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).

Bulk viscosity of liquid noble gases

“…An increased shock wave thickness affects the outer flow's adverse pressure gradient and consequently suppresses the shock induced boundary layer separation, 48 while additionally the shock wave's location and strength are much more accurately predicted when bulk viscous effects are included. 49 Likewise, bulk viscous damping has been observed in compressible turbulent flows. 50 A non-zero bulk viscosity enhances kinetic energy dissipation while additionally inhibiting the energy transfer between translational and configurational energy, thus rendering the flow effectively incompressible.…”

Volume viscosity of inhomogeneous fluids: a Maxwell relaxation model

“…长期以来, 人们对Newtonian流体中的剪切黏 度进行了深入且细致的研究 [4][5][6][7][8] . 相比之下, 体积黏 度却未受到广泛关注, 甚至在一些研究中被忽略不 计, 即Stokes假设 [9] . 对单原子理想气体或不可压 缩流体而言, 该假设并无不妥.…”