Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound

Abstract

In this paper, we continue to study the mechanisms of the receptivity of the supersonic boundary layer to free-stream disturbances by using both direct numerical simulation and linear stability theory. Specifically, the receptivity of a Mach 4.5 flow over a flat plate to free-stream fast acoustic waves is studied. The receptivity to free-stream slow acoustic waves, entropy waves and vorticity waves will be studied in the future. The oblique shock wave induced by the boundary-layer displacement plays an important role in the receptivity because the free-stream disturbance waves first pass through the shock before entering the boundary layer. A high-order shock-fitting scheme is used in the numerical simulations in order to account for the effects of interactions between free-stream disturbance waves and the oblique shock wave. The results show that the receptivity of the flat-plate boundary layer to free-stream fast acoustic waves leads to the excitation of both Mack modes and a family of stable modes, i.e. mode I, mode II, etc. It is found that the forcing fast acoustic waves do not interact directly with the unstable Mack modes. Instead, the stable mode I waves play an important role in the receptivity process because they interact with both the forcing acoustic waves and the unstable Mack-mode waves. Through the interactions, the stable mode I waves transfer wave energy from the forcing fast acoustic waves to the second Mack-mode waves. The effects of incident wave angles, forcing wave frequencies, and wall temperature perturbation conditions on the receptivity are studied. The results show that the receptivity mechanisms of the second mode are very different from those of modes I and II, which leads to very different receptivity properties of these discrete wave modes to free-stream fast acoustic waves with different incident wave angles, frequencies, and different wall boundary conditions. The maximum receptivities of the second mode, mode I and mode II to planar free-stream fast acoustic waves are obtained when incident wave angles approximately equal 26 • , 45 • , and 18 • , respectively. The results of receptivity to a beam of free-stream fast acoustic waves show that the leading edge is one of the most efficient regions for receptivity.

Response and receptivity of the hypersonic boundary layer past a wedge to free-stream acoustic, vortical and entropy disturbances

“…DNS investigations by Ma & Zhong (2003b, 2005 and by Balakumar (2003Balakumar ( , 2005) have indicated too that planar acoustic, vortical and entropy disturbances alone can excite instability modes in a supersonic flat-plate boundary layer. These careful numerical studies have provided much important information about supersonic boundary-layer receptivity.…”

Numerical simulation of the supersonic boundary layer interaction with arbitrary oriented acoustic waves

“…This method makes it possible to obtain detailed information on the perturbation field, which is difficult in experimental studies. A numerical simulation of the receptivity of a two-dimensional boundary layer on a flat plate with a sharp leading edge to acoustic waves was carried out in [10] by using a numerical scheme of a high order of approximation with the separation of the head jump. This scheme is not applicable in a small region near the leading edge of the plate, where a shock wave is formed.…”

“…This scheme is not applicable in a small region near the leading edge of the plate, where a shock wave is formed. This region was not considered in [10], although it can play an important role in the receptivity process. In [10], only fast acoustic waves with a positive inclination angle (12 different angles) were investigated with M =4.5.…”

“…This region was not considered in [10], although it can play an important role in the receptivity process. In [10], only fast acoustic waves with a positive inclination angle (12 different angles) were investigated with M =4.5. In [11] for the same regime, other types of perturbations in the incoming flow (slow acoustic waves, entropy waves and vorticity) are considered.…”

Active control of hypersonic shock layer disturbances

“…The VSL consists of a thick boundary layer and a thin layer of an inviscid §ow behind the SW. Like the boundary layer, the laminar shock layer is unstable, and perturbations developed in this layer induce its transition to the turbulent §ow regime. The evolution of perturbations in supersonic §ows with Mach numbers 6 and 10 was studied by Egorov et al [1,2] and Ma and Zhong [3,4]. However, mechanisms governing emergence and development of perturbations in the VSL with higher Mach numbers may di¨er from those investigations with lower Mach numbers.…”