Application of compact neural network for drag reduction in a turbulent channel flow at low Reynolds numbers

Abstract

The aim of the present work is to develop neural networks for flow estimation and control in a turbulent channel flow at low Reynolds number. The control strategy considered here is the opposition strategy of Choi et al. [“Active turbulence control for drag reduction in wall-bounded flows,” J. Fluid Mech. 267, 75 (1994)]. The idea is to identify which velocity length scales are associated with substantial drag reduction, and to determine how the flow at these length scales can be estimated from a grid of sensors with limited extent and finite spacing. Numerical experiments are carried out in a restricted computational domain at Rτ=140 as well as in a full flow unit at Rτ=180. Evidence is shown that the flow is more complex in the larger domain than in the reduced one. In the larger domain, the estimation is performed on independent subdomains spanning at most a few coherent structures. We obtain up to 13% drag reduction in the simplified flow and 12% in the full flow unit. The essential scales for control are found to roughly match the characteristic dimensions of the coherent structures: On the order of a few hundred wall units in the streamwise direction and about 25 to 50 wall units in the spanwise direction. Controlling the flow with a Fourier-filtered estimate for the velocity resulted in about the same drag reduction as was obtained with the exact, Fourier-filtered velocity field. In addition, we found that the neural-based estimation remained adequate in the presence of moderate aliasing.