# Drag Reduction in Compressible Channel Turbulence with Periodic Interval Blowing and Suction
## 1 Introduction  
Minimizing aerodynamic drag significantly enhances the performance and efficiency of contemporary high-speed aircraft. It is reported that a 1% reduction in drag results in at least a 0.75% reduction in fuel consumption and a reduction of roughly 2-3 tonnes CO\({}_{2}\) emission per flight [1]. Studies showed that friction drag constitutes approximately 50% of the total drag, and a 40% reduction in viscous drag is roughly equivalent to a 15% reduction in total drag [2, 3]. Hence, reducing friction drag exhibits significant application prospects and research value for flow-control technologies. Blowing/suction control, a prevalent active control technique, has emerged as a significant focus in flow-control research [4]. In contrast to passive control technologies like riblet control [5; 6], blow/suction control can be dynamically modified in real time based on the flow field conditions to achieve optimal control efficacy. In comparison to active control technologies like energy deposition [7; 8], it can attain a substantial drag reduction effect at a comparatively small energy cost. Blowing control infuses high-energy fluids into the boundary layer, and simultaneously modifies the velocity gradient of the viscous sublayer, thereby reducing skin friction drag. Additionally, suction control can also reduce drag by removing low-energy fluids from the boundary layer. However, suction control sometimes demonstrates a contrary effect to blowing control. [PERSON] and [PERSON] [9] applied direct numerical simulation (DNS) to incompressible spatially developed turbulence at Reynolds number \(Re_{\rm b}=3000\) based on the boundary layer thickness. The result confirmed that uniform blowing reduces the skin friction and uniform suction increases it. Additionally, turbulent fluctuations are enhanced by blowing and suppressed by suction. The FIK identity revealed that the mean convection term plays an important role in the drag reduction/augment due to blowing/suction. [PERSON] et al. [10] examined the control effect exerted by blowing and suction at Reynolds number \(Re_{\rm b}=3000\) based on the bulk velocity and Mach number \(Ma=0.8,\,1.5\). The findings showed that the drag reduction rate (\(DRR\)) is affected by the blowing/suction amplitude instead of the Mach number. On the contrary, the control gain rises with the growing Mach number due to increasing density near the wall. [PERSON] et al. [11] conducted an investigation on the drag reduction in the turbulent channel at \(Re_{\rm b}=2800\). The spanwise traveling wave generated by wall blowing and suction is used to simulate wall oscillation. The study achieved a drag reduction of \(24\%\) with the mechanism of drag reduction closely linked to pressure-strain correlations. The opposition control effect of the turbulent channel at \(Re_{\rm b}=3000\) was examined by [PERSON] and [PERSON] [12] at bulk Mach number \(Ma_{\rm b}=0.3,0.8,1.5\). The sensing plane location \(y_{\rm d}^{+}\) shifted from \(y_{\rm d}^{+}=12.5\) for \(Ma_{\rm b}=0.3\) to \(y_{\rm d}^{+}=20\) for \(Ma_{\rm b}=1.5\), which corresponds to the upward shift of the Reynolds stress peaks. [PERSON] et al. [13] investigated the incompressible channel turbulence at \(Re_{\rm b}=3000\) with various blowing/suction coefficients on the bottom/top wall. The drag reduction rate increased with the blowing coefficient. Nevertheless, drag reduction was achieved when the suction coefficient was \(0.01\), and the friction drag increased with the suction coefficient. [PERSON] et al. [14] investigated the drag reduction effects of opposition control and uniform blowing/suction on turbulent flow in a channel with a bump on the lower wall at \(Re_{\rm b}=5600\) and \(12,600\). Opposition control can diminish friction drag, but has limited efficacy in reducing pressure drag. Uniform blowing reduces friction drag and pressure drag on the lower wall, but uniform suction amplifies friction drag on the upper wall. The disparity arises from the divergence in the two control mechanisms.