Recent experimental work has succeeded in retarding or removing boundary-layer separation by means of blowing supersonic microjets transversely through the wall. To provide some theoretical context for such work, the current study examines the removal of separation by transverse blowing within the framework of the standard Prandtl scalings for incompressible boundary layers. One key result, obtained using asymptotic analysis, is that such removal is not possible for two-dimensional flow. Neither is removal of separation possible by three-dimensional blowing in an initially two-dimensional separated boundary layer if the blowing distribution has a finite-scale spanwise variation. The second key result obtained is that the previous conclusion is no longer valid when there is nontrivial short-scale spanwise variation of the blowing distribution. This result is obtained by providing a numerical counter-example in which blowing, with a Gortler scale spanwise variation, creates an attached boundary layer flow where none existed before the blowing. One consequence is that there are at least some flows in which transverse Gortler-scale blowing can turn a separated flow into an attached flow, with a vanishingly small drag that is inversely proportional to the square root of the Reynolds number. The flow physics of the computed example is analyzed to obtain a better understanding of how the Gortler-scale blowing affects the flow. (C) 2014 Elsevier Masson SAS. All rights reserved.

This paper is an extension of work on separation from a downstream moving wall by Ruban et al. (J. Fluid. Mech., vol. 678, 2011, pp. 124-155) and is in particular concerned with the boundary-layer separation in unsteady two-dimensional laminar supersonic flow. In a frame attached to the wall, the separation is assumed to be provoked by a shock wave impinging upon the boundary layer at a point that moves downstream with a non-dimensional speed which is assumed to be of order Re-1/8 where Re is the Reynolds number. In the coordinate system of the shock however, the wall moves upstream. The strength of the shock and its speed are allowed to vary with time on a characteristic time scale that is large compared to Re-1/4. The 'triple-deck' model is used to describe the interaction process. The governing equations of the interaction problem can be derived from the Navier-Stokes equations in the limit Re -> infinity. The numerical solutions are obtained using a combination of finite differences along the streamwise direction and Chebyshev collocation along the normal direction in conjunction with Newton linearization. In the present study with the wall moving upstream, the evidence is inconclusive regarding the so-called 'Moore-Rott-Sears' criterion being satisfied. Instead it is observed that the pressure rise from its initial value is very slow and that a recirculation region forms, the upstream part of which is wedge-shaped, as also observed in turbulent marginal separation for large values of angle of attack.

A novel iterative method for solving the incompressible, fully parabolized Navier-Stokes equations is described. It is a modification of the classical so-called P′ method. The central modification is to boost the computed pressure changes during the iterations. The method is shown to produce robust convergence for the considered application in a simple way.

Boundary-layer separation can be prevented or delayed by sucking part of the boundary layer into the surface, but in a straightforward application the required hydraulics entail significant penalties in terms of weight and cost. By means of computational techniques, this paper explores the possibility of autogenous suction, in which the local pressure differences that lead to separation drive the suction used to prevent it. The chosen examples include steady and unsteady laminar flows around leading edges of thin airfoils. No fundamental theoretical limit to autogenous suction was found in the range of angles of attack that could be studied, but rapidly increasing suction volumes suggest that practical application will become increasingly difficult for more severe adverse pressure gradients.

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.

Direct summation of the velocity field introduced by point vortices tends to be time consuming since the velocity of each vortex is found as a sum over all other vortices. The resulting number of numerical operations is proportional to the square of the number of vortices. Here a relatively simple procedure is outlined which significantly reduces the number of operations by replacing selected partial sums by asymptotic series. The resulting number of operations appears to vary roughly in proportion to the number of unknowns, corresponding to a “fast” solver.