Effect of Shape of Two-Dimensional Smooth Hump on Boundary Layer Instability

Effect of hump shape on boundary layer instability is investigated for incompressible, supersonic, and hypersonic speed regimes. Flat-plate boundary layers over a two-dimensional smooth hump of five different geometries are considered. The linear evolution of instability waves is analyzed by using the parabolized stability equation. The resulting growth rate and N -factor are compared for several frequencies. The destabilization effect of the hump is evaluated in terms of the change in N -factor. The overall influence of the hump is also assessed by comparisons of N -factor envelopes and predicted transition locations based on e N -method. Results show that the destabilization effect is the greatest for the incompressible case. The degree of destabilization appears to depend not only on the hump area but also the other geometric parameters. The variation of the predicted transition Reynolds number depending on the hump shape is pronounced only in a certain range of hump heights. Although the supersonic boundary layer also exhibits similar characteristics, the effectiveness of hump is rather low, and relatively insensitive to the hump shape. In the case of the hypersonic boundary layer, the hump exhibits either destabilization or stabilization effect, depending on the relative location of a synchronization point. The degree of destabilization depends strongly on the both hump area and frequency. Either the transition delay or early transition could be predicted depending on the hump location and critical N -factor value employed. Unlike the incompressible case, the dependency on the hump shape is not confined to a certain range of hump heights.