Experimental Study and Performance Analysis of a Recuperative Supercritical CO₂ Brayton Cycle

Abstract

To investigate the operational characteristics of the supercritical carbon dioxide (S-CO₂) Brayton cycle and enhance its applicability in practical operating conditions for micro-scale reactors, an experimental platform for a recuperative S-CO₂ Brayton cycle is constructed and investigated. Several controllable operational parameters, including compressor pump frequency, expansion valve opening, and electric heating power, each intrinsically linked to the thermal characteristics of its corresponding equipment, as well as the cooling water flow rate, are systematically adjusted and analyzed. Experimental results demonstrate that the cooling water flow rate has a significantly greater impact on the temperature and pressure of the cycle system compared to other operational parameters. Based on these findings, steady-state experiments are conducted within a pressure range of 8 MPa to 15 MPa and a temperature range of 70 °C to 150 °C. It is observed that the heat exchange capacity of the recuperator decreases as the cooling water flow rate is reduced, suggesting that sufficient cooling efficiency is required to maximize the recuperative function. Under the condition of a maximum system temperature of 150 °C, the isentropic efficiency of the expansion valve decreases with an increase in the inlet pressure of the valve. However, the overall thermal efficiency of the cycle system requires further calculation and assessment following the optimization of the experimental platform. The result of validation of experimental results is less than 20%. The findings presented in this study offer essential data that encompass the potential operational conditions of the CO₂ Brayton cycle section applicable to small-scale reactors, thereby providing a valuable reference for the design and operation of practical cycle systems.

1. Introduction

Against the backdrop of escalating global tensions and energy shortages, the development of advanced power generation technologies has become a primary objective for many nations. Among various thermal energy conversion technologies, the supercritical carbon dioxide (S-CO₂) Brayton cycle has emerged as a promising solution. This cycle is an efficient thermal energy conversion technology that leverages the unique physical properties of carbon dioxide in its supercritical state to facilitate the conversion of thermal energy into mechanical or electrical energy.

The S-CO₂ Brayton cycle is characterized by its high thermal efficiency and compact system configuration, making it well suited for a broad range of heat sources, including nuclear energy, solar energy, and fossil fuels. Compared to conventional steam Rankine cycles, the S-CO₂ Brayton cycle exhibits significantly improved thermal performance, with efficiency enhancements often exceeding 10% [1]. In addition, it offers the advantages of a reduced equipment footprint and lower operational costs. Carbon dioxide, as the working fluid, is non-toxic, environmentally friendly, and readily available, further increasing the attractiveness of this power conversion technology. Due to its excellent thermoelectric conversion efficiency and compact structure, the S-CO₂ Brayton cycle is especially compatible with the requirements of small modular reactors, which demand both space efficiency and high energy conversion performance.

Since 2005, the demonstration projects of the supercritical carbon dioxide (S-CO₂) Brayton cycle have been initiated by national laboratories across several countries. In the United States, a 250 kWe recompression S-CO₂ Brayton cycle test facility was established at Sandia National Laboratories (SNL), where comprehensive system-level testing was conducted [2]. Conboy et al. [3] investigated the performance of key components in the power cycle, including printed circuit heat exchangers (PCHEs), turbines, and compressors, under the conditions of increased flow rate, pressure, and temperature, using S-CO₂ as the working fluid. In 2012, the research team successfully developed a recompression test assembly consisting of a split-shaft turbine, a heat exchanger, and a compressor configuration [4]. This system demonstrated the potential for improved power conversion efficiency, although it also introduced greater control system complexity. To address this, control testing was performed, and the control system programming was completed accordingly [5]. Subsequently, Moore et al. [6] developed a novel, high-efficiency S-CO₂ turbo-expander and validated its performance and mechanical durability through experiments conducted in a 1 MW-scale test loop. These research efforts have primarily aimed at improving the thermal efficiency of the S-CO₂ cycle and advancing the performance of turbomachinery, thereby providing essential theoretical support and experimental data for system-level modeling and simulation.

Additionally, a 100 kWe simple S-CO₂ Brayton cycle system was developed by Bechtel Marine Propulsion Corporation (BMPC) at its nuclear propulsion research facility. Detailed investigations were conducted on the system’s operation, control strategies, and dynamic characteristics, with a specific focus on startup, shutdown, and operating condition transitions [7]. In Japan, a 10 kWe simple S-CO₂ Brayton cycle test facility was constructed at the Tokyo Institute of Technology (TIT), and a 110 We power generation experiment was subsequently carried out. The research primarily emphasized the compressor’s working performance [8]. In 2014, a 10 kWe simple S-CO₂ Brayton cycle system was developed at the Korea Institute of Energy Research (KIER) to facilitate advancements in system operation and control technologies. Additionally, evaluations were conducted on the performance of key components, including heat exchangers and turbomachinery [7,8,9,10]. In China, a 5 MWe once-through reheated recompression S-CO₂ Brayton cycle test facility was designed by the Xi’an Thermal Power Research Institute (TPRI). A 72 h trial operation applied to a coal-fired power system was successfully completed in December 2021 [11,12]. Meanwhile, in the United States, a 1 MW S-CO₂ test facility was developed by the Southwest Research Institute (SWRI), where the primary focus was placed on testing axial-flow turbines used in the cycle system [13]. In recent years, research efforts at academic institutions have also been directed toward the construction of S-CO₂ cycle systems. In 2018, a CO₂-based Transcritical Rankine Cycle (CTPC) prototype multi-cycle system was developed by Dr. Shi’s team at Tianjin University, where a steady-state detection method for waste heat recovery systems was proposed, utilizing dynamic characteristics as the basis [14]. An investigation was carried out to examine the effects of turbine inlet pressure and temperature on the performance of the CTRC system, revealing that the pressure ratio has a significantly positive impact, while the influence of mass flow rate was found to be less evident [15]. The dynamic response of the CTPC system to variations in flow rate and pressure ratio was further analyzed. Based on these findings, the flexible control of waste heat pumps and heat exchanger valve groups enabled the switching of four different cycle configurations [16]. In addition, a separate study by the same research group verified the feasibility of using CO₂-based gas mixtures to improve the performance of Organic Rankine Cycle (ORC) systems [17].

In 2019, an S-CO₂ recompression Brayton cycle test facility was built by Dr. Cheng’s team at the Institute of Engineering Thermophysics, Chinese Academy of Sciences, with a primary focus on optimizing the performance conditions of printed circuit heat exchangers (PCHEs) under supercritical conditions [18]. In 2020, an S-CO₂ Brayton cycle experimental system was developed by Dr. Liu’s team at Southeast University to evaluate the thermal performance of PCHEs, leading to structural improvements in heat exchanger design [19]. In 2021, a small-flow T-CO₂ test platform was utilized by Dr. Xing’s team at Zhejiang University to investigate the critical heat transfer characteristics of S-CO₂ in horizontal tubes. Heat transfer correlations were summarized, and dynamic experiments were conducted using an infrared spectroscopy testing system. Building on these findings, solutions were proposed to address issues such as low flow rates, large pressure drops, and slow system response. Subsequently, the Qingshan Lake large-flow T-CO₂ test platform was constructed, where more precise heat transfer correlations for vertical tube conditions were established [20,21].

These studies have laid a solid foundation for the practical application of S-CO₂ Brayton cycle technology. However, most research efforts have been concentrated on key system components, such as compressors, turbines, and heat exchangers, while experimental investigations on the dynamic characteristics and control strategies of the entire S-CO₂ Brayton cycle system under various operating conditions remain limited. Such studies are crucial for the practical design and operational optimization of S-CO₂ Brayton cycle systems. Unlike studies that concentrate on individual key components within the cycle, research on the integration of the CO₂ Brayton cycle into small modular reactors places greater emphasis on the overall thermodynamic behavior of the complete cycle system. This focus is primarily driven by the complex and variable operating conditions that such reactors are likely to face in real-world applications, which necessitate a system-level approach to design and analysis. To address this research gap, an S-CO₂ Brayton cycle experimental platform is designed and constructed in this study. Following the successful validation of stable operation under design conditions, a series of experiments are conducted to analyze the influence of controllable operating parameters, including compressor pump frequency, expansion valve opening, electric heating power, and cooling water pump flow rate, on the cycle system. The findings from this study provide valuable guidance for the practical implementation and optimization of S-CO₂ Brayton cycle systems.

2. Experimental Setup and Methodology

2.1. Experimental Rig Description

As shown in Figure 1, the system studied is a recuperative Brayton cycle which consists of heat exchange components, including a heater, a cooler, and two recuperators, as well as turbomachinery components, comprising a compressor and a turbine. In this system, the working fluid is pressurized from the low-pressure state to the high-pressure state by the compressor. Subsequently, it sequentially passes through the two recuperators, where it is preheated using the heat from the exhaust gas. The working fluid is then further heated to the maximum system temperature in the heater before entering the turbine, where it expands to the low-pressure state, performing work. After expansion, the fluid returns to the two recuperators for pre-cooling before being further cooled in the cooler to reach the minimum system temperature. Finally, the working fluid is directed back to the compressor, thus completing one full thermodynamic cycle.

Figure 2 illustrates the layout of the constructed S-CO₂ Brayton cycle system. The cycle system primarily consists of a gas source, cooling system, three-piston compression plunger pump, low-temperature recuperator, high-temperature recuperator, straight-tube electric heater, expansion valve, and cooling system. Considering the practical constraints of system construction, a three-piston compression plunger pump equipped with a frequency controller is selected to pressurize the working fluid and regulate the CO₂ flow rate. The application of a two-regenerator cycle structure enables the heat return process to be separated into two stages, which not only makes the resulting arrangement of the system more flexible, but also leads to an increase in the heat exchange efficiency of the cycle system. Since a customized turbine was not available at this stage, an expansion valve was chosen as an alternative to carry out the pressurization process, taking into account the design of other people’s experimental benches. The straight-tube electric heater is composed of a copper column and six thermistors, ensuring uniform heating, with a maximum heating power of 15 kW.

Carbon dioxide gas (99% purity) is used as the working fluid in the experiment. The mass flow rate is regulated by a three-piston pump, operating at a frequency range of 0 to 50 Hz. To ensure real-time monitoring and data recording, temperature and pressure sensors are installed at 12 measurement points throughout the primary cycle system. A mass flow meter, positioned upstream of the compression pump, is utilized to measure the mass flow rate of the main cycle system.

Table 1. Measurement instruments of the S-CO₂ Brayton cycle system.

Measurement Parameter	Measurement Location	Instrument Type	Measurement Range	Accuracy
Flow rate	Plunger pump inlet	Coriolis flow meter	0–220 kg/h	0.2%
Flow rate	Chiller outlet	Electromagnetic flow meter	0–1.4 m3/h	0.2%
Temperature	Measurement points 1–10	PT100 sensor	−50–400 °C	Class A
Pressure	Measurement points 1–10	Pressure sensor	0–100 MPa	0.3%

provides a detailed summary of all measurement instruments used in the experimental setup.

2.2. Experimental Methodology

2.2.1. Determination of Steady-State Conditions

To conduct a system performance analysis, it is essential to determine whether the system has reached a steady-state condition. After adjusting the working fluid pump speed and expansion valve opening, the system undergoes a transient response phase before its parameters gradually stabilize. Figure 3 illustrates the steady-state point extraction method, where pressure is selected as the steady-state criterion. Following a change in operating conditions, the system parameters exhibit transient fluctuations before eventually stabilizing. The system is considered to have reached a steady state when the pressure remains constant for a duration exceeding five minutes.

2.2.2. Uncertainty Analysis

For parameters that are not directly measured, the Kline–McClintock uncertainty propagation method is employed to conduct the uncertainty analysis:

$$\Delta \mathrm{R}=\sqrt{{\left({\displaystyle \frac{\partial \mathrm{R}}{\partial {\mathrm{x}}_1}}\right)}^2\Delta {\mathrm{x}}_1+{\left({\displaystyle \frac{\partial \mathrm{R}}{\partial {\mathrm{x}}_2}}\right)}^2\Delta {\mathrm{x}}_2+{\left({\displaystyle \frac{\partial \mathrm{R}}{\partial {\mathrm{x}}_3}}\right)}^2\Delta {\mathrm{x}}_3+\dots \dots +{\left({\displaystyle \frac{\partial \mathrm{R}}{\partial {\mathrm{x}}_{\mathrm{n}}}}\right)}^2\Delta {\mathrm{x}}_{\mathrm{n}}}$$

In the experimental cycle system, the calculation error of the recuperator heat exchange capacity primarily originates from measurement uncertainties associated with the main cycle flow meter, temperature sensors, and pressure sensors. The measurement uncertainties of parameters at various system points, as well as the uncertainty in the recuperator heat exchange capacity, are detailed in

Table 2. Uncertainty of measured and calculated parameters.

Measured or Calculated Parameter	Uncertainty
Temperature	±0.5%
Pressure	±10 kPa
Primary cycle flow rate	±0.2%
Recuperator heat exchange rate	±3.56%

.

2.2.3. Controllable System Variables

During the experiment, the control panel allows for the independent adjustments of key operational parameters, including compressor frequency, expansion valve opening, electric heating power, and cooling water pump flow rate. The adjustment range and precision of each parameter are specified in

Table 3. Range and precision of controllable variables on the control panel.

Variable	Control Panel Adjustment Range	Corresponding Adjustment Range	Minimum Adjustment Increment	Corresponding Minimum Adjustment
Compressor frequency	0~50 Hz	0~50 Hz	1 Hz	1 Hz
expansion Valve opening	0~100%	0~100%	0.1%	0.1%
Electric heating power	0~100%	0~15 kW	0.1%	Nonlinear relation between increment and adjustment value
Cooling water pump flow rate	0~60%	0~9.2 L/min	0.1%	Measured by cooling water flow meter (accuracy: 0.1 L/min)

.

The steady-state condition is established at a maximum system pressure of 13 MPa and a maximum temperature of 324.3 °C at the selected measurement point. Under these conditions, a series of tests are conducted to evaluate the effect of each controllable variable. The specific adjustments of each parameter during the tests are detailed in

Table 4. Adjustment parameters for testing controllable variables.

Test Phase	Control Panel Display Values
	Compressor Frequency	Expansion Valve Opening	Electric Heating Power	Cooling Water Flow Rate
Steady-state experiment	35 Hz	55%	58%	11%
Adjusting compressor frequency	(35 Hz → 34 Hz → 33 Hz)	55%	58%	11%
Adjusting expansion valve opening	35 Hz	(55% → 54% → 53% → 52%)	58%	11%
Adjusting electric heating power	35 Hz	55%	(58% → 55% → 52% → 50% → 48% → 45%)	11%
Adjusting cooling water flow rate	35 Hz	55%	58%	(11% → 12% → 13%)

. Before and after each adjustment, the steady-state evaluation criteria, as defined in the previous section, are strictly applied to ensure experimental consistency and accuracy.

2.2.4. Steady-State Experimental Condition

The experiment is conducted under the condition that the cooling water target temperature is maintained at 11 °C. The highest pressure measurement point (HP6 point) and the highest temperature measurement point (inside the electric heating section) are considered as the steady-state pressure and temperature reference points. Adjustments are made through the computer-controlled interface to achieve the target steady-state pressure and temperature for the cycle system. In this experiment, the investigation was initiated from the critical point of carbon dioxide, with temperature and pressure gradually increased to explore the system’s behavior under varying conditions. Steady-state experiments have been conducted within a pressure range of 8 MPa to 15 MPa and a temperature range of 60 °C to 160 °C. The specific steady-state conditions tested in this experiment are detailed in

Table 5. Steady-state experimental conditions and control panel adjustments.

Temperature (°C)	Pressure (MPa)	Compressor Frequency (Hz)	Expansion Valve Opening (%)	Electric Heating Power (%)	Cooling Water Pump Flow Rate (%)
70	9	35	49.5	48	18
70	10	35	43	40	6
70	11	35	38	36	5.7
85	9	35	53	49.8	48
85	10	35	45	38.3	5.8
85	11	33	43	34.5	5.2
100	9	35	67.5	59	65
100	12	35	44.5	46.5	9
100	13	35	42.5	43	6.5
100	14	40	37	39	5.3
150	9	33	69	60	65
150	12	38	50	48.2	7.2
150	13	38	49	48.3	6.9

.

3. Results and Discussion

3.1. Cooling System Adjustment

As summarized in the previous test results, cooling water flow rate adjustment is found to have the most significant impact on the cycle system. Therefore, before discussing the experimental results, a comprehensive analysis of the cooling water flow rate variations under different steady-state experimental conditions is conducted. The summarized data and graphical analysis are presented in Figure 4.

By examining the cooling water flow rates under different steady-state conditions, it is observed that, for steady-state temperatures of 70 °C and 85 °C, the adjustment range of the cooling water flow rate is relatively similar. However, in comparison, for steady-state temperatures of 100 °C and 150 °C, the adjustment range exhibited a significantly larger variation. Therefore, in the experimental results and analysis section, the data will be categorized for further examination. The group with steady-state temperatures of 70 °C and 85 °C is referred to as Cooling Mode 1, while the group with steady-state temperatures of 100 °C and 150 °C is referred to as Cooling Mode 2.

3.2. Working Fluid Flow Rate Analysis

The trend of the working fluid flow rate under different steady-state conditions is shown in Figure 5. It is first observed that the two data groups, Cooling Mode 1 and Cooling Mode 2, exhibited noticeable differences in their flow rate trends, which corresponded to the variation in cooling water flow rate adjustment range. Specifically, a larger adjustment range of cooling water flow rate is associated with a broader range of working fluid flow rate variation.

Both compressor pump frequency and expansion valve opening are identified as the primary factors influencing the working fluid flow rate, but their effects are opposite in nature. An increase in compressor pump frequency led to an increase in the primary cycle flow rate, whereas an increase in the expansion valve opening resulted in a decrease in flow rate. From Table 5 and Figure 5, it is observed that, when both factors are increased simultaneously, the main circulation flow rate exhibited an overall downward trend, indicating that the influence of the expansion valve opening degree is predominant. For instance, under a steady-state temperature of 100 °C, the operating condition at a pressure of 13 MPa results in a 5% increase in the piston pump speed and a 4% decrease in the expansion valve opening on the control panel, compared to the condition at 14 MPa. Moreover, the steady-state flow rate at 13 MPa is significantly higher than that observed at 14 MPa. This phenomenon can be attributed to the differences in their mechanisms of action: the expansion valve directly restricts the cross-sectional area of the flow passage through throttling, while the compression pump increases the mass flow rate of the working fluid per unit time by enhancing the speed of the plunger movement.

A comparison of individual steady-state conditions further confirms that an increase in compressor pump frequency promotes an increase in primary cycle flow rate. For instance, at a steady-state temperature of 70 °C and pressure of 10 MPa, and a steady-state temperature of 85 °C and pressure of 11 MPa, the expansion valve opening remains the same for both cases. However, since the compressor pump frequency is higher in the former case, the working fluid flow rate is also slightly higher compared to the latter.

3.3. Pressure Analysis

The pressure at Point 5 (the expansion valve inlet) is designated as the reference pressure for steady-state regulation, and the pressure trends at the remaining high-pressure points followed a similar pattern to that shown in Figure 6. According to the pressure values of high-pressure points at the maximum system temperature of 150 °C (as listed in

Table 6. High-pressure point pressures at 150 °C.

Expansion Valve Inlet Pressure (MPa)	Compressor Outlet Pressure (MPa)	Low-Temperature Recuperator High-Pressure Side Outlet Pressure (MPa)	High-Temperature Recuperator High-Pressure Side Outlet Pressure (MPa)	Electric Heater Outlet Pressure (MPa)
9	9.127 ± 0.01	9.037 ± 0.01	9.033 ± 0.01	9.046 ± 0.01
12	12.109 ± 0.02	12.037 ± 0.02	12.006 ± 0.01	12.043 ± 0.01
13	13.134 ± 0.04	13.066 ± 0.03	13.052 ± 0.03	13.092 ± 0.03

), it is observed that the pressure slightly decreased along the flow direction of the working fluid, with a slight increase occurring after passing through the electric heater. These results indicate that the target steady-state pressure at each measurement point is effectively controlled, demonstrating good consistency with the expected pressure distribution within the high-pressure section of the system.

Expansion valve opening directly determines the relationship between high pressure and low pressure, expansion valve outlet pressure curve shown in Figure 7. Similarly the trend of the curves for Cooling Mode 1 and Cooling Mode 2, which have different cooling water flow regulation ranges, can be clearly distinguished: the trend of the curves for Cooling Mode 1 and Cooling Mode 2 is more consistent in their respective groups, and since the pressure on the high-pressure side is the parameter to be regulated, the pressure ratio of the circulating system is more consistent.

Based on Figure 7 and Figure 8 and the low-pressure point pressure parameters in

Table 7. Low-pressure point pressures at 150 °C.

Expansion Valve Inlet Pressure (MPa)	Expansion Valve Outlet Pressure (MPa)	High-Temperature Recuperator Low-Pressure Side Outlet Pressure (MPa)	Low-Temperature Recuperator Low-Pressure Side Outlet Pressure (MPa)	Condenser Outlet Pressure (MPa)
9	7.387 ± 0.01	7.385 ± 0.01	6.055 ± 0.01	6.052 ± 0.01
12	8.145 ± 0.01	8.138 ± 0.01	7.619 ± 0.01	7.627 ± 0.01
13	8.730 ± 0.03	8.715 ± 0.035	8.349 ± 0.04	8.361 ± 0.04

for the 150 °C condition, it can be observed that the overall trend of the low-pressure point pressure curves remains consistent. As the working fluid flows through the system, the pressure at each measurement point gradually decreases. Points located closer to the condenser exhibit a more significant pressure drop, which is attributed to the influence of the condenser. This observation aligns with the previous test results, which demonstrated that the cooling water flow rate has a significant impact on the system pressure.

Although both Cooling Mode 1 and Cooling Mode 2 exhibit a general trend where an increase in high-pressure side pressure leads to an increase in the low-pressure side pressure across all temperature conditions, notable differences in the pressure curves of the two modes can still be observed. Specifically, the pressure increase trend at different points is more pronounced in Cooling Mode 1 (with a smaller cooling water flow rate) compared to Cooling Mode 2. Furthermore, in Cooling Mode 2, the pressure variation between different points is more significant than in Cooling Mode 1. In particular, when comparing the expansion valve inlet pressures of 9 MPa and 12 MPa, the difference in measured point pressures increase along the flow direction in Cooling Mode 2, whereas in Cooling Mode 1, the pressure difference remains nearly constant. According to the previous cooling water flow rate analysis, the difference in cooling water flow rates corresponding to the two pressure values in Cooling Mode 2 is significantly larger than that in Cooling Mode 1. This result is consistent with the earlier findings, further confirming that cooling water flow rate has a substantial impact on the overall pressure distribution in the cycle system.

3.4. Temperature Analysis

(a)

High-Temperature Points

By analyzing the temperature trends at high-temperature measurement points in Figure 9, Figure 10 and Figure 11, it is observed that the temperature at the point closest to the electric heater outlet follows a trend similar to the maximum cycle temperature, although with a temperature deviation (approximately 10 to 15 °C). The temperature profile at this point remains nearly parallel to the maximum cycle temperature, indicating a strong thermal influence from the electric heater. As the distance from the electric heater increased along the working fluid flow direction, the influence of the heater on the measurement points weakened. This effect is reflected in both the absolute temperature values and the overall temperature curve trend: points located farther from the heater exhibited a significant temperature drop. Under the same maximum cycle temperature, the temperature difference between points corresponding to different expansion valve inlet pressures increase noticeably.

For most high-temperature points, the measured temperature increases with increasing expansion valve inlet pressure, following a consistent trend. However, a notable exception is observed for the temperature at the expansion valve outlet point in Cooling Mode 2. In this case, the temperature decreases as the expansion valve inlet pressure increased. This phenomenon is attributed to the significant increase in pressure difference across the expansion valve in Cooling Mode 2. As analyzed in previous sections, the pressure drop across the expansion valve increased significantly with inlet pressure, reaching a maximum of approximately 4 MPa. This higher pressure drop enhances the expansion cooling effect, leading to a reduction in temperature at the expansion valve outlet point.

(b)

Low-Temperature Points

By analyzing the temperature trends at low-temperature measurement points in Figure 12, Figure 13 and Figure 14, it is observed that these points are closest to the cooling heat exchanger, making them the most significantly affected by a cooling water flow rate. It is clearly observed that the temperature curves in Cooling Mode 2 (with a larger cooling water flow rate) are entirely positioned below those in Cooling Mode 1, indicating a more effective cooling effect in Cooling Mode 2. In Figure 13, the temperature values of the 10 MPa and 11 MPa points in Cooling Mode 1 are noticeably higher compared to those in Figure 12. As analyzed in the previous section, the cooling water flow rate at the 11 MPa point is relatively lower, reducing the cooling effect on that point. As a result, the temperature at the 11 MPa point in Figure 13 remains nearly unchanged compared to Figure 12, leading to the observed trend in the temperature curve.

(c)

Intermediate-Temperature Points

Analysis of the temperature trends at intermediate-temperature measurement points shows that these points are situated between the previously examined high-temperature and low-temperature regions. As a result, their temperature trends exhibit a gradual increase with rising steady-state pressure.

The temperature curves for Cooling Mode 1 and Cooling Mode 2 display a similar pattern to those in Figure 11. However, in Figure 15 and Figure 16, the two sets of curves appear closer to each other, indicating a less pronounced difference in temperature distribution between Cooling Mode 1 and Cooling Mode 2 in this intermediate temperature range.

3.5. Heat Exchange Analysis

From the heat exchange trends observed in Figure 17, it can be noted that the heat transfer rates on both sides of the low-temperature recuperator exhibit a corresponding relationship. Specifically, the heat absorbed on the low-pressure side decreases as the steady-state pressure increases, while the heat released on the high-pressure side also decreases with increasing pressure. Additionally, the heat absorption on the low-pressure side increases as the steady-state temperature rises, and similarly, the heat released on the high-pressure side increases with temperature. These trends indicate a direct correlation between temperature, pressure, and recuperator heat transfer performance.

From the heat exchange trends observed in Figure 18, it can be noted that the heat transfer rates on both sides of the high-temperature recuperator exhibit a corresponding relationship. Specifically, the heat absorbed on the low-pressure side decreases as the steady-state pressure increases, while the heat released on the high-pressure side also decreases with increasing temperature and pressure. Additionally, the heat transfer on the low-pressure side increases as the steady-state temperature rises, and similarly, the heat released on the high-pressure side increases with temperature.

The difference in heat transfer between the hot side and the cold side of the recuperators is basically between −14% and 20%, and the heat transfer on the hot side is generally greater than that on the cold side. Both recuperators follow the same variation pattern, where heat exchange increases with temperature, aligning with the inherent properties of the recuperator. However, the observed trend with pressure does not entirely conform to general expectations. Upon further analysis, the primary reason for this phenomenon is attributed to variations in cooling water flow rate. As the cooling water flow rate decreases, the temperature difference between the high-temperature and low-temperature sides of the cycle system diminishes, leading to a reduction in recuperator efficiency. Therefore, in practical applications, it is essential to ensure sufficient cooling capacity within the system to maximize the recuperative function of the single-stage compression recuperative Brayton cycle.

3.6. Expansion Valve Related Calculations

Based on the experimental data obtained under steady-state conditions, further calculations are performed to analyze the expansion valve and relevant cycle system parameters. The specific calculation results are presented in

Table 8. Calculated results of cycle system parameters at a maximum system temperature of 150 °C.

Cycle Parameters	Expansion Valve Inlet Pressure (MPa)
	9	12	13
Isentropic Efficiency of Expansion Valve ${\eta }_{valve}$	0.372	0.210	0.143
Electric Heater Heat Input $Q_{heater}$/(kJ/s)	7.571	3.698	3.011
Potential to Realize Work $W_{potential}$/(kJ/s)	0.219	0.140	0.095

It can be observed that, when the maximum system temperature is 150 °C, the isentropic efficiency of the expansion valve decreases as the expansion valve inlet pressure increases. As analyzed in previous sections, the pressure difference across the expansion valve increases with the rising inlet pressure, leading to an increase in the ideal entropy value at the expansion valve outlet, which consequently reduces the isentropic efficiency of the expansion process. Although the expansion valve effectively reduces the working fluid pressure, it differs from a turbine in that it does not convert the pressure drop into mechanical energy output. According to Table 6 and Table 7, as the steady-state pressure increases, the ideal enthalpy rise associated with isentropic expansion at the outlet of the expansion valve becomes substantially greater than the actual enthalpy difference between the inlet and outlet. As a result, the isentropic efficiency calculated using the relevant equation decreases with increasing steady-state pressure. Within the pressure range of 8 to 15 MPa, higher pressure typically suppresses the gas-phase separation of CO₂, leading to more stable flow and, theoretically, improved system efficiency. Therefore, it is inferred that the observed decline in isentropic efficiency is not primarily driven by thermodynamic behavior. Instead, it is more likely attributed to the combined effects of the expansion valve characteristics and the behavior of the working fluid under high-temperature and high-pressure conditions.

3.7. Validation of Experimental Result

Based on the experimental cycle loop built by RELAP5 MOD4.0, the steady state simulation was carried out for the two working conditions of 12 MPa and 13 MPa for the maximum system pressure at the maximum system temperature of 150 °C, and the results are shown in

Table 9. Cycle system simulation results.

Simulation Working Condition	System Parameters	Experimental Value	Simulation Value	Error
Cycle system Maximum temperature: 150 °C Maximum pressure: 12 MPa	Piston pump inlet pressure P1 (Pa)	7.63 × 106	7.69 × 106	0.78%
	Piston pump inlet temperature T1 (K)	303.75	305.98	0.73%
	Piston pump outlet pressure P2 (Pa)	1.21 × 107	1.22 × 107	0.71%
	Piston pump outlet temperature T2 (K)	315.14	322.41	2.31%
	Low-temperature heat exchanger low-temperature side outlet pressure P3 (Pa)	1.20 × 107	1.20 × 107	0.31%
	Low-temperature heat exchanger low-temperature side outlet temperature T3 (K)	328.70	331.37	0.81%
	Electric heater inlet pressure P4 (Pa)	1.20 × 107	1.20 × 107	0.05%
	Electric heater inlet temperature T4 (K)	340.46	342.98	0.74%
	Electric heater outlet pressure P5 (Pa)	1.20 × 107	1.20 × 107	0.36%
	Electric heater outlet temperature T5 (K)	408.35	408.21	0.03%
	High-temperature heat exchanger high-temperature side outlet pressure P7 (Pa)	8.14 × 106	8.09 × 106	0.58%
	High-temperature heat exchanger high-temperature side outlet temperature T7 (K)	351.57	353.09	0.43%
	Condenser inlet pressure P8 (Pa)	7.62 × 106	7.69 × 106	0.93%
	Condenser inlet temperature T8 (K)	315.94	319.29	1.06%
	Main cycle mass flow rate (kg/s)	0.029	0.029	0.76%
	Cooling water mass flow rate (kg/s)	0.037	0.037	0.33%
	Cooling water inlet temperature (K)	285.15	288.37	1.13%
	Cooling water outlet temperature (K)	313.04	306.65	2.04%
	Electric heater power (W)	3708.00	3268.50	11.85%
	Condenser power (W)	3711.60	3067.50	17.35%
	High-temperature heat exchanger power (W)	1399.60	1173.40	16.16%
	Low-temperature heat exchanger power (W)	1723.20	1673.50	2.88%
	Piston pump power (W)	300.00	252.12	15.96%
Cycle system Maximum temperature: 150 °C Maximum pressure: 13 MPa	Piston pump inlet pressure P1 (Pa)	8.36 × 106	8.41 × 106	0.62%
	Piston pump inlet temperature T1 (K)	308.06	308.19	0.04%
	Piston pump outlet pressure P2 (Pa)	1.32 × 107	1.33 × 107	1.14%
	Piston pump outlet temperature T2 (K)	320.88	322.94	0.64%
	Low-temperature heat exchanger low-temperature side outlet pressure P3 (Pa)	1.31 × 107	1.31 × 107	0.20%
	Low-temperature heat exchanger low-temperature side outlet temperature T3 (K)	333.86	338.61	1.42%
	Electric heater inlet pressure P4 (Pa)	1.31 × 107	1.31 × 107	0.30%
	Electric heater inlet temperature T4 (K)	344.69	349.29	1.33%
	Electric heater outlet pressure P5 (Pa)	1.31 × 107	1.31 × 107	0.00%
	Electric heater outlet temperature T5 (K)	406.29	405.45	0.21%
	High-temperature heat exchanger high-temperature side outlet pressure P7 (Pa)	8.71 × 106	8.73 × 106	0.17%
	High-temperature heat exchanger high-temperature side outlet temperature T7 (K)	353.38	356.97	1.02%
	Condenser inlet pressure P8 (Pa)	8.35 × 106	8.73 × 106	4.55%
	Condenser inlet temperature T8 (K)	321.39	325.07	1.15%
	Main cycle mass flow rate (kg/s)	0.025	0.0294	18.63%
	Cooling water mass flow rate (kg/s)	0.028	2.80 × 10−2	0.27%
	Cooling water inlet temperature (K)	285.15	289.28	1.45%
	Cooling water outlet temperature (K)	318.60	313.54	1.59%
	Electric heater power (W)	3023.63	2910.10	3.75%
	Condenser power (W)	2790.60	3111.9	11.51%
	High-temperature heat exchanger power (W)	1029.40	945.68	8.13%
	Low-temperature heat exchanger power (W)	1323.4	1564.6	18.23%
	Piston pump power (W)	83.93	97.68	16.38%

below.

Comparison of the experimental and simulation values shows that the errors of the low-temperature heat exchanger heat recovery, the cooling water inlet and outlet parameters, and the thermal parameters of each node of the cycle are less than 20% from the experimental values. The simulation results are within the reasonable error range, and the results show the accuracy of the simulation modeling.

4. Conclusions

An experimental study is conducted based on the S-CO₂ Brayton cycle system to investigate the effects of various controllable parameters on system performance. The main conclusions are as follows:

(a) The effects of four controllable parameters (piston pump speed, expansion valve opening, electric heating power and cooling water flow rate) on the system performance were explored. The results show that the cooling water flow has the most significant effect on the system and is prioritized for system tuning.

(b) The recuperative efficiency of the recuperator increases with rising steady-state temperature but decreases with increasing steady-state pressure, primarily due to the reduction in cooling water flow rate, which leads to a smaller temperature difference between the high- and low-temperature sides of the cycle.

(c) Further calculations are performed based on steady-state experimental data for conditions with a maximum system temperature of 150 °C, The isentropic efficiency of the expansion valve decreases as the expansion valve inlet pressure increases, ranging from 37% to 14%. It is inferred that this phenomenon is not caused by thermal behavior.

(d) Based on the experimental cycle loop built by Relap5 software, the steady state simulation was carried out for the validation of steady-state experiment results. The difference in the experimental results and simulation values are less than 20%, which are within the reasonable error range.

(e) Due to limitations in the research conditions, an expansion valve was employed in place of a turbine to perform the expansion process in the experimental setup. This substitution has indirectly reduced the significance of analyzing the overall thermodynamic performance of the cycle. Therefore, the present study primarily focuses on the parameters that can be directly measured at various locations within the circulation system. In future work, after the optimization of the experimental platform, experiments will be specifically designed to investigate and analyze the overall thermal parameters of the complete cycle system.