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.

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.

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Direct numerical simulations of the evolution of disturbances in a viscous shock layer on a flat plate are performed for a free-stream Mach number M ∞ = 21 and Reynolds number Re L = 1.44 · 10 5 . Unsteady Navier-Stokes equations are solved by a high-order shock-capturing scheme. Processes of receptivity and instability development in a shock layer excited by external acoustic waves are considered. Direct numerical simulations are demonstrated to agree well with results obtained by the locally parallel linear stability theory (with allowance for the shock-wave effect) and with experimental measurements in a hypersonic wind tunnel. Mechanisms of conversion of external disturbances to instability waves in a hypersonic shock layer are discussed.Introduction. Understanding the mechanisms of receptivity and instability of a viscous shock layer is necessary for developing effective methods of controlling the laminar-turbulent transition in hypersonic flight. When a flying vehicle moves with a high velocity in the upper layers of the atmosphere, the viscous shock layer regime is extended to a significant distance from the leading edges. Origination and evolution of disturbances in the shock layer may be significantly different from those in supersonic near-wall flows with moderate Mach numbers (M ∞ < 10) [1-4] and have been little studied yet. A theoretical study of such flows is difficult because of the interaction of disturbances with the shock wave (SW), significant nonparallelism of the flow, and velocity slip and temperature jump on the wall. Possibilities of wind-tunnel modeling of receptivity and disturbance evolution in a hypersonic shock layer are limited; in particular, wind-tunnel experiments cannot ensure real-flight Reynolds numbers and flow enthalpy. Numerical simulations can fill this gap. There are some recent publications [5][6][7][8], where the problems of receptivity and evolution of disturbances in supersonic and moderate hypersonic flows have been solved by means of direct numerical simulations (DNS) on the basis of full unsteady Navier-Stokes equations. This approach allows obtaining detailed information on the disturbance field, which is necessary for verification of theoretical models and comparisons with measurement data. The studies performed up to now, however, involved flow parameters more typical of the boundary layer (where the SW is rather far from the upper edge of the viscous flow) rather than of the shock layer.Results of a parametric research of shock-layer interaction with external acoustic waves propagating at different angles to the flow with an extremely high Mach number (M ∞ = 21) and a moderate Reynolds number (Re L = 1.44 · 10 5 ) are described in the present paper. Interaction of acoustic perturbations of the external flow (slow and fast modes) with the shock layer is simulated by solving two-dimensional Navier-Stokes equations. The

Results of a numerical and experimental study of characteristics of disturbances in a hypersonic shock layer on a flat plate covered by a sound-absorbing coating and aligned at an angle of attack are presented. Experiments and computations are performed for the free-stream Mach number M ∞ = 21 and Reynolds number Re L = 6 · 10 4 . A possibility of suppressing pressure fluctuations in the shock layer at frequencies of 20-40 kHz with the use of tubular and porous materials incorporated into the plate surface is demonstrated. Results of numerical simulations are found to be in good agreement with experimental data.