Calcul des couches limites tridimensionnelles avec des viscosités turbulentes isotropiques et anisotropiques

Calculation of three-dimensional boundary layers with isotropic and anisotropic turbulent viscosities

Laboratoire de Mécanique des Fluides Ecole Polytechnique Fédérale de Lausanne (Suisse)

Abstract

The three-dimensional turbulent boundary layer equations are solved numerically using a finite difference technique identical to that explained in "The solution of the laminar and turbulent three-dimensional boundary layer equations with a simple finite difference technique", FFA 126, 1974 by T.K. Fannelöp and D.A. Humphreys. The calculations dealt with in the present report put forward new solutions using anisotropie viscosities Ein and eout. The new definitions of Ein, x and Ein, z are arrived at by taking into account the skewing effect discussed by I.L. Ryhming and T.K. Fanne1öp in "A 3-D law-of-the-wall including skewness and roughness effects", IUTAM Symposium on Three-Dimensional Turbulent Boundary Layers, published by Springer-Verlag, Berlin, Heidelberg, New-York, 1982. The expression Eout where the intermittence is generally represented by Klebanoffs function, is modified to advantage by Sarnecki's correlation function. The measurements obtained by the classic experiment BEEL72 done by the NLR (National Aerospace Laboratory, Amsterdam), which simulates the three-dimensional boundary layer on an infmite span swept wing leading to separation have been used to test the calculations. These measurements are sufficiently accurate to allow us to conclude that the anisotropy (Ez/Ex) evaluated experimentally is initially of the order of 0.3, and reaches 0.8 in the separation zone. It is therefore relatively simple to test the validity of the hypothese used in the anisotropic caIculations. However, there is one difficulty which complicates the situation as the formula for anisotropic Ein, z -- 0 is no longer valid Ein, z) when we approach the depth where the speed component w reaches its maximum value. Three possibilities are discussed briefly to try to solve this problem provisionally. The results of the three-dimensional boundary layer ca1culations are given in the form of graphs. The Figures include measurements and values calculated (a) for the integral characteristics of the boundary layer (Rθ, H, βw, CF) as a function of the distance travelled on the distance travelled on the wing surface and (b) for the speed components and shear stress (u, w, tx, tz) as a function of the depth of the layer at a fixed point in the distance travelled. The comparisons show that the anisotropic speed profiles are slightly better, that the integral characteristies differ very little and that the separation region is systematically calculated too early, even if the results are very satisfactory elsewhere.