Application of restricted nonlinear model to drag reduction control of wall turbulence

• Published in: Physics of fluids (1994) Vol. 37; no. 6
• Main Authors: Li, Yi, Xu, Chun-Xiao
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.06.2025
• Subjects: Channel flow; Direct numerical simulation; Drag reduction; Fluid dynamics; Fluid flow; High Reynolds number; Optimal control; Reduced order models; Reynolds number; Reynolds stress; Skin friction; Suction; Turbulence; Turbulent flow
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0272128

Drag reduction of wall-bounded turbulence is an important subject in the fluid dynamics community and engineering applications. Due to the high computation cost of direct numerical simulation (DNS) for high Reynolds number turbulent flows, it is more realistic to resort to the reduced-order models, which can embody the physical mechanism of wall turbulence when developing the control strategy for turbulent drag reduction. In the present work, we apply the restricted nonlinear (RNL) model to the drag reduction controls in turbulent channel flows. The control by spanwise wall oscillation is first considered. The RNL-based DNS in a wide range of parameters have been conducted, and the results show that the RNL model can provide a reasonable estimate of the best oscillation period at different oscillation amplitudes. The RNL-based number of grid points is around 1/8 of that of DNS. The RNL model is also applied to the optimal control employing blowing and suction on the channel walls. The RNL model is used to update the virtual flow field needed to solve the optimal control problem. Application in the turbulent channel flow with Reτ=100 achieves 58% reduction of the skin friction and successfully relaminarizes the flow. The drag reduction mechanisms are explored by analyzing the budget of Reynolds stress and second-order correlations. Two different stages are found during the optimal control, which primarily suppresses streamwise vortices and streaks to weaken the turbulence, respectively.