Roles of bulk viscosity on transonic shock-wave/boundary layer interaction

Abstract

Implicit large eddy simulations are carried out to investigate the influence of the molecular bulk viscosity on transonic shock-wave boundary layer interaction for flow past a natural laminar flow airfoil at a free-stream Mach number M∞ = 0.72 and an angle of attack α = 0.38°. To quantify the nonlinear interactions, we have discarded the putative assumption made by Stokes and used a mathematical model derived from acoustic attenuation measurements to compute bulk viscosity terms. Circumventing the Stokes’ assumption, the time-averaged Cp distributions reveal a much better agreement of the shock strength and location with the available experimental data. Furthermore, due to the additional dissipative term in the energy balance equation, the strength of the upstream propagating Kutta-waves also diminishes along with a decrement in the frequency of the unsteady shock oscillation. Finally, it is observed that the additional bulk viscosity in the fluid flow resulted in an overall increase in the aerodynamic efficiency (the lift-drag ratio).