A review of research on turbines for supercritical carbon dioxide power systems

Supercritical carbon dioxide (S-CO2) Brayton cycle has been known as a potential power cycle technology because of its high efficiency, compact structure and suitability for different heat sources. As one of the key components in the cycle, the turbine has an important impact on the cycle efficiency. Compared with traditional steam and gas turbines, S-CO2 turbines have high working pressure and small size. The internal flow characteristics are significantly different. In this paper, the research progress of S-CO2 turbines in recent years is reviewed. The design and performance evaluation methods for S-CO2 turbines of different types and power levels are summarized, and research on loss correlations and optimization algorithms are introduced. The features of flow field in S-CO2 turbines are discussed. Current studies mainly evaluate the flow field and flow losses through Computational Fluid Dynamics (CFD), and some studies further analyze the influencing mechanism of turbine geometric parameters on flow characteristics. The applications of multi-physical field analysis on S-CO2 turbines are also reviewed. The construction and operation of S-CO2 test loops, and relevant turbine experimental study findings are introduced. Future research directions of S-CO2 turbines are proposed.


Introduction
Supercritical carbon dioxide (S-CO2) closed Brayton cycle is considered as a potential power generation system, which has received extensive attention and research in recent years.S-CO2 has a small compressibility factor near the critical point (7.38 MPa and 30.98 ℃), which makes the cycle have a small compression work.At the same time, S-CO2 has a high density close to that of liquid and a low viscosity close to that of gas.Therefore, the S-CO2 cycle has the advantages of high efficiencies and compact structures.The S-CO2 Brayton cycle has adaptability to heat sources of various temperature [1], and is considered to be a suitable technology choice for different power generation systems.The researchers discussed the availability of nuclear energy [2][3], solar energy [4] [5], coal-fired power plants [6] [7], gas turbines [8] [9], fuel cells [10] [11] and other potential heat sources for S-CO2 cycles.
CO2 undergoes a process of compression, heat absorption, expansion, and heat release in a closed cycle.Ahn et al. reviewed the research progress of S-CO2 cycle under different backgrounds and compared different cycle layouts, believing that the recompression cycle has a high efficiency [1].Crespi et al. systematically organized the different configurations of stand-alone cycles and combined cycles, and conducted in-depth thermodynamic analysis of the cycle performance [12].Xu et al. analyzed the research on the S-CO2 cycle from system design and analysis, energy transfer mechanism and key Figure 1.Cycle efficiencies of different power systems and heat source temperature [1].Some experimental loops or demonstration projects have been built worldwide.Sandia National Labs(SNL) and the Department of Energy(DOE) operated a S-CO2 Brayton cycle power system that is located at Barber Nichols [21].During 2010 the loop was configured with a 260 kW heater, and the simple recuperated Brayton cycle was able to reach break-even conditions.The Institute of Applied Energy (IAE) and Tokyo Institute of Technology constructed a S-CO2 demonstration loop to develop a closed cycle to generate power from industrial waste heat of a not high temperature range [22] [15].Their preliminary test results indirectly proved that S-CO2 as the working fluid would reduce the compression power consumption near the critical point.The part flow S-CO2 cycle has been studied, and the factors affecting the cycle efficiency have been analyzed.Bechtel Marine Propulsion Corporation (BMPC) and the Bettis Atomic Power Laboratory tested a 100 kWe recuperated S-CO2 Brayton system with two shafts [23] [24].Korea Advanced Institute of Science and Technology (KAIST) reported on their experiences of troubleshooting and operation with the S-CO2 Pump Experiment facility (SCO2PE) [25].KIER (Korea Institute of Energy Research) developed three S-CO2 power cycle test loops with power levels of 10kWe, sub kWe, and 80kWe [26].Moore et al. designed a high-temperature and high-pressure S-CO2 flow circuit with a flow rate equivalent to 1 MWe [27].The STEP project executed by Gas Technology Institute (GTI), Southwest Research Institute (SwRI) and General Electric Global Research (GEGR), was to design, construct, commission and operate a 10 MWe pilot plant [28].Xi'an Thermal Power Research Institute (TPRI) designed and constructed a megawatt-level integral test facility, which was operated for more than 1000 hours [29] [30].A set of control modules are used to adjust parameters such as the S-CO2 mass flow rate and inlet temperature of the turbomachinery.As one of the key components, the S-CO2 turbine has a significant impact on the cycle performance.S-CO2 turbines mainly include axial and radial types based on the angle between the flow direction and the rotating axis.This paper introduces the research progress of S-CO2 turbine of different types and power levels, including design and performance prediction, flow characteristics, multi-physical analysis and experimental research.Figure 4. Photographs of SMART@TPRI power system [30].

Design and performance prediction of S-CO2 turbines
The physical properties of S-CO2 differ greatly from those of air.Especially under the working conditions of the turbine, S-CO2 has a high density and low viscosity, which affect the design of the turbine.Due to the lack of a suitable design method for S-CO2 turbines, researchers mostly refer to design methods and loss models of gas or air turbines during the design process.These design methods usually include one-dimensional and three-dimensional methods, which can be used to determine the key design parameters and blade geometric parameters of the turbine.These works have developed in the last century.Soderberg established a correlation system based on a large amount of experimental data from steam turbines and cascades to predict turbine cascade losses [31].Although the Soderberg's correlation is considered a relatively simplified model that only considers a few parameters, it had sufficient accuracy at the time [32].Ainley and Mathieson proposed a method for calculating the performance of axial turbines, which can be performed over a wide range of inlet conditions [33].
According to the A&M method, the total pressure loss of a turbine includes blade profile loss, secondary flow loss, and tip clearance loss.Dunham and Came synthesized new experimental data and performance predictions, and improved the prediction formulas for secondary flow loss and tip clearance loss in the A&M method [34].Carig and Cox [35], Kacker and Okapuu [36] also proposed other methods for estimating the efficiency of axial turbines.Dixon [37] and Horlock [38] provided a detailed introduction to the mean-line design method, which has been widely used.Denton conducted a general discussion using entropy increase to define flow loss and applied the results to turbomachinery flow [39].
The main part of Denton's discussion was focused on axial turbines, but some special issues related to radial turbines have also been discussed.Balje [40][41] and Glassman [42] have established many design criteria for radial turbines and have been widely recognized.Many scholars such as Rohlik [43], Benson [44], and Whitfield [45] have proposed different loss models for predicting the performance of radial turbines using one-dimensional methods.Computational fluid dynamics (CFD) makes it possible to predict the performance of S-CO2 turbines through numerical simulations.The preliminary design method mentioned above is still a suitable method for obtaining relatively optimal turbine geometry, while the CFD method is suitable for use in the later stage of design, where the basic geometric parameters have been determined, to achieve further improvement.However, whether CFD can accurately predict turbine performance still requires extensive experimental research in the future to prove.This section will introduce the research progress of S-CO2 turbine design.
Jeong et al. designed a four stage axial turbine using a one-dimensional gas turbine analysis method.The results indicate that the turbine efficiency increases with the increase of hub radius under the same series conditions [46].Schmitt et al. conducted aerodynamic design for the first stage blade of a 100 MW 6-stage S-CO2 turbine [47].They used the one-dimensional mean-line method to generate blade geometry, and CFD simulation results showed that the stage efficiency was 4% lower than the design target.They believe that the Soderberg loss relationship is insufficient to estimate the entire loss, and suggest further research on the losses considered in designing S-CO2 turbines.Han et al. based on the 5MW supercritical carbon dioxide thermal power platform, designed a two-stage axial S-CO2 turbine [48].Considering the leakage of the stator and rotor blades and mixing loss, the isentropic efficiency of the high-pressure turbine can reach 84.88%, with a shaft power of 3251 kW.Stepanek et al. established a specialized calculation code for S-CO2 turbines of high-power cycles so that the size, efficiency and other parameters could be estimated [49].The design of these turbines is able to be optimized under specific boundary conditions.They believed high power turbines were more suitable for choosing a split flow two stream configuration.The size of a S-CO2 turbine is about one-fifth that of its steam substitute.Kang et al. designed a partial admission impulse axial S-CO2 turbine to meet manufacturing constraints and avoid potential axial thrust [50].The efficiency of the partial intake turbine is reduced by 15% compared to that under full admission.Salah et al. developed and improved a preliminary design tool which is able to calculate passage losses by using loss models, in order to design a 100kW S-CO2 axial turbine [51].A feasible single stage design can be achieved while the turbine has a high load coefficient and a low flow coefficient.Based on response surface optimization methods, the code optimizes turbine geometry by minimizing flow losses.The optimization results for specific geometric shapes indicate that power and total-to-static efficiency values have been improved by 5.34% and 5.30%, respectively.Saeed et al. trained a deep neural network (DNN) using existing CFD simulation results of S-CO2 radial turbines [54].Technologies such as CFD and multi-objective genetic algorithm (MOGA) were used for construction and optimization.It is found that the turbine performance parameters are sensitive to parameters such as velocity ratio and inlet flow angle.Gronman et al. analyzed the design of a S-CO2 radial outflow turbine and compared it with the corresponding radial inflow turbine design [55].Compared with the radial inflow turbines studied, the radial outflow turbines can reach high efficiencies over a wider specific speed range.The maximum loss comes from the relative tip clearance for radial turbines.
Qi et al. used the 1D design code TOPGEN to explore the performance of S-CO2 radial turbines within the power range of 100 to 200 kW [56].Three feasible turbine designs were ultimately determined, with a total-to-static efficiency ranging from 78% to 82%.Holaind et al. used a similarity approach to design a small-scale S-CO2 radial turbine [57].On this basis, CFD numerical simulations were conducted for the optimization design of the stator and impeller.The turbine efficiency is 70%.Ameli et al. conducted unsteady simulations on the radial turbine to study the accuracy of real gas models and impact of model accuracy [58].In their research, Span and Wagner showed good accuracy and they believed that a table with sufficient resolution was necessary.Unglauber et al. reviewed different suggestions on the optimal velocity ratio of gas turbines and developed a mean-line design process for the geometric dimensions of small scale S-CO2 radial inflow turbines [59].They were numerically compared through CFD analysis.For small S-CO2 radial inflow turbines, it is recommended to have a specific speed between 0.2 and 0.4, otherwise it may become a challenge for the manufacturing industry.Lv et al. proposed an method combining design process and Sequential Quadratic Programming optimization algorithm to determine some optimal key parameters [60], including velocity ratio, degree of reaction, geometric ratio and rotor outlet blade angle, under various geometric and aerodynamic constraints.They found and validated a set of optimal loss correlations to predict losses of S-CO2 radial inflow turbines.The predicted performance is consistent with experimental and CFD simulation results.Seshadri et al. designed 20kW S-CO2 turbomachinery for a 140kW simple regenerative S-CO2 cycle [61].They adopted a coupled turbine and compressor to enhance cycle flexibility.Persico et al. proposed a tool considering thermodynamic conditions and flow configurations for blade profile optimization of turbomachinery [62].Its main content includes geometric parameterization, CFD solver, and evolutionary strategies.Shi et al. designed a radial S-CO2 turbine based on one-dimensional flow and numerically simulated it using the RNG k-ε turbulence model [63].The simulation results show that the power is 187 kW and the efficiency is 78.50%.The reason why the numerical simulation efficiency is lower than the thermodynamic design is due to the supersonic flow inside the turbine.In their following study, Shi et al. established a fast thermal design method based on one-dimensional flow theory, which is for S-CO2 radial inflow turbines [64].They proposed a design and optimization method based on Gauss process regression combined with high-precision three-dimensional aerodynamic analysis methods, to shorten the time of design and optimization.
Vijayaraj et al. used NASA 1730 air turbine as a benchmark and adopted a similarity scaling strategy to design a S-CO2 turbine [65].The CFD simulation results show that the dimensionless curve of the S-CO2 turbine is plotted on the corresponding experimental characteristics of NASA turbines with good consistency.Uusitalo et al. used different loss correlations and CFD to predict flow losses of a MW level S-CO2 radial inflow turbine [66].Good consistency could be achieved between 1D loss correlations and CFD results by using a suitable set of loss correlations but different models may lead to high bias in predicting rotor losses.Suggestions were given on how to use loss correlation to predict turbine performance at different specific speeds.In another research, they developed a radial turbine design tool, including loss distribution analysis [67].The turbine design with the highest isentropic efficiency was observed at specific speeds of 0.50 to 0.60.The tip clearance loss is the most significant loss for turbines with a output power of a few hundred kW, while the passage, stator and outlet kinetic losses account for a greater proportion for higher power turbines.Wang et al. improved the simulated annealing algorithm (SAA) and established the optimization process of a kW scale S-CO2 turbine, including rotor meridian plane and nozzle profile optimization [68].They achieved a maximum isentropic efficiency improvement of 4.94% in improved simulated annealing algorithm (ISAA) calculations.Compared with genetic algorithms, the ISAA method saves 59.6% of computational time and 41.5% of computational time compared to the SAA method.[69].First, they carried out parameter sensitivity analysis based on the Gaussian process surrogate model, and then realized the Bayesian optimization (BO) process.The optimized volute showed has more uniform flow characteristics at design and off design conditions than before.Chang et al. obtained several bladeless volute models based on a two-dimensional method by changing the distribution of the cross-sectional area of the volute [70].The interaction between the geometric shape and performance of a bladeless inlet volute was studied through three-dimensional CFD simulation.

Flow characteristics of S-CO2 turbines
The performance of S-CO2 turbine can be calculated by numerical simulation and the internal flow can be simulated with the development of CFD.Researchers conduct studies on the turbine flow characteristics and further discuss the relationship between turbine geometric parameters, flow characteristics, and performances.Shi et al. conducted preliminary thermal design on a 10 MW S-CO2 three-stage axial turbine and obtained key thermal and structural parameters [71].Some transcritical regions were found near the blade root of the leading edge of the first stage rotor, as well as near the leading and trailing edges of the third stage nozzle blades.Peng et al. used the SST k-ω turbulence model to analyze the off design flow characteristics of a 200 kW axial turbine [72].Han et al. designed the turbines of 5MW S-CO2 cycle by using the self-developed mean-line process [73].The maximum isentropic efficiencies of the S-CO2 high-pressure and low-pressure turbines are 82.88% and 82.26%, respectively, and the output powers at the design point are 3251 kW and 6156 kW, respectively.The numerical analysis using RANS equation and SST turbulence model indicates that the Cps curve, finite flow line spectrum, and maximum Mach number profile of each cascade are reasonable.In addition to leakage losses, end wall losses and wake losses account for a significant proportion of turbine aerodynamic losses.The lower separation zone in the blade cascade flow field is significantly larger than the upper separation zone.They conducted numerical research on the secondary flow of the cascade simultaneously.The flow characteristics of logarithmic layer and viscous sublayer in high pressure guide vane cascades were studied using dimensionless vorticity analysis method [74].Ying et al. designed and investigated a 100 kW level S-CO2 axial turbine by using 3D transient viscous flow simulation method [75].The vortex flow is influenced by the geometric parameters of the S-CO2 turbine rotor, such as the aspect ratio and tip-to-hub ratio.The influence is not significant for gas turbines.Vortex interactions exist in the rotor passage, and utilizing these interactions is considered a potential way to improve the turbine efficiency.[76].The blade thickness and blade angle distribution were adjusted.The total-to-static efficiency and power were 89.02% and 10.07 MW respectively.In the follow-up study, Yang et al. synthesized the design method of the axial turbine and the characteristics of the centrifugal turbine and designed the transonic nozzle and rotor cascade [77].The Mach number at the nozzle blade outlet reaches 1.13.Forming at the trailing edge of the nozzle blade, set of expansion waves reflected on the suction side of high pressure rotor blade.Zhou et al. established a threedimensional geometric modeling of a 1.5MW S-CO2 radial inflow turbine [78].The static pressure distribution of stationary blades is basically consistent at different spans, while there is a significant difference in static pressure distribution at different rotor blade spans.A weak secondary flow occurred at the high blade span of the suction side and the flow field at 90% span was complicated.Xia et al. designed and analyzed a radial turbine with a required power of around 100kW [79].There is a lowvelocity zone caused by the large negative incidence at the pressure surface of the rotor inle.The velocity distribution become intricate because of the leakage vortex.Luo et al. investigated the role of turbulence models in the analysis of radial turbine flow structures [80].The Spalart-Allmaras (S-A) turbulence model and the SST-gamma-theta turbulence model showed the lowest and highest efficiency, respectively.The leakage flow and the limit streamline on the suction side sensitive to the turbulence model.El et al. designed and introduced a radial turbine with a diameter of 510 mm and a rotational speed of 21409 rpm [81].The results of CFD simulation show that the low end value of the turbine efficiency is 69.87%.The flow reaches supersonic conditions in the stator passage.The total pressure losses in the rotor passage were also analyzed.These loss mechanisms that lead to reduced turbine efficiency include shock losses, incidence losses, and various mixing zones within the passage.[82].The pressure distribution will become disorderly and unsystematic if the temperature at inlet decreases.The decrease in temperature has the least impact on the maximum leading edge diameter.Wang et al. introduced the aerodynamic performance of radial inflow turbines with S-CO2 and air as working fluid considering different solidity, and provided design references for them [83].In view of the low solidity of the S-CO2 turbine, a new diverter structure is proposed to improve its performance.For S-CO2 and air, a smaller solidity will lead to unsatisfactory flow conditions at the rotor inlet and shield, while a larger solidity will lead to aerodynamic losses at the trailing edge and the outlet hub of the rotor blade.Li et al. proposed a integrated method considering one-dimensional design and three-dimensional optimization of S-CO2 radial inflow turbines with the low specific speed [84].The optimization of the nozzle and impeller is carried out simultaneously.Research has found that the thinner the suction side of the nozzle, the better the flow near the wall.The splitter blades are beneficial for improving turbine performances.Shi et al. used end-to-end deep learning methods to reconstruct the temperature and pressure fields of S-CO2 turbines, thereby achieving off design performance prediction [85].An optimized design for a 60000 rpm S-CO2 turbine was established.The GPU will be able to accelerate the prediction process of physical fields and performance once the deep model is trained.Zhou et al. evaluated the effect of blade tip clearance on the performance of radial S-CO2 turbines [86].The pressure gradient and tip clearance cause the formation of two vortices on the rotor suction surface.When the tip clearance increases from 2% to 8%, the area occupied by leakage flow continues to increase, and the mainstream is hindered.An increase of 6% in blade tip clearance will result in a decrease of 3.84% in turbine efficiency and 4.16% in turbine power output.Wang et al. implemented a system-component coupling optimization method using genetic algorithm [87].The unsteady CFD simulation record the entire process of low-pressure region at the blade leading edge from development to reduction within a calculation period.The pressure wave interaction between the rotor and stator blades as well as the stator wake, lead to obvious unsteady characteristics in the flow field at different spans in the turbine.Although steady-state simulation cannot reflect the transient flow characteristics inside the turbine, the evaluation deviation for the overall performance of the turbine is relatively small.The effects of sealing gap, sealing cavity surface groove, and circular groove shape of labyrinth seals were investigated under different pressure ratios.The configuration performance of circular grooves is the best.The relative leakage, power, and efficiency of stator 1 and rotor under design conditions are 6.34×10 -3 , 8.53×10 -3 , 3.463 MW and 86.61% respectively.Compared with the labyrinth type, the leakage of DGS is reduced by 99.38%.They also arranged LS and DGS on the back of the impeller of the radial inflow turbine [91].The DGS configuration has better performance, while the LS structure has better axial force balance than the DGS structure.Compared with the leak free configuration, the power and efficiency of the DGS configuration are only reduced by 0.27% and 0.35%, respectively.The deformation values of the thermal mechanical seals configured with DGS are all less than 8 μm, which verified its feasibility.Finally, a new type of LS and DGS combined sealing structure was proposed.Ma et al. designed the back of the S-CO2 radial turbine impeller [92].CFD was used to study the back leakage flow rates of 2% and 0.2% under different pump-out vane designs.An improved pump-out vane design method with a two-row layout was proposed.Compared with the benchmark design without pump-out vanes, the cavity outlet pressure was reduced by 1.36 MPa and the back axial force was reduced by 58%.The stage isentropic efficiency is reduced by 2.5 points.Zhao et al. used a typical labyrinth seal for the leakage flow in the back cavity of the S-CO2 radial inflow turbine impeller, and verified the reliability through numerical simulation [93].Excessive or insufficient sealing teeth are not conductive to achieving good effects.When the axial length of the sealing element is given, a number of six teeth is able to achieve the optimum effect in their case.The isosceles trapezoidal teeth demonstrate better performance compared to other shapes.Yang et al. conducted numerical research on different types of labyrinth seals based on a S-CO2 radial inflow turbine [94].The influence of sealing clearance and cavity outlet pressure was analyzed, and the influence of sealing design parameters was evaluated.Numerical method was used to analyze the flow field in the seal chamber.
The CFD method provides assistance for the design of S-CO2 turbines.Compared with gas turbines of the same power level, S-CO2 turbines have the characteristics of small size and high rotational speed, and S-CO2 also has the physical characteristics of high temperature, high pressure, and high density.Researchers simulate the flow characteristics of S-CO2 in the designed turbine by importing CO2 state equations or real gas property files into computational softwares.The calculation results of CFD can serve as an effective reference for evaluating the performance of turbines designed by traditional design methods and flow loss models.CFD can provide good suggestions for design from the perspective of the flow field.Based on the existing research results mentioned above, CFD can capture the threedimensional flow field characteristics of the turbine, such as flow separation and high entropy production areas, thus making targeted improvements.In addition, the flow field of complex and delicate structures such as the internal sealing structure can also be simulated.Numerical simulation significantly reduces time compared to prototype testing, allowing for rapid modification of geometric models and obtaining corresponding calculation results.It can effectively shorten the design cycle, reduce iteration time, and accelerate the design process.In addition, a large number of simulation results can be combined with neural network and other technologies for optimization design, and also contribute to the establishment of a database.Thus loss models and turbine design methods suitable for CO2 could be proposed.

Multi-physical field analysis of S-CO2 turbines
In addition to the flow characteristics, the multi-physical field study of the S-CO2 turbine is also a key aspect.The size of S-CO2 turbines is often significantly smaller than that of air or gas turbines of the same power level, which may pose challenges to structural strength and heat transfer, which are necessary to be considered.Zhang et al. coupled the physical parameters to the FORTRAN code, and carried out the design of 15 MW and 1.5 MW turbines [95].The results of aerodynamic analysis and strength analysis indicate that fluid pressure has a significant impact on the strength performance of the turbine, especially the rotor of a 15 MW axial turbine.Lin et al. used one-dimensional method and stream curvature method to carry out quasi three-dimensional design of flow path, and obtained the geometric modeling of the turbine impeller for a MW power cycle [96].And a numerical model was established to analyze the flow field and structural strength vibration.The maximum stress value meets the strength requirements.Jun et al. conducted a fluid-thermal-solid coupling analysis on a 200 kW S-CO2 turbine [97].The high stress zone is not only related to the shape of the geometric structures, but also tends to appear in areas with large temperature gradients.The maximum equivalent stress occurs at the fillet between the turbine impeller and the seal, with a value of 324MPa, which is less than the yield limit of the material at 500 ° C. In existing research, the equivalent stress values of S-CO2 turbines have not exceeded the yield limit, but their orders of magnitude are consistent, so strength analysis should not be ignored.Figure 14.Thermal-solid coupling analysis results of the turbine impeller [97].Thatte et al. established a fluid-structure-thermal interaction model to predict and evaluate the performance of dry gas seals in the S-CO2 turbine mission cycle, and studied the effects of aerodynamic and thermal disturbances on structural and rotordynamic instability [98].They observed significant changes in surface roughness caused by S-CO2 corrosion and evaluated the impact of this roughness change on the pressure generation ability of dry gas seal films.A three-dimensional fracture mechanics and crack growth model was also developed to predict the life of the hybrid gas bearing [99].Bidkar et al. [88] emphasize that the fluid-structural-thermal analysis is needed.The size of the sealing gap is usually small, and tiny thermal deformation may have a significant impact on the performance of the turbine, which can be determined through thermal-fluid-solid coupling analysis.Du et al. studied a series dry gas seal for a 1.5 stage axial turbine and discussed the effect of seal clearance [100].In their case, the difference in thermal mechanical axial deformation between the inner and outer radii of the sealing face was less than 27 μm, which had little impact on turbine efficiency.
Swann et al. introduced and analyzed an cooling system for the main rotor shaft of a radial turbine, which uses S-CO2 as coolant [101].The heat transfer was conducted through thermal-fluid-structural method to predict temperature distribution.Because of the high convective heat transfer coefficient of S-CO2 in the studied state, large temperature differences can be achieved in short lengths.Chen et al. discussed the flow and heat transfer characteristics of S-CO2 in view of the overheating problem of the turbine shaft [102].The key factors affecting Taylor vortex formation and shaft cooling performance were analyzed and discussed.The position of vortex formation is influenced by factors such as the axial ratio, radius ration, Taylor number and axial Reynolds number.The effect of the rotational velocity and axial velocity on heat transfer performance is more pronounced than that of Taylor vortex.The correlation between S-CO2 Taylor-Couette-Poiseuille (TCP) flow and heat transfer, as well as the effective Reynolds number and Prandtl number has also been given.Jiang et al. established a numerical model for S-CO2 turbine rotor cooling [103].The effects of inlet temperature, mass flow rate, and leakage flow from cylinder to dry gas seal on rotor cooling were studied on the turbine inlet side.At present, there are relatively few studies on the multi physical fields related to S-CO2 turbines.Especially in hightemperature and high-pressure CO2 environments, there is a considerable lack of research on the fatigue and failure of parts.Further multi-physical field analysis may be necessary before the widespread application of S-CO2 turbines.

Experimental studies of S-CO2 turbines
Some institutions around the world have carried out the construction of S-CO2 cycle testing loops and conducted experimental research on the key component turbines.Sandia National Labs [21] selected the configuration of turbo-alternator-compressor in its test loop, and the maximum temperature at the turbine inlet is 810 K.Each TAC unit includes a single-shaft with one radial turbine and one compressor.Gas foil bearings are used for both the journal and for the thrust bearing.For the simple regenerative Brayton cycle, the break even power generation condition is reached at 240 kW heating power, 1.63 kg/s flow rate and 39000 rpm shaft speed.In another recompression Brayton cycle test, the electric power generation efficiency varing from 6% to 7% was achieved.Utamura et al. demonstrated a radial inflow turbine on the bench scale test facility, achieving 110W power generation operation at a rotational angular speed of 1.15 kHz and a CO2 mass flow rate of 1.1kg/s [104].The turbine inlet conditions are 10.6 MPa and 533 K.The main part of loss was considered to be rotor windage.Clementoni et al. introduced the off design performance of components in integrated system test (IST) [24].The performance of IST components under peak power conditions is close to expected.The windage losses of the turbo-generator and turbo-compressor are both more than twice the predicted values, occupying 26% of the turbine peak power.The reasons for the above losses were identified as shaft speed and motor cavity pressure.KIER has developed different turbines for their S-CO2 test loops.Cho et al. designed a high-speed turbine generator for Sub-kWe small scale experimental test loop, with a design speed of 200000 rpm [105].Excessive rotational speed makes it very difficult to select rotating components, balance axial forces, and design rotor dynamics.The partial admission method using a single channel nozzle reduced the rotor speed.A nitrogen cold-run test was conducted under atmospheric pressure conditions, indicating that the influence of partial admission on rotor dynamics is permissible.Shin et al. introduced the development of 60 kWe and sub-kWe turbine generators [106].Cho et al. introduced the S-CO2 turbine, with an average rotor diameter of 73 millimeters [107].The configuration of the S-CO2 turbine adopts impulse and partial admission to reduce the axial force and rotational speed.It ran for 44 minutes, with a maximum power of 25.4 kW.The maximum electrical power of the bench was 10.3 kWe.Hacks et al. introduced the aerodynamic and mechanical design of the S-CO2 turbomachine for a demonstration cycle of a small mass flow in their laboratory [108].One difficulty encountered in practical use was that the ball bearings were limited because the lubricants cannot function in the S-CO2 environment.Ref. [109] focuses on the use of magnetic bearings.The experimental operation shows that an increase in density and speed will lead to greater rotor deflection and greater force on the bearings.In the initial testing of CO2, the speed of the turbine reached approximately 40000 rpm.Huang et al. manufactured a partial admission axial turbine and conducted transcritical tests [110].This turbine adopted traditional carbon ring machanical seals and angular contact ceramic ball bearings.The maximum power generation was 692 W at 14022 rpm and the highest isentropic efficiency was 53.43% at 13366 rpm.They pointed out that failure of dynamic seal might cause leakage and reduce the turbine performance.In the subsequent research [111], the turbine reached a maximum rotational speed of more than 40000 rpm and a maximum output power of 2.27 kW at 20878 rpm.The power generation was proportional to the pressure ratio and mass flow rate.[111].The above studies are all aimed at small-scale cycles and turbines of small power, such as kW level to 100 kW level.Experimental research on MW level turbines has also been carried out.A 10 MWe S-CO2 turbine was manufactured by SwRI(Southwest Research Institute) and GE(General Electric) and tested at 715 ℃ and 27,000 rpm [28].The rotor life increased from 20000 hours to 100000 hours.The length of the rotor is long, but the inner diameter of the turbine casing is small, making it difficult for the machine tool to meet the manufacturing tolerance requirements.The 5-axis Electrical discharge machining technology was used to machine the monolithic turbine rotor.Ref. [30] introduces the cycle test situation of Xi'an Thermal Engineering Institute.Both the high pressure turbine(HPT) and low pressure turbine(LPT) are two-stage axial turbines with a design rotational speed of 9000 rpm.A rapid load regulation test was conducted, including the cold start process, long-term stable operation near the design point, and normal shutdown process.The maximum net power reached 3.866 MW, and the efficiencies of HPT and LPT are 84.3% and 88.2%, respectively.At present, the research on high-power prototype testing is still in its infancy, with only a small amount of data.The low-power S-CO2 turbine prototype is considered to have good performance during the design stage, and the predicted efficiency values in Ref. [21][24] exceed 80%.However, the efficiency values obtained from the experiment were not ideal enough.On the one hand, the design speed of the turbine is too high, which is difficult to achieve in actual operation due to factors such as bearings.On the other hand, the power reduction caused by windage losses also exceeded expectations.Partial admission is one of the solutions for the normal operation of low-power turbines.Although the maximum efficiency value has decreased, it can reduce the impeller speed to an acceptable range.However, further research is needed on partial admission S-CO2 turbines.

Conclusion and prospection
The S-CO2 Brayton cycle is considered to have the advantages of high efficiency, compact structure, and has become a potential power generation system, which has received extensive attention and research in recent years.The turbine is a key component in the cycle, and its efficiency has a significant impact on cycle performance.A review was conducted on the research progress of S-CO2 turbines, which can be divided into the following categories: • At present, the turbine design mainly follows the design method of air or gas turbines, taking into account the physical parameters of S-CO2 in the design codes.The loss correlations in S-CO2 turbines has also been studied to predict turbine flow losses more accurately.Various optimization algorithms have been studied to shorten design time and achieve higher performance turbines.• CFD simulation is used to calculate the flow field and aerodynamic performance of the S-CO2 turbine.On the one hand, it is about the flow field inside the passage.Researchers studied the flow field characteristics under different geometric parameters, such as solidity and tip clearance size.The internal flow state of the passage was evaluated and the secondary flows were captured through patterns such as pressure, temperature, Mach number distribution, and streamline.The flow loss of the turbine was analyzed based on the flow field.Furthermore, some studies have explored the mechanism of vortex flow.On the other hand, due to the small size of the S-CO2 turbine, researchers have discussed the relationship between flow characteristics, leakage flow rate, and efficiency changes under sealing technologies such as labyrinth seals and dry gas seals.• The multi-physical field simulation research of S-CO2 turbine is also a key aspect.The S-CO2 turbine has a moderate operating temperature, but its size is small, making thermal management a challenge.The thermal-fluid-solid coupling method was used to study the deformation and stress of the impeller, sealing performance, shaft and bearing performance during the working process of the turbine.• Existing turbine experimental research is summarized.Early experimental research mainly focused on small-scale cycles and turbines, and in recent years, some institutions have gradually carried out larger scale (MW level) experimental research.In these studies, some issues were reported, mainly including the challenge of high speed on bearing performance, significant windage losses, rotor dynamics design, leakage caused by seal failure, and machining accuracy issues.From these research results, the development directions of future S-CO2 turbine research are proposed: • Further research is needed on the flow mechanism of secondary flows such as vortex structures to explore their impact mechanisms.Flow control is able to improve the turbine efficiency by changing the geometric structures to reduce various flow losses.• The study of multi-physical field coupling analysis needs further development.S-CO2 has a small size and high power density, and issues such as aerodynamics, sealing, and thermal management interact with each other.Only through the multi-physical field analysis method can the turbine performance be known more accurately.• More experimental research on S-CO2 turbines is needed.On the one hand, the feasibility of manufacturing, assembly, bearings and other technologies could be verified, and on the other hand, a database could be established through extensive research to guide the turbine design.• The special physical properties of S-CO2 make existing turbine design methods unsuitable.It is necessary to combine the conclusions of the flow control, multi-physical field coupling analysis and experimental research to form a set of specialized S-CO2 turbine design method.

Figure 5 .
Blade design of S-CO2 turbines for high power cycles[49].Li et al. developed a thermodynamic optimization design program based on genetic algorithm for radial inflow S-CO2 turbines[52].A 5 MW turbine was designed and checked in the design and offdesign conditions by CFD method.Saeed et al. developed a cycle simulation code integrating the turbine design and optimization algorithms, and applied it to an S-CO2 cycle of approximately 10 MWe[53].
(a) Profile of nozzle; (b) Meridian plane of impeller.

Figure 6 .
Optimal curves from three algorithms[68].Bian et al. optimized the cross-sectional geometry of a S-CO2 turbine volute

Figure 8 .
Figure 8. Secondary flow distribution in the impeller passage[75].Luo et al. designed a 10MW single stage S-CO2 centrifugal turbine and evaluated the unsteady threedimensional flow field in the blade passage[76].The blade thickness and blade angle distribution were adjusted.The total-to-static efficiency and power were 89.02% and 10.07 MW respectively.In the follow-up study, Yang et al. synthesized the design method of the axial turbine and the characteristics of the centrifugal turbine and designed the transonic nozzle and rotor cascade[77].The Mach number at the nozzle blade outlet reaches 1.13.Forming at the trailing edge of the nozzle blade, set of expansion waves reflected on the suction side of high pressure rotor blade.Zhou et al. established a threedimensional geometric modeling of a 1.5MW S-CO2 radial inflow turbine[78].The static pressure distribution of stationary blades is basically consistent at different spans, while there is a significant difference in static pressure distribution at different rotor blade spans.A weak secondary flow occurred at the high blade span of the suction side and the flow field at 90% span was complicated.Xia et al. designed and analyzed a radial turbine with a required power of around 100kW[79].There is a lowvelocity zone caused by the large negative incidence at the pressure surface of the rotor inle.The velocity distribution become intricate because of the leakage vortex.Luo et al. investigated the role of turbulence models in the analysis of radial turbine flow structures[80].The Spalart-Allmaras (S-A) turbulence model and the SST-gamma-theta turbulence model showed the lowest and highest efficiency, respectively.The leakage flow and the limit streamline on the suction side sensitive to the turbulence model.El et al. designed and introduced a radial turbine with a diameter of 510 mm and a rotational speed of 21409 rpm[81].The results of CFD simulation show that the low end value of the turbine efficiency is 69.87%.The flow reaches supersonic conditions in the stator passage.The total pressure losses in the rotor passage were also analyzed.These loss mechanisms that lead to reduced turbine efficiency include shock losses, incidence losses, and various mixing zones within the passage.

Figure 10 .
Velocity and Mach number distribution of a 100 kW S-CO2 radial inflow turbine[79].Zhang et al. designed an S-CO2 radial inflow turbine based on concentrated solar power, and the off design performance of different nozzle leading edge diameters was studied

Figure 13 .
The Mach number distribution of an axial turbine using different seal methods[90].

Figure 15 .
The effect of the leakage flow on the rotor cooling[103].

Figure 19 .
Figure 19.Turbine expander (a) Schematic layout; (b) Photo[111].The above studies are all aimed at small-scale cycles and turbines of small power, such as kW level to 100 kW level.Experimental research on MW level turbines has also been carried out.A 10 MWe S-CO2 turbine was manufactured by SwRI(Southwest Research Institute) and GE(General Electric) and tested at 715 ℃ and 27,000 rpm[28].The rotor life increased from 20000 hours to 100000 hours.The length of the rotor is long, but the inner diameter of the turbine casing is small, making it difficult for the machine tool to meet the manufacturing tolerance requirements.The 5-axis Electrical discharge machining technology was used to machine the monolithic turbine rotor.Ref.[30] introduces the cycle test situation of Xi'an Thermal Engineering Institute.Both the high pressure turbine(HPT) and low pressure turbine(LPT) are two-stage axial turbines with a design rotational speed of 9000 rpm.A rapid load regulation test was conducted, including the cold start process, long-term stable operation near the design point, and normal shutdown process.The maximum net power reached 3.866 MW, and the efficiencies of HPT and LPT are 84.3% and 88.2%, respectively.At present, the research on high-power prototype testing is still in its infancy, with only a small amount of data.The low-power S-CO2 turbine prototype is considered to have good performance during the design stage, and the predicted efficiency values in Ref.[21][24] exceed 80%.However, the efficiency values obtained from the experiment were not ideal enough.On the one hand, the design speed of the turbine is too high, which is difficult to achieve in actual operation due to factors such as bearings.On the other hand, the power reduction caused by windage losses also exceeded expectations.Partial admission is one of the solutions for the normal operation of low-power turbines.Although the maximum efficiency value has decreased, it can reduce the impeller speed to an acceptable range.However, further research is needed on partial admission S-CO2 turbines.