Asymptotic structhres for a number of unsteady three-dimensional separating flows follow and depend on the symmetry properties of the flow (e.g. line symmetry, axial symmetry).In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi two-dimensional with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.'Work funded under Space Act Agreement C99066G; presently at
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.
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