Wave processes in a viscous shock layer and control of fluctuations

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.

Response and receptivity of the hypersonic boundary layer past a wedge to free-stream acoustic, vortical and entropy disturbances

“…As is well known, when each of three elementary types of free-stream disturbances strikes a shock in free space, all three types of waves may emerge downstream (McKenzie & Westphal 1968). A similar process takes place when a shock is adjacent to a solid boundary, as was shown theoretically by Duck, Lasseigne & Hussaini (1995, 1997 for the supersonic flow past a wedge, and demonstrated experimentally by Maslov et al (2010) for the flat-plat boundary layer in the strongly interactive regime. In the presence of the boundary layer, the disturbance downstream also consists of reflected acoustic waves.…”

“…We focus on the acoustic part of the perturbation. Vortical and entropy waves are also present (see Appendix A), but they are absorbed by a thin layer located at the outer edge of the boundary layer without entering the latter (Dong & Wu 2013; see also Maslov et al 2010, where such features were observed experimentally). The acoustic wave is governed by the (quasi-steady) Euler equations linearized about the uniform flow, among which the momentum equation in the y-direction reads…”

Influence of Langmuir adsorption and viscous fingering on transport of finite size samples in porous media

“…The study presented in this paper is of vital importance in understanding the role of nonlinear adsorption and viscous fingering in various processes where the motion of species results in the formation of nonlinear waves [31,32] or when the motion of species is encountered by nonlinear waves [33]. Our inferences could be helpful in understanding the role of adsorption parameters and viscosity ratios in chromatography applications, CO 2 capture, subsurface transport as well as in oil recovery.…”

Similarity Solution of Spherical Shock Waves -Effect of Viscosity

“…The similarity solutions of converging spherical and cylindrical shock wave problems with different equation of states (EOS) were investigated by several authors [1,6,7,9,12,15,19,22,24]. The existence and effects of the viscous forces for the similarity solutions to shock wave problems were studied by several researchers [10,17,21,28]. Landau and Lifshitz [14] and Zel'dovich and Raizer [27] have studied the entropy production in a viscous medium and developed an analytical model for the shock process based on Hugoniot curves considering the effects of viscosity and heat conduction.…”