Acoustic receptivity of Mach 4.5 boundary layer with leading-edge bluntness. (English) Zbl 1161.76560
Summary: Boundary layer receptivity to two-dimensional slow and fast acoustic waves is investigated by solving Navier-Stokes equations for Mach 4.5 flow over a flat plate with a finite-thickness leading edge. Higher order spatial and temporal schemes are employed to obtain the solution whereby the flat-plate leading edge region is resolved by providing a sufficiently refined grid. The results show that the instability waves are generated in the leading edge region and that the boundary-layer is much more receptive to slow acoustic waves (by almost a factor of 20) as compared to the fast waves. Hence, this leading-edge receptivity mechanism is expected to be more relevant in the transition process for high Mach number flows where second mode instability is dominant. Computations are performed to investigate the effect of leading-edge thickness and it is found that bluntness tends to stabilize the boundary layer. Furthermore, the relative significance of fast acoustic waves is enhanced in the presence of bluntness. The effect of acoustic wave incidence angle is also studied and it is found that the receptivity of the boundary layer on the ‘windward’ side (with respect to the acoustic forcing) decreases by more than a factor of four when the incidence angle is increased from \(0^\circ\) to \(45^\circ\). However, the receptivity coefficient for the ‘leeward’ side is found to vary relatively weakly with the incidence angle.
MSC:
| 76N20 | Boundary-layer theory for compressible fluids and gas dynamics |
| 76E09 | Stability and instability of nonparallel flows in hydrodynamic stability |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
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