Delft University of Technology

Effect of CO2-based binary mixtures on the performance of radial-inflow turbines for the
supercritical CO2 cycles

Yang, Yueming; Wang, Xurong; Hooman, Kamel; Han, Kuihua; Xu, Jinliang; He, Suoying; Qi, Jianhui

DOI
10.1016/j.energy.2022.126429
Publication date
2023
Document Version
Final published version
Published in
Energy

Citation (APA)
Yang, Y., Wang, X., Hooman, K., Han, K., Xu, J., He, S., & Qi, J. (2023). Effect of CO -based binary
mixtures on the performance of radial-inflow turbines for the supercritical CO cycles. 2Energy, 266, Article
2
126429. https://doi.org/10.1016/j.energy.2022.126429

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 Energy 266 (2023) 126429

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Energy
journal homepage: www.elsevier.com/locate/energy

Effect of CO2 -based binary mixtures on the performance of radial-inflow

turbines for the supercritical CO2 cycles
Yueming Yang a , Xurong Wang b , Kamel Hooman c , Kuihua Han a , Jinliang Xu d , Suoying He a ,
Jianhui Qi a,d,e ,∗
a
School of Energy and Power Engineering, Shandong University, Jinan 250061, China
b School of Energy and Building Environmental Engineering, Henan University of Urban Construction, Pingdingshan 467036, China
c Process and Energy Department, Delft University of Technology, 2628 CB, Delft, The Netherlands
d
Beijing Key Laboratory of Multiphase Flow and Heat Transfer for Low Grade Energy Utilization, North China Electric Power University, Beijing 102206, China
e
Suzhou Research Institute, Shandong University, Suzhou 215123, China

ARTICLE INFO ABSTRACT

Keywords: Recently, the supercritical carbon dioxide (SCO2 ) power cycle has become a hotspot in the field of energy-
Supercritical carbon dioxide efficient utilization. The utilization of additives in the power cycle has been proven to be an effective way
Radial-inflow turbine to improve the SCO2 power cycle efficiency. As one of the core components of the system, the influence of
CO2 -based binary mixture
CO2 -based mixtures on turbine performance needs to be further explored. In this study, the preliminary design
Numerical simulation
and three-dimensional numerical simulation of a 500 kW radial-inflow turbine (RIT) for small-scale SCO2 power
Turbine stage losses
systems were carried out. Furthermore, the design and off-design performance of high Reynolds number and
small size turbine under the change of the CO2 -based binary mixture compositions and mixing ratios were
studied. Increasing the amount of nitrogen, oxygen, or helium into CO2 has a negative effect on the RIT
performance, and the appropriate amount of xenon or krypton can improve the turbine efficiency. Moreover,
mixtures with higher krypton additions adapt to higher heat source conditions. The loss of the turbine stage
passage shows that a large amount of helium greatly reduces the working fluid density, and the high amount
of xenon has a great influence on the dynamic viscosity, which all makes the RIT operation deviate from
the steady state. Therefore, the CFD model simulation fails indicating that RIT designed based on pure CO2
may not run smoothly and continuously. The losses in the stage with pure CO2 and CO2 –Kr mixture were
investigated. The results indicate that the losses originated from the stator cannot be ignored and that the
improvement of efficiency is mainly owed to the reduction in clearance losses. There is no doubt that the
viewpoints proposed in this paper have significant reference value for the practical application of the SCO2
power cycle using mixtures.

1. Introduction the conversion efficiency of conventional power cycles, innovating the

cycle module is necessary. The supercritical carbon dioxide (SCO2 )
Demand for low-carbon energy resources has reached a new peak cycle has attracted extensive attention due to its simple layout, compact
as global efforts to mitigate climate change by reducing carbon emis- system, and high cycle efficiency [2–4], and was first proposed by
sions [1]. Meanwhile, the energy-saving, high-performance, and safe Feher [5] in 1968.
energy conversion system has always been at the leading edge of The SCO2 power cycle overcomes some limitations of the steam
research. As an indispensable subsystem of thermal energy conversion, Rankine cycle, such as the large energy input in the compression
the power cycle module determines the efficiency of the whole system. process, the large heat transfer surfaces, and the large volume of
Selecting an appropriate power cycle module can make low-carbon en- turbomachinery. Moreover, it utilizes the liquid-like properties (the
ergy more flexibly applied to the multi-energy distributed architecture specific volume and compression coefficient are significantly lower
system. This system refers to a regional energy internet that can contain than those in the gas phase) near the critical point of the working fluid
a variety of energy resource inputs and has a variety of output functions to reduce the compressor power consumption. However, while simple
and transport forms. Considering the limited potential for improving cycles benefit from the reduced compression work, their efficiency is

∗ Corresponding author at: School of Energy and Power Engineering, Shandong University, Jinan 250061, China.
E-mail address: j.qi@sdu.edu.cn (J. Qi).

https://doi.org/10.1016/j.energy.2022.126429
Received 2 July 2022; Received in revised form 9 November 2022; Accepted 12 December 2022
Available online 19 December 2022
0360-5442/© 2022 Elsevier Ltd. All rights reserved.
Y. Yang et al. Energy 266 (2023) 126429

Currently, researchers are still attempting to improve the efficiency

Nomenclature
of the SCO2 power cycle. As we know, cycle efficiency is determined
by the temperature and pressure of the high-temperature heat source
Acronyms and the low-temperature heat source. Usually, we try to increase the
1D One-dimensional. temperature and pressure of the high-temperature heat source, i.e. the
3D Three-dimensional. turbine inlet properties. But this way will be limited by the materials of
the cycle. Another way is to lower the minimum operating temperature.
N2 Nitrogen.
However, the lowest-temperature point of SCO2 power cycle is before
O2 Oxygen.
the inlet of the compressor, which should be slightly above the CO2
CFD Computational fluid dynamics.
critical temperature (31.6 °C) to guarantee the high cycle efficiency and
CSP Concentrated solar power. to avoid condensation of CO2 . This requirement limits the potential
DES Distributed energy system of SCO2 power cycle, as the surrounding temperatures are not always
EoS Equations of state. coincident with the CO2 critical points. Hence, the researcher tries to
He Helium. break the constraints of the physical properties of the CO2 by shifting
HTR High temperature recuperator. the critical point of the CO2 . One possible way is to add other gas, such
Kr Krypton. as N2 , O2 , He, etc., into CO2 to alter the critical point. This inspires the
LTR Low temperature recuperator. researchers starting to explore new CO2 -based mixtures, which can be
NIST National Institute of Standards and Technol- potentially used as the working fluid of the SCO2 power cycle.
ogy. To better understand the effect of different additives on the SCO2
Re Reynolds number. cycle efficiency, understanding of CO2 critical point mobility is essen-
tial. Jeong et al. [10,11] addressed that the change direction and range
RGP Real gas property.
of the CO2 critical point depends on the composition and quantity of
RIT Radial-inflow turbine.
additives, such as the addition of helium will decrease the critical tem-
SCO2 Supercritical carbon dioxide.
perature. When helium, xenon, and krypton are used as additives, the
SMR Small modular reactors. cycle efficiency under specific operating conditions will be improved
Xe Xenon. due to the increase in cycle temperature range and pressure ratio. What
Greek Symbols is more, they also proposed that the cycle layouts are crucial to the
selection of additives. According to Hu et al. [12], both CO2 –He and
𝛼 Absolute flow angle, [°] CO2 –Kr mixtures can improve the thermodynamic performance of the
𝛽 Relative flow angle, [°] SCO2 cycle by increasing cycle efficiency and reducing heat transfer in
𝛥 Difference, [–]. HTR (high-temperature recuperator) and LTR (low-temperature recu-
𝜂 Efficiency, [%] perator). However, in the study of Vesely et al. [13,14], for some cycle
𝛾 Isentropic exponent, [–]. layouts, helium showed negative effects like most additives, which
𝜇 Dynamic viscosity, [μPa s]. confirms Jeong’s assertion. Guo et al. [15] carried out a multi-objective
𝜌 Flow density, [kg/m3 ]. optimization in the process of cycle optimization. They recommended
that a medium cooling SCO2 –Xe cycle should be adopted for the con-
𝜀 Tip clearance. [mm].
centrated solar power (CSP) system, as it has good compatibility to the
Roman Symbols large specific power in the thermal storage. On the other hand, some
solar power plants are located in arid regions and high-temperature
𝑚̇ Mass flow rate, [kg/s].
areas where the efficiency of the SCO2 power cycle system is reduced.
ℎ Enthalpy, [J/kg].
This is due to the environmental temperature being higher than the crit-
𝑀 Torque, [N m] ical temperature, and the working fluid cannot be cooled down to the
𝑃 Pressure, [MPa] adjacent region of the critical point. Therefore, specific additives are
𝑠 Entropy, [J/(kg K)]. selected to increase the critical temperature of working fluids, which is
𝑇 Temperature, [K] proved to be effective in improving the system benefit in arid regions.
𝑊 Shaft power, [W] Bonalumi et al. [16] used CO2 -TiCl4 mixtures for solar applications
𝑍 Blade number, [–]. with high-temperature heat sinks. After adding an appropriate amount
of TiCl4 , the mixture reached a higher critical temperature, resulting
Subscripts
in efficiency gains of up to 5% and 3% in the simple cycle and the
0 Reference state point. recompression cycle, respectively. According to Crespi et al. [17], when
1,2, . . . Number or state point. the mole fractions of TiCl4 and C6 F6 were between 10% and 25%,
g Working fluid. the cycle thermal efficiency could reach more than 50% even in the
application of CSP energy systems with ambient temperature up to
s Isentropic process.
50◦ C. Hu et al. [12] also indicated that CO2 -cyclohexane and CO2 -
tur Turbine.
butane mixtures can be applied to Brayton cycles in arid regions or
power conversion cycles with higher heat sink temperatures.
The SCARABEUS project funded by the EU’s Horizon 2020 research
damaged by the significant loss caused by irreversible heat transfer. is studying the use of CO2 -based mixtures in optimizing the oper-
ating range of supercritical fluid, aiming to improve the operation
Angelino [6] also pointed this out, and proposed to construct different
efficiency and reduce the cost of CSP plants. According to the project,
cycle layouts to reduce the irreversibility in heat recuperation. A series
the mixture can broaden the supercritical cycle to the transcritical
of later studies on system configuration and layout optimization have cycle, resulting in the ability to compress the working fluid in the
also laid the foundation for the application of the SCO2 cycle [7–9]. liquid phase using a pump instead of a compressor, and simplify cycle
Thus, it is vital to choose a suitable power cycle configuration for a configuration depending on the chosen mixture composition. Moreover,
given heat source to increase the efficiency of the power cycle. the air-cooled condenser can obtain high cycle efficiency, especially for

2
Y. Yang et al. Energy 266 (2023) 126429

typical CSP plants in high-temperature and arid environments. CO2 -

C6 F6 , as an intensively investigated working fluid in the SCARABEUS
project, obtains a transcritical cycle with high cycle efficiency when
coupled with a solar tower [18]. Some of the above-mentioned addi-
tives are organic compounds, such as C6 F6 , butane, and cyclohexane.
Invernizzi et al. [19] suggested that the feasibility range of system
operating temperatures should take into account the thermal stability
of organic compounds. In summary, the CO2 -based mixture concept
overcomes some limitations of the conventional SCO2 power cycles, and
the mixture types can be tailored according to the specific boundary
conditions of each energy generation plant. Undoubtedly, the CO2 -
based mixture concept has great development potential and broad
application prospects.
Another possible direction for SCO2 power cycle utilization is on
distributed energy systems (DESs). In recent years, the research on
small DESs, especially Small Modular Reactors (SMR), has gradually
become a hotspot. In contrary technical direction to the conventional
Fig. 1. 3D geometric model of the 500 kW SCO2 RIT.
nuclear power plant, i.e. tries to increase the power capacity of the reac-
tor, SMR tries to increase the mobility and flexibility of the reactor. For
example, CLEAR-I (China Lead-based Research Reactor), as a mobile
advanced nuclear energy system, has ultra-safe, ultra-small, and ultra- working fluids. Second, the internal flow fields of the turbine based on
long-term technical characteristics, and uses a particular kind of liquid the pure CO2 and mixtures are analyzed and compared to reveal the
metal (lead, bismuth, lithium, etc.) as the cooling medium [20]. These possible reasons for large losses.
abilities require applications of the advanced small-scale power cycle, This paper is constructed with the following sections. Section 2 de-
which the SCO2 -based mixtures power cycle illustrates their potential. scribes the model construction and verifies the mesh and mixture prop-
As the requirements of SMR in DES, the power cycle capacity about erties. Section 3 analyzes the performance and losses when the turbine
kilowatt to megawatt are within the interest of researchers. is operating with mixtures. Finally, Section 4 gives three conclusions
The previous study [21] addressed that for small-scale power cycle and some future works.
(less than 20 MW), the radial inflow turbines (RITs) are the most
suitable turbomachinery type. RITs work at high temperature, high 2. Methodology
pressure, and high energy density, which makes their aerodynamic
and structure integrative design always the focus of research [22,23]. This paper seeks various binary mixtures consisting of CO2 and
The performance of RITs will greatly affect the whole cycle efficiency, oxygen, nitrogen, helium, xenon, or krypton. These additives can be
hence, lots of research are focused on the performance estimation infiltrated impurities such as oxygen and nitrogen or specific substances
of the RITs. Allison et al. [24] compared the efficiencies for a high- added to improve the cycle efficiency, such as helium, xenon, and
parameter simple Brayton cycle concerning a range of compressor and krypton [10,11]. As inert gases, helium, krypton, and xenon also have
turbine efficiencies. The results show that every 2% increase in turbine no impact on the stability of CO2 at high temperature and pressure.
efficiency results in nearly a 1% increase in cycle efficiency, while The real gas property (RGP) files for the binary mixtures are obtained
the influence of compressor efficiency is approximately half. Similarly, by calling the property data of the REFPROP database [26] with an
Cho et al. [25] pointed out that turbine efficiency has more effect on in-house Python code.
overall thermal efficiency. Therefore, as the core rotating component To explore the influence of CO2 -based binary mixtures with dif-
of the cycle, the turbines must be selected and designed carefully to ferent components and mixing ratios on the performance of RITs, an
reach an exceptional performance. However, those studies are almost efficient computational fluid dynamics (CFD) numerical calculation
using purely CO2 as working fluids, and the influence of mixtures is platform is used to achieve high-precision process simulation.
hardly revealed. The application of mixtures at the system level has Details about the methodologies will be discussed in the following
been studied in-depth, but the effect on system components has not sections.
been thoroughly explored, especially in turbomachinery. Many stud-
ies [11,12,14] have analyzed the cycle efficiency fluctuations caused 2.1. SCO2 radial-inflow turbine model
by the change of the mixture’s physical properties from the perspective
of thermodynamics. However, their research is under a hypothesis that To build a power cycle test-rig suitable for an SMR in DESs, a
the turbine efficiency will remain the designed value when adding ad- small-scale power turbine test platform is necessary. Moreover, the
ditives into the working fluids. It is not clear whether the internal flow RIT’s design can be scaled while maintaining the same aerodynamic
field of turbomachinery changes significantly with the variation of the flows and performance by using the specific speed parameter (𝑁𝑠 ) [21].
mixture’s composition and mixing ratio, and whether the performance Therefore, different RITs can match the kilowatt-level or megawatt-
changes as previously calculated in the cycle optimization. What is level power generation systems through scaling up, which can be
more, the lack of design procedures for CO2 -based mixture turbines flexibly applied to movable nuclear power plants. Finally, a 500 kW
will also distract the attention of researchers. If we plan to study the SCO2 RIT is selected and generated. This turbine, with very high speed
mixture’s influence on the existing power cycle, a fixed turbine model without exceeding the bearing range, can be used as a representative
will be considered. Therefore, this paper adopts a specific turbine of SCO2 RITs used in small DESs. The stator and rotor geometry
geometry model to carry out mixture-related research. of the turbine are generated by using the preliminary design tool
Based on the above-mentioned discussion, the objective of this TOPGEN [21,27], as shown in Fig. 1.
paper is twofold. Firstly, The influence of mixtures on the power output TOPGEN is a University of Queensland in-house code for RITs devel-
and isentropic efficiency of the turbine is explored. Though there are no oped by the Queensland Geothermal Energy Centre of Excellence. This
specific design procedures for CO2 -based mixture turbines, this study in-house code includes the calculation of flow and geometric features
also evaluated the suitability of SCO2 turbine operating with CO2 -based for both the stator and rotor. An iterative calculation process for each
mixture, i.e. should it be replaced or optimized with the change of combination of head and flow coefficients with rotational speed is

3
Y. Yang et al. Energy 266 (2023) 126429

Table 1
The initial conditions of the calculation.
Parameter Value
Power, 𝑊 [kW] 500.00
Rotational speed, 𝑁 [kRPM] 100.0
Inlet total temperature, 𝑇01 [K] 833.15
Inlet total pressure, 𝑃01 [MPa] 20.00
Mass flow rate, 𝑚̇ [kg/s] 5.30
Pressure ratio (Total-Static), 𝑃 𝑅 [–] 2.22
Flow coefficient, 𝜑 [–] 0.38
Head coefficient, 𝜓 [–] 0.86

Fig. 3. Schematic diagram of the turbine meridian plane.

be seen in Fig. 1. Moreover, a meridional-plane projection of the stator

and the rotor is illustrated in Fig. 3.
Fig. 2. An overview of the TOPGEN calculation process [27].

2.2. Numerical method and boundary conditions

illustrated in Fig. 2. The rotor design part takes into account the well- The construction of the cycle system consumes vast labor power
established loss model to estimate the total losses. For the stator design and financial resources, and the assembly of the test-rig is very costly.
process, TOPGEN does not consider the loss and assumes it as an Hence, it is impractical to build a corresponding test-rig to adapt to the
isentropic expansion process [27]. However, in the research process, cycle system of different mixtures. Considering the above situation, the
it is observed that the loss caused by the stator is obvious, so the existing turbine model designed for pure CO2 is selected to simulate
optimized stator structure [28] is selected in this paper. Through the the situations using different CO2 -based binary mixtures. In this study,
efficiency iteration process shown in Fig. 2, the point where the overall the 3D steady and unsteady simulations are conducted by the ANSYS
efficiency matches the geometric losses is obtained. The final detailed platform. ANSYS-BladeGen is used to build the 3D turbine model,
geometric module provides the necessary information for the three- and the structured mesh used in CFD simulation is generated through
dimensional (3D) blade optimization stage. Moreover, the feasibility TurboGrid. Fig. 4 presents the mesh of the computation domain, which
of each design scheme is addressed based on the selection criteria includes two nozzle passages and a single rotor passage. Since the
that comprise not only optimal operating ranges of the aerodynamic existence of 0.1 mm tip clearance has a noticeable impact on the turbine
design, but also manufacturability and structural/vibration constraints. flow performance, the grid at this position is refined.
To obtain the real gas properties, TOPGEN is coupled to the REFPROP ANSYS-CFX is employed to perform the numerical simulation. The
database by the National Institute of Standards and Technology (NIST). boundary conditions of the designed RIT are the same as the design
For SCO2 , TOPGEN gives access to the Span and Wagner equations of conditions, as shown in Table 1. The total pressure, the total tempera-
state (SW EoS) [29]. ture, and the absolute velocity direction are imposed as the stator inlet
The design conditions for the input of the calculation model are boundary conditions, whereas the static pressure is set as the rotor
listed in Table 1. After filtering the feasible data, a set of turbine outlet boundary condition. The Mixing-Plane method between stator
parameter data is obtained as shown in Table 2. According to the and rotor interfaces is set in the steady-state simulation for information
geometric parameters after optimizing the design, the ANSYS-BladeGen exchange. Since using simplified passage model, the interfaces between
module is adopted to construct the 3D model of the turbine stage part. passages are defined as periodic boundaries. The characteristics of
The final calculation 3D model applied in the following simulation can turbine internal flow are complex, as separated flows and vortex mix

4
Y. Yang et al. Energy 266 (2023) 126429

Table 2
Design parameters for turbine.
Rotor parameter Value Stator parameters Value
Inlet radius, 𝑟4 [mm] 31.63 Inlet radius, 𝑟1 [mm] 41.91
Inlet blade height, 𝑏4 [mm] 2.25 Blade height, 𝑏1 [mm] 2.35
Inlet absolute flow angle, 𝛼4 [°] 66.16 Outlet radius, 𝑟3 [mm] 33.21
Inlet relative flow angle, 𝛽4 [°] −20.22 Stator installation angle, 𝛼1 [°] 56.00
Tip clearance, 𝜀𝑡 [mm] 0.10 Stator blade length, 𝑟3 [mm] 15.00
Outlet hub radius, 𝑟6ℎ [mm] 9.49 Outlet absolute flow angle, 𝛼3 [°] 65.08
Outlet shroud radius, 𝑟6𝑠 [mm] 18.53 Outlet relative flow angle, 𝛽3 [°] 67.56
Outlet hub angle, 𝛽6ℎ [°] −38.29 Trailing edge thickness, 𝑡3 [mm] 0.90
Outlet tip angle, 𝛽6𝑡 [°] −57.03 Stator blade number, 𝑍𝑠 [–] 20
Blade thickness, 𝑡𝑟 [mm] 1.00
Rotor blade number, 𝑍𝑟 [–] 13

In this paper, an in-house python code is developed to obtain

the physical properties of the working fluid from the NIST REFPROP
database to generate RGP files for pure CO2 and CO2 -based binary
mixtures. The RGP table contains 9 physical properties of the mix-
ture, such as the ℎ, 𝑠, 𝐶𝑝 , etc. With the tabulated physical properties
supplied, ANSYS CFX can solve the governing equations by directly
reading the physical data in these external tables. The established GERG
2008 EoS [34,35] is employed to calculate the properties of mixtures
CO2 –N2 , CO2 –O2 , and CO2 –He. For CO2 –Kr and CO2 –Xe, the binary
interaction parameters are automatically fitted for the multi-fluid mod-
els’ calculations (Helmholtz-Energy-Explicit mixture models) [36]. The
equation is based on multi-fluid approximations and is explicit in the
Helmholtz free energy.
The mixture model is a specific basic equation in Helmholtz free
energy 𝑎, with independent mixture variable density 𝜌, temperature 𝑇 ,
and the vector 𝑥̄ of molar composition. In the form of dimensionless
Helmholtz free energy 𝛼 = 𝑎∕(𝑅𝑇 ), the equation is as follows:
Fig. 4. Computational grid of SCO2 RIT.
̄ = 𝛼 𝑜 (𝜌, 𝑇 , 𝑥)
𝛼(𝛿, 𝜏, 𝑥) ̄ + 𝛼 𝑟 (𝛿, 𝜏, 𝑥)
̄ (1)

where 𝛿 = 𝜌/𝜌𝑟 and 𝜏 = 𝑇𝑟 / 𝑇 . The 𝜌𝑟 and 𝑇𝑟 are the composition-

along the passage, resulting in highly turbulent flow. The losses are dependent reducing functions for the mixture density and temperature,
generated, due to the flow separation caused by gas impact on the which are calculated by Eqs. (2) and (3). The function 𝑎(𝜌, 𝑇 , 𝑥)
̄ is split
leading edge, the shed vortex of the trailing edge, and the secondary into a part 𝛼 𝑜 , which represents the properties of ideal-gas mixtures at
flow caused by clearance leakage flow. Therefore, the turbulence model given values for 𝜌, 𝑇 , and 𝑥,̄ and a part 𝛼 𝑟 , which takes into account
adopts the 𝑘 − 𝜔 SST model, which is more accurate in predicting the the residual mixture behavior.
flow with strong adverse pressure gradients. Moreover, no slip-wall ∑ 1 ∑ ∑
𝑁 𝑁−1 𝑁
1 𝑥𝑖 + 𝑥𝑗 1 1 1 3
boundary condition is employed on any solid wall. The convergence = 𝑥2𝑖 + 2 𝑥𝑖 𝑥𝑗 𝛽𝑣,𝑖𝑗 𝛾𝑣,𝑖𝑗 ( + )
𝜌𝑟 (𝑥)
̄ 𝜌 𝑐,𝑖 𝛽𝑣,𝑖𝑗 𝑥𝑖 + 𝑥𝑗 8 𝜌1∕3 𝜌1∕3
2
residual values of each physical quantity are marked as 10−5 . When 𝑖=1 𝑖=1 𝑗=𝑖+1 𝑐,𝑖 𝑐,𝑗
the turbine operates under off-design conditions, the outlet pressure of (2)
the turbine is kept constant while the inlet pressure is changed, so as
to fit the variable condition characteristics of the cycle [30]. ∑
𝑁 ∑
𝑁−1 ∑
𝑁
𝑥𝑖 + 𝑥𝑗
𝑇𝑟 (𝑥)
̄ = 𝑥2𝑖 𝑇𝑐,𝑖 + 2 𝑥𝑖 𝑥𝑗 𝛽𝑇 ,𝑖𝑗 𝛾𝑇 ,𝑖𝑗 (𝑇𝑐,𝑖 𝑇𝑐,𝑗 )0.5 (3)
2
𝛽𝑇 ,𝑖𝑗 𝑥𝑖 + 𝑥𝑗
𝑖=1 𝑖=1 𝑗=𝑖+1
2.3. CO2 -based binary mixtures
The binary parameters 𝛽𝑣,𝑖𝑗 , 𝛽𝑇 ,𝑖𝑗 , 𝛾𝑣,𝑖𝑗 , and 𝛾𝑇 ,𝑖𝑗 are fitted to data for
binary mixtures and dependent on each additive. 𝜌𝑐,𝑖 , 𝜌𝑐,𝑗 , 𝑇𝑐,𝑖 , and 𝑇𝑐,𝑗
The NIST REFPROP database [26] is applied to obtain all thermo-
are critical parameters of the pure components.
physical properties of working fluids. The properties of the working
To verify the accuracy of the physical properties of the working fluid
fluid are loaded into RGP tables and used in ANSYS CFX [31,32].
in this study, the CO2 –Xe binary mixture is taken as an example. Fig. 5
Moreover, the use of REFPROP to calculate the thermophysical proper- shows the comparison of the mixture’s isobaric specific heat capacity
ties of CO2 -based binary mixtures in cycle systems has been generally 𝑐𝑝 calculated in this study with Xue’s MD calculation results [33]. The
recognized [10–15]. Besides, the physical property data obtained by line graph depicts the change of the 𝑐𝑝 of the working fluid under
Xue et al. [33] through molecular dynamics (MD) simulation matched the pressure of 15 MPa. The calculated results are similar to the MD
well with the NIST database. Therefore, it is a feasible option to simulation results, and these two groups of data can verify each other,
combine the above two methods to apply the RIT simulation in this which indicates that the physical properties of the supercritical fluid
study. Due to the limitation of existing experimental data, NIST gives used in this study are credible.
suggestions on the selection of pressure and temperature ranges of
the various mixtures [34]. However, to assess a higher turbine inlet 2.4. Verification of computational mesh and property tables
temperature, the selected temperature range is widened to 900 K. The
extended temperature range can be obtained because fluids behave as To carry out the mesh independency study, 4 meshes with different
ideal gases and their properties vary regularly with different pressures resolutions are generated and marked with Mesh 1 to 4, as shown
and temperatures. Meanwhile, the uncertainty of the prediction of in Table 3. Comparing the turbine mass flow rate, 𝑚, ̇ total to static
high-temperature physical properties is difficult to discuss. efficiency, 𝜂𝑡−𝑠 , and total torque, 𝑀, the relative error between Mesh 3

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Y. Yang et al. Energy 266 (2023) 126429

Fig. 5. The isobaric heat capacity, 𝐶𝑝 , of CO2 –Xe binary mixtures as a function of
temperatures, 𝑇 , calculated by this study and MD at 15 MPa.
Fig. 6. Variation of mixtures isentropic exponent vs. the mole fraction of additives.

Table 3
Mesh independency study.
Mesh Rotor cell Stator cell 𝑚/[kg/s]
̇ 𝜂𝑡−𝑠 /% 𝑀(all (enhance the turbine efficiency) is selected to compare the turbine per-
number/×104 number/×104 blade)/[N m] formance under off-design conditions and explore the change of turbine
1 34.0 11.6 5.34 78.95 47.85 operation range. Moreover, to further study the underlying reasons
2 49.4 15.5 5.33 78.62 47.57 for the mixture’s effects through simulations, the entropy change of
3 74.3 19.3 5.30 79.07 47.50 the turbine stage passage is analyzed. Finally, the variation of turbine
4 111.2 30.2 5.29 79.14 47.48
efficiency is calibrated by a transport characteristic, and the source of
losses is revealed by loss breakdown, which provides a reference for
Table 4 optimizing the turbine to adapt to the specific cycle.
Comparison of 1D design and simulation values of SCO2 RIT.
Case 𝑊 /kW 𝜂𝑡−𝑠 /% 𝑚/[kg/s]
̇ 3.1. SCO2 RIT with SCO2 -based binary mixtures at design point
1D TOPGEN results 500.00 79.02 5.30
3D CFD results with CO2 RK 496.78 79.07 5.30 CO2 -based binary mixtures with different components and mixing
3D CFD results with RGP table 498.25 79.05 5.29
ratios are used to explore the influence of additives on the turbine per-
formance. The selected mole fractions, 𝑥, of various additives are 0.5%,
1%, 5%, 10%, 20%, 30%, 40%, and 50%. Then the steady-state simu-
and Mesh 4 for these parameters are 0.18%, 0.08% and 0.04%. These lation is carried out under the design condition. The constant boundary
relative errors are quite limited, indicating that Mesh 3 has sufficient condition at the stator inlet is set to 833.15 K and 20 MPa. At the rotor
resolution for carrying out the following simulations. For the single outlet, the static pressure maintains 9.009 MPa. The additive changes
passage model, the cell number of the stator is 193,000, and the cell the thermodynamic and transport characteristics of the working fluid
number of the rotor is 743,000. in the supercritical region, so it is necessary to use a parameter to
The data in the RGP tables are derived by setting the mole fraction calibrate the working fluid characteristics. Roberts et al. [39] suggested
𝐶
of CO2 to 1 and the mole fraction of the additive to 0 in the mixture that the isentropic exponent, 𝛾 = 𝐶𝑝 , is an important criterion of
𝑣
composition. To study the independence of the RGP table to the res- similarity in the performance of turbomachinery. Their study showed
olution, 5 different RGP tables with different resolutions, 100 × 100, that the choking 𝑚, ̇ the pressure ratio, and the isentropic efficiency
200 × 200, 300 × 300, 400 × 400 and 500 × 500 are generated and of the compressors are all significantly affected by the changes in 𝛾.
applied in simulation. Considering the independence, stability, conver- Under the inspiration of Roberts’s work, this study attempts to use 𝛾 as
gence, and accuracy of the simulation, RGP tables with a resolution of the parameter to calibrate the mixture characteristics for the following
400 × 400 are finally adopted in the following simulations. exploration of their influence on the RIT.
Table 4 shows the comparison between the 3D numerical simulation Through the comparison of 𝛾 of the CO2 -based mixtures for multiple
results and the 1D results. The CFD simulation data are consistent state points, limited change can be found within the operating tempera-
ture range of RIT. So it can be considered that the specific mixture has a
with the TOPGEN design results, which manifests that the simulation
relatively stable 𝛾 in this interval. However, for different additives, the
process and the design process are mutually verified and explains
changes of the mixture 𝛾 are different with the increasing amount of the
the rationality of the RIT model. Furthermore, the simulation results
additives, as shown in Fig. 6. The introduction of xenon has the greatest
based on RGP tables are close to those based on the Aungier-Redlich-
effect on the thermal properties of CO2 , while nitrogen and oxygen have
Kwong cubic equation [37,38], demonstrating the accuracy of the RGP 𝜕𝛾
the smallest impact. In addition, the CO2 –He mixture 𝛾 growth rate, 𝜕𝑥 ,
table resolution and the process of obtaining the mixture’s physical
increases with an increased 𝑥 of helium. This phenomenon indicates
properties.
that with the increase of 𝑥, the effect of adding helium tends to be
more significant to the change of the CO2 properties. Furthermore, the
3. Results and analysis 𝛾 of the CO2 –Kr mixture increases almost linearly with the increase of
𝑥.
A 500 kW SCO2 RIT is designed and discussed. Firstly, the tur- The variations of the RIT isentropic efficiency with different com-
bine operated with various mixtures under a designed condition to ponents and mixing ratios of the mixtures are shown in Fig. 7. As
explore its performance change. Then the mixture with a positive effect the variation of 𝛾 implies, the introduction of xenon has the largest

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Y. Yang et al. Energy 266 (2023) 126429

the output power. The enthalpy difference decreases significantly with

an increased amount of xenon and krypton, leading to a decrease
in the turbine output power. The introduction of helium increases
the enthalpy difference to the maximum extent. However, due to the
decrease in 𝑚,
̇ the final turbine power growth rate decreases. For the
introduction of nitrogen and oxygen, the enthalpy differences between
the turbine inlet and outlet dominate the rise of the output power.
Furthermore, for the five additives in this paper, the mixture has little
effect on the turbine performance when the 𝑥 is less than 1%.

3.2. SCO2 RIT with SCO2 -based binary mixtures under off-design condition

The above analysis shows that under the premise that the inlet and
outlet boundary conditions of the turbine are constant, the influence
of different additives on the turbine is obviously different, and the
turbine performance also changes significantly with the amount of
additives. The influence of mixtures on turbine performance under off-
design conditions is further analyzed. In this section, only CO2 –Kr
binary mixture is analyzed as it is the only helpful additive to improve
turbine efficiency. Fig. 10 shows the efficiency curve of the off-design
Fig. 7. Variation of RIT isentropic efficiency vs. the mole fraction of additives.
conditions when the turbine outlet pressure is constant and the inlet
pressure is changed. When the additive’s 𝑥 is 1%, the mixtures have
little effect on the variable operating conditions of the turbine, and
impact on turbine efficiency. With the increase of xenon amount, the the turbine highest efficiency point almost coincides with the oper-
efficiency shows a trend of first increase and then decrease, and the ation using pure CO2 . However, with the increase in the amount of
highest efficiency point appears at 𝑥 about 10%. When 𝑥 of xenon is krypton, the deviation of the turbine performance curve under off-
higher than 20%, the turbine efficiency decreases rapidly. Contrary design conditions becomes larger. With an increased 𝑥 of krypton,
to adding xenon, the addition of krypton will increase the turbine the highest point of turbine efficiency moves to the right, which is
efficiency. Nitrogen and oxygen are often considered to be inevitable the direction of increasing inlet pressure. Moreover, the mixtures with
impurity gases, but the effect on turbine efficiency is little when mixed higher amount of krypton show detrimental effects under the lower
in a small amount. Helium has been widely used in the applications of turbine inlet pressure. The above results indicate that the operational
power conversion systems, such as the Gas Cooling High-Temperature range of the turbine becomes narrow.
Reactor. When helium is used as an additive, it has a negative effect Fig. 11 shows the influence of different ratios of CO2 –Kr mixture
on turbine efficiency. With the increase of 𝑥, the decline rate of turbine on the turbine shaft power and 𝑚̇ under variable working conditions.
efficiency accelerates. In all, mixing an appropriate amount of krypton For the turbine shaft power in Fig. 11, the distribution is almost linear
or a small amount of xenon into the working fluid can improve the with respect to the inlet pressure when the mixing ratios change. The
turbine performance, while the other three additives negatively affect 𝑚̇ demand increases with the increase of inlet total pressure, and the
turbine operation. binary mixture with higher krypton 𝑥 brings a greater growth rate in 𝑚. ̇
To further analyze the influence of working fluid properties on On the one hand, with an increasing Kr amount and operating pressure,
turbine performance, the following research is carried out. Fig. 8 il- the working fluid 𝜌 increases, resulting in a rise in 𝑚.
̇ On the other hand,
lustrates the variation curves of mixture 𝜌 and turbine 𝑚̇ as the mole for a fixed turbine geometry, 𝑚̇ depends mainly on pressure. A larger
fraction of additive changes under the design condition. The turbine pressure drop accelerates the overall flow speed in the turbine so that
𝑚̇ is closely related to the mixtures 𝜌 when the CFD simulations are 𝑚̇ increases.
carried out with fixed geometry and inlet velocity. When a higher 𝜌
of the mixture is used in the turbine, the operating 𝑚̇ will decrease. 3.3. Turbine stage losses analysis
On the contrary, a lower 𝜌 of the mixture causes a higher 𝑚. ̇ The 𝜌 of
the CO2 –Xe mixture deviates most from pure CO2 with an increased To understand the influence of mixtures on turbine performance
𝑥 of xenon. Therefore, the change of 𝑚̇ is the largest, resulting in the more clearly, the overall loss of the turbine stage is studied. Fig. 12 de-
instability of turbine operation, which is manifested in the significant picts the entropy rise in the passage at different percentages of the blade
reduction of efficiency, as shown in Fig. 7. As a bioinert gas with low spans when the RIT uses pure CO2 . The entropy growth rate fluctuates
molecular weight, helium has low 𝜌 and high kinematic viscosity, 𝜇. It greatly in the middle and downstream part of the rotor passage, which
significantly reduces the working fluid 𝜌, making the 𝑚̇ of the turbine is caused by the vortex generated through the tip clearance leakage
decrease linearly. The shaft power of RIT depends on the 𝑚̇ and the flow. More separated flow and secondary flow in the channel lead to
enthalpy levels of working fluid at the inlet and the outlet, shown in an increase in flow losses. Further, Fig. 13 shows the changes in the
Eq. (4): average entropy in the turbine stage passage under the different mixing
ratios of nitrogen, xenon, helium, and krypton. The losses in the stator
𝑊𝑡𝑢𝑟 = 𝑚𝑔 (ℎ1 − ℎ6 ) = 𝑚𝑔 𝜂𝑡𝑢𝑟 (ℎ1 − ℎ6𝑠 ) . (4) passage gradually decrease with the increase of the xenon 𝑥. However,
Turbine total to static isentropic efficiency can be calculated through: the losses decrease at first and then increase in the rotor passage.
When the 𝑥 of xenon exceeds 20%, the stage losses increase sharply,
ℎ1 − ℎ6
𝜂𝑡𝑢𝑟 = 𝜂𝑡−𝑠 = . (5) indicating that the influence of mixtures on the turbine performance
ℎ1 − ℎ6𝑠 is intensified, and even affects its operation stability. According to the
Then the total enthalpy difference between the inlet and outlet previous analysis, nitrogen and oxygen have similar effects on turbine
of the turbine is calculated. The variations of enthalpy difference performance, so this section only analyzes the influence of nitrogen
and output power with the increased mole fractions of additives are on stage losses. Overall, nitrogen has a negative effect on the rotor
shown in Fig. 9. The power output can be predicted by the enthalpy turbine stage losses. The effect of the CO2 –Kr mixture is opposite to
difference, while the 𝑚̇ has a relatively small effect on the trend of that of the CO2 –N2 mixture, and the losses gradually decrease with

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Y. Yang et al. Energy 266 (2023) 126429

Fig. 8. Variation of mixture density and RIT mass flow rate vs. the mole fraction of additives.

Fig. 9. Variation of mixture enthalpy at stator inlet and shaft power vs. the mole fraction of additives.

For the steady-state simulation, the Stage model (Mixing-plane

method) is used to exchange the information at the stator and ro-
tor interface. The stage model performs a circumferential averaging
of the fluxes at different bands on the interface. Then steady-state
solutions are obtained in each reference frame. The stage averaging
at the interface leads to a one-time numerical mixing loss, which is
characterized by a sudden entropy rise. However, there is a sharp
entropy drop at the interface when the helium 𝑥 is larger than 20%,
which is not logical. Hence, the entropy and Reynolds number at the
interface when the 𝑥 of helium is 1% and 50% are studied and shown in
Fig. 14. The averaging effect is obvious when the amount is small, and
the equivalent regions of entropy and Reynolds number (Re) show a
banded distribution. When the amount of helium is relatively large, the
average effect of entropy at the interface is unsatisfactory, especially at
the trailing edge of the stator. It can be observed from the Re contours
that the interface Re distribution is not regular, indicating that the
information processing results may be inaccurate. To further reveal the
strong unsteady characteristics under this condition, the next study is
conducted.
Fig. 10. Variation of the isentropic efficiency vs. the turbine inlet pressure.
The CO2 –He binary mixture with a 50% helium mole fraction is
selected to conduct a detailed study. Fig. 15 shows the RIT stage
losses under three different simulation settings. On the one hand, an
the 𝑥 of krypton increasing, which also explains why CO2 –Kr can information processing method of the interface called Frozen Rotor is
improve turbine efficiency. The addition of helium also contributes to used for steady-state simulation in this paper. Compared to the Mixing-
the increase in stage loss, and its negative effect is greater than that of plane, Frozen Rotor maps variables directly to the neighbor patch so
nitrogen. There are two purposes for the investigation of the entropy that the computation requirement of steady-state simulation is reduced.
change curve. One is to observe the relationship between efficiency However, the entropy value gradually tends to be consistent at the rotor
and loss more intuitively. Another aspect is to reflect the prediction of passage center with the development of the main flow. Therefore, it
turbine performance through CFD simulations. The entropy drop at the can be considered that the steady-state simulation has a similar effect
interface becomes obvious with the increase in helium amount, which on the overall performance prediction of the turbine when using the
indicates the uncertainty of steady-state simulation prediction. two interfaces. On the other hand, when using the CO2 –He mixture at

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Y. Yang et al. Energy 266 (2023) 126429

Fig. 11. Variation of the shaft power and mass flow rate vs. the turbine inlet pressure.

Fig. 12. Static entropy contours at different spans with pure CO2 .

a high helium amount, the steady-state simulation can hardly reach 3.4. Breakdown of losses
convergence. It is concluded that the unsteady characteristics of the
turbine are strong, and the steady-state simulation cannot predict tur- From the perspective of transport characteristics of the working
bomachinery performance well. Then the transient simulation of the fluids, the influence of the dynamic viscosity, 𝜇, on the turbine stage
turbine under this working fluid is analyzed. Comparing the entropy losses are investigated in this section. Through the transport model
increase between the steady-state and transient simulations in Fig. 15, calculation based on the thermophysical properties from REFPROP
the two performance predictions are significantly different. It is mainly database, it can be found that different additives have variant levels
of increase effect on the 𝜇. The dynamic viscosity of the mixture obeys
reflected in the loss prediction produced by the interaction effect
a states principle shown in Eq. (6) [40]:
between the stator and rotor. Under the real situation (transient simu-
lation), the entropy rise is obvious from the stator outlet to the rotor ̄ = 𝜇 ∗ (𝑇 , 𝑥)
𝜇(𝑇 , 𝜌, 𝑥) ̄ = 𝜇 ∗ (𝑇 , 𝑥)
̄ + 𝛥𝜇(𝑇 , 𝜌, 𝑥) ̄ + 𝛥𝜇0 (𝑇0 , 𝜌0 )𝐹𝜇 (𝑇 , 𝜌) , (6)
leading edge. However, the stage averaging between static and dynamic ∗
where the superscript denotes a dilute gas value, and the subscript 0
passages only accounts for the time average interaction effects. Even
denotes a reference fluid value. 𝐹𝜇 is a mixture’s factor that contains
though the stage averaging assumes a sufficiently large physical mixing
the use of mixing rules.
generated by the relative motion, the neglected transient interaction When nitrogen and oxygen are introduced as impurity gases with
still plays an important role. This is because the 𝜌 of the mixture has a slight amount, the change of 𝜇 is little, and the influence on the
been greatly reduced at high helium amount, which is significant for turbine performance can be ignored. The amount of helium also has
small size and high-speed RITs. Then the turbine operation tends to a limited effect on the 𝜇 of the mixture, only reducing the 𝜌 to a
be more unstable as the transient interaction between the stators and great extent. Therefore, the turbine efficiency deviates from the nor-
rotors intensified. Therefore, the turbine designed with pure CO2 is no mal working condition after the 𝑚̇ changes, which will cause larger
longer suitable for high mixing ratio CO2 –He mixtures. losses. The addition of krypton and xenon has a great influence on

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Y. Yang et al. Energy 266 (2023) 126429

Fig. 13. Variation of the passage entropy change vs. the streamwise location.

the transport characteristics of CO2 , and the influence from xenon slip-wall on the blade walls). Endwall and secondary flow losses are
is more intense. The simulation results show that the working fluid determined as the entropy rise over each component caused by viscous
pressure and temperature levels are in the range of 8 MPa to 20 MPa endwall effects and induced secondary flows (i.e., by setting a slip-wall
and 700 K to 835 K during turbine operation. As shown in Fig. 16, the on the shroud and hub surfaces, which also prevents in large part the
𝜇 of the mixtures under different mixing ratios are analyzed in com- development of secondary flows). Tip clearance loss is calculated as
bination with the turbine operation efficiency. For the binary mixtures the proportional entropy rise on the rotor due to the existence of tip
of CO2 –Kr and CO2 –Xe, there is a reasonable 𝜇 range that makes the clearance. Mixing loss is determined from the entropy rise across the
turbine efficiency higher than that by adopting pure CO2 . However,
mixing-plane in the steady CFD predictions. All these procedures can
when the 𝜇 exceeds the reasonable range, it will have a negative effect
be done by adjusting the CFD simulations.
on the turbine operation and reduce the turbine efficiency. The reason
for this phenomenon is analyzed from the level of the turbine flow Fig. 18 shows a breakdown of the different contributions to losses
field. The Mach number contours of the 50% blade span under the from the turbine stage passage. Tip leakage loss decreases with the
different amounts of krypton are obtained, as shown in Fig. 17. The increase of krypton amount. It can be explained that the dynamic
local low Mach number region begins to appear at the blade inlet viscosity 𝜇 of the mixtures increases with the increase of the krypton
pressure side, which is unfavorable to the normal condition, seriously 𝑥. In the meantime, smaller tip clearance is more sensitive to the
hindering the output work of the turbine. Therefore, when substances change of transport characteristics of the working fluid. As a result,
similar to krypton and xenon are added, the appropriate amount can the tip clearance leakage decreases, and losses accordingly decrease.
ensure the 𝜇 of the mixture in a reasonable range so that conducive to The loss reduction caused by the rotor section is obvious, which is
improving the turbine performance. assumed to be related to the decrease of the flow Re. An increase
The cause of turbine loss has been preliminarily analyzed, but the in the 𝜇 of the mixtures reduces the overall Re of the fluid flow.
exploration of the loss mechanism of the CO2 -based mixture turbine Therefore, the decrease in turbulence intensity will mitigate the flow
is not detailed enough. Therefore, to assess the performance of the separation. Moreover, the losses caused by the stator passage cannot
turbine stage when CO2 -based mixture is applied, a loss breakdown
be ignored compared with the rotor passage. Most of the loss models
study is performed. The purpose of this loss breakdown is twofold:
in the 1D preliminary design now focus on the rotor losses of the
firstly, to clarify the difference in the loss mechanism of SCO2 RITs
turbine, such as incidence loss, passage loss, tip clearance loss, and
between using pure CO2 and mixtures; secondly, to seek high loss
regions to inform future preliminary design methods for the design exit energy loss. However, limited attentions are focused on modeling
of efficient turbomachinery. In this section, the CO2 –Kr mixture is of the stator losses. With the increase of the krypton 𝑥, the endwall
used as an example. To study loss mechanism, the way to distinguish and secondary flow losses in the stator are reduced, but the stator
different losses are presented. Entropy loss is determined following the profile and trailing edge losses are gradually increased. Therefore, the
method of Wheeler and Ong [41,42]. Profile and trailing edge losses efficiency improvement of the CO2 –Kr mixture is mainly due to the
are determined as the entropy rise over each component resulting from reduction of the tip clearance loss and the endwall and secondary flow
the blade boundary layer and trailing edge losses (i.e., by setting a losses of the passage.

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Y. Yang et al. Energy 266 (2023) 126429

4. Conclusion

In this study, a 500 kW CO2 radial-inflow turbine is designed and

demonstrated. The effects of different additives (N2 , O2 , helium, xenon,
and krypton) on the turbine performance are analyzed. Real gas prop-
erties of pure CO2 and CO2 -based mixtures are accurately encoded for
numerical simulation. Computational fluid dynamics simulations are
carried out to explore the turbine performance and loss mechanism
when using CO2 -based mixtures. At last, the loss breakdown analysis
is investigated to illustrate the components of stage overall loss. The
main conclusions are as follows:

(1) Additives have different effects on turbine performance.

According to the calibration of thermodynamic properties by
isentropic exponent 𝛾, xenon, krypton, and helium have a great
influence on the turbine. The small amount of xenon or appro-
priate amount of krypton added into the mixtures will increase
the turbine efficiency, but reduce the turbine output power
as the enthalpy differences dropped. However, helium behaves
opposite to krypton and xenon. Nitrogen and oxygen, often
introduced as inevitable impurity gas, bring a slightly negative
impact.
(2) The off-design performance and robust analysis of 𝐒𝐂𝐎𝟐 tur-
bines under different mixtures are studied. With the increase
of krypton amount, the high-efficiency point moves toward the
direction of higher inlet pressure, and the RIT performance de-
teriorates gradually under the low inlet pressure, indicating that
the operation adaptation range of the turbine becomes narrow.
The density of the CO2 –He mixtures is greatly reduced compared
with the pure CO2 density when the mole fraction of helium is
high. Through the steady and transient simulations, it is assumed
that the turbine designed with pure CO2 is no longer suitable for
the mixtures with high mole fraction helium.
(3) The stage loss is analyzed detailedly with different mix-
tures, a properly dynamic viscosity range is proposed, and
the loss breakdown analysis is also presented. As the ad-
ditive mole fraction increases, nitrogen and helium increase
the entropy acceleratedly, while krypton increases the entropy
hinderingly. Moreover, the total loss decrease at first and then
Fig. 14. Entropy and Reynolds number contours when the mole fraction of helium is
1% and 50%. increase with the increase of the xenon amount. A properly
dynamic viscosity range is proposed so that the turbine can reach
a high efficiency when the dynamic viscosity of the working
fluids is in this range. Adding a predefined amount of rare gases,
such as xenon and krypton, can change the dynamic viscosity
of the mixtures into this range. The loss breakdown study is
performed with the CO2 –Kr mixture, which indicates that the
introduction of krypton can reduce tip clearance loss and end-
wall and secondary flow losses. Moreover, the loss generated in
the stator is significant.

In the future, it is suggested that full-scale turbine design proce-

dures using different SCO2 -based mixtures should be explored. Also,
a full robust examination of SCO2 -based mixture turbines based on
𝛾 and off-design conditions should be carried out. More important,
as the compressor inlet condition is close to the CO2 critical point,
it is worth examining the performance of SCO2 compressors oper-
ating with different CO2 -based mixtures. In addition, experimental
and CFD comparisons should be performed for SCO2 turbomachinery
applications.
In all, the research carried out in this study will eventually ben-
Fig. 15. The passage entropy change vs. the streamwise location under three different efit the SCO2 power cycle community, and will contribute to the
settings.
application of advanced power cycles.

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Y. Yang et al. Energy 266 (2023) 126429

Fig. 16. Variation of the dynamic viscosity vs. the temperature.

Fig. 17. Mach number contours of the turbine with different krypton mole fraction.

CRediT authorship contribution statement

Yueming Yang: Investigation, Conceptualization, Methodology,

Software, Writing – original draft. Xurong Wang: Conceptualization.
Kamel Hooman: Conceptualization. Kuihua Han: Conceptualization.
Jinliang Xu: Formal analysis. Suoying He: Conceptualization. Jianhui
Qi: Supervision, Funding acquisition, Methodology, Writing – review &
editing.

Declaration of competing interest

The authors declare that they have no known competing finan-

cial interests or personal relationships that could have appeared to
influence the work reported in this paper.

Fig. 18. Breakdown of predicted losses. Data availability

The data that has been used is confidential.

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Y. Yang et al. Energy 266 (2023) 126429

Acknowledgments [20] Wu Y, Bai Y, Song Y, Huang Q, Zhao Z, Hu L. Development strategy and

conceptual design of China lead-based research reactor. Ann Nucl Energy
2016;87:511–6.
The authors gratefully acknowledge the support of the National
[21] Qi J, Reddell T, Qin K, Hooman K, Jahn IH. Supercritical CO2 radial turbine
Natural Science Foundation of China (Grant No: 52106049), the Natu- design performance as a function of turbine size parameters. J Turbomach
ral Science Foundation of Shandong Province, China (ZR2021ME118, 2017;139(8).
ZR2020QE191), the Natural Science Foundation of Jiangsu Province, [22] Zhou A, Song J, Li X, Ren X, Gu C. Aerodynamic design and numerical analysis
China (BK20210113), the Beijing Natural Science Foundation, China of a radial inflow turbine for the supercritical carbon dioxide Brayton cycle. Appl
Therm Eng 2018;132:245–55.
(3222048), and the Young Scholars Program of Shandong University, [23] Zhou K, Wang J, Xia J, Guo Y, Zhao P, Dai Y. Design and performance analysis
China (31380089964175). of a supercritical CO2 radial inflow turbine. Appl Therm Eng 2020;167:114757.
[24] Allison T, Moore J, Pelton R, Wilkes J, Ertas B. Turbomachinery. In: Brun K,
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