Stability of air flow past thin liquid films on airfoils

High-speed incompressible flow past a thin airfoil in a uniform stream is considered. When the angle of attack for a solid airfoil exceeds a certain critical value, the boundary layer in the leading-edge region separates in a process known to lead to dynamic stall. Here suction near the leading edge is studied as a means of controlling separation and thereby inhibiting dynamic stall. First, steady boundary-layer solutions are obtained to determine the nature of suction distributions required to suppress separation on an airfoil at an angle of attack beyond the critical value (for a solid wall). Unsteady boundary-layer solutions are then obtained, using a combination of Eulerian and Lagrangian techniques, for an airfoil at an angle of attack exceeding the critical value; the effects of various parameters associated with the finite-length suction slot, its location and the suction strength are considered. Major modifications of the Lagrangian numerical method are required to account for suction at the wall. It is determined that substantial delays in separation can be achieved even when the suction is weak, provided that the suction is initiated at an early stage.

Boundary-layer separation control on a thin airfoil using local suction

Publisher Summary This chapter discusses that separation in a steady boundary layer is directly associated with flow reversal, which in turn implies vanishing shear at the wall. Observations seem to support that an adverse pressure gradient is indeed a prerequisite to separation. For the steady, two-dimensional boundary-layer equation, a mathematical analysis with an adverse pressure gradient over fixed wall and in the vicinity of the point of flow reversal is also explored in this chapter. The problem of the flow structure near the steady separation point, capable of getting around the Goldstein singularity and penetrating further downstream into the wake region, has attracted many investigators. The direct approach of unraveling the flow structure including the unknown pressure modification near the separation point requires a more refined boundary-layer theory. The chapter reviews the recent studies of unsteady boundary-layer equation relevant to the separation problem: the asymptotic approach to separation is aimed at the prediction of separation without the boundary-layer details that must be obtained by accurate stepwise integration. Attention is only focused on the behavior of the u-component boundary-layer velocity at the outer edge of the boundary layer.

Unsteady Separation According to the Boundary-Layer Equation

Unsteady laminar separation over impulsively moved cylinders

Nonlinear axisymmetric bending of annular plates with varying thickness

: The laminar boundary-layer equations were solved for incompressible flow past a parabola at angle of attack. Such flow experiences a region of adverse pressure gradient and thus can be employed to study the boundary-layer separation process. The present solutions were obtained numerically using both implicit and Crank Nicholson type difference schemes. It was found that in all cases the point of vanishing shear stress (the separation point) displayed a Goldstein type singularity. Based on this evidence, it is concluded that a singularity is always present at separation independent of the mildness of the pressure gradient at that point. (Author)

Incompressible Laminar Boundary Layers on a Parabola at Angle of Attack: A Study of the Separation Point

The boundary layer technique of matched asymptotic expansions is used to obtain a solution for the deflection of a highly prestressed thin annular plate. The plate is fixed at the outer boundary and has a central rigid inclusion that is rotated out of the plane of the plate. The exact solution is also derived, and it is shown that the boundary layer solution compares favorably with the exact solution.

R. T. Davis

Papers

Incompressible Laminar Boundary Layers on a Parabola at Angle of Attack: A Study of the Separation Point

Unsymmetrical Bending of Prestressed Annular Plates

Nonlinear Unsymmetrical Bending of an Annular Plate