# Control of Corner Separation with Plasma Actuation in a High-Speed Compressor Cascade
## 2 Numerical Methods and Plasma Actuation Layouts  
The typical high-speed compressor cascade, NACA65-K48, is studied. This high-speed compressor cascade model is designed by the research group DLR (German Aerospace Center) and has been used broadly to study the flow control of high-speed compressor cascade corner separations (see, for example, [4; 5; 8; 9; 10]). Its main geometrical and aerodynamic parameters are shown in Table 1.  
Previously, [PERSON] et al. [24] have investigated the suitable RANS (Reynolds-averaged Navier-Stokes) numerical method to simulate the NACA65-K48 high-speed compressor cascade flow accurately and reliably. Based on their findings, the following numerical method is used in this paper to simulate the high-speed compressor cascade flow, and the comparisons between the experimental and numerical results, which can be found in reference [24], are omitted here. The high-speed compressor cascade flow is simulated with Ansys CFX, and the calculation grid is established with ICEM. Figure 1 shows the calculation grid model. The topological structure of the calculation grid model is an H-O-H type, and the grid model consists of 2.8 million nodes. Grids near solid surfaces are refined to ensure y\({}^{+}\) < 2. To better simulate the influence of plasma actuation on the flow field, grids near plasma actuators are clustered. The two-equation \(k\)-\(\omega\) eddy viscosity model is used to solve the Reynolds Stress in the RANS equations. \begin{table}
\begin{tabular}{c c} \hline \hline
**Main Parameters** & **Value** \\ \hline Chord (c)/mm & 60 \\ Span (\(h\))/mm & 100 \\ Turning angle (\(\theta\))/\({}^{\circ}\) & 42 \\ Inlet flow angle (\(\beta_{1}\))/\({}^{\circ}\) & 132 \\ Outlet flow angle (\(\beta_{2}\))/\({}^{\circ}\) & 90 \\ Stagger angle (\(\beta_{3}\))/\({}^{\circ}\) & 112.5 \\ Inlet Mach number & 0.7 \\ Solidity & 0.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters of NACA65-K48 high-speed compressor cascade. Figure 1: Calculation grid model. According to the experimental study by [PERSON] et al. [24], for the incidences studied in this paper, the corner separation will not develop to the mid-span. Hence, the symmetrical boundary is used at mid-span to reduce the simulation cost. The inlet boundary is 1.5 chord lengths upstream of the blade's leading edge, and the outlet boundary is 2.5 chord lengths downstream of the blade's trailing edge. At the inlet, total pressure distributions along the spanwise direction together with a fixed total temperature from experiments (see for example in [24]) are imposed. At the outlet, the average static pressure boundary is applied to guarantee that the inlet Mach number is kept constant at 0.7 at different incidence angles. During the simulations, the fluid is treated as compressible and solid walls are treated as adiabatic and non-slipping. Figure 2 shows the sketch of the DBD plasma actuator. Two electrodes are separated by the dielectric barrier, and when an AC voltage of several kilovolts is applied between the upper and lower electrodes, weakly ionized gases (plasma) are generated over the lower electrode in the air. As the plasma moves under the force of the electric field, it collides with the air. Through the momentum exchange within the collision, body force is imposed on the air. This paper uses the phonologic model developed by [PERSON] et al. [25] to simulate the body force induced by the plasma actuators. The accuracy of this model in simulating the body force of the plasma actuation has been validated by [PERSON] et al. [25] as well as [PERSON] et al. [21], and, according to the discussion of [PERSON] et al. [26], this model could qualitatively simulate the distribution of the body force of the plasma actuation. Figure 3 shows the plasma actuation layouts studied in this paper. Both the suction surface and the endwall plasma actuation layouts consist of six plasma actuators. For each plasma actuator, the width of the upper and lower electrodes are 1 mm and 5 mm, respectively.