The feasibility of using Kr as an additive in the sCO
2 recompression Brayton cycle has already been proven [
29]. Compared to pure CO
2, using a CO
2–Kr mixture working fluid improves the cycle’s energy efficiency. Additionally, the CO
2–Kr mixture helps reduce exergy losses, especially by effectively controlling exergy destruction in the high-temperature heat exchanger, further optimizing the system overall performance. With the same exergy efficiency, the CO
2–Kr cycle has a lower cost than the pure CO
2 cycle, indicating that Kr as an additive improves cycle efficiency and provides better economic benefits [
29]. However, in practical operation, the system will inevitably experience continuous fluctuations, and the dynamic performance of the CO
2–Kr mixture as the working fluid remains unclear. Therefore, to predict and evaluate the dynamic response characteristics of the system under disturbance factors and explore the reasons for dynamic performance differences between different working fluids, a comparative analysis of the system’s dynamic response characteristics under mass flow, heat source power, and rotational speed disturbances was conducted.
4.1. Effects of Mass Flow Rate Step Change
Figure 6 shows the temperature response distribution at key locations in the CO
2 and CO
2–Kr systems under mass flow disturbance. When the system reaches steady operation, a downward step disturbance in mass flow is applied. The figure shows that, after the disturbance is applied, the temperature at key locations first decreases and then increases. This is because, with constant rotational speed and heat source power, a decrease in mass flow increases the heat absorbed per unit of working fluid, which causes the temperature to rise. However, in the early stages of the disturbance, due to the thermal inertia effect caused by the working fluid properties and the lag effect of the heat source, the temperature change at key locations initially shows a downward trend. Around 53 s, the thermal inertia and lag effects gradually disappear, and the temperature rises. Therefore, the final stable temperature at the turbine inlet and outlet is higher than the pre-disturbance temperature. For the re-compressor, during the final stable phase, the effect of the mass flow decrease on the re-compressor temperature is higher than the effect of efficiency decrease on the temperature. As a result, the temperature during the stable phase of the re-compressor is slightly lower than in the initial phase.
Taking the turbine outlet temperature as an example, a comparison of the response time and overshoot between the two working fluids reveals that, during the initial stage, the CO2–Kr system has a response time that is 3.5 s faster than the CO2 system. However, it also results in a larger response amplitude, with a value that exceeds CO2 by 6.25 K. After the disturbance is applied, in the turbine outlet temperature dynamic response, the pure CO2 system experiences a sharp drop in temperature followed by significant fluctuations (beginning to recover after 53 s), while the CO2–Kr mixed working fluid system shows a gentler fluctuation and a smooth decline, quickly recovering to the steady state. The response time is shortened by 10 s, and the final steady-state temperature is lower than that of the CO2 system. In the turbine inlet temperature response curve, the green shaded area clearly shows that the overshoot of the CO2–Kr system is much more pronounced than that of the CO2 system. Similarly, at the re-compressor inlet and outlet, the CO2–Kr system has a better temperature response time than the CO2 system, with a 1.5 s reduction in response time.
By comparing the temperature responses of the CO2 and CO2–Kr systems, it can be observed that the CO2-Kr mixture generally performs better dynamically after disturbances than the pure CO2 system. When faced with disturbances, the CO2 system experiences larger temperature fluctuations, longer recovery times, and a higher final stable temperature. In contrast, the CO2-Kr system exhibits smaller fluctuations, faster recovery, and a lower final temperature after the disturbance. This indicates that the addition of Kr improves the system’s stability and thermal efficiency, allowing the system to maintain smoother operation under disturbances.
Similarly, a decrease in mass flow leads to changes in the compression ratio of the compressor and turbine, which in turn causes a step change in the pressure at key locations.
Figure 7 shows the pressure response at key locations. According to the compressor performance curve, underrated speed and a decrease in mass flow leads to an increase in the compression ratio, which increases the main compressor outlet pressure and turbine inlet pressure. However, the reduction in mass flow causes a decrease in the turbine compression ratio. In the early stages of the disturbance, the turbine outlet pressure decreases, followed by a decrease in the re-compressor inlet pressure. As the main compressor outlet pressure continues to increase, the system’s pressure gradually rises, leading to an increase in both the turbine outlet pressure and the re-compressor inlet pressure.
In addition, comparing the pressure response curves of CO2 and CO2–Kr, it is observed that both systems follow similar overall trends, but there are significant differences in overshoot and response time. Specifically, during the pressure response process, the overshoot for the pure CO2 system is 1.2 MPa, while the CO2–Kr system has an overshoot of only 0.5 MPa, with the difference being approximately 0.7 MPa. This difference indicates that the CO2–Kr mixture exhibits better stability during regulation and can effectively suppress excessive fluctuations. Regarding response time, under the same disturbance conditions, the CO2–Kr system’s response time is about 1.2 s shorter than that of the CO2 system. This reduction is approximately 16.7%, significantly improving the system’s dynamic performance. This improvement is attributed to the differences in thermophysical properties between CO2 and CO2–Kr, as the introduction of Kr enhances the gas’s density and viscosity, leading to lower overshoot and faster response speeds during pressure regulation. These properties enable the CO2–Kr system to reach a steady state more quickly and maintain smaller fluctuation amplitudes when facing disturbances.
During the system operation, the decrease in mass flow directly affects the turbine output power and compressor power consumption. As the mass flow decreases, the turbine output and the compressor power consumption reduce. However, the impact of the decrease in compressor power consumption is much greater than that of the turbine output power change. This is because the compressor power consumption has a more significant impact on the system’s overall energy consumption. Specifically, after the reduction in compressor power consumption, the overall system efficiency improves, leading to an increase in the net output power of the system. This change increases the system’s specific work and improves the thermal efficiency, provided that the heat source conditions remain unchanged, as shown in
Figure 8.
By comparing the system performance of two different working fluids, it is observed that there are certain differences in turbine output power and compressor power consumption between the CO2 and CO2–Kr mixture systems. These differences mainly arise from the thermodynamic property differences of the working fluid at key locations, especially the differences in physical parameters such as density and viscosity under different operating conditions. The CO2 system has a specific work of 42.52 kW/kg and a thermal efficiency of 30.37% after the disturbance. In comparison, the CO2–Kr system demonstrates better performance with a specific work of 50.39 kW/kg and a thermal efficiency of 35.21%. These results indicate that the CO2–Kr mixture performs better than the pure CO2 system, particularly in specific work and thermal efficiency, showing a clear advantage.
4.2. Effects of Heat Source Step Change
When the system operates stably at the design operating point, a heat source disturbance is applied, reducing the heat source from 810 kW to 730 kW.
Figure 9 shows the dynamic temperature response of the system after the heat source disturbance. It can be observed that, during the 50 s heat source decrease, the temperature response curves at the inlet and outlet of the re-compressor and turbine exhibit significant dynamic changes. For the CO
2 working fluid, the re-compressor inlet temperature stabilizes at 353 K before the disturbance. However, a sudden change occurs after the heat source decreases, and the temperature drops sharply to 344 K at 50.4 s, a decrease of approximately 2.5%. Then, the temperature gradually rises to 346.7 K at 50.8 s, entering a state of slight fluctuation. The turbine inlet temperature initially stabilizes at 828 K before the disturbance. Following the decrease in heat source, the turbine inlet temperature drops rapidly to 822.08 K at 50.4 s. Similarly, the turbine outlet temperature also exhibits a decreasing trend.
This overall trend is primarily driven by the thermodynamic response mechanism of the system caused by decrease in the heat source. The reduction in heat source power directly leads to a decrease in the thermal load of the cycle system. The re-compressor needs to adjust its compression ratio to maintain flow balance, causing the inlet temperature to fluctuate due to changes in the working fluid’s heat absorption capacity. The brief rise in turbine inlet temperature results from the delayed response due to the system’s thermal inertia, followed by a gradual decrease as the heat source disruption continues.
In contrast, the CO2–Kr mixture shows a more gradual temperature change. The re-compressor inlet temperature, initially stable at 352.83 K, drops to 341.94 K at 50.4 s after the heat source disturbance, with a decrease of approximately 3.1%, slightly higher than pure CO2. The turbine inlet temperature is 828.06 K at 50 s, which is 2.07 K lower than that of CO2, and the subsequent fluctuation is smaller. Notably, the difference in turbine outlet temperature between the two working fluids is more significant. At 50 s, the CO2–Kr outlet temperature is 767.07 K, 1.53 K lower than CO2’s 765.44 K. This indicates that the mixture has better thermal stability.
These differences can be attributed to the inert gas properties of Kr. Its larger molecular weight alters the working fluid’s heat capacity and thermal diffusion resistance [
16]. After a disturbance occurs, CO
2–Kr, with its lower specific heat capacity and thermal conductivity, experiences relatively slow heat transfer, resulting in smaller temperature fluctuations from the disturbance, which effectively reduces system oscillations.
Similarly, the pressure response curves at the inlet and outlet of the re-compressor and turbine show dynamic changes, with significant differences between the CO
2 and CO
2–Kr working fluids, as shown in
Figure 10. For the CO
2, the re-compressor inlet pressure gradually rises from the initial value of 7.75 MPa to 7.90 MPa at 50 s. However, after the heat source decreases, the inlet pressure drops only slightly and then further decreases to 7.895 MPa at 50.7 s, accompanied by small fluctuations. The outlet pressure slowly increases from the initial 13.73 MPa to 13.91 MPa at 50 s, and after the disturbance, it gradually stabilizes at 13.81 MPa, with a small overall fluctuation. The turbine inlet pressure in the CO
2 system gradually rises from 13.49 MPa to 13.68 MPa at 50 s and then continues to fluctuate, reaching 13.569 MPa at 100 s. The turbine outlet pressure rises from 7.89 MPa to 8.04 MPa at 50 s, then quickly drops to 8.00 MPa after the heat source decreases, finally stabilizing at 7.93 MPa at 100 s. This trend is primarily driven by the thermodynamic imbalance caused by the sudden drop in heat source power. The reduced thermal load leads to a decline in the heat absorption capacity of the working fluid. To maintain flow balance, the re-compressor needs to adjust its compression ratio, which causes fluctuations in the inlet pressure due to changes in the fluid density. The brief increase in turbine inlet pressure results from the system’s inertia, causing a delayed response and a gradual decrease due to the interruption of the heat source.
In contrast, the pressure variations in the CO2–Kr mixture are more gradual. The re-compressor inlet pressure increases from 7.75 MPa to 7.89 MPa at 50 s, then decreases to 7.85 MPa at 50.3 s after the heat source decreases, with a decrease of only 0.04 MPa. The turbine inlet pressure at 50 s is 13.65 MPa, which is 0.03 MPa lower than that of CO2, and during subsequent fluctuations, the maximum decrease is 0.12 MPa. The difference in turbine outlet pressure is more noticeable, with CO2–Kr at 50 s being 8.041 MPa, 0.001 MPa lower than CO2. However, at 100 s, it stabilizes at 7.92 MPa, which is 0.01 MPa lower than CO2’s 7.93 MPa, indicating that the CO2–Kr mixture has superior long-term stability. This difference is mainly due to the distinct thermodynamic properties of the two working fluids. As a single fluid, CO2 shows significant pressure changes when the heat source fluctuates. However, introducing the additive Kr alters the thermodynamic characteristics of the system. Kr’s low-temperature properties make the CO2–Kr system more stable during heat source fluctuations. Kr optimizes the thermodynamic performance of the gas mixture, leading to smaller pressure fluctuations and faster responses when the heat source changes in the CO2–Kr system.
Due to the impact of the aforementioned key parameters, the system’s thermal performance changes, as shown in
Figure 11, which illustrates the system’s dynamic performance response curve during heat source disturbances. In the CO
2 system, before the heat source disturbance (0–50 s), the efficiency and specific work stabilized at 28.47% and 39.49 kW/kg, respectively. At 50.3 s, after the sudden drop in the heat source, the efficiency sharply rises to 29.70%, while the specific work drops to 37.64 kW/kg. Subsequently, at 50.7 s, the efficiency further increases to 30.20%, a 1.73% improvement from the initial value, and the specific work rebounds to 38.25 kW/kg, gradually stabilizing in subsequent fluctuations. Finally, the efficiency stabilizes at 31.24%, and the specific work stabilizes at 39.52 kW/kg, reflecting an increase of 2.77% and 0.03 kW/kg, respectively, from the initial values.
This change is due to the reduction in heat load, which causes the turbine output power to decrease. The system achieves a new energy balance, leading to a stable state. The rise in efficiency is primarily driven by the positive effect of reduced compressor power consumption, which outweighs the negative effect of reduced turbine work, leading to the overall efficiency increase. Similarly, the specific work shows a similar trend.
In contrast, the efficiency and specific work of the CO2–Kr system are significantly higher than those of the CO2 system before the heat source decreases. After the heat source decreases, the efficiency of the CO2–Kr system drops to 35.23% at 50.3 s, and the specific work drops to 44.58 kW/kg. However, the recovery is faster. By 51.5 s, the efficiency rebounds to 36.11%, and the specific work returns to 45.68 kW/kg. By 100 s, the efficiency stabilizes at 37.01%, 5.77% higher than CO2, and the specific work stabilizes at 46.81 kW/kg, 7.29 kW/kg higher than CO2. The above results show that the CO2–Kr system exhibits less fluctuation in efficiency during heat source disturbances and reaches a stable specific work value more quickly, demonstrating superior disturbance resistance. The larger molecular weight of Kr leads to a lower specific heat capacity of the CO2–Kr mixture, allowing the mixture to respond more quickly to temperature disturbances and recover to a steady state faster. This helps reduce the impact of temperature fluctuations on system performance when there are sudden changes in the heat source. Furthermore, CO2-Kr’s viscosity is higher than pure CO2, which increases flow resistance but reduces compressor power consumption, thus making efficiency improvements more pronounced.
In summary, CO2–Kr, due to its optimized thermodynamic properties—specifically, the increase in density—significantly reduces the actual volumetric flow rate compared to pure CO2. The reduction in volumetric flow lowers the flow velocity of the working fluid in pipes and equipment, thus minimizing the amplification effect of flow inertia on disturbances. Under dynamic operating conditions, in the CO2–Kr mixture, the addition of Kr moderately increases the mixture’s viscosity compared to pure CO2, thereby suppressing flow instabilities, while Kr’s inertness improves thermodynamic stability under high-temperature conditions. Although Kr’s thermal conductivity is slightly lower than CO2 at standard conditions, the mixture’s enhanced density and adjusted transport properties promote more efficient heat transfer in certain regimes. These combined effects contribute to an improvement in isentropic efficiency during compression/expansion and significantly dampen pressure fluctuations.
4.3. Effects of Speed Step Change
In the recompression Brayton cycle system, the compressor and turbine are arranged with a single shaft, and disturbances in the rotational speed affect the performance curves of the compressor and turbine, which in turn impact the system’s key parameters and, ultimately, the system performance. The temperature response characteristics of the two working fluids are shown in
Figure 12. For the CO
2 system, the re-compressor inlet temperature gradually rises from 335.20 K at 0.2 s to 353.20 K just before 50 s. After a speed decrease at 50.2 s, it sharply increases to 353.20 K then rises to 355.99 K by 50.6 s, with small fluctuations thereafter, stabilizing at 354.17 K by 100 s. The outlet temperature rises from 389.95 K to 411.81 K just before 50 s. After the speed decreases, it reaches 415.13 K at 50.6 s, eventually stabilizing at 412.91 K. The turbine inlet temperature increases from 815.99 K to 829.20 K just before 50 s, and after the speed decreases, it jumps to 831.28 K at 50.2 s, fluctuating to 829.20 K by 100 s. The turbine outlet temperature rises from 754.40 K to 769.81 K just before 50 s. After the speed decrease, it reaches 771.12 K at 50.6 s, finally stabilizing at 768.82 K. This trend is mainly caused by the thermodynamic inertia effects triggered by the rotational speed decrease. The speed decrease causes an imbalance in the power output of the compressor and turbine. The reduction in the compressor compression ratio lowers the temperature rise of the working fluid, while the weakening turbine power output delays heat expulsion, leading to instantaneous temperature accumulation. In contrast, the CO
2–Kr mixture exhibits better temperature stability from the beginning. Specifically, the re-compressor inlet temperature rises from 344.17 K to 352.83 K before 50 s, slightly lower than the CO
2 system. After the speed decrease, the peak temperature reaches 359.47 K, finally stabilizing at 355.17 K. The turbine inlet temperature starts at 842.24 K, and the fluctuation is only 0.6% after the speed decrease, eventually stabilizing at 829.78 K. The superiority of CO
2–Kr stems from its physical property parameters, as the specific heat capacity of CO
2–Kr is lower than that of pure CO
2. This allows the CO
2–Kr system to respond more quickly to disturbances and recover to a steady state faster, thereby suppressing temperature fluctuations during sudden changes in rotational speed. Therefore, CO
2–Kr mitigates temperature fluctuations through its lower specific heat capacity, demonstrating better performance under dynamic conditions. It provides a reliable working fluid choice for recompression Brayton cycle systems in high fluctuation scenarios.
During the speed drop disturbance, the pressure response characteristics of CO
2 and CO
2–Kr show significant differences, as shown in
Figure 13. After the speed disturbance occurs, the system enters the dynamic adjustment phase. Taking CO
2 as an example, the re-compressor inlet pressure gradually rises from 7.757 MPa to 7.89 MPa, while the turbine outlet pressure rises from 7.897 MPa to 8.04 MPa. The speed drop directly leads to a reduction in the compressor power consumption and a decrease in the compression ratio. It thus causes a redistribution of the working fluid’s flow and pressure. In contrast, the CO
2–Kr re-compressor inlet pressure rises from 7.758 MPa to 7.922 MPa, and the turbine outlet pressure rises from 7.898 MPa to 8.040 MPa. This indicates that the pressure response of CO
2 is more intense at the initial stage of the speed drop, while the pressure change of CO
2–Kr is relatively more gradual. However, both systems show an increasing pressure trend during the transition phase before reaching a steady state. It is worth noting that the change in turbine inlet pressure is more pronounced. In the CO
2 system, the pressure rises from 13.730 MPa to 13.682 MPa, while in CO
2–Kr, it drops from 13.730 MPa to 13.676 MPa. This difference may be due to the thermodynamic properties of the working fluid affecting the turbine’s energy conversion efficiency.
Similarly, the system performance exhibits corresponding response characteristics after the disturbance, as shown in
Figure 14. The efficiency and specific work response curves of CO
2 and CO
2–Kr show significant differences. During the initial stable phase, the efficiency and specific work of CO
2–Kr are significantly higher than those of CO
2. As the speed decreases, both working fluids exhibit a decreasing trend in efficiency and specific work, but the rate of decrease and the final stable values differ. At 50 s, the efficiency of CO
2 drops to 28.48%, a decrease of 0.74% from the initial value, while the efficiency of CO
2–Kr drops to 33.76%, a decrease of 1.17%. Regarding specific work, CO
2 drops from 39.51 kW/kg to 38.49 kW/kg, while CO
2–Kr drops from 47.29 kW/kg to 45.64 kW/kg. Between 50 and 100 s, the efficiency and specific work of CO
2 tend to stabilize. The efficiency and specific work of CO
2–Kr also stabilize, but the drop is more significant, and the values remain consistently higher than those of CO
2.
This is related to the thermodynamic properties of the working fluids and the system’s dynamic response. CO2–Kr performs excellently during the initial high-speed phase due to its heat capacity and better compressibility, which allows for more efficient energy transfer under high-pressure and high-temperature conditions, thereby improving cycle efficiency and output power. However, as the speed decreases and the system enters a low-load state, the working fluid’s flow resistance and heat losses gradually become dominant. CO2, with its lower viscosity and higher thermal diffusivity, can maintain more stable flow characteristics at low speeds, thus slowing down the rate of decrease in efficiency and specific work. In contrast, the thermophysical properties of CO2–Kr are more sensitive to flow rate changes, leading to a more significant performance degradation.
4.4. Analysis of Working Fluid Property Differences
The above analysis discussed the dynamic performance of CO2 and CO2–Kr as working fluids under different disturbance factors. In this section, a detailed analysis will be conducted from the perspective of the working fluid properties, providing a theoretical basis for system optimization and operational control.
Figure 15 compares the density, viscosity, specific heat capacity, and thermal conductivity of two working fluids, CO
2 and CO
2–Kr, within the temperature range of 300 K–900 K and pressure range of 5 MPa–30 MPa. The figure shows that the CO
2–Kr mixture exhibits significant differences from pure CO
2 in terms of density, viscosity, specific heat capacity, and thermal conductivity. The density of the CO
2–Kr mixture is higher than that of pure CO
2. As the temperature increases, the density decreases more significantly, indicating that its volume expansion effect is more pronounced under high-temperature conditions. CO
2–Kr generally has a higher viscosity than pure CO
2, with the difference becoming more pronounced at higher temperatures and pressures. This results in lower friction losses in the CO
2–Kr system, thus improving system efficiency. Regarding specific heat capacity, the CO
2–Kr mixture has a lower specific heat capacity than pure CO
2, especially at high temperatures and low pressures. This means that the CO
2–Kr system has weaker heat absorption and release capabilities, allowing for a faster response to temperature changes but with a relatively weaker thermal buffering capacity. The CO
2–Kr mixture also has a lower thermal conductivity than pure CO
2, indicating weaker heat transfer capabilities, which may slow heat transfer during thermal regulation, thus affecting the system’s thermal efficiency and dynamic response characteristics.
In summary, the density of pure CO2 is lower than that of the CO2–Kr mixture and decreases more significantly with increasing temperature. This is due to the introduction of Kr, which significantly increases the working fluid’s molecular weight and enhances the thermal inertia effect. Its inert gas properties cause the mixture to exhibit a delayed temperature response during the initial phase of dynamic disturbances. In contrast, the more pronounced volume expansion effect at high temperatures results from changes in intermolecular forces. The pure CO2 generally has a lower viscosity than the CO2–Kr mixture, with this difference being more significant under high temperature and pressure conditions. This allows the mixture to suppress turbulent fluctuations and reduce the amplitude of pressure fluctuations. Its optimized compressibility enables pressure disturbances to be more efficiently transmitted downstream and reduces pressure oscillations through enhanced damping effects, thereby shortening the system’s response time.
Regarding thermodynamic properties, the mixture’s specific heat capacity and thermal conductivity are lower than those of the pure CO2 system. While this weakens the heat absorption and conduction capabilities, it restructures the transient energy transfer mechanism. The lower specific heat capacity makes the CO2–Kr system more sensitive to temperature changes. At the same time, the decrease in thermal conductivity, in conjunction with the viscosity and density, forms a unique thermal buffering mechanism. During the later stages of the disturbance, the system’s higher thermal capacity effectively dampens temperature fluctuations. The coupling effects of these physical properties enable the CO2–Kr mixture to exhibit superior thermal stability during dynamic disturbances, thereby enhancing the dynamic response capability and disturbance resistance of the Brayton cycle system.