# Drag Reduction in Compressible Channel Turbulence with Periodic Interval Blowing and Suction
## 4 Conclusions  
In this paper, direct numerical simulation (DNS) is employed on infinitely long compressible channel turbulence. The blowing strips are arranged intermittently on the bottom wall and the suction strips are assigned symmetrically on the top wall. A periodic unit is selected as the computational domain. In the controlled cases, the wall mass flow rate is kept constant at each Mach number. The main conclusions are summarized as follows:  
1. The global drag reduction is strongly related to the wall mass flow rate, instead of the injected energy or blowing/suction intensity. Although the increasing blowing/suction intensity leads to a more significant control effect in the controlled region, the reduced controlled area will weaken the effect on the entire wall. In conclusion, when the Mach number and wall mass flow rate are identical, the velocity gradient within the viscous sublayer remains constant.
2. At the subsonic speed, the skin friction coefficient \(C_{\text{f}}\) increases in the blowing region and decreases in the suction region. The \(C_{\text{f}}\) variation in the controlled region rises with the blowing/suction intensity. At the supersonic speed, the \(C_{\text{f}}\) curve oscillates in the controlled region. Generally, \(C_{\text{f}}\) decreases in the blowing region and increases in the suction region, but this phenomenon becomes pronounced when the blowing/suction intensity reaches 0.5%.
3. In the controlled region, blowing will result in the peak position of the Reynolds stress shifting upward, whereas suction will cause the peak position to move closer to the wall. Within the controlled region, the variation in the peak position caused by blowing/suction will progressively diminish. When the wall mass flow rate is constant, the spatially averaged peak position of the Reynolds stress on the entire wall remains nearly the same.  
The findings of this research may offer assistance and guidance for engineering applications, including long-distance pipeline transport of high-velocity gas or engine intake ducts. To minimize friction drag, it is essential to maximize the wall mass flow rate of the blowing control. If the wall mass flow rate is fixed, global blowing is recommended, or the blowing area should be expanded, which can diminish the blowing intensity and thus lower the necessary input power for blowing and enhance the control gain.  
Conceptualization, S.L. and C.Z.; data curation, Y.Z. ([PERSON]); formal analysis, S.L.; funding acquisition, Y.Z. ([PERSON]), J.L., and Y.Z. ([PERSON]); investigation, S.L. and C.Z.; methodology, Y.Z. ([PERSON]); resources, C.Z. and Y.Z. ([PERSON]); software, Y.Z. ([PERSON]); supervision, Y.Z. ([PERSON]), J.L. and Y.Z. ([PERSON]); visualization, S.L.;writing--original draft, S.L.; writing--review and editing, Y.Z. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This work was supported by National Natural Science Foundation of China (12202383 and 92152202).  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The Center for Engineering and Scientific Computation in Zhejiang University provided the computing resources for the simulations in this paper.  
The authors declare no conflicts of interest.