Active control for drag reduction of turbulent channel flow based on convolutional neural networks

An active controller based on convolutional neural networks (CNNs) is designed for drag reduction of turbulent channel flow. CNNs are constructed to predict the normal velocities on the detection plane as wall blowing and suction using measurable quantities at the wall, i.e., spanwise or streamwise wall shear stress. The training data of CNNs are generated from the direct numerical simulation of channel flow. With different wall quantities, we design and train different CNNs for flow prediction. The purpose is to identify which wall quantity is associated with substantial drag reduction. A linear neural network based on the spanwise wall shear stress shows sufficient capability to predict the inflow field and obtain almost the same drag reduction rate as the opposite control, which does not perform well when using the streamwise wall shear stress as the input. Hence, a nonlinear CNN model with activation function and multiple convolutional layers is established to use the streamwise wall shear stress for flow prediction and drag reduction control. Applying the trained CNNs to a low Reynolds number turbulent channel flow at Re-tau = 100, we obtain up to 19% and 10% drag reduction rates based on the spanwise and streamwise wall-shear stresses, respectively. These networks are also tested at different Reynolds numbers, i.e., Re-tau = 180 and Re-tau = 390, where substantial drag reduction rates are obtained as well. Effects of the controller on turbulent instantaneous flow field and statistics are presented.