Large eddy simulations of a turbulent channel flow with a deforming wall undergoing high steepness traveling waves

Abstract

Backward traveling waves over a wall of a fully developed turbulent channel are known to reduce the drag coefficient, flow separation, and turbulence intensity. Based on previous studies of traveling waves with a small steepness (s = a/λ < 0.0625, a: nondimensional amplitude, λ: nondimensional wavelength), it is thought that the nondimensional wave-speed (C = C*/U*, C*: dimensional wave-speed, U*: mean channel velocity) is required to be more than one to have a zero net drag and a high reduction in the turbulent kinetic energy (TKE). This idea is tested here for waves with higher wave steepness (0.05 < s < 0.15) at various wave-speeds using large eddy simulations of a fully developed turbulent channel in which one wall is undergoing a traveling wave. It is found that the increase in wave steepness decreases the wave-speed at which a net zero drag is obtained, e.g., for waves with steepness of s = 0.05, 0.075, and 0.15, the wave-speed is, approximately, C = 1.6 ± 0.1, 0.9 ± 0.1, and 0.7 ± 0.1, respectively. Similarly, the increase in wave steepness decreases the wave-speed at which TKE of the flow in the vicinity of the wave is highly reduced, e.g., qualitatively minimized. In fact, the wave-speeds at which the high reduction in TKE is observed in this study are C = 1.2, 1.2, and 0.6 for waves with wave steepness of 0.05, 0.075, and 0.15, respectively.