Injection-ejection fluid influence on velocity and vorticity distributions in laminar-turbulent transition of unsteady incompressible boundary layer on porous surface

Abstract

Through the porous contour in pependicular direction, the fluid of the same properties as the incompressible fluid in the basic flow, has been injected or ejected. The corresponding equations of unsteady boundary layer, by introducing the appropriate variable transformations, momentum and energy equations and two similarity parameter sets, being transformed into generalized form. These parameters are expressing the influence of the outer flow velocity, the injection or ejection velocity and the flow history in the boundary layer, on the boundary layer characteristics. The numerical integration of the generalized equation with boundary conditions has been performed by means of difference schemes and by using the Tridiagonal Algorithm Method with iterations in the three once localized approximations, where the first unsteady, dynamic and porous parameters will remain, while all others will be let to be equal to zero, and where the derivatives with respect to the first porous parameter will be considered equal to zero. The obtained generalized solutions are used to calculate the shear stress, velocity and vorticity distributions in the laminar-turbulent transition of the unsteady boundary layer on the porous aerofoil when the center velocity changes with time as a degree function and when the potential external velocity on the aerofoil is measured in free flight. As well as for both the accelerating and decelerating flows, the ejection of fluid postpones the boundary layer separation, and vice versa the injection of fluid favours the separation.