9
300 9
7
7, 8 3
38
200 3
Cycle thermal efficiency (%)

7, 8

6, 6 4
6, 6
100 3, 3, 4 36
4(5), 5
4(5), 5
0
1.5 2.0 2.5 3.0 34
Entropy (KJ (kg–K))

Water-cooled SBC Water-cooled RBC

Dry-cooled SBC Dry-cooled RBC 32
Figure 16: Temperature-entropy comparison among water-cooled
and dry-cooled SBC and RBC.
30
cases whose total UA is larger has less validated points in
Figure 14. The cases whose total recuperator UA is higher
0.84 0.86 0.88 0.90 0.92 0.94 0.96
than 9000 kW/K will make the minimum temperature
Isentropic efficiency
difference of HTR or LTR less than 10°C and these cases
are ignored here. Turbine for water-cooled RBC
For the dry-cooled Brayton cycle, the higher compressor Optimized configuration for water-cooled RBC
Compressor for water-cooled RBC
inlet temperature results in cycle thermal efficiency decrease.
Recompression compressor for water-cooled RBC
Figure 15 shows the cycle thermal efficiency performance at Turbine for dry-cooled RBC
different compressor inlet temperatures. For each case ap- Optimized configuration for dry-cooled RBC
plying different compressor inlet temperatures, the total Compressor for dry-cooled RBC
recuperator UA, UA distribution between LTR and HTR, and Recompression compressor for dry-cooled RBC
the recompression flow ratio are optimized to get the highest
Figure 17: Cycle efficiency variation with turbomachinery for
cycle efficiency. From Figure 15, it can be found out that the
water-cooled and dry-cooled recompression Brayton cycles.
overall cycle efficiency decreases almost linearly with com-
pressor inlet temperature decrease. Every 5°C increase in CIT
will result in around 1.2% cycle efficiency decrease for RBC. conditions (CIT assumed to be 55°C) is listed in Table 6. The
The detailed cycle configuration of optimized RBC for entropy and temperature comparison of water-cooled and
water-cooled (CIT assumed to be 32°C) and dry-cooled dry-cooled SBC and RBC are shown in Figure 16.
Science and Technology of Nuclear Installations 13

Start

Read the input

Calculate the pressure of

each point

Compressor
Turbine model
model
T6
T2

Assume a value to T3
(T6 < T3 < T2)

Assume a value to T4
(T6 < T4 < T3)

No Recompression
Brayton?

Yes

Recompression model

T10
Low temperature Increase the value of T4 Decrease the value of T4
recuperator
Yes

UA equals to No No
UA > UAset?
fixed value?

Yes

Calculate the value of T8

T8 < T3?

High temperature Increase the value of T3

recuperator
Yes
No No
UA euqalsto
UA > UAset? Decrease the value of T3
fixed value?

Yes

Calculate the loop flowrate

M = Q/(h1–h9)

Output

End

Figure 18: Calculation flowchart of SASCOB.

4.2.4. Turbomachinery Efficiency Effects. Turbomachinery efficiency. Every 1% increase of turbine efficiency will result
efficiency varies in different literatures. The increase of in 0.5% increase in cycle efficiency for water-cooled RBC and
turbomachinery efficiency helps improve the cycle effi- 0.6% increase for dry-cooled RBC. Every 1% increase of the
ciency. It is obvious from Figure 17 that increasing the compressor efficiency brings around 0.15% increase in the
turbine efficiency is more efficient in improving the cycle cycle efficiency for water-cooled RBC and 0.3% increase for
14 Science and Technology of Nuclear Installations

dry-cooled RBC. The recompression compressor efficiency increasing turbine inlet pressure. For RBC, in-
has less impact on cycle efficiency compared with that of the creasing TIP not only makes the turbine produce
turbine. Every 1% increase of the recompressor brings about more power but also consumes more work to drive
0.1% increase for the recompression Brayton cycle and 0.2% the compressor. The combined effect of turbine and
increase for dry-cooled RBC. Conclusion can be made that compressor makes the cycle efficiency decrease with
improving the turbine efficiency is the most effective way to TIP after a certain point.
improve the Brayton cycle efficiency. (3) For water-cooled Brayton cycle design (CIT equals to
32°C), when the total recuperator UA is less than
5. Conclusion 2000 kW/K, SBC has a higher cycle thermal effi-
ciency than RBC. When total recuperator UA is
The Brayton cycle design is carried out in this paper for a higher, RBC starts to show its advantage over SBC.
lead fast reactor concept which owns a core outlet tem- The optimal recompressor flow rate fraction varies at
perature of 480°C. A steady state thermal analysis solver different total recuperator UAs.
named SASCOB is developed for the S-CO2 Brayton cycle-
cooled reactor. The solver includes necessary modules like (4) For dry-cooled Brayton cycle design, the optimal cycle
heat exchanger, turbomachinery, and CO2 property package. efficiency decreases with the CIT increasing from 35°C
The solver is capable to obtain the parameters like pressure, to 55°C. Every 5°C increase in CIT will result in
temperature, enthalpy, and density along the cycle for simple around 1.2% cycle efficiency decrease for RBC. In-
and recompression Brayton cycles. The accuracy of SASCOB creasing the compressor inlet pressure is helpful to
is validated through comparison with the MIT design. With increase the overall cycle efficiency for RBC. Every 5°C
the aid of SASCOB, a feasible simple and recompression increase in CIT will result in around 0.7% cycle ef-
Brayton cycle design for the lead fast reactor concept has ficiency decrease for SBC. Compressor inlet pressure
been achieved under water-cooled and dry air-cooled moving close to critical pressure is helpful to increase
condition through sensitivity analysis. For SBC, the optimal the overall cycle efficiency for SBC.
cycle efficiency can be 35.9% under water-cooled condition (5) The increase of turbomachinery help improves the
(CIT equals to 32°C) and 32.6% under dry air-cooled con- cycle efficiency. For turbomachinery, improving the
dition (CIT equals to 55°C) with a turbine inlet temperature turbine efficiency is the most effective way to im-
of 460°C. For RBC, the optimal cycle efficiency can be prove the Brayton cycle efficiency. Every 1% increase
40.48% under water-cooled condition (CIT equals to 32°C) of turbine efficiency will result in 0.5% increase in
and 34.36% under dry air-cooled condition (CIT equals to cycle efficiency for water-cooled RBC and 0.6% in-
55°C), a turbine inlet temperature of 460°C. The following crease for dry-cooled RBC.
detailed conclusions can be made:
The above optimized configuration for SBC and RBC
(1) Here are some discussions about the compressor under water-cooled and dry air-cooled conditions will
parameter effect on the overall cycle efficiency. For provide promising choices of the power conversion system
both SBC and RBC, coolant at the compressor inlet for the lead fast reactor power. Further system analysis for
working close to critical or pseudocritical point the lead fast reactor coupled with the S-CO2 Brayton cycle
achieves the highest cycle efficiency. When the will be carried out to study the system transient behavior,
compressor inlet temperature is over 35°C, in- safety behavior, and control strategy.
creasing the compressor inlet pressure will result in
cycle efficiency decrease for SBC while it will bring
cycle efficiency increase for RBC. In the dry air
Nomenclature
cooling condition, increase the minimum cycle C: Capacitance rate/ kW/K
pressure is helpful for RBC because it can help re- W: Work consumed by turbomachinery, MW
duce the power consumed by recompression com- UA: Heat exchanger conductance, kW/K
pressor and is harmful for SBC because it can Qheat: Heat source, MW
increase the power consumed by the main com- φ: Mass flow rate fraction of the recompression
pressor. When dry air cooling is considered, the CIT compressor
is assumed as 55°C, the recuperator UA is set con- •
m: Mass flow rate, kg·s− 1
stant, the cycle efficiency of SBC is 4.7% lower than h: Enthalpy, J·kg− 1
that of SBC cooled by water, while the cycle efficiency N: Total number of subheat exchangers
of RBC is 9% lower than that of RBC cooled by water. NTU: Dimensionless number of transfer units
(2) The effects of TIP on cycle efficiency of SBC and RBC (NTUs) for a subheat exchanger
are different. For SBC, higher TIP helps increase the p: Pressure, MPa
cycle thermal efficiency. However, it is also inter- r: Pressure ratio
esting to see that the efficiency increase rate de- s: Specific entropy, J·(kg·K)− 1
creases when turbine inlet pressure is over 20 MPa. c1: Compressor inlet
For RBC, cycle efficiency increases first and then c2: Compressor outlet
decreases after reaching a peak value with the c2s: Ideal compressor outlet condition
Science and Technology of Nuclear Installations 15

i: The ith number of subheat exchanger the cold-side inlet and hot-side out enthalpy of each subheat
exchanger will be calculated:
min: Minimum
mc: Main compressor i ∗ 􏼐hc,in − hc,out 􏼑
rc: Recompression compressor hc,in,i � hc,out,i + ,
N
tur: turbine (A.3)
recom: Recompression compressor i ∗ 􏼐hh,in − hh,out 􏼑
Greek letters: hh,out,i � hh,in,i − .
N
η: Turbomachinery efficiency
ε: Heat exchanger effectiveness The inlet and outlet temperature of each subheat ex-
Acronym: changer can be calculated with pressure and enthalpy.
The heat capacity at hot side and cold side of the subheat
CIT: Compressor inlet temperature exchanger can be determined:
CIP: Compressor inlet pressure
HX: Heat exchanger h − hh,out,i
Ch,i � mh ∗ h,in,i ,
HP: Recuperator’s high-pressure side Th,in,i − Th,out,i
LFR: Lead fast reactor
LP: Recuperator’s low-pressure side hc,in,i − hc,out,i
Cc,i � mc ∗ ,
min_dt: Minimum temperature difference Tc,in,i − Tc,out,i
RBC: Recompression Brayton cycle
(A.4)
S-CO2: Supercritical carbon dioxide Cmin � min􏼐Ch,i , Cc,i 􏼑,
SBC: Simple Brayton cycle
SMR: Small modular reactor Cmax � max􏼐Ch,i , Cc,i 􏼑,
TIT: Turbine inlet temperature
TIP: Turbine inlet pressure. Cmin
CR � .
Cmax
Appendix
The effectiveness of the heat exchanger can be cal-
A. Derivation of Recuperator Conductance culated with the following equation:

In order to reduce the calculation error, the heat exchanger is

divided into N parts through the channel. The pressure drop Q
εi � . (A.5)
inside the heat exchanger is assumed to be linearly distributed. N ∗ Cmin,i ∗ 􏼐Th,in,i − Tc,in,i 􏼑
The cold-side inlet pressure and hot-side outlet pressure of the
subheat exchanger can be expressed as follows: And, the UA value of the total heat exchanger can be
obtained:
i ∗ Δpc N
pc,out,i � pc,in,i − ,
N UA � 􏽘􏼐NTUi ∗ Cmin,i 􏼑. (A.6)
(A.1) i�1
i ∗ Δph
ph,out,i � ph,in,i − ,
N where
where pc,in,i denotes the cold-side inlet pressure of the ith ⎪
⎧
⎪ lg􏼐1 − εi CR,i /1 − εi 􏼑, CR ≠ 1,
⎪
⎪
subheat exchanger, kPa, pc,out,i denotes the cold-side out ⎨
NTUi � ⎪ (A.7)
pressure, kPa, N denotes the subheat exchanger number, ⎪
⎪ εi
⎪
⎩ CR � 1.
ph,in,i denotes the hot-side inlet pressure of the ith subheat 1 − εi ,
exchanger, kPa, ph,out,i , denotes the hot-side outlet pressure
of the ith subheat exchanger, kPa, and Δph and Δpc denote
the pressure drop through the heat exchanger at hot and cold B. Calculation Flowchart of SASCOB
sides, which will be defined by the user.
With the energy conservation equation, we can get the Calculation flowchart of SASCOB is given in Figure 18.
enthalpy at cold and hot sides of the heat exchanger:
Q Data Availability
hc,out � hc,in + ,
mc The data used to support the findings of this study are
(A.2)
Q available from the corresponding author upon request.
hh,out � hh,in − .
mh
Conflicts of Interest
The enthalpy inside the heat exchanger is assumed to
vary linearly along with the heated or cooled length. Thus, The authors declare that they have no conflicts of interest.
16 Science and Technology of Nuclear Installations

Acknowledgments [14] J. H. Park, J. Yoon, J. Eoh, H. Kim, and M. H. Kim, “Opti-

mization and sensitivity analysis of the nitrogen Brayton cycle
The authors would like to express their special thanks for the as a power conversion system for a sodium-cooled fast re-
financial support from the National Natural Science Foun- actor,” Nuclear Engineering and Design, vol. 340, pp. 325–334,
dation of China (Grant Nos.: 11605132 and U1867218) and 2018.
financial support from the Nuclear Power Institute of China. [15] V. Dostal, M. J. Driscoll, and P. Hejzlar, A Supercritical
Carbon Dioxide Cycle for Next Generation Nuclear Reactors,
Massachusetts Institute of Technology, Department of Nu-
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