Theoretical and numerical analyses of turbulent plane Couette flow controlled using uniform blowing and suction

Abstract

We theoretically and numerically investigate the control effect of the uniform blowing and suction (UB/US) in a turbulent plane Couette flow under a constant velocity difference condition in terms of the net energy saving. First, the effective range of UB/US amplitude is derived theoretically. According to the theoretical analysis, the effective range of UB/US amplitude decreases as the Reynolds number increases. The upper bound of the ratio between UB/US amplitude and the wall velocity, Vwc/Uw, is about 0.45% even at very low Reynolds numbers, i.e., Rew∼1000, while it is less than 0.1% at practically high Reynolds numbers, i.e., Rew>107. Next, using a direct numerical simulation (DNS), we investigate the control effect of UB/US in a turbulent plane Couette flow at Rew=3200. In the cases with smaller UB/US amplitude, i.e., Vw/Uw≤0.1%, little control effect can be observed. In the cases with larger UB/US amplitude, i.e., Vw/Uw≥0.3%, although not only a significant decrease of the contribution from the Reynolds shear stress (RSS) but also relaminarization of flow field can be observed, the total drag is increased due to the increase of the contribution from the UB/US beyond the decrease of the contribution from the RSS. Based on the present study, we can draw a conclusion that overall drag reduction by UB/US is hardly possible for turbulent Couette flows.