Propagation Of Weak Shock Waves Research Articles

A computational study of a laminar methane–air flame assisted by nanosecond repetitively pulsed discharges

Nanosecond repetitively pulsed (NRP) discharges have been considered a promising technique for enhancing combustion efficiency and control. For successful implementation, it is necessary to understand the complex plasma–combustion interactions involving chemical, thermal, and hydrodynamic pathways. This paper aims to investigate the mechanisms enhancing a laminar methane–air flame assisted by NRP discharges by high fidelity simulations of the jet-wall burner employed in a previous experimental study. A phenomenological plasma model is used to represent the plasma energy deposition in two channels: (1) the ultrafast heating and dissociation of O2 resulting from the relaxation of electronically excited N2 , and (2) slow gas heating stemming from the relaxation of N2 vibrational states. The flame displacement, key radical distribution and flame response under plasma actuation are compared with experimental results in good agreement. The computational model allows a systematic investigation of the dominant physical mechanism by isolating different pathways. It is found that the kinetic effect from atomic O production dominates the flame dynamics, while the thermal effect plays a minor role. Hydrodynamic perturbations arising from weak shock wave propagation appear to be sensitive to burner geometry and is found to be less significant in the case under study.

Modeling of dynamic phenomena in aqueous foams (review)

Analytical review of investigations aimed at studying the aqueous foam behavior under the shock-wave impact is given. The main approaches and theoretical approximations used in the development of aqueous foams models are analyzed. The two-phase gas-drop model of aqueous foam is considered, based on the laws of conservation of mass, momentum, and energy in accordance with one-pressure, two-velocity, two-temperature approximations. The model describes foam dynamics under a high - intensity impact, which destroys the foam structure into microdroplets, and takes into account interfacial heat transfer, interfacial drag and virtual mass forces and the phenomenon of foam syneresis (deposition). The numerical implementation of the model was carried out using new solvers in the OpenFOAM software. The analysis of the numerical solution of the spherical explosion in aqueous foam is given for the conditions of the literature experimental data. The syneresis influence on the intensity and velocity of shock wave propagation is shown. The two-phase model of aqueous foam is considered, which takes into account its elastic- viscous-plastic properties for conditions of weak impact that does not destroy foam structure. The model takes into account the elastic properties of aqueous foam at small deformations and describes it as a non-Newtonian fluid when the foam changes its state from the elastic to viscoplastic. The weak shock wave propagation dynamics in the layer of aqueous foam with the formation of a two-wave structure, consisting of the main wave and the elastic precursor ahead of it, is analyzed. The process of local aqueous foam compaction zone formation, followed by a gaseous region, behind the shock wave front is shown. The reliability of the obtained results of numerical studies is confirmed by their agreement with the literature experimental data.

Analytical Study of Weak Shock Waves in Gas with dust particles

In the present paper, the exact solution of quasilinear hyperbolic system of equations governing the propagation of weak shock waves in a one-dimensional dusty adiabatic gas flow with generalized geometries is derived. Here, the density behind the shock front is assumed to vary according to a power law of the distance. An analytical expression for the total energy carried by weak shock wave in dusty gas is also derived.

The propagation of weak shock waves in non-ideal gas flow with radiation

In the present paper, the evolutionary behavior of weak shock waves propagating in an unsteady one-dimensional flow in non-ideal radiating gas is analyzed. The effect of thermal radiation under optically thin limit is included in the energy equation of the governing system. The method of asymptotic analysis is used to derive the transport equation describing the propagation of waves under the high-frequency conditions which is also used to determine the time of first wave-breaking conditions. The equation governing the propagation of acceleration waves is also obtained. Furthermore, the movement of disturbance in the shape of saw-tooth profile is discussed. The effect of parameter of non-idealness under the influence of radiative heat transfer, on the decay of sawtooth profile is analyzed.

Weak-shock wave propagation in polymer-based particulate composites

Shock waves are common in polymer-based particulate composites that are subjected to intermediate to high-velocity impact loading. However, quantitative information on the spatial variation of stress, particle velocities, and energy dissipation during the formation and propagation of weak-shock waves is limited. In this paper, a systematic experimental study is conducted to understand the characteristics of weak-shocks in polymer-bonded particulate composites. Specimens made of polymer-bonded sugar are subjected to a projectile impact loading, at varying velocities, using a modified Hopkinson pressure bar apparatus. Full-field displacement and strains of the deformed samples are obtained with the help of an ultrahigh-speed imaging and digital image correlation technique. Using the full-field displacement data, the shock wave velocity, shock front thickness, and the full-field stress fields are calculated. From the spatial stress field and the strain rate data, the spatial energy dissipation profile is also estimated. The effect of impact velocity on the spatial stress profile, shock wave velocity, and energy dissipation are discussed.

Evolution of weak shock wave in two-dimensional steady supersonic flow in dusty gas

The present paper concerns with the propagation of weak shock waves in a dusty gas governed by the quasilinear hyperbolic partial differential equations. Using the method of wavefront analysis the transport equations governing the evolution of weak discontinuities are derived. Transport equations are used to determine the shock formation distance and conditions which ensure that there will not evolve any shock. Also the influence of dust particles, ratio of specific heats and upstream flow Mach number on the shock formation distance is analyzed.

Exact Solution of the Weak Shock Wave in Non-ideal Gas

In the present paper the exact solution of quasilinear hyperbolic system of equations governing the propagation of weak shock waves in a one dimensional non-ideal adiabatic gas flow with generalized geometries is derived. Here the density ahead of the shock front is assumed to vary according to a power law of the distance. The effect of van der Waals parameter on the radius of weak shock wave is analyzed. An analytical expression for the total energy carried by weak shock wave in non-ideal gas is also derived.

On the propagation of weak shock waves in compressible thermohyperelastic solids

In the present paper, a study of the weak shock waves propagation into thermohyperelastic solids is presented using the theory of singular surfaces. The equation of motion of the weak shock waves, which is obtained by the later theory, reduces to an eigenvalue problem. The propagation speeds of weak shock waves are obtained from the eigenvalues of the isentropic acoustic tensor for a particular state of deformation. The constitutive equation of a near-incompressible thermohyperelastic solid is considered. This constitutive model derives from a Helmholtz free energy which does not seem to be used in published scientific literature. The shock waves speeds are expressed in the framework of standard loadings: simple uniaxial tension, biaxial stretching, and uniform dilatation. The material seems to be always stable, and no singularity of the isentropic acoustic tensor has been found which corresponds to a critical state.

Growth and decay of weak shock waves in magnetogasdynamics

The purpose of the present study is to investigate the problem of the propagation of weak shock waves in an inviscid, electrically conducting fluid under the influence of a magnetic field. The analysis assumes the following two cases: (1) a planar flow with a uniform transverse magnetic field and (2) cylindrically symmetric flow with a uniform axial or varying azimuthal magnetic field. A system of two coupled nonlinear transport equations, governing the strength of a shock wave and the first-order discontinuity induced behind it, are derived that admit a solution that agrees with the classical decay laws for a weak shock. An analytic expression for the determination of the shock formation distance is obtained. How the magnetic field strength, whether axial or azimuthal, influences the shock formation is also assessed.

One-way approximation for the simulation of weak shock wave propagation in atmospheric flows.

A numerical scheme is developed to simulate the propagation of weak acoustic shock waves in the atmosphere with no absorption. It generalizes the method previously developed for a heterogeneous medium [Dagrau, Rénier, Marchiano, and Coulouvrat, J. Acoust. Soc. Am. 130, 20-32 (2011)] to the case of a moving medium. It is based on an approximate scalar wave equation for potential, rewritten in a moving time frame, and separated into three parts: (i) the linear wave equation in a homogeneous and quiescent medium, (ii) the effects of atmospheric winds and of density and speed of sound heterogeneities, and (iii) nonlinearities. Each effect is then solved separately by an adapted method: angular spectrum for the wave equation, finite differences for the flow and heterogeneity corrections, and analytical method in time domain for nonlinearities. To keep a one-way formulation, only forward propagating waves are kept in the angular spectrum part, while a wide-angle parabolic approximation is performed on the correction terms. The numerical process is validated in the case of guided modal propagation with a shear flow. It is then applied to the case of blast wave propagation within a boundary layer flow over a flat and rigid ground.

Shielding of elastic nonstationary waves by interfaces

The ray method is used to solve the problem of the propagation of discontinuous (weak shock) waves in inhomogeneous elastic media. A procedure for drawing the fronts of reflected and refracted waves at interfaces and calculating their intensities is proposed. The effect of shielding discontinuous waves by one or two interfaces is studied. The cases of slipping and non-slipping contact are examined

Propagation of weak shock waves in a non-ideal gas

AbstractThis paper investigates the problem of propagation of planar and non-planar weak shock waves in a non-ideal medium. The mathematical formulation developed in this work leads to a closed system of coupled transport equations which efficiently describes the strength of a shock wave and the first order discontinuities induced behind it. The influence of the parameter of non-idealness and the non planar configuration of the wavefront on the nonlinear distortion, attenuation and shock formation of pulses, are discussed in detail. An analytical expression for the shock formation distance is obtained and a direct comparison between the ideal versus the non ideal gas flow is established. Also, the usual asymptotic decay laws for weak shock are recovered.

Features of wave propagation in the sand of different saturation

There are the results of experimental and theoretical studies on the propagation of weak shock waves in the wet sand at different water saturation. There are mathematical model and numerical analysis of propagation of pressure pulses in porous media, taking into account capillary forces. Non-monotonic dependence of the amplitude of the wave resulting in a wet porous medium vs. the degree of water saturation is installed. The evolution of the fast, slow and filtration waves depends on the saturation of the system with water is analyzed. The influence of capillary forces on the propagation of longitudinal waves is evaluated.

Rayleigh mechanism of local elevation of energy in propagation of a shock wave in an active medium

A mechanism of action of a shock wave on an active medium, which leads to an additional energy release source, is considered. This source moves together with the shock wave front and depends on the magnitude and direction of the electric field applied to the plasma and on the current density in the plasma. The study is a continuation of an earlier publication devoted to the propagation of weak shock waves. Here, we consider shock waves of an arbitrary intensity with an arbitrary mechanism of formation of an additional energy contribution due to variation of the parameters of the medium as a result of passage of the shock wave. Special cases of this effect are the propagation of a shock wave in a plasma and detonation burning.

Study and Analysis of Shock Wave Propagation in Excavation Laneway during Methane Explosion

Coal mine can be damaged by extremely strong methane explosion, and the importance of suppressing anti-methane explosion in coal mine production safety is self-evident. The basic assumptions are used to analyze the shock wave propagation and the strength characteristics during methane explosion. The expressions among parameters in wave-front are derived during strong and weak shock wave propagation. Meanwhile, the cylinder shock wave overpressure parameter while propagating and attenuating with distance is deduced. In a certain distance away from the source location of explosion, the overpressure are basically in inverse proportion to the square root of the distance and laneway section, and is proportional to the square root of the amount of pure methane involved in the explosion. Through comparison and analysis of theoretical calculations and numerical simulation data, the data are almost identical.

Propagation of weak shock waves in non-uniform, radiative magnetogasdynamics

A problem of propagation of weak planer shock wave in radiative magnetogasdynamics is theoretically investigated. The gas is taken to be sufficiently hot for the effects of thermal radiation to be significant, which are of course treated by the optically thin approximation to the radiative transfer equation. The density of the medium ahead of the shock wave is assumed to be exponentially varying. A systematic perturbation scheme is used to obtain the analytical solution of the flow field. Also, an approximate solution near the front shock is determined. The effect of radiation and magnetic field strength on the shock wave propagation is examined.

Shock waves evolution in a porous media with different internal structure

There are the results of experimental and theoretical researches of processes of reflection and propagation of weak shock waves in gas-saturated porous structures. A mathematical model describing the evolution of shock waves in granular medium is offered. It is studied the influence on the properties of the transmitted and reflected waves of such parameters of the porous medium as a characteristic particle size of the skeleton and its granulometric composition. The interaction of shock waves with layered inhomogeneous media is considered. The obtained results are of interest for the development of methods of explosion protection and acoustic sensing.

Weak shock waves and shear bands in compressible, inextensible thermoelastic solids

A study of weak shock waves propagating into a solid, which is compressible but temperature-dependent extensible in a specified direction is presented. The inextensible solid is also considered. The constitutive equations of constrained thermoelastic material are written as the summation of constrained and unconstrained counterparts of the relevant quantities. The equation of motion of weak shock waves, which is recovered by the theory of singular surfaces, reduces to an eigenvalue problem. The solution of this eigenvalue problem yields the speeds of propagation of weak shock waves. In the case of an undeformed solid, the speeds of these waves are explicitly expressed. Additionally, a discussion on the ductility limits of constrained thermoelastic material subjected to the uniaxial and biaxial extensions is presented.

Weak shock waves and shear bands in thermoelastic solids

The linear weak shock wave (acoustic wave) propagation and the existence of shear bands are examined in finitely deformed thermoelastic solids within the framework of the theory of singular surfaces. The jumps of certain field variables across the shock wave front are obtained by using Taylor series expansions of them. The propagation condition of shock waves in a thermoelastic solid is obtained by using the strain–energy function corresponding to Duhamel–Neumann expression. The propagation speeds of weak shock waves are determined for a particular state of deformation, that is, general dilation. The formation of shear bands and the magnitudes of critical stretches are obtained for the deformation states of uniaxial, biaxial extension and for uniform dilation.

A study of the weak shock wave propagating through an engine exhaust silencer system

The present study addresses a computational work of the weak shock wave propagating inside a silencer system of automobile exhaust pipe. The second order total variation diminishing (TVD) scheme is employed to solve the two-dimensional, compressible, unsteady, Euler equations. Eight different models of the silencer systems are explored to investigate the effects of the silencer configuration that has on the weak shock wave propagation phenomena. The incident plane shock wave is assumed at the inlet of the silencer and its Mach number is changed between 1.01 and 1.30. The present computational analysis clearly reveals the detailed shock wave reflections/diffractions and vortical flows inside the silencer models. These results are detailed by the pressure time histories at several locations inside the silencer model. Of the eight different silencers applied, the silencer model with a series of the baffle plates inside the expansion chamber reduces the first peak pressure at the exit of the exhaust pipe by about 27%. The present computational results predict the experimental results with a quite good accuracy.