Structure of shock waves with emission in a gas flow impinging on a barrier

The parameters of emitting shock waves generated upon high-velocity rarefied-gas flow impingement on a plane barrier are investigated with account for the reflecting capacity of the barrier. In the case of aluminum plasma impingement the unsteady radiation-gasdynamic flows are numerically calculated using the Lax-Wendroff scheme at different values of the radiation reflection coefficient. The radiation transport is accounted for in the gray gas approximation. In the quasi-stationary stage the structure of compressed shock layer on the wall is considered in the radiant heat conduction approximation.     

Mechanism of self-oscillations in a supersonic jet impact onto an obstacle 1. Obstacle with a spike

Results of numerical simulations and experimental investigations of self-oscillations arising in the case of impingement of an overexpanded or underexpanded jet onto an obstacle with a spike are reported. The mechanisms of the emergence and maintaining of self-oscillations for overexpanded and underexpanded jets are elucidated. It is demonstrated that self-oscillations are caused by disturbances in a supersonic jet, which induce mass transfer between the supersonic flow and the region between the shock wave and the obstacle. The feedback is ensured by acoustic waves generated by the radial jet on the obstacle. These waves propagate in the gas surrounding the jet, impinge onto the nozzle exit, and initiate disturbances of the supersonic jet parameters. In the overexpanded jet, these disturbances penetrate into the jet core, where they are amplified in oblique shock waves.     

Gas content factor in the interaction of shock waves of different intensity in a two-phase gas-liquid medium

The transition from regular to Mach interaction is investigated in connection with the interaction of two plane weak or moderate shock waves of different intensity in a two-phase gas-liquid medium over the entire range of gas contents. A nonmonotonic dependence of the transition limit and the flow parameters on the gas content is detected. The investigation extends the results of [1] corresponding to the reflection of a shock wave from a wall. At intermediate gas contents in the case of opposing shock waves, analogous to the normal reflection of a shock wave from a solid wall, the results are in agreement with [2]. In the case of weak shock waves non-linear asymptotic expansions [3] are employed. In the extreme cases of single-phase media the results coincide with the findings of [3, 4]. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 172–174, November–December, 1986.     

Initial stage of the collision of blast waves

The collision of two blast waves is analyzed for the case of variable parameters of the gas behind the wave front and wave reflection at a plane, a cylindrical, and a spherical obstacle. The reflection of a blast wave from a nonmoving obstacle is investigated in detail. The problem of the collision of two shock waves with constant parameters behind the front is solved both in the symmetrical case (reflection from a nonmoving wall) and in the case of waves of different amplitudes by a system of algebraic relations for the compression shocks. The reflection of a strong point-source spherical shock wave from a wall has been treated in [1, 2]. The present article examines the initial stage of wave collision for an arbitrary distribution of the parameters behind the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 41–48, September–October, 1971.The authors are grateful to V. P. Korobeinikov for a discussion of the results and to V. P. Kolgan for furnishing the numerical solutions.     

Spontaneous acoustic emission from strong shocks in solids

Summary  The role of free electrons in the stability of strong shock waves in metals under spontaneous acoustic emission is investigated. For that purpose, a three-term form of the equation of state is employed in order to describe the cold pressure, the thermal atomic pressure and the thermal pressure of free electrons. The equation of state enables the calculation of the sound velocity behind the shock, which in turn is utilized in the Dyakov–Kontorovich criteria for the shock stability. The integral over the Fermi–Dirac distribution function that describes the specific internal energy of free electrons is replaced by a model algebraic function that possesses correct asymptotic limits at low and high temperatures. It is shown that strong shock waves in all metals are prone to instability under spontaneous emission. However, the threshold for that instability is shifted to higher Mach numbers if free electrons are taken into account. It is further shown that the stabilizing effect of free electrons is vastly overestimated if the expressions for degenerate electron gas are employed for temperatures that are larger than the Fermi temperature. Received 22 November 1999; accepted for publication 12 July 2000     

Structure of the heating layer ahead of the front of a strong intensely emitting shock wave

The problem of the structure and brightness of strong shock waves arises in the investigation of such phenomena as the motion of large meteoroids in the atmosphere, optical and electrical discharges, the development of strong explosions, and other similar processes and in the creation of powerful radiation sources based on them. This problem also has a general physics interest. As the propagation velocity of a strong shock wave increases the gas temperature behind its front and the role of emission grow. Part of the radiation emitted by the gas heated and compressed in a shock wave is absorbed ahead of the front, forming the so-called heating layer. The quasisteady structure of a strong intensely emitting shock wave was studied in [1, 2]. In this case a diffusional approximation and the assumption of a gray gas were used to describe the radiation transfer. They introduced the concept of a wave of critical amplitude, when the maximum temperature T_- in the heating layer reaches the temperature T_a determined on the basis of the conservation laws, i.e., from the usual shock adiabat; it is shown that behind a compression shock moving through an already heated gas there is a temperature peak in which the maximum temperature T₊ exceeds T_a. The problem of the quasisteady structure of an emitting shock wave in air of normal density was solved numerically in [3]. The angular distribution of the radiation was approximately taken into account — it was assigned by a simple cosinusoidal law. The spectral effects were taken into account in a multigroup approximation. They introduced 38 spectral intervals, which is insufficient to describe a radiation spectrum with allowance for the numerous lines and absorption bands.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 86–92, September–October, 1978.     

Propagation of nonlinear waves along a viscoelastic bar

Various types of nonlinear waves propagating along a viscoelastic bar are considered. The rheological equation of state has strong physical and geometric nonlinearities, and nonisothermal effects are included. Both weak (isentropic) and shock waves of loading and unloading are investigated. It is shown that, for certain rubber-like materials, stable shock waves of extension can exist along with the shock waves of compression at very large strains. We then consider the strike of a viscoelastic bar of finite length against a rigid obstacle. Numerical solutions to this problem illustrate the influence of stress relaxation on nonlinear wave processes. A model for sticking and bouncing off is formulated and the mass-averaged velocity of the bar at the moment when it bounces off the obstacle is calculated.     

Numerical modeling the dynamics of flow in explosion above a surface

The hydrodynamics of processes occurring in explosion of condensed explosives in air is considered. The physical model, computation technique, and results of simulation of a two-dimensional hydrodynamic flow arising in explosion of cylindrical charges are discussed. In this case, the explosions are considered at some distance above the ground. To close the gas-dynamics equations, the Jones–Wilkins–Lee equation of state is used. The results of calculation allow one to obtain a detailed space–time pattern of the arising flow and to study the origination, propagation, and subsequent attenuation of shock waves. Cylindrical charges of the same mass but with different diameter-to-length ratios are considered. It is shown that the charge shape can render essential influence on dynamics of flow and the parameters of shock waves (in the near and medium fields of explosion).     

Application of background oriented schlieren for quantitative measurements of shock waves from explosions

This paper describes application of a background oriented schlieren technique in order to obtain quantitative measurements of shock waves from explosions by processing high speed digital video recordings. The technique is illustrated by an analysis of two explosions, a high explosive test and a hydrogen gas explosion test. The visualization of the shock front is utilized to calculate the shock Mach number, leading to a predicted shock front pressure. For high explosives the method agreed quite well with a standard curve for side-on shock pressures. In the case of the gas explosion test we can also show that the shock front is non-spherical. It should be possible to develop this technique to investigate external blast waves and external explosions from vented gas explosions in more details. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Lifting of Disperse Particles from a Cavity Behind the Front of an Unsteady Shock Wave with a Triangular Velocity Profile

The gas flow in plane shock waves slipping along an impermeable surface with a rectangular cavity where solid disperse particles are suspended is considered numerically. The motion of the gas and particles (gas suspension) is modeled by equations of mechanics of multiphase media. Some laws of the behavior of the dusty cloud in the cavity are established for the case of wave interaction with the cavity.     

Triple configurations of traveling shock waves in inviscid gas flows

Triple configurations of shock waves in supersonic inviscid flows of a perfect gas are considered. The basic parameters of triple configurations are determined, and the conditions of solution existence are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 3–10, May–June, 2008.     

Regular reflection of a shock wave from a solid wall in a stream of fuel mixture

The two-dimensional stationary problem of regular reflection of a shock wave from a plane solid wall in a fuel gas mixture is examined in the case when the mixture is ignited at the intersection of the incident wave with the wall and a flame front is formed behind the reflected shock wave. The shock waves and the flame front are considered plane surfaces of discontinuity. The fuel mixture and the reaction products are considered perfect, inviscid, and non-heat-conducting gases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 161–163, July–August, 1978.     

Spectral Stability of Ideal-Gas Shock Layers

Extending recent results in the isentropic case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the spectral stability of shock-wave solutions of the compressible Navier–Stokes equations with ideal gas equation of state. Our main results are that, in appropriately rescaled coordinates, the Evans function associated with the linearized operator about the wave (i) converges in the large-amplitude limit to the Evans function for a limiting shock profile of the same equations, for which internal energy vanishes at one end state; and (ii) has no unstable (positive real part) zeros outside a uniform ball |λ| ≦ Λ. Thus, the rescaled eigenvalue ODE for the set of all shock waves, augmented with the (nonphysical) limiting case, form a compact family of boundary-value problems that can be conveniently investigated numerically. An extensive numerical Evans-function study yields one-dimensional spectral stability, independent of amplitude, for gas constant γ in [1.2, 3] and ratio ν/μ of heat conduction to viscosity coefficient within [0.2, 5] (γ ≈ 1.4, ν/μ ≈ 1.47 for air). Other values may be treated similarly but were not considered. The method of analysis extends also to the multi-dimensional case, a direction that we shall pursue in a future work.     

Special and extreme triple shock-wave configurations

Triple shock-wave configurations in steady supersonic flows of an inviscid perfect gas are considered. Triple configurations with special intensities of shock waves and extreme ratios of various flow parameters behind these configurations are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 39–53, July–August, 2006.     

Evolution of shock waves in polydisperse gas suspensions with a nonuniform particle concentration distribution

The results of a numerical investigation of the laws of shock wave propagation in polydisperse (two-fraction) gas suspensions with a non-uniform initial particle concentration distribution are presented. Examples of shock wave propagation in extended layers of a gas suspension with linearly increasing, linearly decreasing and sinusoidal laws of variation of the particle concentration are considered. It is shown that when shock waves pass through layers of a gas suspension with increasing and decreasing laws of variation of the particle concentration, respectively, amplification and attenuation of the waves are observed; when shock waves travel through gas suspensions with a periodic law of variation of the particle concentration the pressure distribution behind the wave fronts is nonmonotonic. The solutions corresponding to polydisperse and monodisperse gas suspensions with an effective particle size are examined. The nonequilibrium and thermodynamic-equilibrium solutions are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 183–190, September–October, 1991.     

Analogy between soap film and gas dynamics. II. Experiments on one-dimensional motion of shock waves in soap films

This paper presents an experimental investigation of one-dimensional moving shock waves in vertical soap films. The shock waves were generated by bursting the films with a perforating spark. Images of propagating shock waves and small disturbances were recorded using a fast line scan CCD camera. An aureole and a shock wave preceding the rim of the expanding hole were clearly observed. These images are similar to the x-t diagrams in gas dynamics and give the velocities of shock and sound waves. The moving shock waves cause jumps in thickness. The variations of the induced Mach number, M₂ and the ratio of film thickness across the shock wave, δ ₂/δ ₁, are plotted versus the shock Mach number, M _s. Both results suggest that soap films are analogous to compressible gases with a specific heat ratio of γ≅1.0. Published online: 15 October 2002     

Establishment of circumfluence (steady-state flow) when a shock wave strikes a cylinder or a sphere

The problem of the diffraction of a shock wave at a stationary sphere or cylinder is considered. The finite-difference method proposed by S. K. Godunov [1, 2] is employed Numerical solutions are obtained for the stage of the diffraction of the shock wave and for the subsequent steady state of flow around the object (circumfluence). Cases of sub-, trans-, and supersonic flow behind the shock wave are considered. When strong shock waves undergo diffraction, zones of reverse flow appear in the neighborhood of the tail part of the obstacle.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 97–103, September–October, 1972.     

Wave propagation in a non-ideal dusty gas

In this paper we have studied the behavior of wave motion as propagating wavelets and their culmination into shock waves in a non-ideal gas with dust particles. In the absence of non-ideal effect the gas satisfies an equation of state of Mie–Gruneisen type. An expansion wave resulting from the action of receding piston is considered and the solutions to this problem showing effects of dust particles and non-idealness are obtained. The propagation of weak waves is considered and the flow variables in the region bounded by the piston and the characteristic wave front are found out. The expansive action of a receding piston undergoing an abrupt change in velocity is discussed. Cases of central expansion fan and shock fronts are studied and the solutions up to first order in the physical plane are obtained. The effects of non-idealness and dust particles are discussed in each case.     

Stability of fast parallel MHD shock waves in polytropic gas

The stability of plane shock waves in Magnetohydrodynamics for an ideal medium is studied. Stability results are obtained for the special case of fast parallel shock waves in a polytropic gas. Linear stability is proved for a polytropic gas with arbitrary γ. The domain of structural (nonlinear) stability, where the uniform Lopatinsky condition is fulfilled for the stability problem, is found.