Stability of the Hypersonic Shock Layer on a Flat Plate

Маслов, А. А.; Mironov, S. G.; Poplavskaya, T. V.; Smorodskii, B. V.

doi:10.1023/b:flui.0000030302.15633.26

Cited by 3 publications

(5 citation statements)

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“…This means that vortex disturbances arise in the shock layer. Near the leading edge of the flat plate, the phase velocities obtained by the linear stability theory [4] are significantly different from the DNS data. A possible reason is that the linear stability theory [3,4] ignores nonparallelism of the mean flow, which is fairly noticeable in the vicinity of the leading edge.…”

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confidence: 56%

“…It is seen in Fig. 1 that the DNS results for the slow mode are in good agreement [3,4] and direct numerical simulations, respectively; curves 1 and 2 refer to the slow and fast modes, respectively; the points are the experimental data [9].…”

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confidence: 57%

“…In the present work, we compare the growth rates α i and phase velocities C x of disturbances on the SW with computations within the framework of the linear stability theory with allowance for the SW effect, which were performed in [4] and showed that the SW presence near a viscous boundary layer shifts the maximum of density fluctuations on the SW (Fig. 1).…”

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confidence: 99%

“…Results of direct numerical simulations of the evolution of disturbances in the shock layer on the plate for f = 38.4 kHz and θ = 0 can be compared with computations by the locally parallel linear stability theory with allowance for the shock-wave effect [3,4] and with the data of [9]. The distributions of the amplitude spectra of density fluctuations along the coordinate normal to the plate surface in cross sections along the model axis were obtained in experiments.…”

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Numerical simulation of receptivity of a hypersonic boundary layer to acoustic disturbances

Маслов

Kudryavtsev

Mironov

et al. 2007

J Appl Mech Tech Phys

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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

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Numerical simulation of receptivity of a hypersonic boundary layer to acoustic disturbances

Маслов

Kudryavtsev

Mironov

et al. 2007

J Appl Mech Tech Phys

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“…In this case, it is necessary to take into account the influence of the shock wave and viscous-inviscid interaction on stability characteristics. The boundary conditions for disturbances on the shock wave were derived from the linearized Rankine-Hugoniot conditions (Chang, Malik & Hussaini 1990;Maslov et al 2004a;Maslov, Poplavskaya & Smorodsky 2004b). It was demonstrated that reflection of disturbances from the shock wave results in branching of the solutions of the linear stability problem; i.e.…”

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Wave processes in a viscous shock layer and control of fluctuations

et al. 2010

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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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