An instability in supersonic boundary-layer flow over a compression ramp

Abstract

Separation of a supersonic boundary layer (or equivalently a hypersonic boundary layer in a region of weak global interaction) near a compression ramp is considered for moderate wall temperatures. For small ramp angles, the flow in the vicinity of the ramp is described by the classical supersonic triple-deck structure governing a local viscous-inviscid interaction. The boundary layer is known to exhibit recirculating flow near the corner once the ramp angle exceeds a certain critical value. Here it is shown that above a second and larger critical ramp angle, the boundary-layer flow develops an instability. The instability appears to be associated with the occurrence of inflection points in the streamwise velocity profiles within the recirculation region and develops as a wave packet which remains stationary near the corner and grows in amplitude with time.

Instability of supersonic compression ramp flow

“…Our observations are qualitatively similar to [7] but not [6]. The same equations with a slight change in boundary conditions for the moving wall problem show no instabilities.…”

“…Of course, this does not preclude other types of instability modes or global instability at much larger ramp angles. The numerical results of Cassel et al [6] and Fletcher et al [7] suggest that there are instabilities present for all the angles studied in figures 2 and 3. …”

“…In the first approach, we write the perturbations to the flow as 6) with similar expressions for the other quantities. Expression (2.6) were substituted into (2.1)-(2.4) which were then linearized for small leading to the unsteady linear perturbation equations ∂ũ ∂x + ∂ṽ ∂y = 0, (2.7) 9) and homogeneous boundary conditions.…”

Instabilities in supersonic compression ramp flow

“…In both situations, an increase in the controlling parameter leads to local breakdown of the laminar boundary layer. Cassel, Ruban & Walker (1995) carried out a series of calculations for progressively higher ramp angles using a time-marching algorithm to solve the unsteady triple-deck equations, starting from an initial configuration where the ramp angle was abruptly changed from zero. The original objective of these computations was to carry the solutions through to a presumed steady state and this was accomplished without complication for relatively low ramp angles.…”

“…However at a very moderate angle (well below the maximum values considered by Smith &Khorrami 1991 andKorolev et al 2002) an apparent absolute instability, † was encountered which precluded carrying out solutions to higher ramp angles. At the time Cassel et al (1995) went to considerable effort to attempt to confirm that the observed instability was physical, as opposed to numerical in nature. The oscillations that were observed in the wall shear and pressure appeared for all grids considered.…”