Subcritical instability on the attachment-line of an infinite swept wing

The leading-edge contamination (LEC) problem of an infinite swept wing is shown here as vortex-induced instability. The governing equation for receptivity is presented for LEC in terms of disturbance energy based on the Navier-Stokes equation. The unperturbed shear layer given by the swept Hiemenz boundary-layer solution is two-dimensional and an exact solution of incompressible the Navier-Stokes equation. Thus, the LEC problem is solved numerically by solving the full two-dimensional Navier-Stokes equation. The contamination at the attachment-line is shown by solving a receptivity to a convecting vortex moving outside the attachment-line boundary layer, which triggers subcritical spatio-temporal instability. The mechanism of LEC is shown to be due essentially to a convecting Counter-clockwise rotating vortex, whereas a clockwise rotating vortex displays much weaker receptivity. These results are consistent with experimental results for the bypass mechanism. The role of linear and nonlinear mechanisms in the contamination problem is discussed as interactions between vorticity and velocity terms of the developed receptivity equation. The computed temporal growth rates reveal pattern formation during such instabilities. Proper orthogonal decomposition (POD) of the numerical solution shows the structure of the leading eigenvector as the coherent eddy excited during the bypass transition.