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.     

Amplification of shock waves in a bubble-filled liquid with gas concentration gradient

The properties are studied of the propagation of unsteady shock waves in a gas-liquid system of bubble structure in the case when the volume concentration of the gas changes in the direction of motion of the shock wave. It is established that when there is a sufficiently rapid drop in the gas content, an effect of amplification of the shock wave is observed which is due to the deceleration of the medium behind the shock wave. A study is made of the laws of the evolution of long- and short-wave pulsed perturbations in such systems. The authors consider processes of reflection of waves from obstacles and their passage from a gas into a bubble liquid, from a two-phase mixture into a pure liquid. The contribution is determined of nonequilibrium effects to the process of amplification of a wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 49–54, January–February, 1988.The authors wish to express gratitude to R. I. Nigmatulin for his interest in the study and for useful discussions.     

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.     

Propagation of shock waves in a porous medium saturated by a liquid with bubbles of a soluble gas

The process of evolution and reflection of shock waves of moderate amplitude from a rigid boundary in a porous medium saturated by a liquid with bubbles of a soluble gas is studied experimentally. Experimental values of the amplitude and velocity of the reflected wave are compared with the calculated results obtained using mathematical models. The process of dissolution of gas bubbles in the liquid behind the shock wave is studied. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 91–102, September–October, 2000.     

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.     

Structure of shock waves in a liquid with vapor bubbles

The aim of the present paper is to investigate the influence of interphase heat and mass transfer in a vapor-liquid bubble medium on the structure of a steady shock wave formed by steady or fairly prolonged action on the medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 109–118, March–April, 1982.     

Nonstationary gas flow with shock waves in a supersonic compressor

Shock waves are formed in the channels between blades in a compressor working in the transsonic state, and the positions of these vary periodically and produce strong vibrations in the blades. The effect is extremely complex and is dependent on a large number of parameters. Here we present a simplified model for the effect, which can be examined theoretically. It is assumed that the nonstationary pulsations in the flow and the amplitudes in the oscillations of the shock waves are small, and therefore one can employ a steady-state flow whose characteristics may be taken as given, including the mean position of the shock waves.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 41–47, September–October, 1973.     

Motion of shock waves in an inhomogeneous gas

Whitham [1] has proposed a method of approximate calculation of the motion of shock fronts giving results in fairly good agreement with the experiments when one considers various nonstationary problems of the interaction of shock waves with one another and solid surfaces. However, the method gives rise to fundmental difficulties when one considers the propagation of shock waves in a moving medium [1, 2]. In the present paper, the method is generalized to the case of a gas which is moving nonuniformly in front of the shock wave, no restrictions being made on the nature of the motion or the variation of its parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 175–178, January–February, 1981.I thank M. D. Gerasimov for interest and assistance in the work.     

Nonlinear magnetoacoustic waves in a conducting liquid containing gas bubbles

The propagation of long waves in an incompressible conducting liquid saturated with nonconducting gas bubbles is considered on the basis of the equations of magnetohydrodynamics of a homogeneous gas-liquid medium. It is shown that the propagation of weakly nonlinear MHD waves in such a medium is described by the Burgers-Korteweg-de Vries (BKdV) equation. The influence of MHD interaction effects on the parameters of fast and slow weak magnetoacoustic shock waves is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 142–147, March–April, 1991.     

Diffraction of weak shock waves by deformed bodies submerged in a liquid

Conclusion On the basis of an analysis of theoretical and experimental data obtained up to now by various investigators, we can note the following major advances in the field of the interaction of shock waves with barriers submerged in a liquid:Exact solutions have been obtained for problems in the diffraction of acoustic shock waves by rigid and stationary bodies of specified shape (plates, wedges, cones, parabolic, elliptical, and circular cylinders, spheres, paraboloids of revolution); approximate schemes have been worked out for estimating hydrodynamic loads, making it possible to investigate various stages of the interaction of shock waves with elastic shells of revolution and solid bodies; studies have been conducted in the exact formulation of the interaction of plane (spherical) nonstationary waves with elastic barriers (unbounded plates, plates in a screen, infinitely long thin-walled and thick-walled cylindrical shells, closed thin-walled and thick-walled spherical shells); an exact solution has been found for the internal problems in the case of cavities (circular and elliptical cylinders, spheres, spheroids) and elastic shells of revolution (infinitely long cylindrical and closed spherical shells); methods have been worked out for the approximate determination of the parameters of objects (elastic thin-walled infinitely long cylindrical and closed spherical shells) from reflected echo signals; estimates have been given for the influence of the structural characteristics of an object (support, concentrated masses), the nonlinear properties of interacting media, cavitation in liquid, and plastic deformations in the barrier material on the process of hydrodynamic interaction.We should also mention the main lines of further investigation and the problems which require solution: designing new experimental apparatus and measuring complexes for studying the nonstationary behavior of deformed bodies and structures in a liquid; solution of problems in diffraction by oonical and cylindrical shells of finite length, and by compound structures of complicated form in which account is taken of the structural characteristics and the internal elements; calculation of three-layer and multilayer shells acted upon by shock waves, taking account of the transverse compression of the filler; construction of more exact schemes (models) for the nonlinear and cavitation-type interaction of waves with barriers; development of numerical and combined methods for the solution of the problems in hydroelasticity.Mechanics Institute, Moscow State University. Translated from Prikladnaya Mekhanika, Vol. 16, No. 5, pp. 3–11, May, 1980.     

On the structure of MHD shock waves in a viscous non-ideal gas

The structure of one-dimensional magnetohydrodynamics (MHD) shock waves is studied using the Navier–Stokes equations for the non-ideal gas phase. The exact solutions are obtained for the flow variables (i.e. particle velocity, temperature, pressure and change-in-entropy) within the shock transition region. The equation of state for a non-ideal gas is considered as given by Landau and Lifshitz. The effects of the non-idealness parameter and coefficient of viscosity of the gas are analysed on the flow variables assuming the magnetic field having only constant axial component. The findings confirm that the thickness of MHD shock front increases with decreasing values of the non-idealness parameter.