On the stability of attachment-line boundary layers. Part 1. The incompressible swept Hiemenz flow

Publisher Website
Google Scholar
Abstract
The stability of the incompressible attachment-line boundary layer is studied by solving a partial-differential eigenvalue problem. The basic flow near the leading edge is taken to be the swept Hiemenz flow which represents an exact solution of the Navier-Stokes (N-S) equations. Previous theoretical investigations considered a special class of two-dimensional disturbances in which the chordwise variation of disturbance velocities mimics the basic flow and renders a system of ordinary-differential equations of the Orr-Sommerfeld type. The solution of this sixth-order system by Hall, Malik & Poll (1984) showed that the two-dimensional disturbance is stable provided that the Reynolds number . Both symmetric and antisymmetric two- and three-dimensional eigenmodes can be amplified. These unstable modes with the same spanwise wavenumber travel with almost identical phase speeds, but the eigenfunctions show very distinct features. Nevertheless, the symmetric two-dimensional mode always has the highest growth rate and dictates the instability. As far as the special two-dimensional mode is concerned, the present results are in complete agreement with previous investigations. One of the major advantages of the present approach is that it can be extended to study the stability of compressible attachment-line flows where no satisfactory simplified approaches are known to exist.