The effects of suction on the nonlinear stability of a three-dimensional compressible boundary layer

Influence of suction/blowing on the finite amplitude disturbances having non-stationary modes of a compressible boundary layer flow

“…The effects of non-linearity are then explored by deriving a finite amplitude equation governing the evolution of the non-linear lower branch modes and also allowing the finite amplitude growth of a disturbance close to the neutral location determined from a prior stability analysis. Although the form of the amplitude equation is not at all surprising (given a similar result for the stationary vortices in Seddougui and Bassom (1996)), the dependence of the coefficients of the Landau-type modulated vortex amplitude equation on the frequency parameter is established here. A close examination of the coefficients of this evolution equation indicates strongly that the non-linearity has a destabilizing effect for both suction and blowing through the surface of the disk, the effect of which is much more stronger for a suction.…”

“…Non-linearity has been taken into account in [40], and it was shown that a smaller initial finite amplitude of the disturbance with a positive frequency is sufficient to give rise to an exponential growth of the lower branch non-stationary modes, which would then cause the transition to turbulence in the rotating disk boundary layer flow, of course in the absence of other dominant instability mechanisms. The impacts of applying suction or injection through the disk surface were discussed for the absolute instability in the work of [13] and for the convective instability in the works of [12] and [1], but these were limited to the case of the incompressible Von Karman's boundary layer flow. Motivated by the latter works, we in the present study aim to study the influences of not only the compressibility but also the mass transfer on the lower branch non-stationary neutral modes as studied in the case of zero-suction in [39].…”

“…A close examination of the coefficients of this evolution equation indicates strongly that the non-linearity has a destabilizing effect for both suction and blowing through the surface of the disk, the effect of which is much more stronger for a suction. Also the impact of non-linearity is higher for the non-stationary compressible modes than for the stationary waves of Seddougui (1990) and Seddougui and Bassom (1996). Moreover, in the case of suction, there occurs a regime of non-stationary modes that cover not only the positive frequency waves, but also waves having negative frequencies, and these modes are always unstable no matter whether the wall is insulated or isothermal.…”

“…In this paper, a weakly non-linear stability analysis is pursued to explore the effects of suction and blowing on a compressible mode of instability of the threedimensional boundary layer flow induced by a rotating disk. The main thrust of the research is to extend the stationary work of Seddougui and Bassom (1996) to cover for the non-stationary mode so that it is targeted to determine whether the major role in finite amplitude destabilization of the boundary layer is played by the stationary mode of Seddougui and Bassom (1996) or the non-stationary mode as calculated from the present study. Within this perspective, the basic compressible flow obtained in the large Reynolds number limit, together with a suction parameter entering into the wall with normal velocity at the wall, is perturbed by disturbances which are constituted as the non-linear interaction of fundamental modes and harmonics.…”

Viscous modes within the compressible boundary-layer flow due to a broad rotating cone

“…Although it has not been attempted in the present study, a further possible extension to this stability analysis is therefore to consider the effects of surface suction. This would thereby extend the study of Seddougui & Bassom (1996) to the cone.…”