This section comprises two main parts. Firstly, we conduct a thermodynamic analysis of the environmental wind tunnel refrigeration system designed for high-speed trains, which utilizes an air compression refrigeration system to ascertain its thermodynamic performance, and we compare our design to a conventional evaporative refrigeration system. Secondly, a sensitivity analysis was conducted for the key parameters in the refrigeration system using the established model. The main methodology involved determining the impact of different parameters on system performance via simulation numerical modeling.
4.1. Comparison of Air Compression Refrigeration Cycle and Evaporative Refrigeration Cycle
The impact of the air cooling cycle on the cooling efficiency of air compression refrigeration systems was studied under the assumption of demand conditions that are identical to those of evaporative cooling. In the experimental section of the train, the temperature was maintained at −70 °C, and the wind speed was set at 100 m/s. Previous field simulations indicated that the required cooling capacity for the application of air compression refrigeration is approximately 1.8 × 107 W. This is because during the actual working process, a certain amount of air needs to be extracted from the wind tunnel for the air compression refrigeration cycle. As a result, the airflow in the second half of the wind tunnel decreases since the real air flow becomes smaller. Due to the constant air density, this reduction in airflow leads to a decrease in the air velocity within the wind tunnel, thereby reducing flow losses. Consequently, the actual amount of cooling required to achieve the same experimental conditions (100 m/s wind speed and −70 °C) in the experimental section is lower compared to evaporative cooling.
In addition to accounting for the cooling requirements of the wind tunnel, the quality of the external air also impacts the efficiency of the cooling cycle. Air compression cooling necessitates the compression of external air to obtain a cooling source. For the analysis, dry air with a temperature of 25 °C and a pressure of 1.0 × 105 Pa was selected. Other main equipment parameters include an inlet compression ratio of 2.5, a cooling water temperature of 40 °C for the water cooler, and a source gas temperature of −40 °C for the return cooler. The return cooler is connected to the ambient wind tunnel and possesses a sufficiently large heat transfer area to ensure the adequate cooling of the compressed air. This process allows the final compressed air to exit the return cooler at the same temperature as the gas drawn from the wind tunnel.
The mechanical energy generated by the turbine expander, through the work of air expansion, is fully utilized in the turbo compressor air compression system. The pressure–enthalpy and temperature–entropy diagrams for the system are shown in
Figure 9.
The operating conditions of the different components in the different air cooling systems were also obtained in
Table 1.
At this stage, the air compression system energy flow diagram is shown in
Figure 10, and an external energy input of approximately 28.3 MW is required to supply the refrigeration system, considering the cooling efficiency of the water-cooling tower as 4.5. This yields a coefficient of performance (COP) for the system of approximately 0.636, and the energy flow diagram of the refrigeration system is shown below.
To compare the cooling effect of the air compression system, a conventional cascade refrigerating system was introduced, and the system schematic is shown in
Figure 11.
Assuming that the temperature in the experimental section of the train is still −70 °C and the wind speed is 100 m/s, the power loss of the system is reduced due to the air extraction required for air compression cooling. Additionally, the resistance in the wind tunnel increases as a result of the additional heat exchange network. Therefore, under the same conditions in the experimental section, the evaporative cooling cycle method needs to provide more cooling capacity in order to achieve the desired experimental environment. Simulation calculations indicate that the refrigeration system needs to deliver a cooling capacity of approximately 2.0 × 107 W to achieve the same experimental conditions in the wind tunnel section.
With an external ambient temperature of 25 °C, an evaporator temperature of −70 °C, a condensing temperature of 40 °C, and an evaporator–condenser temperature difference of 5 °C, the midpoint temperature of the evaporative refrigeration cycle was determined to be −23 °C. By observing the characteristics, R23 was selected as the refrigerant for the low-temperature part of the refrigeration system, and R404A was chosen for the high-temperature part, allowing for the design of the experimental state at each point. Calculations are carried out using Solkane, and the completion of pressure enthalpy and temperature entropy diagrams are shown on
Figure 12.
The operating conditions of the various components in different evaporative refrigeration systems were obtained, as shown in
Table 2.
At this point, an external energy input of approximately 32.1 MW is required to supply the refrigeration system (assuming a cooling efficiency of 4.5 for the water-cooled tower), resulting in an approximate system cooling efficiency COP of 0.624.
The comparison reveals that, although the cooling efficiency of air compression refrigeration is not significantly different from evaporative refrigeration, the air compression system has a lesser impact on the cooling section of the wind tunnel. Consequently, it requires less energy for the refrigeration system under the same experimental conditions. Specifically, the air compression system necessitates approximately 3.72 MW less energy, resulting in an improvement of approximately 13.15% over the efficiency of the evaporative refrigeration system.
4.2. Systematic Sensitivity Analysis
A sensitivity analysis is conducted for the design parameters of the aforementioned components, encompassing two main areas. The first area involves studying the influence of various parameters of the refrigeration equipment on the system under specific external conditions. The second area explores the impact of different external conditions on the cooling sensitivity of the system once the refrigeration equipment has been selected.
The initial step is to assess the effect of different design parameters on the heat transfer capacity of the system’s return cooler and the cooling efficiency of the air compression refrigeration system. For this particular case, a plate heat exchanger was chosen as the return cooler. Design parameters for the plate heat exchanger include total heat transfer area, single plate heat transfer area, plate configuration form, plate spacing, plate thickness, individual flow path cross-section, etc. While these design parameters are somewhat inter-related, the total heat transfer area of the heat exchanger exhibits the greatest relative impact on heat transfer performance. It serves as an essential indicator for evaluating the heat transfer capacity of the plate heat exchanger and can be derived from the product of the heat transfer area per single plate and the number of heat exchanger plates.
Assuming that the other design parameters of the return cooler remain constant, and with inlet temperatures of 313 K and 228 K, respectively, for the hot and refrigeration sides of the return cooler, as well as inlet pressures of 350 Kpa and 110 Kpa, the sole parameter adjusted is the total heat transfer area of the heat exchanger (achieved by altering the number of heat exchanger plates). The relationship between the heat exchanger area and the outlet temperature of the return cooler is presented in
Figure 13a below, indicating a considerable decrease in the outlet temperature as the system’s flow rate changes. Moreover, the outlet temperature reduces at a faster rate when the flow rate is smaller. When the temperature drops to a certain level, the capacity for heat transfer of the heat exchanger reaches its limit. Increasing the heat transfer area will not lead to a reduction in outlet temperature. When the flow rate of the heat exchanger remains constant, adjusting the inlet temperature of the cooler return, heat exchanger heat transfer area, and export temperature are shown in
Figure 13b below. It can be observed from the graph that the increase in heat transfer area results in a decrease in the heat exchanger export temperature. Similarly, the graph reveals that the outlet temperature of the heat exchanger drops faster with an increase in the inlet temperature of the heat exchanger. It is observable from
Figure 13c that, as the heat transfer area increases, the outlet pressure of the heat exchanger decreases. Furthermore, with an increase in flow rate through the heat exchanger, the decrease in outlet pressure becomes more pronounced. However, the overall decrease in pressure is insignificant when compared to the inlet pressure of the system.
Further analysis of the effect of changes in the heat transfer area of the return cooler on the cooling efficiency of the air compression refrigeration system assumes that the system is as described above, with unchanged parameters for the components. In this system, the compressor increases the atmospheric gas to 250 Kpa and subsequently recovers it to 110 Kpa through a turbine–compression system. The high-pressure gas then passes through a water cooler, reducing its temperature to 45 °C. A certain amount of gas is extracted through the wind tunnel and used as the cold source gas in the recooler, where the temperature of the cold source gas is −45 °C. It should be noted that if the system efficiency is below 0.2, the air compression refrigeration system will not function effectively. With variations in the heat exchanger area, the system experiences changes in heat transfer efficiency, as shown in
Figure 14. It can be observed that an increase in heat transfer area leads to a rapid improvement in the system’s heat transfer efficiency. Additionally, it can be seen that a higher mass flow rate in the system results in a slower increase in cooling efficiency. Furthermore, by examining the pattern of heat exchanger outlet temperature and pressure in the graph above, it becomes evident that this is due to the rapid decrease in outlet temperature as the heat transfer area increases. As the outlet temperature of the return cooler decreases, the temperature of the refrigerant gas is lower after expansion, allowing for more cooling capacity per unit mass flow rate, thereby increasing the refrigeration efficiency of the system.
However, once the heat transfer efficiency reaches its peak value, any further increase in heat transfer area results in a gradual decline in system cooling efficiency. Moreover, this decline is more pronounced with higher mass flow rates in the system. This phenomenon occurs because after reaching a certain limit of heat transfer efficiency, further increases in heat transfer area no longer reduce the outlet temperature of the system. Instead, they increase the resistance within the heat exchanger, leading to a drop in outlet pressure within the system. Consequently, the subsequent expander work is reduced, resulting in a decrease in air temperature and an increase in the refrigeration efficiency of the system.
It can be concluded that for the air compression system, the heat transfer area of the return cooler should be appropriately increased to ensure a lower exit temperature. This is essential as reducing the exit temperature effectively improves the refrigeration efficiency of the system. Although excessive heat transfer area may have a certain impact on system efficiency, it is smaller compared to other factors. Therefore, during design selection, it is advisable to choose a heat exchanger with a larger heat transfer area as the system’s return cooler.
During the operation of the environmental wind tunnel for high-speed trains, various operating conditions arise, necessitating the study of unified heat exchanger performance at different mass flow rates. Assuming the system’s design parameters remain constant, the hot side inlet temperature and pressure of the return cooler are 313 K and 350 Kpa, respectively, while the cooling side’s inlet temperature and pressure are 228 K and 110 Kpa, respectively. Only the heat exchanger’s mass flow rate is varied to observe how the outlet temperature and pressure change with different heat transfer areas. As depicted in
Figure 15a, as the system’s mass flow rate increases, the heat exchanger’s outlet temperature rises initially, and then reaches a peak before declining. This trend becomes more pronounced when the heat exchanger area is smaller. When the heat transfer area is sufficiently large and the overall heat transfer rate within the system is low, the system consistently operates near its cooling limit. The relationship between the heat exchanger’s mass flow rate and its outlet pressure is demonstrated in the following
Figure 15b. It can be observed that increasing the fluid’s mass flow rate through the heat exchanger leads to a decrease in outlet pressure. Moreover, as the total heat transfer area within the heat exchanger expands, the outlet pressure reduction becomes more significant. However, this overall decline in pressure remains relatively small compared to the system’s inlet pressure.
Further analysis of the effect of using different heat transfer areas on the cooling efficiency of air compression refrigeration systems with variations in mass flow rates is presented. This study assumes that the remaining components of the system operate at constant efficiency. In this system, the compressor increases the atmospheric gas pressure to 250 KPa, and then the turbine–compressor component restores the system pressure to 110 Kpa. The high-pressure gas passes through a water cooler, reducing its temperature to 45 °C. A certain amount of gas is extracted through the wind tunnel and used as the source gas in the recooler, where the temperature of the source gas is −45 °C. It is assumed that when the system efficiency falls below 0.2, the air compression refrigeration system cannot function effectively.
With changes in the heat exchanger area, the system’s heat transfer efficiency varies, as shown in
Figure 16a,b. When the heat exchanger’s working mass flow rate is low, the system’s refrigeration efficiency remains mostly constant. Additionally, the heat transfer efficiency of the smaller heat exchanger is slightly higher than that of the larger heat exchanger. However, when the mass flow rate of air in the system reaches a certain point, the efficiency of the smaller heat exchanger starts to rapidly decrease, while the larger heat exchanger continues to decrease slowly. This trend can be attributed to the fact that at lower mass flow rates, the outlet temperature of the system cooler remains within a low range. Hence, the main factor influencing the system’s efficiency becomes the change in outlet pressure. However, as the mass flow rate in the system increases, the heat transfer area of the system cooler fails to maintain the outlet temperature within the lower range. Consequently, the outlet temperature of the system cooler rises rapidly, leading to a decline in the system’s overall efficiency. Simultaneously, the outlet pressure in the system continues to gradually decrease. The combined effect of these factors results in a rapid decrease in the cooling efficiency of the system.
While the cooling efficiency of the system is an important parameter, more attention is typically given to the cooling capacity of the air compression system. The cooling capacity is determined by the difference between the inlet and outlet temperatures and the mass flow rate of air in the system. If the mass flow rate of the system changes significantly while the two parameters of the system gas remain largely unchanged, the cooling capacity can be affected. In this study, it was observed that an increase in the mass flow rate of the system leads to an increase in the outlet temperature of the return cooler, subsequently raising the temperature of the system’s cold air. As a result, the cooling efficiency of the system decreases, directly affecting its cooling capacity. Moreover, when the mass flow rate exceeds a certain range, the refrigeration efficiency of the air compression system falls below 0.2, rendering the entire refrigeration system incapable of delivering a qualified cooling source for the high-speed train’s environmental wind tunnel. When the mass flow rate in the system is low, the cooling capacity increases proportionally with the mass flow rate, and the growth rate remains relatively consistent. The heat exchanger with a larger heat transfer area exhibits only slightly lower efficiency than the heat exchanger with a smaller heat transfer area. However, as the mass flow rate increases, it becomes evident that insufficient heat exchange area in the system causes the cooling capacity to decrease instead of increasing.
From the above analysis, it can be concluded that the heat transfer area of the return cooler has a significant impact on both the cooling efficiency and cooling capacity of the system. However, this impact is mainly notable when the heat transfer area of the return cooler fails to meet the system’s mass flow rate requirements. At this point, an increase in the mass flow rate leads to a rapid decline in the system’s cooling efficiency, while the cooling capacity remains unchanged. Conversely, when the heat transfer area of the return cooler is sufficiently large, the system’s refrigeration efficiency only experiences a gradual decline. Therefore, during system design and selection, it is advisable to choose a heat exchanger with a slightly larger heat transfer area based on the system’s requirements. This decision facilitates the improvement of the system’s efficiency. Although increasing the heat transfer area may raise the construction cost to some extent, as indicated by the previous analysis, the overall impact on the system’s economy is insignificant compared to operational and maintenance costs. Hence, it can be assumed that when the heat transfer area of the recuperator in the system is adequately large, any subsequent changes in heat transfer area or mass flow rate will have minimal impact on the system’s economic performance. Consequently, the change in heat transfer area can be considered to have a low sensitivity.
- 2.
Turbine Expander
The sensitivity of turbine expander design parameters has been extensively studied in previous articles [
30,
31]. These studies employed the extreme difference method to analyze the impact of different parameters on expander efficiency. In a practical expander design, it is often challenging to optimize every parameter due to considerations of aerodynamic characteristics and design feasibility. Therefore, this paper focuses on investigating expander inversion as the main design parameter. However, since expander inversion is a dimensionless number, it cannot solely determine the values of other expander design parameters. For this reason, we refer to the expander design parameter selection principles described by Li Peng [
28] as a guideline.
In our study, an expander with an applicable mass flow rate of approximately 360 kg/s and a design inversion ranging from 0.3 to 0.8 was selected. It should be noted that the original expander might not meet the requirements of the wind tunnel for high-speed train environments. Hence, based on similar principles, three times the amplification parameters were set and used to select the final compressor. We acknowledge that using multiple compressors in parallel could achieve the same effect, but we do not investigate this approach in this paper.
Figure 17a,b depicts the efficiency and outlet temperature of the expander for different mass flow rates, showing that the expander achieves maximum efficiency at approximately 0.51. As inversion increases, expander efficiency gradually improves until it reaches the optimum value, after which it rapidly declines. The graphs also reveal that changes in mass flow rate have a limited impact on the overall trend of expander efficiency, but they do affect the maximum efficiency value. Similarly, the outlet temperature of the expander follows a similar pattern to its efficiency, initially decreasing with increasing inversion and then rapidly rising after reaching a minimum temperature. In the context of an air compression refrigeration system, assuming the system follows the description mentioned above with constant efficiency for the remaining components, the compressor is capable of increasing atmospheric gas pressure to 250 KPa. By employing a booster compressor, the system further pressurizes the gas and utilizes the expander to return the pressure to 110 KPa. The high-pressure air’s outlet temperature in the water cooler is maintained at 45 °C, and the return cooler features a heat transfer area of 800 m
2, with an outlet temperature consistently maintained at −40 °C. The outlet pressure follows the aforementioned model law. The expander’s efficiency under these conditions is illustrated in
Figure 17c. This behavior can be attributed to the fact that the expander converts the internal energy of high-pressure air into mechanical energy during system operation, which drives the booster compressor. Consequently, the compressed air pressure decreases, leading to lower enthalpy within the system. As the high-pressure gas enters the expander, the reduced work capacity of the air causes the outlet air temperature to rise, resulting in a reduced cooling capacity for the system.
The changes in turbine performance, system performance, and cooling capacity at different air mass flow rates, while keeping the degree of reactivity constant, are further investigated. The remaining settings of the turbine model remain the same as before. The simulation results are shown in
Figure 18a–c. When the turbine operates at an air mass flow rate lower than its design mass flow rate, the turbine efficiency increases as the mass flow rate increases. The turbine achieves its highest efficiency when the mass flow rate matches the design mass flow rate, resulting in the lowest turbine outlet temperature and the highest external work capacity. However, when the mass flow rate exceeds the design mass flow rate, the turbine can still function, but its operating efficiency decreases. Additionally, the outlet temperature of the turbine increases, reducing the system’s cooling capacity. Nevertheless, although the turbine’s efficiency decreases, more air passes through the turbine, resulting in increased external work capacity. It is worth noting that the decrease in the system’s efficiency due to the increase in air mass flow rate has a greater impact than the decrease in turbine efficiency. Consequently, the external power output of the turbine decreases, but at a slightly slower rate than the decrease in system efficiency.
The performance of air compression refrigeration systems follows similar to turbine operation, with an initial increase in efficiency followed by a decrease. However, the rate of change in the system is much greater than the rate of change in the turbine itself, as explained in the previous section. Comparing
Figure 19a,b reveals that the mass flow rate at which the system operates at maximum efficiency differs from the mass flow rate at which the system produces maximum cooling capacity. The latter value is slightly greater than the former because the cooling efficiency characterizes the cooling capacity of the air per unit mass. As the air mass flow rate increases, the total cooling capacity of the system also increases, despite a decrease in the cooling capacity per unit mass of air.
In the daily selection process, it is necessary to match the equipment’s scale factor with the operating mass flow rate so that the turbine system can operate at the appropriate mass flow rate. An expander with a rated flow rate of 360 kg/s was selected as a benchmark. In order to study the impact of different magnitude coefficients on the expander’s performance, 330 kg/s and 390 kg/s expanders were built using similar principles for comparison.
Figure 20a illustrate how the turbine operating efficiency varies with the turbine mass flow rate for different scale factors. The graph demonstrates that all turbines have the same maximum efficiency point of approximately 82.14% due to identical turbine design parameters. Furthermore, the turbines exhibit a consistent trend of first increasing and then decreasing. Although the rate of change in turbine efficiency differs slightly across various scale factors, larger scale factor turbines generally experience a slightly lower rate of change compared to smaller turbines. However, it is important to note that turbines with different scale factors are not suitable for the same operating range, and the corresponding optimum mass flow rate for turbine operation varies. The turbine outlet temperature and efficiency display a similar trend, as shown in
Figure 20b, albeit in opposite directions. Additionally, the external work capacity of the turbine is a crucial aspect of interest as it directly impacts the cooling efficiency of the system.
Figure 20c depicts the external work power of a turbine for different scale factors plotted against the mass flow rate of the compressed gas. This graph reveals that the external power output of the turbine increases with the mass flow rate and begins to decline rapidly after reaching its peak. Moreover, the magnitude of the turbine’s external power output is influenced by its scale factor, with higher scale factors resulting in greater turbine external power and corresponding mass flow rates of compressed air.
For the entire air compression refrigeration system,
Figure 21a show the variation in air mass flow rate versus refrigeration efficiency. As depicted, the change in system efficiency remains essentially the same across different scale factors, except that larger turbine magnitude factors require a higher mass flow rate to achieve optimum system efficiency. The maximum cooling efficiency remains constant
Figure 21b, irrespective of scale factors. Furthermore,
Figure 20b illustrates the change in system cooling capacity with system air mass flow rate for different magnitude factors. A comparison reveals that although the maximum cooling capacity of the system differs, the pattern of change is similar to that of the system’s cooling efficiency, initially decreasing and then increasing. It is also evident that when the air mass flow rate of the system is small, a smaller turbine size may result in a larger cooling capacity. This phenomenon occurs because operating the system outside the suitable mass flow rate range significantly reduces its cooling efficiency, thus affecting the overall cooling capacity. Therefore, selecting a turbine with an appropriate scale factor that matches the air mass flow rate is crucial for enhancing system performance.
Regarding the relationship between the turbine’s gauge coefficients (rated flow) and the maximum cooling capacity of the system,
Figure 22a,b illustrates that the cooling efficiency of the system slightly decreases with increasing turbine gauge coefficient and the drop in pressure of the recooler outlet may have caused this reduction. However, as the mass flow rate of air in the system increases with the turbine gauge coefficient, the maximum cooling capacity of the system also rapidly increases (
Figure 22b). Therefore, when selecting an air compression refrigeration system, particular attention should be paid to the actual size of the turbine to ensure it meets the maximum cooling capacity requirements of the system.
This analysis demonstrates that the scale factor and degree of inversion of the turbine have a significant influence on the system’s operating efficiency and cooling capacity. These design parameters are highly sensitive in air compression refrigeration systems and should be considered as important optimization parameters in subsequent parameter optimization processes. Additionally, since the compressor and turbine belong to the same rotating machinery and operate based on similar principles, the design parameters of the compressor in the air compression refrigeration system are equally important. The compressor plays a crucial role in increasing the gas pressure and is considered to be no less significant than the turbine in the system. Thus, the design parameters of the compressor should be an important target for subsequent optimization.
Based on these results, the design parameters identified as highly sensitive in air compression refrigeration systems include the inverse motion and magnitude coefficients of the compressor and turbine. Conversely, the system exhibits relatively low sensitivity parameters for the design parameters of the heat exchanger.