Allowance for nonstationary heat and mass transfer in the propagation of small perturbations in a liquid with bubbles

The propagation of small perturbations in a liquid with vapor-gas bubbles is studied. Heat and mass transfer between the phases is taken into account on the basis of the exact equations of heat conduction and diffusion. The aim of the present investigation is to make more precise the results of an earlier paper [1] of the author and verify the applicability of using fixed coefficients of heat and mass transfer for nonstationary heat and mass transfer between a pulsating bubble and the liquid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 157–162, July–August, 1979.     

Study of two-phase bubbly flow dynamics in binary mixtures

The results of an investigation of the bubble dynamics and wave phenomena in two-component vapor-liquid mixtures are presented. These mixtures are widely used in industrial systems as heat transfer media. The effects of various additives on the wave dynamics of vapor-liquid mixtures are of particular interest. A single-velocity two-pressure model was used which takes into account both the liquid radial inertia due to medium volume changes, and the temperature distribution around the bubbles. The claim that mixture composition may have a peculiar effect on the bubble dynamics of a boiling non-ideal solution is substantiated. It is noted that the small free radial oscillation damping ratio for some binary systems lies outside the domain defined by the damping ratio of the constituents as a result of phase change diffusion effects. A criterion is proposed to identify cases of diffusion resistance responsible for the anomalous effect of component concentration on bubble behavior. The phase change delay due to diffusion results in observably higher mixture wave velocities and a smaller damping ratio than for respective single-component systems.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1992 and the AMS fonts, developed by the American Mathematical Society.     

Interphase momentum interaction effects in the averaged multifield model: Part I: Void propagation in bubbly flows

The volume-averaged form of the linear momentum conservation equations for twophase flow is examined to clarify momentum interaction effects between phases. The case of an accelerating sphere of varying radius in an accelerating fluid is used to derive the form of the interphase force terms. The analysis is extended to assemblies of noninteracting spheres and an interphase force term related to the spatial gradient of phase volume fraction is seen to arise. For the case of bubbly flow, two real characteristics are obtained for dispersed phase volume fractions less than about 0.25. If the term involving the spatial gradient of the phase volume fraction is neglected, then the characteristics are always complex for velocity differences between the phases. The interphase force model is applied to predict experiments on void propagation in bubbly flows. There are no adjustable constants in the model. The experimental data were obtained in our laboratory using cross correlation of signals from a pair of gamma densitometers. The predictions are in excellent agreement with the data. In addition, the predictions are compared with data from several other laboratories, taken over different sets of flow conditions. The predictions are again in close agreement with the data.     

Numerical simulation of shock propagation in a polydisperse bubbly liquid

The effect of distributed bubble nuclei sizes on shock propagation in a bubbly liquid is numerically investigated. An ensemble-averaged technique is employed to derive the statistically averaged conservation laws for polydisperse bubbly flows. A finite-volume method is developed to solve the continuum bubbly flow equations coupled to a single-bubble-dynamic equation that incorporates the effects of heat transfer, liquid viscosity and compressibility. The one-dimensional shock computations reveal that the distribution of equilibrium bubble sizes leads to an apparent damping of the averaged shock dynamics due to phase cancellations in oscillations of the different-sized bubbles. If the distribution is sufficiently broad, the phase cancellation effect can dominate over the single-bubble-dynamic dissipation and the averaged shock profile is smoothed out.     

Shock-wave formation in flowing bubbly mixtures by steepening of compression waves

The formation and propagation of shock waves in a two-component flowing bubbly mixture has been investigated experimentally. The structure of shock waves formed by steepening of compression waves is compared with the corresponding features of shocks produced spontaneously in shock tubes. Experimentally determined values of the speed of propagation of the shock compare favorably with the Hugoniot relationship based upon a homogeneous two-phase model. The effect of the gravitational and frictional pressure gradients on the shock characteristics is also examined.     

Behavior of detonation propagation in mixtures with concentration gradients

Behavior of detonation waves in mixtures with concentration gradients normal to the propagation direction was studied experimentally. Mixtures with various concentration gradients were formed by sliding the separation plate which divides a detonation chamber from a diffusion chamber in which a diffusion gas was initially introduced. A stoichiometric hydrogen–oxygen mixture was charged in the detonation chamber, while oxygen or nitrogen was filled in the diffusion gas chamber. Temporal concentration measurement was conducted by the infrared absorption method using ethane as alternate of oxygen. Smoked foil records show a deformation of regular diamond cells to parallelogram ones, which well corresponds to local mixture concentration. Schlieren photographs reveal the tilted wave front whose angle is consistent with the deflection angle of the detonation front obtained from trajectories of the triple point. The local deflection angle increases with increase in local concentration gradient. Calculation of wave trajectory based on the ray tracing theory predicts formation of the tilted wave front from an initial planar front.      

Derivation of a non-linear model equation for wave propagation in bubbly liquids

Summary Though the use of an asymptotic approach, it is deduced a fourth order partial differential equation governing the evolution of nonlinear (sound) wave propagation in bubbly liquids. Remarkably it involves also higher order nonlinear terms. Some results concerning the steady-state solution as well as the dispersion relation are obtained.

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Sommario Mediante l'usa di uno schema asintotico viene dedotta una equazione differenziale alle derivate parziali del quarto ordine, atta a descrivere l'evoluzione di un'onda non lineare propagantesi con la velocità del suono in un liquido con bolle. Tale equazione in particolare presenta delle non linearità anche nette derivate di ordine più elevato. Infine vengono discussi alcuni risultati numerici connessi con la ricerca di soluzioni del tipo onda stazionaria e con la relazione di dispersione.

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This work was supported by M.P.I. through Fondi per la ricerca scientifica 40% e 60%.     

A numerical study of weak shock wave propagation in a reactive bubbly liquid

A numerical study is presented on the response of a weakly shock compressed liquid column that contains reactive gas bubbles. Both the liquid and gas are considered compressible. Compressibility of the liquid allows calculation of shock and rarefaction waves in the pure liquid as well as in the gas/liquid mixture. A microscopic model for local bubble collapse is coupled with a macroscopic model of wave propagation through the gas/liquid mixture. In the particular cases presented here, the characteristic times of propagation of the shock wave and bubble collapse are of the same order of magnitude. Consequently, the coupling between various phenomena is very strong. The present model based on fundamental principles of two-phase fluid mechanics takes into account the coupling of localized bubble oscillations. This model is composed of a microscopic one in the scale of a bubble size, and a macroscopic one which is based on the mixture theory. The liquid under study is water, and the gas is a reactive mixture of argon, hydrogen and oxygen. Received 18 December 1995 / Accepted 2 June 1996     

Multivelocity effects in high-pressure-gradient flows of dilute bubbly media

The multivelocity effects associated with the behavior of gas or vapor bubbles in a region with high pressure gradients typical of the flows around a cavity in which the pressure is higher than that in the surrounding space are considered. For a low volume bubble concentration, the problem of fluid flow perturbation by the bubbles is examined. For gas bubbles, it is shown that taking multivelocity effects into account considerably reduces the additional jet momentum. It is found that, with time, the temperature distribution in the wake behind a vapor bubble becomes nonmonotonic and the maximum temperature may even exceed the initial bubble temperature. It is demonstrated that the bubbles may accumulate and a flow regime with a sharply pronounced two-phase jet extending to the outer edge of the main liquid jet may develop. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 87–100, January–February, 1998. The work received financial support from the Russian Foundation for Fundamental Research (project No.96-01-01442).     

Water hammer and propagation of perturbations in elastic fluid-filled pipes

A Korteweg—de Vries (KV) approximation is constructed in this paper for the perturbations being propagated in elastic pipes filled with fluid. On the basis of the approximation constructed and the equation obtained for the perturbations of a finite-amplitude velocity, the water-hammer phenomenon is analyzed in the Zhukovskii formulation, and the water hammer in systems with preliminary longitudinal tension is considered separately. Special attention in the study of the perturbations is paid to the signal structure and evolution in the hydraulic line. Taking account of the inertial properties of the pipe in the approximation mentioned permitted the indication of new effects, in principle, which are essential for applied problems of the propagation of perturbations in elastic hydraulic lines. In particular, it is shown that the initial signal can be doubled in such lines by redistributing its intensity over the frequencies. It is established that the origination of an oscillating forerunner is possible in hydraulic lines with preliminary tension. Starting with [1], the water-hammer phenomenon was investigated in many papers, in [2], for example. The main attention in these papers was paid to the propagation velocity of the water hammer and its intensity. After simplification, the initial system of Zhukovskii equations contains no mechanism hindering the twisting of the wave profile, and, therefore, there is no possibility of stationary shock formation within the framework of this theory. Moreover, the Zhukovskii theory of the water hammer and of propagation of perturbations in elastic pipes results in the conclusion that the wave structure, velocity, and amplitude depend essentially on the characteristics of the initial perturbation and can differ significantly from the water hammer predicted by theories for powerful signals in sufficiently long pipes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–8, July–August, 1976.     

Free wave propagation in binary gas mixtures

The problem concerning the propagation of free waves in binary mixtures of monatomic ideal gases is analyzed by using a kinetic model of the Boltzmann equation which is compatible with the two-fluid hydrodynamic theory. Comparison of the theoretical results with available experimental data shows that the two-fluid model equation can be used to describe the wave-vector dependence of the free sound waves in both continuum and kinetic regimes.     

Quasi-steady regimes of wave propagation in active mixtures

Regimes of multifront, spinning, marginal, and galloping detonation, quasi-detonation, and supersonic and subsonic (turbulent and laminar) flames are discussed. Criteria for identification of different wave regimes include not only the wave velocity or its deficit, but also the relation between the cell size (or the size of the induction zone) and the characteristic size of equipment. New applications of detonation and combustion are also discussed. This paper is based on an invited presentation at the 21st International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Finite propagation velocity and local perturbations in nonlinear relaxation filtration

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 102–106, September–October, 1991.     

Certain magnetohydrodynamic flows associated with the propagation of waves

The propagation of waves in an absorptive medium is accompanied by unidirectional motion of this medium — a flow which develops due to the fact that the wave loses a portion of its momentum along with energy loss. It is this loss which is compensated by the flow by virtue of the momentum-conservation law. In a conducting medium the momentum losses via the waves are associated not only with the viscosity and thermal conductivity but also with the Joule-heat losses. Moreover, the magnetic field itself also affects the configuration and character of the flow in this case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 30–33, July–August, 1970.The authors thank N. A. Roi for his useful comments.