## 3 Experimental Facility and Numerical Validation  
### Experimental Facility  
The supersonic cascade wind tunnel is an intermittent facility at the Innovation Academy for Light-Duty Gas Turbines of the Institute of Engineering Thermophysics, Chinese Academy of Sciences (IET), with traditional schlieren apparatus and pressure systems incorporated (PSI). This tunnel is driven by dry air from three tanks with a total of 120 m\({}^{3}\) storage through a series of solid converging-diverging nozzles, which provides supersonic flow at 1.5 Mach to 2.5 Mach with an interval of 0.25 Mach. At inlet Mach number 1.75, the tunnel has a stable operating time of more than 50 s for aerodynamic measurements. Four pressure taps and several temperature sensors are installed at the inlet of the nozzle to achieve total pressure and total temperature. Wall static-pressure probes are installed at the nozzle outlet region, cascade inlet region, and outlet region. The maximum measured error of the inlet deviation angle, total pressure, static pressure, and total temperature is less than \(\pm\)0.5\({}^{\circ}\), 0.3%, 0.2%, and 1%, respectively. A five-hole probe for the supersonic range is placed downstream from the cascade trailing edge traversing along the outlet plane. This five-hole probe is driven by a stepping motor and is controlled by LabVIEW data acquisition procedures. The error range for the five-hole probe is about \(\pm\)1%, and the accuracy of the stepping motor is \(\pm\)0.01 mm. The data from the pressure probes are collected by PSI electronic pressure scanners (This PSI electronic pressure scanner was purchased from Mexico, USA, and produced by Pressure Systems International, San Antonio, TX, USA). The employed model is PSI9816, with a sensor measurement accuracy of 0.05%. This tunnel is equipped with a set of CQW300 schlieren apparatus (The CQW300 was purchased from Sichuan, China and produced by Sichuan Wake Optical Precision Machinery Co., Ltd., Mianyang, China), which is composed of a spherical primary mirror system, a light-source slit system, a knife-edge camera system, and a plane mirror system. It can be employed to visualize the shockwave structure inside the internal channels of the tested cascade. For a supersonic compressor cascade with an inlet Mach number of 1.75, the tunnel operates at a total pressure of 270 kPa and a total temperature of 320 K. The Reynolds number based on the vane chord is about 7.54 \(\times\) 10\({}^{6}\) at a Mach number of 1.75. The height and width of the flow channel inside its test section are 200 mm and 130 mm, respectively. The baseline cascade test modules are composed of two sets for different test purposes, each of which consists of six vanes with a 150 mm chord. One of the sets has a pair of transparent plexiglass plates for schlieren visualization, as shown in Figure 6. Another set has steel plates to fix one or two drilled vanes with taps on both suction and pressure surfaces and other vanes for the static pressure values on both surfaces, as shown in Figure 7. A pair of adjustable straight plates are hinged at the end of the upper and lower plenum chamber for the adjustment of the upper and lower spillage passage flow, which are at 5 deg and 3 deg, respectively, in design conditions. The upper and lower tailboards are installed at the trailing edges of the uppermost and lowest vanes with cylindrical pins, which are fitted to provide back-pressure adjustment for the cascade exit flow by regulating the passage area between the two tailboards. To obtain the inlet flow conditions, static pressure taps are located along a line at a distance of 26.5 mm (50% of the axial chord length) axially upstream of the inlet plane. The downstream aerodynamic parameters of static pressure, total pressure, exit Mach number, and lag angle are obtained at the midspan by traversing a combination probe located at 39.5 mm (\(\xi_{2}/l_{ax}\) = 0.75) downstream from the cascade exit plane.