The evolution of disturbances in a hypersonic viscous shock layer on a flat plate excited by slowmode acoustic waves is considered numerically and experimentally. The parameters measured in the experiments performed with a free-stream Mach number M ∞ = 21 and Reynolds number Re L = 1.44 · 10 5 are the transverse profiles of the mean density and Mach number, the spectra of density fluctuations, and growth rates of natural disturbances. Direct numerical simulation of propagation of disturbances is performed by solving the Navier-Stokes equations with a high-order shock-capturing scheme. The numerical and experimental data characterizing the mean flow field, intensity of density fluctuations, and their growth rates are found to be in good agreement. Possible mechanisms of disturbance generation and evolution in the shock layer at hypersonic velocities are discussed.Introduction. In high-velocity high-altitude flight, the entire space between the surface of the flying vehicle and the bow shock wave (SW) even at a large distance from the leading edges is the viscous flow zone where the socalled viscous shock layer is formed. Like the boundary layer, the laminar shock layer is unstable, and perturbations developed in this layer induce a transition to a turbulent flow regime. The evolution of perturbations in the viscous shock layer and in supersonic flows with lower Mach numbers, however, may be caused by different mechanisms. The presence of numerous instability modes plays an important role in the development of instability at hypersonic velocities. Factors that can also affect the character of instability evolution are the interaction of instability waves and the SW [1], substantial deviations from a parallel flow, and velocity slip and temperature jump on the wall. In addition, one should take into account that instability waves can be excited not only by the conventional mechanism of receptivity but also by means of direct amplification of free-stream perturbations in the SW [2]. Finally, of great importance in flight conditions at high stagnation temperatures of the flow are real gas effects capable of changing the stability characteristics to a large extent.Because of the above-listed factors, a sufficiently large amount of experimental measurements, results of the linear analysis of hydrodynamic stability (see [3,4]), and data of direct numerical simulations [5,6], which were accumulated during long-time research of the laminar-turbulent transition of the boundary layer at moderate hypersonic Mach numbers (M ∞ = 5-8), cannot be extrapolated to the case of a viscous shock layer at extremely high Mach numbers (M ∞ = 15-25). Meanwhile, the knowledge of mechanisms controlling the evolution of disturbances in a viscous shock layer is necessary to develop efficient methods of predicting and controlling the laminar-turbulent transition in hypersonic flows. This will allow a significant reduction of the drag force and heat loads and offer engineering background for production of efficient hypersonic flying vehicles.

No abstract

Generation and development of disturbances in a hypersonic viscous shock layer on a flat plate is studied both experimentally and numerically. The study is performed at the Mach number M∞ = 21 and the Reynolds number ReL = 1.44 × 105 and is aimed at elucidating the physical mechanisms that govern the receptivity and instability of the shock layer at extremely high hypersonic velocities. The experiments are conducted in a hypersonic nitrogen-driven wind tunnel. An electron-beam fluorescence technique, a Pitot probe and a piezoceramic transducer are used to measure the mean density and Mach number contours, as well as density and pressure fluctuations, their spectra and spatial distributions in the shock layer. Direct numerical simulations are performed by solving the Navier–Stokes equations with a high-order shock-capturing scheme in a computational domain including the leading and trailing edges of the plate, so that the bow shock wave and the wake behind the plate are also simulated. It is demonstrated that computational and experimental data characterizing the mean flow field, intensity of density fluctuations and their spatial distributions in the shock layer are in close agreement. It is found that excitation of the shock layer by external acoustic waves leads to generation of entropy–vortex disturbances with two maxima of density fluctuations: directly behind the shock wave and on the external edge of the boundary layer. At the same time, the pressure fluctuations decay inward into the shock layer, away from the shock, which agrees with the linear theory of interaction of shock waves with small perturbations. Thus, the entropy–vortex disturbances are shown to dominate in the hypersonic shock layer at very high Mach numbers, in contrast with the boundary layers at moderate hypersonic velocities where acoustic modes are most important. A parametric numerical study of wave processes in the shock layer induced by external acoustic waves is performed with variations of frequency, amplitude and angle of propagation of external disturbances. The amplitude of generated disturbances is observed to grow and decay periodically along the streamwise coordinate, and the characteristics of these variations depend on the frequency and direction of incident acoustic waves. The hypersonic shock layer excited by periodic blowing and suction near the leading edge is also investigated; in the experiments, this type of excitation is obtained by using an oblique-cut whistle. It is shown that blowing/suction generates disturbances resembling those generated by external acoustic waves, with similar spatial distributions and phase velocities. This result paves the way for active control of instability development in the shock layer by means of destructive interference of two types of disturbances. Numerical simulations are performed to show that instability waves can be significantly amplified or almost entirely suppressed, depending on the relative phase of blowing/suction and acoustic disturbances. Wind-tunnel experiments completely confirm this numerical prediction. Thus, the feasibility of delaying instability development in the hypersonic shock layer has been demonstrated for the first time.

No abstract