## 3 Experimental Facility and Numerical Validation
### General Flow Characteristics and Numerical Validation  
The pressure distribution and shock configuration at different static pressure ratios (p\({}_{2}\)/p\({}_{1}\)) of 1.78 and 2.52 were analyzed at an inlet Mach number of 1.75. Both the simulation results and schlieren photographs during experiments are shown in Figure 10. Due to a lack of suction devices on the side walls of the wind tunnel, the boundary layer effect of the side walls should have a certain impact on the experimental results. In order to reduce this part of the impact, we increased the height of the blade in the process of modeling in the experimental and numerical domain. The blade height was 220 mm to minimize the side-wall boundary layer effect. It was found that shock configuration inside the vane passages of the supersonic compressor cascade is composed of four sections involving bow shock, first-passage shock, passage reflected shock system, and last normal-passage shock. Under design conditions, the experimental results indicate that the first-passage shockwave impacts the suction surface of the adjacent vane at 55.3% of the chord from the leading edge. With the gradual increase in back pressure, the last normal shockwave approaches upstream from far downstream to the outlet plane of the baseline cascade and then marches into the vane passages, as shown in Figure 10b. In the light of the unique incidence requirement for supersonic compressor vane passages with axial subsonic components, the inlet flow does not change with the outlet flow of the supersonic compressor cascade. Hence, the inlet flow of the cascade remains unchanged, to some extent, with the outlet static pressure variations. Moreover, the position of the first-passage shock foot on the suction surface of the adjacent vane is almost the same as that of the experimental schlieren photographs, as shown with a blue dotted box in Figure 10. Therefore, the numerical method adopted in this manuscript can meet the accuracy requirements of the subsequent research.  
Due to the projection of schlieren images from one side of the blade to the other, 3D effects can cause shockwave thickening, which has a certain impact on testing accuracy. In this article, the numerical results and experimental results of the blade surface isentropic Mach number distribution are compared and analyzed to further evaluate the accuracy of the numerical method. Figure 10 shows the comparative analysis of isentropic Mach number distribution on the vane surface based on the CFD numerical results and experimental data under the conditions of an inlet Mach number of 1.75 and a static pressure ratio of 2.52. There are forty pressure holes across the region of SWBLI on both the suction and pressure surfaces of the vane; the first starts at 22.7% of the vane chord from the leading edge and the last ends at 78.2% of the chord. In processing the test results, it is necessary to analyze their measurement error. According to the uncertainty analysis and error analysis  
Figure 9: Analysis of computational mesh independence with different mesh nodes.  
principle of the test instrument, the standard deviation and standard error of the test data are calculated, and the error bar is drawn, as shown in Figure 11. Compared with the experimental data, for most simulation results, the deviations of the isentropic Mach number and shock location on the vane surface are in the range of 2.1-4.3%, i.e., less than 5%. For less than 4% of the data are such deviations greater than 5%. Therefore, the simulation method can meet the precision requirements of the numerical study. The numerical prediction method employed here is capable of predicting the flow characteristics of the SWBLI within a supersonic compressor cascade.