Airfoils with separation and the resulting wakes

Abstract

A viscous/inviscid interaction method is described and has been used to calculate flows around four distinctly different airfoils as a function of angle of attack. It comprises an inviscid-flow method based on conformal mapping, a boundary-layer procedure based on the numerical solution of differential equations and an algebraic eddy viscosity. The results are in close agreement with experiment up to angles close to stall. In one case, where the airfoil thickness is large, small difficulties were experienced and are described. The method is shown to be capable of obtaining results with large flow separation and quantifies the role of transition on the lift coefficient.

Analysis of transitional separation bubbles on infinite swept wings

“…If there is no wall transpiration, 1/Jw = 0, then the boundary conditions (21) given in equations (20) and (21) revert back to those given in equation (16).…”

Computation of steady and unsteady control surface loads in transonic flow

“…For the purpose of estimating viscous corrections, each computational span station is treated as being locally two dimensional, and the boundary layer computed using Cebeci's inverse technique. 14 ' 15 An equivalent blowing velocity is obtained and used as a correction to the normal boundary condition to account for the addition or subtraction of mass flux through the surface to simulate the growth or decay of the displacement thickness on the wing surface. Any viscous effects on the wake are not accounted for in the present formulation.…”

Essential ingredients of a method for low Reynolds-number airfoils

“…The need to include the wake as part of the calculation at higher angles of attack has been demonstrated by Cebeci et al 3 , who also showed that interaction between the inviscid-and viscous-flow solutions was necessary at the higher angles of attack and at any angle where separated flow existed. As a consequence, the interactive boundary-layer approach described in Ref.…”

“…It assumes that transition starts when a small disturbance is introduced at a critical Reynolds number and is amplified by a factor of e 9 or about 8 x 10 3 : the effect of freestream turbulence can be represented by where n = -8.43-2.4£nr T = (3) as proposed by Mack. 10 The amplitude at a fixed point is independent of time and the spatial theory provides the required amplitude change.…”