Instability of supersonic compression ramp flow

Abstract

The instability of supersonic compression ramp flow is investigated. It is assumed that the Reynolds number is large and that the governing equations are the unsteady triple-deck equations. The mean flow is first calculated by solving the steady equations for various scaled ramp angles α , and the numerical results suggest that there is no singularity for increasing ramp angles. The stability of the flow is investigated using two approaches, first by solving the linearized unsteady equations and looking for global modes proportional to e λ t . In the second approach, the linearized unsteady equations are solved numerically with various initial conditions. Whereas no globally unsteady modes could be found for the range of ramp angles studied, the numerical simulations show the formation of wavepacket type disturbances which grow and convect and reach large amplitudes. However, the numerical results show large variations with grid size even on very fine grids.

Hypersonic compression corner flow with large separated regions

“…(2002), based on Neiland’s (1970) reattachment theory, found that their computations were smooth past the second minimum without encountering singularity for up to 7.5. These findings were also confirmed by Logue, Gajjar & Ruban (2014).…”

“…(Blue symbols: compression corner) ▴, ○, ▪, ▾ & ▸: Smith & Khorrami (1991); ▫, ♦, & ♢: Logue et al. (2014); * & : Korolev et al. (2002).…”

Tollmien–Schlichting wave cancellation via localised heating elements in boundary layers

“…Previous studies involving numerical simulations of the unsteady triple-deck equations have encountered difficulties and unexplained behaviour in the results. For example in the recent paper by Logue, Gajjar & Ruban (2014) on unsteady flow past a compression ramp the results showed the development of a wave packet that grew in amplitude and convected downstream. The techniques used in Logue et al.…”

“…The techniques used in Logue et al (2014) to solve the unsteady triple-deck equations utilised high-order finite differencing in the streamwise direction, combined with Chebychev collocation in the wall-normal direction, and a variety of time-marching schemes were tested. In grid-refinement studies, the wave packet signal was not resolved spatially or temporally as seen in figure 6 of Logue et al (2014). No convincing explanation was available to explain this behaviour.…”

“…In grid-refinement studies, the wave packet signal was not resolved spatially or temporally as seen in figure 6 of Logue et al. (2014). No convincing explanation was available to explain this behaviour.…”