The Theory of Skin Friction Reduction by a Compliant Coating in a Turbulent Boundary Layer

Abstract

The response of a compliant surface to pressure fluctuations is known to modify (sometimes decrease) the skin friction in a turbulent boundary layer. This paper develops the surface response (receptance) of a compliant coating to a pressure perturbation. The compliant coating was assumed to be composed of a thin membrane stretched over a shallow layer of liquid. This type of coating has been used successfully by several experimenters to reduce the skin friction. After the surface response equation was developed, the technique developed by Lin and Ffowcs Williams was utilized to determine the Reynolds stresses induced near the vibrating compliant surface. The technique is generalized to allow for random turbulent pressure fluctuations and surface motion, but it is restricted to two-dimensional surface oscillations. The interesting result is that certain combinations of the properties of the compliant coating may induce a negative Reynolds stress in the layer of fluid adjacent to the coating. This layer of fluid may then be responsible for starving the turbulent eddies of their energy supply and causing a reduction in turbulence intensity and skin friction.