Curvature effects on the stability of three-dimensional laminar boundary layers

The linear stability equations which govern the growth of small periodic disturbances for compressible, three-dimensional laminar boundary layer flow are derived in an orthogonal curvilinear coordinate system. The parallel flow assumption is utilized in the derivation. The system of equations is solved using a finite difference scheme similar to that in a current state-of-the-art stability analysis code, COSAL. The LR method and the inverse Rayleigh iteration procedure are used to calculate the eigenvalues.

The stability of the three-dimensional compressible laminar boundary layer including the effects of streamline and surface curvature for flows past swept wings where crossflow type disturbances dominate is calculated. A parametric study is performed varying Reynolds number and sweep angle on an airfoil with a concave cutout in the leading edge region of the lower surface. It is known that convex curvature has a stabilizing effect on the laminar boundary layer. Conversely, concave curvature has a destabilizing effect. The magnitude of these effects for swept wing flows is determined. Non-stationary as well as stationary disturbances are calculated, and the most amplified frequencies are identified.

N-factor correlations at the measured location of transition are made utilizing flight test data. Results indicate that amplification rates and hence, N-factors, for swept wing flows over convex surfaces are reduced by about 30 to 50 percent when curvature effects are included in the linear stability analysis. In addition, comparisons are made with some experimental results on a swept concave-convex surface. Calculated velocity vector plots show good agreement with observed disturbances in the laminar boundary layer over the concave surface. The results of the calculations show that concave curvature destabilizes "crossflow” type disturbances with a 30 percent increase in amplification rate.