SUBCRITICAL INSTABILITY ON THE ATTACHMENT-LINE OF AN INFINITE-SWEPT WING

BY T K Sengupta and A Dipankar

Abstract

The leading edge contamination (LEC) problem of an infinite-swept wing is shown here as vortex-induced instability - a mechanism discussed in Sengupta et al. (2003)- that is referred to as SDS hereafter. The governing equation for receptivity is presented for LEC in terms of disturbance energy based on Navier-Stokes equation. The unperturbed shear layer given by the Hiemenz boundary layer solution is two-dimensional and an exact solution of incompressible 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, that triggers sub-critical spatio-temporal instability. The mechanism of LEC is shown essentially due to a convecting counterclockwise rotating vortex- while a clockwise rotating vortex display much weaker receptivity. These results are conisistent with the experimental ones in Lim et al. (2004) for the bypass mechanism. Role of nonlinear mechanism of 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 instabilites. Proper orthognal decomposition (POD) of numerical solution show the structure of the leading eigenvector as the coherent eddy excited during the bypass transition.