Interaction Of Weak Shock Waves Research Articles

Numerical simulation of the interaction between weak shock waves and supersonic boundary layer on a flat plate with the blunt leading edge

The interaction of weak shock waves in form of an N-wave with the supersonic laminar boundary layer on a flat plate with blunt leading edge at the free-stream Mach number M = 2.5 is numerically studied. The numerical results are compared with known experimental data. The combined influence of the N-wave and the leading edge bluntness on the laminar-turbulent transition process is discussed.

Numerical Simulation of the Interaction between Weak Shock Waves and Supersonic Boundary Layer on a Flat Plate with the Blunt Leading Edge

The interaction of weak shock waves in form of an N-wave with the supersonic laminar boundary layer on a flat plate with blunt leading edge at the free-stream Mach number M = 2.5 is numerically studied. The numerical results are compared with known experimental data. The combined influence of the N-wave and the leading edge bluntness on the laminar-turbulent transition process is discussed.

Interaction of weak shock waves with highly porous materials

Interaction of weak shock waves with highly porous materials

Interaction of weak shock waves with perforated metal plates

Interaction of weak shock waves with perforated metal plates

Interaction of weak shock waves with rectangular meshes in plate

Interaction of weak shock waves with rectangular meshes in plate

Towards front-tracking based on conservation in two space dimensions III, tracking interfaces

This is the third paper in the series of our conservative front-tracking method. In this paper, we describe how our method tracks fluid interfaces in multi-fluid flows. Two important ingredients in our conservative front-tracking method in tracking fluid interfaces are: (1) the velocities and pressures of the left and right cell-averages in a discontinuity cell are respectively maintained to be equal to each other, and in doing so the physics that the normal velocity and pressure are continuous cross the interface is simulated but that the tangential velocity may be discontinuous is ignored, and (2) a so-called numerical surface dissipation is designed on the tracked interface to eliminate possible numerical instability there, and we believe that this numerical surface dissipation is a good substitute for the missing physical dissipation acting on the interface. We then present numerical simulation of Haas–Sturtevant’s two shock–bubble interaction experiments [J.F. Haas, B. Sturtevant, Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, J. Fluid Mech. 181 (1987) 41–76] using this method. Our numerical results are in good agreement with the experimental and other numerical results in the early times of the flow. Moreover, our numerical results are also in good agreement with the experimental results in the later times of the flow and give clear pictures of the bubble deformation then, which show that the right boundaries of the bubble behave just as Rychtmyer–Meshkov instabilities with the shock coming from either heavy or light gases.

Shock wave attenuation by grids and orifice plates

The interaction of weak shock waves with porous barriers of different geometries and porosities is examined. Installing a barrier inside the shock tube test section will cause the development of the following wave pattern upon a head-on collision between the incident shock wave and the barrier: a reflected shock from the barrier and a transmitted shock propagating towards the shock tube end wall. Once the transmitted shock wave reaches the end wall it is reflected back towards the barrier. This is the beginning of multiple reflections between the barrier and the end wall. This full cycle of shock reflections/interactions resulting from the incident shock wave collision with the barrier can be studied in a single shock tube test. A one-dimensional (1D), inviscid flow model was proposed for simulating the flow resulting from the initial collision of the incident shock wave with the barrier. Fairly good agreement is found between experimental findings and simulations based on a 1D flow model. Based on obtained numerical and experimental findings an optimal design procedure for shock wave attenuator is suggested. The suggested attenuator may ensure the safety of the shelter’s ventilation systems.

A transonic small-disturbance model for the propagation of weak shock waves in heterogeneous gases

The interaction of weak shock waves with small heterogeneities in gaseous media is studied. It is first shown that various linear theories proposed for this problem lead to pathological breakdowns or singularities in the solution near the wavefront and necessarily fail to describe this interaction. Then, a nonlinear small-disturbance model is developed. The nonlinear theory is uniformly valid and accounts for the competition between the near-sonic speed of the wavefront and the small variations of vorticity and sound speed in the heterogeneous media. This model is an extension of the transonic small-disturbance problem, with additional terms accounting for slight variations in the media. The model is used to analyse the propagation of the sonic-boom shock wave through the turbulent atmospheric boundary layer. It is found that, in this instance, the nonlinear model accounts for the observed behaviour. Various deterministic examples of interaction phenomena demonstrate good agreement with available experimental data and explain the main observed phenomena in Crow (1969).

Interaction of weak shock waves with a layer of a powdered medium

Results of analytical and numerical studies of the interaction of linear and weakly nonlinear air shock waves with an infinite layer of a powdered medium and with a finite-thickness layer are presented. Approximate analytical expressions for phase-pressure distributions in the powdered medium are obtained. It is found that the gas pressure at the “gas-powder” interface is continuous for linear waves and experiences a sudden change for nonlinear waves. The dependences of phase pressures on a shielded solid wall obtained by solving a general nonlinear system of equations of motion of a powdered medium and an approximate analytical solution of linear equations are compared.

Interaction of Weak Shock Waves with Current Sheets in an Active Region to Produce Nanoflares and Chains of Type I Radio Bursts

Interaction of weak shock waves with a current sheet is investigated by a two-dimensional numerical magnetohydrodynamic model. In accordance with solar coronal conditions, a ratio of thermal to magnetic pressures of 0.1 and a shock Alfven Mach number slightly above 1 are considered. It is found that even weak shock waves trigger magnetic field reconnection in current sheets. Based on this result, it is suggested that drifting chains of type I radio bursts are radio manifestations of the interactions of weakly super-Alfvenic shock waves with pre-existing current sheets distributed in an active region. This model of type I noise storms is then discussed in connection with the concept of nanoflares (localized reconnections) and the heating of the solar corona.

Mach reflection and interaction of weak shock waves under the von Neumann paradox conditions

The problem of weak Mach reflection, known as the von Neumann paradox, and the more general case of Mach interaction of relatively weak shock waves are studied on the basis of the short-wave asymptotics.

Numerical simulation of the propagation of shock waves in compressible open-cell porous foams

A numerical model for the simulation of the interaction of weak shock waves with open-cell compressible porous foams is developed. It is assumed that the foam is infinitely weak and that its volume fraction, which was 0.05 in the cases studied herein, is relevant only when the interaction between the gaseous and the solid phases is considered. The gas is assumed to be inviscid and thermally nonconductive, except for the viscous drag interaction and the heat transfer between the two phases. It is also assumed that the heat transfer between the two phases is extremely efficient, i.e. that the heat transfer coefficient is infinitely large. The range of incident shock wave Mach numbers investigated herein is between 1.08 and 1.40, and the range of foam densities is between 14.8 and 57.4 kg/m 3. The numerical results are in very good agreement with experimentally obtained pressure histories and foam particle paths when the incident shock wave Mach numbers are between 1.25 and 1.40 (weak shocks). The agreement between experimentally and numerically obtained pressure histories is poor when the incident shock wave Mach numbers are between 1.08 and 1.18 (very weak shocks). The results of the study indicate that when weak shocks interact with open-cell compressible foam, the transfer of momentum between the gaseous and the solid phases is of paramount importance. On the other hand, if the shocks are very weak, then the elasticity of the foam is an important parameter as well. It is therefore suggested that, while yielding very good results for weak shocks, the assumption of infinitely weak foam is inadequate for very weak shocks.

Cavity collapse in a liquid with solid particles

An experimental study of the interaction of weak shock waves in a liquid with bubbles and solid particles has been conducted. Cavities were punched, and solid particles were cast, into a thin sheet of gelatine clamped between two transparent blocks. A shock of pressure 0.3 GPa was introduced by impacting the gelatine layer with a flyer plate. The subsequent collapse of the cavities was photographed using high-speed framing cameras, and waves in the gelatine were visualized using schlieren optics. Assorted cavity/particle geometries were studied. In the first, cavity and particle were aligned on an axis parallel to the incident shock front. The jet crossing the cavity was found to deviate from the perpendicular to the shock front. This deviation was towards the solid particle when separations were small and away from the particle when separations were increased. When a cavity was placed upstream of a solid particle the collapse time was reduced. Conversely, when a cavity was placed downstream of a solid particle, collapse time was increased and the closure was more symmetrical. These observations were explained in terms of wave reflections. Collapses where the cavity/particle axis was inclined to the incident shock showed features of each of the geometries described above.

The reflected pressure field in the interaction of weak shock waves with a compressible foam

This paper deals with the waves that are reflected from slabs of porous compressible foam attached to a rigid wall when impacted by a weak shock wave. The interest is in establishing possible attenuation of the pressure field after a shock or blast wave has struck the surface. Foam densities from 14 to 38 kg/m3 were tested over a range of shock wave Mach numbers less than 1.4. It is shown that the initial reflected shock wave strength is accurately predicted by the pseudo-gas model of Gelfand et al. (1983), with a pressure ratio of approximately 80% of the value for reflection off a rigid wall. Evidence is presented of gas entering the foam during the early stages of the process. A second wave emerges from the foam at a later stage and is separated from the first by a region of constant velocity and pressure. This second wave is not a shock wave but a compression front of significant thickness, which emerges from the foam earlier than predicted by the pseudo-gas model. Analysis of the origin of this wave points to much more complex flows within the foam than previously assumed, particularly in an apparent decrease in average wave front speed as the foam is compressed. It is shown that the pressure ratio across both these waves taken together is slightly higher than that for reflection off a rigid wall. In some cases this compression wave train is followed by a weak expansion wave.

An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves

The signal speed, namely the local sound speed plus the flow velocity, behind the reflected shocks produced by the interaction of weak shock waves (M i < 1.4) with rigid inclined surfaces has been measured for several shock strengths close to the point of transition from regular to Mach reflection. The signal speed was measured using piezo-electric transducers, and with a multiple schlieren system to photograph acoustic signals created by a spark discharge behind a small aperture in the reflecting surfaces. Both methods yielded results with equal values within experimental error. The theoretical signal speeds behind regularly reflected shocks were calculated using a non-stationary model, and these agreed with the measured results at large angles of incidence. As the angle of incidence was reduced, for the same incident shock Mach number, so as to approach the point of transition from regular to Mach reflection, the measured values of the signal speed deviated significantly from the theoretical predictions. It was found, within experimental uncertainty, that transition from regular to Mach reflection occurred at the experimentally observed sonic point, namely, when the signal speed was equal to the speed of the reflection point along the reflecting surface. This sonic condition did not coincide with the theoretical value.

Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities

The interaction of a plane weak shock wave with a single discrete gaseous inhomogeneity is studied as a model of the mechanisms by which finite-amplitude waves in random media generate turbulence and intensify mixing. The experiments are treated as an example of the shock-induced Rayleigh-Taylor instability. or Richtmyer-Meshkov instability, with large initial distortions of the gas interfaces. The inhomogeneities are made by filling large soap bubbles and cylindrical refraction cells (5 cm diameter) whose walls are thin plastic membranes with gases both lighter and heavier than the ambient air in a square (8.9 cm side shock-tube text section. The wavefront geometry and the deformation of the gas volume are visualized by shadowgraph photography. Wave configurations predicted by geometrical acoustics, including the effects of refraction, reflection and diffraction, are compared to the observations. Departures from the predictions of acoustic theory are discussed in terms of gasdynamic nonlinearity. The pressure field on the axis of symmetry downstream of the inhomogeneity is measured by piezoelectric pressure transducers. In the case of a cylindrical or spherical volume filled with heavy low-sound-speed gas the wave which passes through the interior focuses just behind the cylinder. On the other hand, the wave which passes through the light high-sound-speed volume strongly diverges. Visualization of the wavefronts reflected from and diffracted around the inhomogeneities exhibit many features known in optical and acoustic scattering. Rayleigh-Taylor instability induced by shock acceleration deforms the initially circular cross-section of the volume. In the case of the high-sound-speed sphere, a strong vortex ring forms and separates from the main volume of gas. Measurements of the wave and gas-interface velocities are compared to values calculated for one-dimensional interactions and for a simple model of shock-induced Rayleigh-Taylor instability. The circulation and Reynolds number of the vortical structures are calculated from the measured velocities by modeling a piston vortex generator. The results of the flow visualization are also compared with contemporary numerical simulations.

Effect of a spherical acoustic pressure wave on a fluid-filled elastic cylindrical shell

problems of interaction of weak shock waves with cylindrical shells which permit one to rigorously take into account the effect of the hydrodynamic forces. Both approaches are based on the application to the sought functions of the Fourier series expansion in the angle variable, the integral Laplace transform of the time and the Fourier transform of the lengthwise coordinate. The first approach [3] consists in obtaining for each vibrational mode an integral Volterra equation to be solved numerically. In the second approach [6], the inversion of the Laplace and Fourier transforms is done numerically using the Gauss-Laguerre quadratures and ultraspherical polynomials. Both methods require the use of a computer and are quite time consuming. In this article the calculation of the Fourier series coefficients is performed by means of numerical integration on the explicit finite-differenc e scheme of the system of differential equations of motion of the shell and the acoustic media. High precision of calculation of discontinuous and fast varying solutions is achieved thanks to the application of the method of minimization of numerical dispersion [4]. The advantage of the given method consists in the simplicity of the numerical algorithm and the possibility of finding the solution for various harmonics with the same accuracy (in the regions of slow variation of perturbations as well as in the region of the front breakups). The method can be successfully applied to solution of more complex problems of nonstationary hydroelasticity,

Interaction of Weak Shock Waves with Screens and Honeycombs

The interaction of weak shock waves with screens and honeycombs is examined to facilitate the design of a pulsed flowing gas laser system operating at a high repetition rate. Interactions with zero and finite base flow (M<0.3) are studied using a shock tube capable of generating weak shock waves. By reflecting the incident wave from the driven section end plate, interactions with and without base flow can be studied in a single experiment. A quasi-steady flow theory is developed to model shock interaction with screens, while a quasi-one-dimensional flow code is used for the interaction between shock waves and honeycombs. Comparisons between analytical and experimental results are made.

Deformation of a laminated spherical shell under the action of a weak shock wave

Problems of the nonsteady interaction of acoustic waves with structural elements have been most completely investigated for cases in which rigid bodies or thinwalled isotropic shells are the obstacle. In addition to appearing in periodicals, these results have been generalized in monographs [7, 14, 15]. Reference [i] is devoted to the determination of the nonsteady loads in connection with the action of internal wave sources. The interaction of weak shock waves with shell systems has been discussed in [2, 6]. Solutions for a cylindrical shell reinforced with periodically positioned ribs are obtained in [ii, 16] with the use of simplifying assumptions valid for initial instants of time. Along with this, the widespread practical application of laminated articles produces interest in wave problems of nonsteady interaction with the medium of plates and shells with their lamination taken into account. Here we should note [5, 8, 9, i0, 12, 17], in which nonsteady processes for three-layer objects are discussed with the help of approximate approaches. An exact solution is obtained in this paper, and numerical results of the problem of the interaction of a plane weak shock wave and a laminated spherical shell are given.

Interaction of weak shock waves with random media

Recent studies of the scattering of weak shock waves by continuous and discrete scatterers in random media, and of the flow generated in the scattering medium by shock propagation are described. Consideration of the coupling between shock propagation and vorticity and/or entropy fluctuations in a fluid is particularly difficult if the wave is of finite amplitude, for basic nonlinearities of fluid mechanics become important both in the wave propagation and in the turbulent motion. In one experiment, wave propagation through a cubical volume of incompletely and randomly mixed gases at the end of a large shock tube has been studied. In a second, interaction with a random array of discrete scatterers (small helium-filled soap bubbles) is studied in a smaller facility. Both of these flows are visualized by schlieren and shadowgraph photography. The scattered pressure field behind the initial disturbance is measured. Methods for measuring the characteristics of the “turbulence” before and after passage of the wave using laser scattering in the random medium have been developed; the laser speckle pattern at the focal plane of the schlieren system has been recorded photographically and has been analyzed with a computer-controlled photodensitometer to yield information about the scale and intensity of the inhomogeneities in the scattering medium. [Work supported by NSF.]