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.     

Evolution equation for unsteady shock waves of moderate intensity in a viscous heat-conducting gas

A simple model equation that takes into account the nonisentropicity of the flow is. obtained from the equations of a viscous heat-conducting gas. It differs from the Burgers equation in possessing an additional term with a clear physical significance. This equation is suitable for one-dimensional traveling waves on the Mach number interval 1M1.3. The equation obtained gives the asymptotic laws of damping of weak shock waves correct to small terms of the leading and next order for plane [2], cylindrical [3] and spherical [4] symmetry.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 187–190, September–October, 1989.     

粘性金属中的正激波稳定性问题

G.H.Miller等把高压金属中的粘性激波作为强间断面处理,解析推论出:在大粘性系数条件下小扰动激波是不稳定的,物质粘性是导致失稳的因素。本文中针对平面正激波,认为高压金属中的粘性激波的物理量是连续变化的,利用线性稳定性理论,用数值解推论出:在有粘性条件下小扰动激波都是稳定的,物质粘性是致稳的因素。指出G.H.Miller等获得错误结论的原因在于:从无粘流动解推出的小扰动边界条件导致粘性激波小扰动增长。给出实验确定的小扰动速度梯度的边界条件,这样既可以把粘性正激波作为强间断面处理,也能够保证粘性正激波的稳定性。     

One dimensional steepening of waves in non-ideal relaxing gas

In this paper, we studied the behavior of different modes of wave propagation and breaking of wave front by employing the theory of singular surfaces in a plane and radially symmetric flow of a non-ideal relaxing gas. The one dimensional steepening of waves is considered and the transport equation for the jump discontinuity of velocity gradient is obtained. The effects of relaxation and van der Waals excluded volume of the medium on the jump discontinuity of velocity gradient are analyzed.     

On the structure of shock waves in liquid-bubble mixtures

Asbtract The structure of shock waves in liquids containing gas bubbles is investigated theoretically. The mechanisms taken into account are the steepening of compression waves in the mixture by convection and the effects due to the motion of the bubbles with respect to the surrounding fluid. This relative motion, radial and translational, gives rise to dissipation and to dispersion caused by the inertia of the radial flow associated with an expanding or compressed bubble. For not too thick shocks the dissipation by radial motion around the bubbles dominates over the dissipation by relative translational motion, in mixtures with low gas content. The overall thickness of the shock appears to be determined by the dispersion effect. Dissipation, however, is necessary to permit a steady shock wave. It is shown that, analogous to undular bores, a stationary wave train may exist behind the shock wave.     

The propagation of shock waves in viscous media

The question of the thickness of shock waves in a viscous gas was treated in papers [1, 2]. The present paper derives general equations for solving problems concerning the flow of a medium inside a shock wave layer, and the change of this layer in viscous media. By way of an example we consider a problem of this type for a Kelvin medium.     

Gas-dynamic shock waves in a relaxing gas

St. Petersburg State University, St. Petersburg 199004. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 3, pp. 92–97, May–June, 1995.     

Similarity solutions for the flow behind an exponential shock in a non-ideal gas

Similarity solutions for the flow of a non-ideal gas behind a strong exponential shock driven out by a piston (cylindrical or spherical) moving with time according to an exponential law are obtained. Similarity solutions exist only when the surrounding medium is of constant density. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic. It is found that the assumption of zero temperature gradient brings a profound change in the density distribution as compare to that of the adiabatic case. Effects of the non-idealness of the gas on the flow-field between the shock and the piston are investigated. The variations of density-ratio across the shock and the location of the piston with the parameter of non-idealness of the gas are also obtained.     

Blowing of a foreign gas in a hypersonic viscous shock layer

We consider the problem of a hypersonic viscous flow of a nonreactive mixture of ideal gases around smooth thick bodies in the framework of a two-layer model of a thin shock layer for moderately small Reynolds numbers. We investigate the effect of blowing of a foreign gas through a permeable surface in the bow region of a spherical blunt body. We introduce a transformation of variables that gives a number of important advantages in the numerical solution of the problem under consideration. The problem of mass blowing from the surface of a body into a boundary layer has an extensive literature. The effect of blowing for moderately small Reynolds numbers has been considerably less studied [1–5], and in the majority of papers on this question either the critical point of a blunt body or the blowing of a gas homogeneous with the gas in the incoming flow is investigated.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 110–116, July–August, 1972.     

Supersonic motion of bodies in a gas with shock waves

The authors consider the problem of supersonic unsteady flow of an inviscid stream containing shock waves round blunt shaped bodies. Various approaches are possible for solving this problem. The parameters in the shock layer on the axis of symmetry have been determined in [1, 2] by using one-dimensional theory. The authors of [3, 4] studied shock wave diffraction on a moving end plane and wedge, respectively, by the through calculation method. This method for studying flow around a wedge with attached shock was also used in [5]. But that study, unlike [4], used self-similar variables, and so was able to obtain a clearer picture of the interaction. The present study gives results of research into the diffraction of a plane shock wave on a body in supersonic motion with the separation of a bow shock. The solution to the problem was based on the grid characteristic method [6], which has been used successfully to solve steady and unsteady problems [7–10]. However a modification of the method was developed in order to improve the calculation of flows with internal discontinuities; this consisted of adopting the velocity of sound and entropy in place of enthalpy and pressure as the unknown thermodynamic parameters. Numerical calculations have shown how effective this procedure is in solving the present problem. The results are given for flow round bodies with spherical and flat (end plane) ends for various different values of the velocities of the bodies and the shock waves intersected by them. The collision and overtaking interactions are considered, and there is a comparison with the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 141–147, September–October, 1984.     

Flow of a viscous gas in a shock layer with equilibrium chemical reactions

Steady flow of supersonic air over a sphere is examined, allowing for viscosity, heat conduction, and actual physical and chemical processes. Flow in the shock layer at flight speeds in the range 3 km/sec V10 km/sec (10⁴R10⁶) is investigated, under the assumption of local thermodynamic equilibrium. The flow is described by simplified Navier-Stokes equations, which are solved by a finite difference method. The case of a cooled surface is examined. The distribution of gasdynamic parameters is obtained in different flow regimes. The distribution of heat flux and friction coefficient is investigated as a function of the oncoming-stream parameters and the sphere radius. The shape and position of the shock wave are determined, and the stream lines and sonic lines are constructed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 150–153, July–August, 1970.The authors thank Yu. P. Lun'kin and F. D. Popov for their help in formulating the problem and their constant interest.     

Breakup of gas bubbles in a liquid by shock waves

The nature of the propagation of shock waves in various media is related to the characteristics of the latter, including their compressibility, thermophysical properties, the presence of multiple phases, etc. The structure of a shock wave varies appreciably as a function of the properties of the medium. The most significant property of a liquid mixture with gas bubbles is the compressibility of the latter under the influence of an externally applied pressure, for example, in a shock wave propagating in the liquid—gas medium. The transfer of momentum and energy between phases and the pressure variation behind the wave depends on the behavior of the gas bubbles behind the shock front.     

Dynamics of shock waves in a liquid containing gas bubbles

Results are presented of a numerical solution of the Korteweg-de Vries-Burgers equation that describes the propagation and establishment process for a stationary structure to a shock wave in a gas-liquid medium. Data are obtained on the time for the establishment of a stationary structure of a shock wave, propagation velocity, and amplitude oscillations in the front of the shock wave. Experiments are discussed on the basis of the results obtained for the study of shock waves in a liquid containing gas bubbles.