Stabilization of laminar boundary layers by compliant membranes

Abstract

Direct numerical simulations have been performed to study boundary layer flow over a compliant membrane. While coupling directly to the fluid dynamics code through the wall boundary condition, this membrane model displays many of the important features of other compliant coatings. While membrane parameters are identified that increase the critical Reynolds number by a factor of 2 compared with the rigid wall, this is mitigated by a significant increase in the growth rates in the unstable region. A detailed analysis of the temporal evolution and spatial structure of the terms in the kinetic energy balance equation shows significant differences in the behavior of two different classes of modes of the system: class A waves, which are destabilized by increased dissipation in the membrane, and class B waves, which are stabilized by membrane dissipation. For class A waves, the dominant dissipative mechanism is viscous damping in the fluid augmented by negative energy production, the principal stabilization mechanism seen in the ‘‘smart wall’’ algorithm simulations. For class B waves, direct transfer of energy to, and dissipation by, the membrane dominates stabilization of the flow. For class A waves, the membrane stabilizes the flow not by dissipating energy, but by modifying the flow to decrease energy production and enhance viscous dissipation in the fluid.