The effect of compressibility on the primary global instability of unforced laminar separation bubbles

Abstract

Laminar separation bubbles present a three-dimensional self-excited instability mechanism which leads to the appearance of spanwise-periodic structures. In incompressible flow, this mechanism was found to become active at conditions in which wave-like, two-dimensional perturbations are only convectively unstable. In the absence of continuous external excitation, the three-dimensional instability is expected to dominate the flow dynamics and initiate the laminar-turbulent transition. This work extends previous analyses by incorporating the effect of compressibility at subsonic conditions. Two-dimensional numerical simulations of a flat-plate boundary layer with a prescribed free-stream deceleration and acceleration are carried out to obtain a set of model laminar separation bubbles. A linear stability analysis is applied then, to study the influence of Reynolds and Mach numbers on the three-dimensional instability.

Self-excited primary and secondary instability of laminar separation bubbles

“…2008; Cherubini et al. 2010 b ; Rodríguez & Theofilis 2010 a ; Gennaro, Souza & Rodríguez 2019). Figure 2( b ) shows the neutral curve corresponding to the baseline LSBs .…”

Investigation of Mach number effects on flow over a flat plate at Reynolds number of 1.0 × 104 by schlieren visualization

“…Therefore, the reduced growth rate of the Kelvin-Helmholtz instability is one of the possibilities of delay of the three-dimensionalization in the higher-M conditions. The self-exited global instability, which leads to the three-dimensionalization of flow, is also reduced by increasing M with fixed freestream Re (Gennaro et al 2019). Although there might be other possibilities such as the influence of the freestream turbulence, the visualized images at least show that the twodimensional structure remains to some extent up to the trailing edge at the high-M conditions and this trend corresponds to the stabilized LSB in the previous study by Gennaro et al (2019).…”

“…Their result implies that the LSB is stabilized by increasing M with fixed freestream Re. Although there might be several other possibilities, the visualized images at least show that the two-dimensional structure remains to some extent up to the trailing edge at the high-M conditions and this trend corresponds to the stabilized LSB in the previous study by Gennaro et al (2019).…”

“…The self-exited global instability, which leads to the three-dimensionalization of flow, is also reduced by increasing M with fixed freestream Re (Gennaro et al 2019). Although there might be other possibilities such as the influence of the freestream turbulence, the visualized images at least show that the twodimensional structure remains to some extent up to the trailing edge at the high-M conditions and this trend corresponds to the stabilized LSB in the previous study by Gennaro et al (2019). Figure A2(a) illustrates the frequency spectra acquired by the present study at M = 0.66, α = 0 • .…”

“…Therefore, the influence of the level of the freestream turbulence on the present result cannot be accurately evaluated. The compressibility effect on the self-exited global instability on the LSB was investigated by Gennaro et al (2019). Their result implies that the LSB is stabilized by increasing M with fixed freestream Re.…”