Wave processes in the shock layer on a flat plate at an angle of attack

Abstract

A numerical and experimental study of receptivity of the viscous shock layer on a flat plate aligned at an angle of attack to external acoustic perturbations is performed. Density and pressure fluctuations are measured in experiments at the free-stream Mach number M ∞ = 21 and Reynolds number Re 1 = 6 · 10 5 m −1 . Direct numerical simulations of receptivity of the viscous shock layer to external acoustic perturbations in wide ranges of the governing parameters are performed by solving the Navier-Stokes equations with the use of high-order shock-capturing schemes. The calculated intensities of density and pressure fluctuations are found to be in good agreement with experimental data. Results of the study show that entropy-vortex disturbances dominate in the shock layer at small angles of attack, whereas acoustic perturbations prevail at angles of attack above 20 • . Introduction.A viscous shock layer is formed on the leading edges of hypersonic flying vehicles where the local Reynolds number is not too high and viscous forces prevail. The characteristics of disturbances in a hypersonic shock layer are determined by the following basic processes: action of free-stream perturbations on the shock layer, generation of disturbances inside the shock layer (receptivity), and evolution of disturbances during their downstream convection. These processes are interrelated, proceed simultaneously over the entire length of the shock layer, and can be defined as a unified process of distributed receptivity. Receptivity is an important characteristic of the initial stage of the laminar-turbulent transition. Acting on arising disturbances, one can control the laminar-turbulent transition in a high-velocity flow.Previous experimental and numerical investigations of the characteristics of fluctuations generated by external acoustic waves in a hypersonic shock layer on a flat plate aligned at a zero angle of attack [1] showed that the main features of the formation of the field of density fluctuations are generation of entropy-vortex disturbances and their domination inside the shock layer. Interacting with the mean flow, these disturbances form the field of density fluctuations. In particular, there are two peaks of density fluctuations: on the shock wave (SW) and on the boundary-layer (BL) edge where the mean density gradient reaches high values. Vortices propagate in the inviscid layer between the SW and the BL edge. It was also demonstrated [1, 2] that the role of the acoustic mode of disturbances is enhanced as the angle between the direction of external acoustic disturbances and the SW increases.Subsequent experimental and numerical studies [2] made it possible to supplement and refine the characteristics of the entropy-vortex mode disturbances developed in the shock layer on a flat plate at a zero angle of attack. It was shown that specific features of these disturbances are the coincidence of the spatial distributions of fluctuations in the shock layer and the equality of the streamwise phase velocities of disturbances rega...

Effect of sound-absorbing materials on intensity of disturbances in the shock layer on a flat plate aligned at an angle of attack

“…It was demonstrated [2] for a flat plate with a sharp leading edge that acoustic waves from the free stream induce entropy-vortex disturbances whose intensity can be controlled by introducing local controlled perturbations (such as blowing/suction with an appropriate amplitude and frequency) into the shock layer (interference control method). As the angle of attack of the flat plate increases, however, non-decaying pressure fluctuations corresponding to the acoustic mode of disturbances arise in the shock layer on the windward side of the plate [3]. With a further increase in the angle of attack, the pressure fluctuations rapidly grow, and their maximum is shifted toward the plate surface, whereas the relative level of fluctuations of the entropy-vortex mode decreases.…”