The effect of bulk viscosity on compressible couette flow with blowing

Abstract

The effect of bulk viscosity on a compressible couette flow is considered between two porous parallel walls in which the lower wall is at rest and the upper wall is moving at a constant velocity. The flow between the walls is steady, two dimensional, and the gas is perfect. At the lower wall, there is vertically oriented blowing; suction occurs at the upper wall.

The bulk viscosity μb is introduced through the second viscosity coefficient, A = μb - 2/3μ, where μ is the shear viscosity and μb provides the viscous stresses due to dilatational motion of the gas. Typically μb is set equal to zero (Stokes' hypothesis). This case is generally true for monatomic gases and air, but for certain polyatomic gases, such as C02 , the ratio μb/μ can exceed 103. Such a large value can significantly effect the flow field.

Compressible couette flow with blowing is governed by four first-order ODE's which are formulated from the conservation equations. These equations are numerically solved using a fourth-order Runge-Kutta method with variable step size and the shooting method, which transforms a two point boundary value problem into an equivalent initial value problem. The shooting method is applied to the temperature boundary conditions to assist in determining the initial temperature gradient. This same method also assists in defining an initial x-velocity gradient that governs the determination of the distance between the walls. The physical significance of computed results for both subsonic and supersonic blowing are discussed.