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

Abstract

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.

Accelerated flow past a symmetric aerofoil: experiments and computations

“…The disturbance vorticity is calculated by subtracting the mean over this time period from the instantaneous data. The details of the exact method are also given in Sengupta & Dipankar (2005) and are not repeated here. Vortical structures obtained from the POD analysis provide a statistical fit of the ensemble during the time period, by minimizing the projection error of the data onto a set of deterministic eigenvectors.…”

Symmetrized compact scheme for receptivity study of 2D transitional channel flow

“…og 2 using an explicit representation of the second derivative by one-sided formula, as described in [26,33]. The VTE is solved by discretizing the convection terms of Eq.…”

“…We have taken 1001 points in the streamwise direction and 201 points in the wall-normal direction using hyperbolic tangent stretched grids -as given by Eq. (33). The computational domain extends 30H in the streamwise direction.…”

“…In [22], this was demonstrated experimentally and in [28], the physical mechanism was identified in terms of a new energy based receptivity/ stability theory without any approximation. In [33], this was shown responsible for the hitherto unexplained leading edge contamination problem of swept-wing flow field at the attachment line.…”

“…In the present work, we will use an upwind scheme of [27] (called the OUCS3-scheme) that has good numerical properties. These numerically stable near-neutral upwind compact schemes have been used to solve external flow problems in [27,28,33] where the directional and signal attenuating properties near the outflow of compact schemes have been used for high Reynolds number transitional flow problems.…”