Separation Control by Co-Flow Wall Jet

Abstract

This paper analyzes 2D differential and integral wall jet momentum equations for separation control. The analysis is used to investigate the separation control mechanism of co-flow wall jet, which utilizes an upstream tangential injection and downstream streamwise suction simultaneously to achieve zero-net-mass-flux flow control. The previous separation control guideline to obtain negative ∂u^2/∂y^2 at the wall is found to be excessive for energy expenditure and may not be achievable, because ∂u^2/∂y^2>0 is necessary in adverse pressure gradients at the wall regardless the flow is separated or attached. A more energy efficient separation control criterion is suggested to seek an attached elevated flow with the wall shear stress (tau_w) >0 and ∂u^2/∂y^2≥0. The co-flow wall jet working mechanism includes three factors to offset adverse pressure gradients: 1) The spanwise vorticity established at the wall by the injection and suction is essential to enhance turbulent diffusion and the wall vorticity flux via the suction. 2) The streamwise mass flux provided by the wall jet enhances the streamwise inertia force. 3) The adverse pressure gradient enhances the streamwise inertia force and turbulent diffusion, which offset the adverse pressure gradient itself. Co-flow wall jet has a mechanism to grow its control capability with the increasing adverse pressure gradient. The NASA hump is numerically simulated and validated to support the theoretical analysis based on 2D Unsteady Reynolds averaged Navier-Stokes equations. The numerical analysis indicates that the turbulent diffusion plays the most dominant role to offset adverse pressure gradient.