Computational analysis of compressibility effect on flow field and aerodynamics at low Reynolds numbers

Abstract

The flow around the wing of exploration aircraft flying in the very dilute Martian atmosphere experiences very specific low-Reynolds-number compressible flows. A fundamental understanding of compressibility effects, especially on a separation bubble, is an important issue in the aerodynamic wing design. We investigated the effect of compressibility on the laminar separation bubbles and aerodynamic properties of a blunt flat plate with a thickness of 5% of the chord length in unsteady two-dimensional laminar and large-eddy simulations at chord-based Reynolds numbers ( Re) of 6100 and 11 000 in the Mach number ( M) range from M = 0.1 to 0.8. In the incompressible flow below M = 0.2 at Re = 11 000, the separated shear layer rolled up due to the Kelvin–Helmholtz (KH) instability reattaches to the surface with turbulent transition and then forms a laminar separation bubble. In contrast, with increasing Mach number, the transition and reattachment are delayed, and the separation bubble is stretched. In particular, at M = 0.8, the rolled-up vortex is not distorted in the span direction and advects downstream with a strong spanwise two-dimensionality. This is due to the compressibility effect that suppresses the KH instability. On the other hand, at Re = 6100, the separated shear layer is stable without spanwise distortion even in the incompressible flow due to the stronger influence of viscous forces. With increasing Mach number, such stable separated shear layer reattaches without rolling up further downstream, and the Strouhal number of the vortex also gradually decreases. This leads that the large lift oscillation owing to periodic and two-dimensional spanwise vortex shedding is significantly suppressed with an increasing Mach number. This is also due to the weakening of the KH instability due to the compressibility effects. However, at Re = 11 000, the reattachment points move downstream more significantly with the increasing Mach number, indicating that the suppression of the KH instability due to the compressibility effect is more pronounced at Re = 11 000 than at Re = 6100. Consequently, the negative skin friction shear stress owing to the reverse flow inside the expanded separation bubble becomes relatively large, decreasing the total drag with the increasing Mach number.