Energy Reports 8 (2022) 2480–2489

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journal homepage: www.elsevier.com/locate/egyr

Research paper

Properties of Nitrous Oxide and Helium mixtures for space nuclear

recompression Brayton cycle
∗
Xinyu Miao a , Haochun Zhang a , , Dong Zhang a , Chenxu Zhang b , Ziliang Huang a
a
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
b
Harbin Electric Company Limited, Harbin 150028, China

article info a b s t r a c t

Article history: Space nuclear reactors are the research foundation of space nuclear power and nuclear propulsion.
Received 2 August 2021 Thermoelectric conversion efficiency and mass of high-power nuclear reactors have always been
Received in revised form 27 December 2021 essential factors that restrict aerospace design. Supercritical nitrous oxide (S-N2 O) Brayton cycle is
Accepted 22 January 2022
becoming hot research due to its high-power conversion efficiency, low energy loss, compact and
Available online xxxx
simple system structure, making it widely used in space nuclear reactor application. The recompression
Keywords: cycle is proposed to improve the thermal efficiency of the S-N2 O cycle and effectively weaken the
Nuclear power spacecraft ‘‘pinch point’’ phenomenon that may occur in the regenerators. The thermodynamic of the S-N2 O
Supercritical N2 O-He Brayton cycle has been studied but has little research on the nitrous oxide (N2 O) and helium (He)
Recompression Brayton cycle mixtures as the working medium for the Brayton cycle. In this paper, physical properties were
Thermodynamic properties
studied on the mixture of supercritical nitrous oxide and helium (S-N2 O+He) as the working medium
Thermoelectric conversion efficiency
of the space power system based on a recompression Brayton cycle. Consider the thermodynamic
properties of the mixture at seven different temperature nodes, analyze the variation trend of
compressibility factor, specific heat, specific heat ratio, thermal conductivity, and dynamic viscosity
with temperature, respectively. Finally, determined the mixing ratio of the working medium at the
maximum thermoelectric conversion efficiency of the cycle and estimated the mass and specific mass
of the Brayton rotating unit.
© 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction shield, and pressure shell. A NEP system can be defined in six
subsystems: reactor, shield, thermoelectric conversion, heat re-
With the deepening exploration of space, spacecraft missions jection, power management and distribution (PMAD), and electric
have been farther and farther away from the earth in recent propulsion (EP). The thermoelectric conversion part of the space
years. Space nuclear power systems are favored due to the advan- nuclear power system is significant. Thermoelectric conversion
tages such as high-power density, stable performance, and long efficiency is related to the operational efficiency and safety of
working life. Space nuclear reactor power systems have simple the aircraft and has a significant influence on the structure and
lightweight structures, making them more suitable for deep space mass of the spacecraft. Thermoelectric conversion technologies
exploration missions and Mars and Lunar Outposts in the future
for a space nuclear power system include dynamic (Gryaznov,
(Liu et al., 2021). Space reactor power system can be operated
2000) and static methods (Mason and Schreiber, 2007). Static
continuously or intermittently, starting and shutting down mul-
conversion methods are designed for a specific situation by mod-
tiple times for more than 1000 years or even longer, with the
power ranging from 100 kWe to 1 MWe, to replace where the so- ular modes, but conversion efficiency is usually about 10% (Fang
lar energy options are not feasible or non-existent (El-Genk et al., et al., 2017). Dynamic conversion methods based on the Stirling,
2010). The nuclear power system of spacecraft can be divided Rankine, and Brayton cycles can provide high thermal efficiency
into two types: nuclear thermal propulsion (NTP) system and of 20% to 30% (Fang et al., 2017). The recompression Brayton cycle
nuclear electric propulsion (NEP) system. NTP consists of three is suitable for the space system (Yuan et al., 2021). Supercritical
highly integrated subsystems: a nuclear reactor, a rocket engine, fluids in power systems have been regarded as a potential techni-
propellant storage, and management subsystem. The reactor sub- cal choice for different types of power conversion systems (Antti
system consists of the core, control drums, actuators, reflector, et al., 2021). The Brayton cycle can be combined with the fourth-
generation nuclear energy system to meet the different power
∗ Corresponding author. requirements of spacecraft. The fourth-generation nuclear energy
E-mail address: zhc7@vip.163.com (H. Zhang). system generally operates with high temperature and pressure

https://doi.org/10.1016/j.egyr.2022.01.186
2352-4847/© 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-
nc-nd/4.0/).
X. Miao, H. Zhang, D. Zhang et al. Energy Reports 8 (2022) 2480–2489

(Hoffelner, 2010), strong corrosion (Murty and Charit, 2008), and

high dose neutron irradiation (Kurtz and Odette, 2019).
Carbon dioxide (CO2 ), nitrous oxide (N2 O), ethyne (C2 H6 ), and
sulfur hexafluoride (SF6 ) can be used as the working mediums
in the recompression supercritical Brayton cycle (Zheng, 2018).
CO2 is widely used for its inert chemical properties, such as high
thermal stability, high density, non-toxic, non-combustible, not
support combustion, low cost, etc. Supercritical CO2 (S-CO2 ) has
become a research hotspot in the field of space power generation
(Li et al., 2021). Compared with other working mediums, their
critical point and physical properties are suitable for supercritical
cycles and easy to reach (Linares et al., 2015). The research of the
S-CO2 Brayton cycle started in the 1940–1950s (Feher, 1968) and
achieved significant achievements in the 1960–1970s (Angelino,
1968). Angelino performed a detailed investigation of SCO2 cycles
and introduced novel cycle configurations such as recompression,
pre-compression, and partial cooling to overcome the internal Fig. 1. Diagram of the megawatt nuclear powered spacecraft with Brayton cycle
irreversibility problem in the recuperator and then improve the (Zhu et al., 2017).

cycle performance (Angelino, 1967).

During that period, the development was slow due to the im-
mature mechanical manufacturing technology (Gokhstein, 1969). nuclear power systems. Moreover, He is difficult to compress,
At the beginning of the 21st century, the study of S-CO2 rose which will also increase the stages of compressors. Therefore,
again (Dostal, 2004). Most development work with S-CO2 cycles pure He cannot be used as a suitable working medium for the
has been applied on large-scale systems with MWe outputs of space Brayton cycle in space power systems with strict volume
space nuclear power systems. S-CO2 cycle has the advantages of and mass constraints. The Brayton cycles using mixture working
high cycle efficiency, simple and compact structure, higher safety, fluids have obvious performance advantages compared with the
has a broad application prospect, and can be combined with S-CO2 Brayton cycle (Liu et al., 2019). Analyzing four supercritical
fourth-generation reactors such as high temperature gas cooled working fluids, when obtaining the same thermal efficiency, CO2 ,
reactor or liquid metal cooled fast reactor (Ahn et al., 2015). A net C2 H6 , and SF6 require a high-pressure ratio and primary flow
efficiency of 41% is calculated for a compressor outlet pressure on rate, while the N2 O cycle requires are smaller. He is an inert
20 MPa and nuclear reactor outlet temperature of 555 ◦ C (Coco- gas, and then adding it to the pure S-N2 O is very beneficial for
Enrıquez et al., 2017). The thermodynamic performance of the avoiding corrosion of the equipment materials. These advantages
S-CO2 Brayton cycle can be improved by increasing the working make N2 O-He mixture as a working medium of recompression
medium’s critical temperature and operating conditions (Khatoon supercritical Brayton power cycle in nuclear reactors.
and Kim, 2019). Research on supercritical ethyne (S-C2 H6 ) as In view of previous literature, this work focuses on new mix-
the working medium for the Brayton cycle was first proposed tures’ properties with mixing ratio and new fluids in the re-
by Perez et al. as a power conversion system of a fast neutron compression Brayton cycle. In Section 2, the composition of the
breeder reactor that can replace S-CO2 as a liquid metal coolant recompression Brayton cycle, physical properties prediction mod-
(Perez, 2008). The main problem for S-C2 H6 is chemical stability els, and thermodynamic models of the mixture are described.
and flammability; the former is the crucial issue. Enriquez et al. The performance of mixtures with different mole fractions of
studied the application of the S-C2 H6 Brayton cycle focused on the N2 O and He, obtained the maximum thermal efficiency of the
solar thermal power stations (Luis et al., 2016). In the research, system, compared and analyzed the thermal efficiency with the
Enriquez pointed out that reducing the residence time of the corresponding supercritical working fluid recompression Brayton
working medium at high temperature was a solution to the cycle are analyzed in Section 3. Conclusions and future work are
decomposition problem of C2 H6 at high temperature. At present, discussed in Section 4. An increase in the thermal efficiency of the
there is no relevant research literature on the supercritical sulfur recompression Brayton cycle using N2 O-He mixtures is the main
hexafluoride (S-SF6 ) Brayton cycle. SF6 also has problems with conclusion of this manuscript.
chemical stability and may not be suitable for high temperature
conditions (Calderazzi and Paliano, 1997). In addition, scholars
2. System description and thermodynamic analysis
from Sandia Laboratory in the United States mixed alkanes (in-
cluding C2 H6 ), nobles gases, SF6 , and other working mediums into
The spacecraft with the Brayton cycle consists of electric
CO2 to change its critical point and improve circulation efficiency
thruster, radiator, central truss, reactor, Brayton unit, and radi-
(Wright et al., 2013). The critical temperature and pressure of
ation shielding. The spacecraft diagram with the Brayton cycle is
N2 O are:36.5 ◦ C/7.24 MPa, which is not much different from the
critical point of CO2 (31.1 ◦ C/7.39MPa). The physical properties shown in Fig. 1. Brayton device is a crucial thermoelectric con-
of N2 O and CO2 are similar. The influence of critical pressure version component of the spacecraft, with flexibility in working
and temperature of N2 O on system temperature, pressure, and medium selection and arrangement.
performance is almost the same as that of CO2 , making N2 O have
the potential as a working medium of supercritical cycles (Jahar, 2.1. System description
2010). Compared with the CO2 system, the N2 O system exhibits
higher pressure ratio and higher thermal efficiency (Jahar, 2010). According to the different loop structure, the Brayton cycle can
Helium (He) is an inert gas commonly used in the Brayton cycle be divided into different modes according to different configu-
(El-Genk and Tournier, 2007) and considered as a working fluid rations. For supercritical N2 O-He working medium, the physical
for terrestrial and space (Labus et al., 1989). The small molar properties change dramatically near the critical point, and then
mass of He will increase the aerodynamic load of impeller blades, the recompression supercritical Brayton cycle system is a suitable
thus increasing the mass and size of turbomachinery in space and high-performance thermal cycle for this study. Components
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X. Miao, H. Zhang, D. Zhang et al. Energy Reports 8 (2022) 2480–2489

Fig. 2. Schematic diagram of the recompression Brayton cycle.

2.2. Physical properties prediction model of N2 O-He mixture gas

Chapman–Enskog theory is widely used in the calculation of

the physical properties of gases. State Equation for the actual gas
is shown as:
pv
Z = (1)
Rg T
Where p is the pressure of the gas (Pa), Rg is the perfect gas
constant, Rg = 8.314 J/mol K, T is the temperature of the gas
(K), v is the gas molar volume (m3 /mole), Z is the compressibility
factor of the actual gas, if Z > 1, the real gas is more difficult to
compress than the ideal gas, otherwise it is easier to compress, if
Z = 1, the properties of the gas are close to that of the ideal gas.
Eq. (1) also can be written as:
pv B C D
Z = =1+ + + + ··· (2)
Rg T v v2 v3
Where B, C, D. . . respectively represent second order, third order,
Fig. 3. T–s diagram of the recompression Brayton cycle. and fourth-order virial coefficients, which relate to the inter-
molecular potentials.
The ‘‘perfect fluid’’ correlation developed by Pitzer and Curl
of the recompression system include main compressor (MC), re- in 1957 (National Institute of Standards and Technology (NIST),
compressor (RC), turbine, high-temperature regenerator (HTR), 2010) for the second virial coefficient, B is in excellent agreement
low-temperature regenerator (LTR), reactor, and other compo- with the experimental data when 0.7 < θ < 3.0 [θ = (T /Tcr )] (Pitzer
nents. A schematic diagram and the corresponding T–s diagram and Curl, 1957), but N2 O can be deviated by the data when 1.0 <
of the recompression power system are shown in Figs. 2 and 3, θ < 5.0.
respectively. In the primary loop, the coolant of the reactor is The expression for the normalized second virial coefficient,
B, is shown as (National Institute of Standards and Technol-
lithium (Li). The Li absorbs the reactor’s heat and then directly
ogy (NIST), 2010):
into the regenerator (RE) to heat the working medium of the
Brayton cycle is the secondary loop. The mixture of N2 O and He B = v ∗ ΨB (T /Tcr )
is heated in the RE and then flows into the turbine (1-2) and 0.44
[ ( )
produces power (2-3). The stream then flows to the HTR and then = v −102.6 + 102.732 − 0.001 × θ − 1.22
∗
θ
to the LTR to heat the gas compressed in the main compressor ( √ )]
(7-8a-8-1). The cooled stream exiting LTR (5) is divided into two × tanh 4.5 θ (3)
parts. The split ratio of one part is x∗ , and another part is 1-x∗ .
The part with the higher mass flow rate (1-x), 5a, is cooled in the Where Tcr is the critical temperature of pure gas (K), v* is the
cooler (5a-6) before flows into the MC and then compressed to characteristic molar volume of gas mixture (m3 /mol), θ is the
higher pressure (6-7) and heated through the LTR (7-8a). Stream reduced temperature, θ = T/T cr , ΨB is the dimensionless function
5b, with a lower mass flow rate x, is compressed by the RC to of reduced density of second virial coefficient.
the same pressure as the main compressor (5b-8b). The stream For He, the following relationship is developed for the second
out from the LTR and the RC are mixed at state 8 and then being virial coefficient as Jean and Mohamed (2008):
heated in the HTR (8-1), afterward to the RE. Thus, the circulation 115 835
BHe cm3 /mole = 8.4 − 0.0018 × T + √ −
[ ]
of the secondary cycle is completed. (4)
T T
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X. Miao, H. Zhang, D. Zhang et al. Energy Reports 8 (2022) 2480–2489

Similarly, the data for the normalized third virial coefficient are Where ρ is the density of the mixture(kg/m3 ), Rg is the gas
correlated as Jean and Mohamed (2008): constant of the mixture, and presented below:
0.0237 8314
[ ( )
C = v ∗2 0.0757 + −0.0826 − 3.6 × 10−5 θ + 0.059
Rg = (13)
θ M
Where M is the average molar mass of the mixture and presented
]
× tanh (0.84θ) (5) below (Zhang et al., 2021):
The B, C for mixture can be presented as Brewer and Vaughn M = x1 M1 + (1 − x1 )M2 (14)
(1969):
2.2.3. Dynamic viscosity
B = x21 B11 + 2x1 x2 B12 + x22 B22
The dynamic viscosity of the mixture is shown as Jean and
B12 = v12
∗
ΨB T /Tcr ,12
( )
Mohamed (2008):
(6)
B11 = v11
∗
ΨB T /Tcr ,11 1 0.291 × v ∗
( )
µmix = µ0 + (1 − )µ∗ × ψµ ( ρ) (15)
2.3 M
B22 = v22 ΨB T /Tcr ,22
∗
( )
The critical viscosity of the mixture, µ∗ is calculated using Eq. (16)
C = x31 C111 + 3x21 x2 C112 + 3x1 x22 C122 + x32 C222 by Mason and Uribe (1996),
) 13 √ as:
C112 = C12 C2
( MT ∗
(7) µ = 0.204 × 10
∗ −7
)1 (0.291 × v ∗ )2/3 (16)
C1 C22 3
(
C122 =
ψµ (ρ ) = 0.221ρ + 1.062ρ 2 − 0.509ρ 3 + 0.225ρ 4
Where Bii is the second virial coefficient for a pure gas (mol/m3 ),
The average critical specific volume v∗ and average critical
Bij is the second virial interaction coefficient (mol/m3 ) i ̸ = j, Ciii
temperatures T ∗ are calculated as Jean and Mohamed (2008):
is the third virial coefficient of pure gas (mol2 /m6 ), Cijj is the
third virial interaction coefficient (mol2 /m6 ) i ̸ = j, v*ii is the v ∗ = x1 v11 + x2 v22 (17)
characteristic molar volume of pure gas (m3 /mol) v*ii = v* =
x2 V11 T11 + x222 V22 T22 + 2x1 x2 V12 T12
Rg∗ (Tcr /Pcr ), v*ij is the characteristic interaction molar volume T ∗ = 11 (18)
(m3 /mol) i ̸ = j, v∗12 is the average specific volume of the mixture, x1 V11 + x2 V22
1 and 2 respectively stand for He and N2 O. xi is the molar fraction The viscosity of the gas mixture is calculated using the pro-
of component i in the gas mixture. posed by Sutherland and Wassiljewa:
Tcr,12 is the average critical temperature of mixture and pre- µ01 µ02
sented as Prausnitz (1959): µ0 = x2 + (19)
1 + φ12 x 1 + φ21 x1
x
1 2
4b √
Tcr ,12 = Tcr ,1 Tcr ,2 (8) The interaction coefficient φij are calculated by Mason and Uribe
(1 + b)
(1996):
v11
∗
µ0 2M1 M2 5 M2
b=
v22
∗ φ12 = 1 ×( + )
µ12 (M1 + M2 )2 3A12 M1
(20)
2.2.1. Enthalpy and specific heat µ0 2M1 M2 5 M1
φ21 = 2 × ( + )
In this paper, Cp and Cv of the working medium are consid- µ12 (M1 + M2 )2 3A12 M2
ered as strength parameters (unrelated to the total amount of In these equations, the A12 is the ratio collision integrals, A12 =
(2,2)
substance) and Cp , Cv can be calculated by the weighted aver- Ω / Ω (1,1) , and the interaction viscosity is shown below (Jean
age of the mass fraction. Therefore, the calculation formulas for and Mohamed, 2008):
the thermal parameters of N2 O-He mixed working medium are
shown as Zhang et al. (2021): µ12 = Aµ (T − Tµ )n (21)

ymix = w y1 + (1 − w )y2 (9) Where Aµ is the coefficient used in viscosity correlation, Tµ is

the temperature used in viscosity correlation (K), and n is the
Where y is the thermal physical property parameters of the exponent used in viscosity correlation. Aµ = 3.4*10−7 , Tµ =
working medium. 45.89, n = 0.66.
The mass fraction of He in the mixed working medium is
shown as Zhang et al. (2021): 2.2.4. Thermal conductivity
Thermal conductivity of mixture for the cycle is calculated as
x1 M1
w= (10) Jean and Mohamed (2008):
x1 M1 + (1 − x1 )M2
0.291 × v ∗
( )
1
Where x1 is the mole fraction of He in the mixture, γmix is the λmix = λo + 1 − λ ∗ × ψλ ( ρ) (22)
2.94 M
specific heat ratio of the mixed working medium (Zhang et al.,
2021). In this relation, the ‘‘Pseudo-critical’’ conductivity of the mixture,
λ∗ is calculated by Eq. (23) proposed by the van der Waals’ rules,
Cp,mix
γmix = (11) as:
Cv,mix (T ∗ )0.271
λ∗ = 0.304 × 10−4 ×
M 0.465 (0.291 × V ∗ )0.415 (23)
2.2.2. Density
The density of mixed working medium is calculated as follow: ψλ (ρ ) = 0.645ρ + 0.33ρ 2 + 0.0368ρ 3 − 0.0128ρ 4
Using the Van der Waals’ mixing rules can calculate the
p ‘‘Pseudo-critical’’ temperature and volume of the mixture, Eqs. (17)
ρ= (12)
and (18).
ZRg T
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X. Miao, H. Zhang, D. Zhang et al. Energy Reports 8 (2022) 2480–2489

In Eq. (22), the thermal conductivity of the mixture is calcu- h7s − h6

ηMC = (31)
lated by Chapman–Enskog kinetic theory approached (Mason and h7 − h6
Uribe, 1996) as: h8s − h5
ηRC = (32)
x21 x22 2x1 x2 L12
h8 − h5
L11
+ L22
− L11 L22
λ0 = (24) Where s is isentropic.
L212 The effectiveness of the HTR and LTR can be defined as Juhasz
1− L11 L22
(2005):
Where T3 − T4
15 25
x2 x1 x2 M12 + M22 − 3M22 B12 + 4M1 M2 A12 εHTR = (33)
L11 = 1o + × 2 4
T3 − T8
λ1 2λ12 (M1 + M2 )2 A12 T4 − T5
εLTR = (34)
( )
x1 x2 M1 M2 55
L12 = − × × − 3B12 − 4A12 T4 − T7
2λ12 (25)
(M1 + M2 ) A12 4 2
The first law efficiencies for working medium is given by Jahar
15 25
x22 x1 x2 M + 4 M1 − 3M12 B12 + 4M1 M2 A12
2 2
(2010),
L22 = + × 2 2
λ o
2 2λ12 (M1 + M2 )2 A12 Wnet
ηth = (35)
In these equations, the λ12 is related to the interaction viscos- QR
ity µ12 by Jean and Mohamed (2008): Where QR is the rate of heat transfer of reactor (kW), Wnet is the
15 k net produced power for the system, ηth is the thermal efficiency
λ12 = µ12 f12 (26) of the cycle.
4 m12
The Wnet is calculated by Jahar (2010):
Where correction factor f12 is determined by the experiments, for
f12 (N2 O-He) = 1.08; Boltzmann number k = 1.38 × 10−23 (J/K); Wnet = WT − (WMC + WRC ) (36)
m12 is the average molecular weight of the mixture. Where WT is the total turbine power output (MW), WMC is the
total main compressor power consumption (MW), WRC is the total
2.2.5. Prandtl number re-compressor power consumption (MW).
Prandtl number of the mixture for the cycle is calculated as: The Brayton rotating unit is mainly composed of the compres-
µCp sor, turbine, and generator. With the same system output power,
Pr = (27) a nuclear reactor can be connected to multiple Brayton Rotating
λ units, which can eliminate system failure caused by a single unit
2.3. Thermodynamics model failure.
Assuming that the total number of Brayton Rotating units in
the system is N, the mass is expressed as Webb and Gross (2011):
The thermodynamic analysis of the recompression Brayton
cycle based on the ‘‘First Law of Thermodynamics Analysis’’ (Shen
1 + 0.52 ln π
and Dong, 2007), and the assumptions considered for the system MBRU = C αBRU Pe0.7 N 0.3 (37)
are Jahar (2010): 1.93
Where C is an empirical constant, N is the number of Brayton
(1) The system works under steady state conditions;
Rotating units, Pe is the system power, αBRU is the specific mass
(2) Only consider the pressure drop in the reactor, high and
of a single Brayton Rotating unit, π is the gas compression ratio.
low temperature regenerator, and cooler;
Akbari and Mahmoudi (2014) based on the existing experi-
(3) Changes in kinetic energy and potential energy of compo- mental data of space Brayton rotating unit, the quadratic fitting
nents are not considered; formula of specific mass and turbine outlet temperature is as
(4) Circulation and heat exchange between components and follows:
the environment are ignored. ( )2
T3 T3
During the analysis, only concerned the overall performance of αBRU = −5.893 + 5.829 + 12.19 (38)
1000 1000
the components and the thermal state at the inlet and outlet,
ignored the internal parameters and dimensional changes of the Where T3 is the turbine outlet temperature.
components. Each component of the cycle is based on the mass
and energy balances, which are presented below (Mohammadi 3. Results and discussion
et al., 2019):
∑ ∑ 3.1. Thermophysical properties of pure gas and mixture gas
mi = mo (28)
∑ ∑ When calculating the physical properties of the working
Q −W = mo ho − m i hi (29) medium, operation pressure is 7.4 MPa and selected seven tem-
perature nodes: 315.00 K, 400.00 K, 600.00 K, 800.00 K, 1000.00
Where h is the specific enthalpy (kJ/kg), m is the mass flow
K, 1200.00 K, 1400.00 K. Properties of the working medium have
rate (kg/s), Q is the rate of heat transfer (kW), W is the power
great significance to the thermal heat efficiency of the Brayton
(kW), subscript i, o stands for inlet and outlet.
cycle.
The key of thermodynamic analysis of system components is
to calculate the outlet state parameters and component perfor- 3.1.1. Basic thermophysical properties of N2 O
mance parameters under the specified inlet state. The efficiency In order to simplify the calculation, N2 O is regarded as an ideal
of the turbine, MC, and RC are shown below (Mohammadi et al., gas, and the thermodynamic properties of N2 O are calculated by
2019): using the REFPROP software (Lemmon et al., 2010), and develop
h2 − h3 a thermodynamic property subroutine ‘‘PUREN2OPROP’’ to esti-
ηT = (30) mate thermodynamic properties of nitrous oxide in supercritical
h2 − h3s
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X. Miao, H. Zhang, D. Zhang et al. Energy Reports 8 (2022) 2480–2489

Table 1
Constant value of the empirical formula for N2 O physical properties calculation.
T (K) 298–1400 1400–6000
A 27.67988 60.30274
B 51.14898 1.034566
C −30.64454 −0.192997
D 6.847911 0.012540
E −0.157906 −6.860254

region, which based on the literature report earlier (Lemmon

and Span, 2006) and the National Institute of Standards and
Technology (NIST) (National Institute of Standards and Technol-
ogy (NIST), 2010) database. The REFPROP software can calculate
the properties of N2 O up to 525 K and use Eq. (38) to calculate
properties of N2 O above 525 K. The maximum accuracy of the
NIST REFPROP software error is 0.1%; the average accuracy error Fig. 4. Effect of He mole fraction on compressibility factor of mixture, Z.
can be controlled within 0.02%.
The empirical formula for Cp , Cv are as follows:

Cp◦ = A + Bt + Ct 2 + Dt 3 + E /t 2
(39)
Cv◦ = A − Rg + Bt + Ct 2 + Dt 3 + E /t 2

where A, B, C, D, E are constants from NIST, the data are shown

in Table 1; t = T (K)/1000; Rg (N2 O) = 188.95 J/(kg K).

3.1.2. Basic thermophysical properties of He

The corresponding properties data of He used REFPROP soft-
ware to search. When p = 7.40 MPa, T = 400.00–1400.00 K,
the Cp , Cv , γ for He are little changed with temperature, Cp ≈
5.199 kJ/(kg K), Cv ≈ 3.13 kJ/(kg K),γ ≈ 1.66. REFPROP software
can be used to calculate the properties of CO2 up to 2000 K.

3.1.3. Thermophysical properties of N2 O-He Fig. 5. Effect of He mole fraction on heat capacity of the mixture, Cp .
The properties of the mixture depending on the properties of
the pure gas substance. Python software was used to program
and iteratively calculate the parameters related to the working 3.4. Specific heat ratio, γ
medium properties of the mixtures.
The specific heat ratio, γ , is shown in Fig. 6. The range of
γ is from 1.15 to 1.7. The Cp of He is not easily affected by
3.2. Compressibility factor, Z temperature, but the Cp of N2 O is greatly affected by temperature.
In the low region of xHe , the γ of mixture has a more significant
When Z = 1, the mixed gas obeys the ideal gas law; Z < 1, the variation with temperature. The γ is increased with the increase
gas is compressed easily; Z > 1, the gas is compressed difficultly. of xHe . When the xHe > 0.6, the γ change trend tends to be
The compressibility factor of the mixture, Z, is shown in Fig. 4. gentle. When T = 315.00 K, the corresponding line of γ has
The compressibility factor of the mixture gas is changed from a bit different from other lines because near the critical point
0.75 to 1.15. When T = 315.00 K–600.00 K, Z of the mixture properties of N2 O changed drastically.
increase slowly with the increase in the mole fraction of He,
xHe . When T = 800.00 K–1400.00 K, Z is decreases with the 3.5. Thermal conductivity, λ
increases of xHe . For the mixture, if xHe < 0.3, Z decreases with the
The thermal conductivity, λ, is shown in Fig. 7. Thermal con-
temperature decrease; if xHe > 0.3, Z decreases with the increase
ductivity is sensitive to temperature changes. The thermal con-
of temperature. When T = 800.00 K, Z ≈ 1.0, nearly has no
ductivity of pure N2 O at 1200.00 K is 2.8 times that at 400.00 K.
change with xHe . The thermal conductivity of He is much higher than that of N2 O.
Therefore, with the increase of xHe , the thermal conductivity
3.3. Specific heat, Cp of the gas mixture increases, and the higher temperature, the
greater the λ rise. The 315.00 K thermal conductivity line is
slightly different from other lines because 315.00 K is close to
The heat capacity of the mixture, Cp , is shown in Fig. 5. In the critical point of N2 O.
Fig. 5, the Cp is increased with the increase of xHe . At high xHe ,
the Cp has little change with temperature, the lines approximately 3.6. Dynamic viscosity, µ
overlap; at low xHe , lower temperature more minor smaller Cp .
With the same xHe , Cp increases slower by temperature, and the The dynamic viscosity, µ, is shown in Fig. 8. Due to the
lines have small change in high temperature. molecular interaction of the working medium, the viscosity of the
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Fig. 6. Effect of He mole fraction on specific heat ratio, γ . Fig. 9. Effect of He mole fraction on Prandtl number, Pr.

Table 2
The selected Brayton cycle parameters (Zhang, 2019; Feng et al., 2020;
Mohammadi et al., 2019; Meng et al., 2021).
Parameters Description Values
p3 (MPa) Main compressor inlet pressure 7.40
T2 (K) Reactor outlet temperature 1200.00
T6 (K) Cooler outlet temperature 315.00
m (kg/s) Mass flow rate 5.00
x∗ Split ratio 0.30
π Pressure ratio 3.00
ηMC Main compressor efficiency 0.85
ηRC Re-compressor efficiency 0.85
ηT Turbine efficiency 0.88
εHTR Effectiveness of High-temperature recuperator 0.86
εLTR Effectiveness of Low-temperature recuperator 0.86

3.7. Prandtl number

Fig. 7. Effect of He mole fraction on thermal conductivity, λ. The Prandtl number, Pr, is shown in Fig. 9. The Prandtl number
of mixtures is always lower than those of pure gases in the
mixtures and very significant with the mixture composition and
temperature. The Prandtl number of He is between 0.5–0.7, and
N2 O is between 0.7–1.5. When T = 315.00 K–325.00 K, the
Prandtl number increases rapidly with increasing Helium mole
fraction xHe . At the same time, when T > 400.00 K and xHe < 0.5,
the Prandtl number of the mixture gradually decreases, then but
when xHe > 0.5, the Prandtl number almost changes little. The
Prandtl number is an important parameter that affects the heat
transfer coefficient of the working fluid and has an essential effect
on the cycle.

3.8. System thermal efficiency, ηth

In this paper, a space nuclear power system with recom-

pression supercritical Brayton cycle and high temperature gas
cooled reactor is adopted. The reactor outlet temperature T2 is
between 1000.00 K and 1400.00 K. In space, the radiator has
Fig. 8. Effect of He mole fraction on dynamic viscosity, µ. different temperatures in different directions due to the different
operating positions of the spacecraft. The outlet temperature of
the cooler T6 is generally 315.00 K∼600.00 K. The specific cycle
mixture increases slowly with the addition of He. The viscosity system parameters are based on some data in Akbari and Mah-
values of He and N2 O are similar, so the viscosity changes little moudi’s report (Akbari and Mahmoudi, 2014), and cycle operation
after mixing. At the same time, as the temperature increases, parameters are shown in Table 2.
the viscosity of the mixed gas increases, the increase of viscosity The thermal efficiency of the given conditions of the system,
will lead to the increase of pressure loss of the mixture, which ηth , is shown in Fig. 10. As shown in the figure, with the increase
has an adverse effect on the circulation. The initial period of the of He content, the thermal efficiency of the system increases
viscosity line at 315.00 K is slightly different from the others rapidly at first and then decreases slowly. When 0 < xHe < 0.15,
trends because 315.00 K is close to the critical point of N2 O. xHe greatly influences on the thermal efficiency, ηth increases with
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Fig. 10. Effect of He mole fraction on system thermal efficiency, ηth . Fig. 12. Effect of He mole fraction on specific mass of Brayton Rotating unit,
αBRU .

4. Conclusion

A detailed study on thermophysical properties of the N2 O and

He mixtures as Brayton cycle working medium for MW space
nuclear reactor system has been presented in this study. The
developed expression for the gas mixture properties is valid at
a temperature between the critical value, Tcr and 1200 K, pres-
sure up to 21 MPa. The recompression cycle is a competitive
power cycle that can avoid the pinch point due to the sharply
changed properties of supercritical N2 O-He. He added in the N2 O
reduces the critical temperature and increases the power cycle
thermal efficiency. The working medium mixture 85%N2 O-15%He
increases the power cycle efficiency from 43% to 48.1%. Using
the new working medium for the cycle results in higher thermal
efficiency and better performance of the cycle configurations.
Fig. 11. Effect of He mole fraction on mass of Brayton rotating unit, MBRU . The provided evaluation can be used to select the suitable cycle
working medium specified environmental conditions. According
to the results and analysis of the cycle, the following conclusions
can be drawn.
the increase of xHe . When xHe > 0.15, the ηth decrease slowly. It
can be seen that the thermal efficiency is maximum at xHe = 0.15 (1) When He mole fraction, xHe < 0.3, the compression factor,
and ηth(max) = 0.4814. Z, varies possibility with temperature; when xHe > 0.3, the
compression factor decreases with the increase of temper-
3.9. Mass of brayton rotating unit, MBRU ature and the mixture When He mole fraction, xHe < 0.3, the
compression factor, Z, varies possibility with temperature;
The spacecraft mass is an important parameter. The mass when xHe > 0.3, the compression factor decreases with the
(MBRU ) and specific mass (αBRU ) of the Brayton Rotating unit are increase of temperature and the mixture is more easily
shown respectively in Figs. 11 and 12. In Fig. 10, the MBRU in- compressed. When T = 800.00 K, Z ≈ 1.0, it means that
creases with the increases of the He content in the beginning and the mixture can be regarded as an ideal gas under this
then decreases slowly. The MBRU range is 3242–3706.6 kg, and at condition, and the compression factor has little change
xHe = 0.32, the mass value reaches the maximum MBRU(max) = with xHe .
3706.6 kg. In Fig. 11, the specific mass of the Brayton Rotating (2) Specific heat, Cp , and specific heat ratio, γ , increase with
the increase of xHe , but have different variation trends. At
unit first grows rapidly and then stabilizes with the increase of
high xHe , Cp changes little with temperature. In the lower
xHe . The range of specific mass is 7.51–8.12.
region of xHe , the γ of the mixture varies greatly with
temperature. When xHe > 0.6, the γ change trend of the
3.10. Performance comparison with CO2 , He, N2 O, and N2 O-He cycle mixture tends to be gentle.
(3) Thermal conductivity, λ, increases with the increases of xHe .
The comparison between CO2 , N2 O, He, and 85%N2 O–15%He as Dynamic viscosity, µ, increases slowly with the addition
working mediums in both supercritical recompression cycles for of He. Temperature greatly influences on dynamic viscos-
various operating parameters are shown in Table 3. The essential ity; the higher the temperature, the greater the dynamic
input operating conditions of these working mediums in Table 3 viscosity. These two properties of the mixture at 315.00 K
are: the mass flow rate is 5 kg/s, the effectiveness of HTR and LTR are different from other lines because the temperature line
is 86%, the efficiency of the MC and RC is 85%, the efficiency of of 315.00 K is close to the critical point of N2 O. Prandtl
the turbine is 88%, the split ratio is 0.30, and the pressure ratio number, Pr, increases rapidly with increasing Helium mole
is 3.00. Results show that N2 O–He has better thermal efficiency fraction xHe as the T ≤ 325 K. When T ≥ 400.00 K, the
than CO2 , He, and N2 O for all operating conditions applied in the Prandtl number of the mixture gradually decreases at xHe
Brayton cycle. < 0.5, and then, the Prandtl number almost changes little.
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Table 3
Comparison of CO2 , N2 O, He, and 85% N2 O - 15% He recompression Brayton cycle.
Operating parameters CO2 N2 O 85% N2 O and 15% He He
Tmin (K) Tmax (K) Pmin (MPa) ηth (%) ηth (%) ηth (%) ηth (%)
315 1200 7.4 41.6 43.0 48.1 43.2
315 1200 8.4 39.9 40.9 45.3 41.2
315 1000 7.4 40.4 41.8 47.1 41.7
315 1000 8.4 38.2 39.7 44.5 39.4
325 1200 7.4 38.3 39.2 47.5 39.8
325 1200 8.4 36.1 36.9 44.8 37.5
325 1000 7.4 34.5 40.0 46.4 36.3
325 1000 8.4 31.2 37.5 43.6 33.3

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