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

Abstract

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

Response of a Hypersonic Boundary Layer to Wall Blowing-Suction

“…In this case, the excitation of Mack's second mode was because of a two-step resonant process, i.e., the resonant between fast acoustic waves and mode F near the leading edge and the resonant between mode F and mode S. The twostep receptivity scenario observed from numerical simulations was consistent with that described by Fedorov and Khokhlov [19]. Maslov et al [20] studied the evolution of disturbances in a Mach 21 flat-plate boundary layer by solving the unsteady Navier-Stokes equations with a high-order shock-capturing scheme. The numerical results were agree well with the data obtained from the locally parallel linear stability theory and experimental measurements in a hypersonic wind tunnel.…”

“…where q 0 is an amplitude constant depending on the location of the actuator, and is a small dimensionless parameter. The function l is the profile function defined as (20) where s i and s e are the coordinates of the leading and trailing edges of the actuator. Figure 2 shows the profile of the blowing-suction disturbances in the forcing region.…”

Interaction of two counter-rotating supersonic vortices

“…In this paper, in paragraph 3, the main results of the previous works of the authors concerning the study of the wing tip vortex dependence on the Mach number at large distances from the wing in supersonic regimes for steady state incoming flow are briefly presented. The results for the influence of acoustic type disturbances on the wingtip vortex may be found in [6,7,8], where the disturbances were introduced in steady state incoming flow in the form of a monochromatic plane wave with small amplitude at the inlet boundary by analogy with the [9].…”

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

“…The pressure fluctuations were measured by a piezoceramic sensor, and the distributions of the mean density and density fluctuations were measured by the method of the electron-beam fluorescence [5]. The procedure of reconstruction of the mean density and the field of density fluctuations from the fluorescence signal was described in [2]. The fluctuations were measured in the frequency range from 3 to 50 kHz.…”

“…It was demonstrated in [1][2][3], where the flow in a hypersonic shock layer on a flat plate aligned at a zero angle of attack was considered, that this algorithm and calculation method can be used to solve problems of BL receptivity and stability.…”