# Investigation of the Effects of Different Working Fluids on Compressor Cascade Performance
## 4 Performance Analysis
### Effect of Physical Properties on Static Pressure Ratio  
The relationship of specific heat ratio and static pressure ratio on matching Reynolds number and Mach number is presented in Figure 10. The compressor cascade using a higher heat ratio fluid has a higher static pressure ratio. Equation (15) accurately predicts the static pressure ratio of compressor cascade with helium and carbon dioxide. The prediction relative error is less than 8%, which is enough to meet the engineering demand. Mach number and attack angle also have a significant effect on total pressure loss of compressor cascade. Once the attack angle is fixed, compressor cascade static pressure ratio increase with the increase in Mach number. When Mach number is fixed, the static pressure ratio of compressor cascade increases initially and the former decreases with the increase in attack angle. Attack angle at maximum static pressure is 3\({}^{\circ}\). When the attack angle increases to 6\({}^{\circ}\), the decrease of the inlet area caused by the increase of the attack angle is smaller than that instigated by corner separation, which results in a decrease in compressor cascades static pressure ratio.  
The static pressure coefficient and static pressure ratio distribution at 98% span for dissimilar working fluids are presented in Figure 11. The difference of static pressure coefficients at 98% span with different working fluids is not obvious and the difference of  
Figure 10: Static pressure ratio at different attack angles.  
Figure 9: Contour of coefficient of total pressure loss at different plane.  
static pressure ratio at 98% span with different working fluids is obvious, so it is established that the difference of specific heat ratio is cause of difference in the compressor cascade static pressure ratio with dissimilar fluids.  
Figure 12 illustrates limiting streamlines of compressor cascade with carbon dioxide and helium on the suction surface. As shown in Figure 12, at the same attack angle, the separation of suction surface of a compressor with carbon dioxide is significantly smaller than that of helium. It happened because the static pressure ratio in the compressor cascade with helium is higher than carbon dioxide, and the larger reverse pressure gradient leads to the larger corner separation. The separation scale of the compressor cascade increases with the increase of attack angle for same working fluid. It happened due to increases in inverse pressure gradient with the increase of attack angle. In view of the above analysis, it can be concluded that physical properties of fluid affect the separation structure of the flow in the compressor cascade by affecting the static pressure ratio of the compressor cascade.  
Figure 11: Static pressure coefficient (Cp) and static pressure ratio (\(\pi\)) distribution at 98% span for dissimilar working fluids (i = 0, Ma = 0.7).  
Figure 13 shows the relative position of transition at matching Reynolds number and Mach number. As presented in figure, the transition of working fluid using large specific heat ratio occurs earlier at the same attack angle. Thus, specific heat ratio is also one of the factors inducing transition of working fluid. Therefore, for the same working fluid, the larger the attack angle, the earlier the transition will occur.  
Figure 12: Representations of suction surface skin-friction lines under different attack angle (Ma = 0.7).