## 3 Compressor Test Model  
The rotor stage of a low-speed axial compressor test rig shown in Figure 1 in Beihang University [12] was applied in this analysis. The test rig consists of a 13-blade stator row and a 19-blade rotor row with the C4 profile (Figure 2). At the mid-span, the rotor blade has a chord length of 52 mm, a solidity of 0.605, a stagger angle of 34.49 degree, and an outlet angle of 41.99 degree. The design speed of the test rig is 3000 rpm, and the mass flow is 2.40 m\({}^{3}\)/s at the design point with a total pressure rise equal to 1500 Pa. A detailed introduction of the test rig is presented in [PERSON] [12] and [PERSON] [20]. In this study, a blade cascade extended from the rotor's mid-span profile was applied as the compressor test model. The length in the vertical direction was set as 20% span according to the literature. An axial total pressure fluctuation in the inlet boundary was added as the source of unsteady excitation, which was set to physically imitate the periodic sound excitation generated by pneumatic speakers. The schematic plot of the sound generator and the figure in the experiment by [PERSON] [12] are shown in Figure 3.  
To imitate the inlet unsteady excitation, the total pressure at inlet condition was set as Equation (4), where \(P_{inlet}\) was the total pressure on the inlet boundary, \(t\) was the physical time during the unsteady simulation, \(A_{m}\) was the maximum excitation amplitude of pressure, and \(f\) was the frequency of the excitation. Total temperature and velocity at inlet directions were kept constant in the computations. \[P_{inlet}=101325\ +A_{m}\times\sin(f\times 2\pi\times t). \tag{4}\]  
The maximum excitation amplitude of pressure was set to be 600 Pa in the experiment, and the maximum flow control effect under unsteady excitation could be obtained at that amplitude. In the computations, the maximum amplitude was extended to 1000 Pa. The computation boundary conditions were set up based on the parameters of a near-stall working state with a total pressure  
Figure 1: Compressor test rig. Figure 2: Blade sections at three spanwise locations. rise over 1600 Pa in the calculation. Periodic boundary conditions were set between the up and down side of the computation domain as well as between the left and right side. The total pressure boundary condition was used at the inlet and the averaged static pressure boundary condition was set to the outlet. Since DES results can be sensitive to grid resolution, four sets of mesh solutions with the same topology were studied to guarantee the accuracy of results. The Y-plus of the meshes near the blade surface were kept smaller than one in all four cases. The separation positions were chosen as the reference of shedding vortex structure (identification of separation position would be described in Section 4), and the results with the four meshes were shown in Figure 4. When the amount of mesh grids exceeded 7.36 million, the simulated separation positions were beginning to converge. Therefore, the mesh solution with 7.36 million mesh grids was chosen as the basic solution, which contained 347 nodes in the axial direction, 134 nodes in the pitchwise direction, and 125 nodes in the spanwise direction near the blade region. From the numerical results, it could be concluded that the separation positions were varying less than 5% between 30% and 70% of the blade span, which indicated that the vortex shedding flow could be possibly considered as a quasi-3D phenomenon in circumferential direction at the middle span of this blade. In order to exclude the influence of hub/shroud secondary flow and focus on the separation flow, a 1 mm-thick curved slice at 50% span of the rotor blade was applied as a quasi-3D mode. Reliability of the quasi-3D model on the simulation of shedding vortex structure by high-fidelity simulation was verified by [PERSON] [21]. The quasi-3D model shared the same mesh grid distribution in the B2B section with the 3D mesh grid.