Examination of the Thermal Equilibrium Assumption in Transient Natural Convection Flow in Porous Channel

The local thermal equilibrium assumption in the transient natural convection channel flow is investigated numerically. The Darcy–Brinkman–Forchheimer model is used to model the flow inside the porous domain. The effect of different parameters on the validity of the local thermal equilibrium assumption is examined. It is found that the volumetric Nusselt number has the most significant effect on the local thermal equilibrium assumption.     

Displacement of oil by solutions of an active additive from a uniform stratum with allowance for gravity

Self-similar solutions describing the displacement of oil by solutions of an adsorbed active additive have been obtained and investigated [1–3] in the framework of a one-dimensional flow model with neglect of diffusion, capillary, and gravity effects. In the present paper, a self-similar solution is constructed for the problem of oil displacement by an aqueous solution of an active additive from a thin horizontal stratum with allowance for gravity under the assumption that there is instantaneous vertical separation of the phases. This makes it possible to estimate the effectiveness of flooding a stratum by solutions of surfactants and polymers in the cases when gravitational segregation of the phases cannot be ignored.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 87–92, January–February, 1984.     

Shift of chemical equilibrium in a binary reacting mixture of molecular gases under the action of resonance laser radiation

At the present time, great attention is being paid to the problem of the final state of molecular gas systems originating from a steady external effect. This is associated, first of all, with intensive investigations of the properties of molecular gas lasers and also laser initiation of chemical reactions and the isotope separation. The theoretical feasibility is shown in [1, 2] for effectively shifting the chemical equilibrium in dissociation—three-particle recombination reactions, initiated in a single-component gas by resonance laser radiation. The purpose of this paper is to analyze the shift of chemical equilibrium in a binary mixture of molecular gases as a function of the intensity and nature of the laser pumping. It is well known [3] that the equilibrium constant of a chemical reaction can be expressed in terms of the dissociation equilibrium constant of the molecules participating in the reaction This factor permits the problem to be reduced to calculation of the dissociation equilibrium constants.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 3–9, January–February, 1978.The authors express thanks to B. F. Gordiets for numerous discussions of the results obtained and also to R. V. Khokhlov and P. K. Khabibullaev for support and interest in the work.     

Numerical calculation of the problem of cooling of a spherical volume of nonequilibrium-ionized radiating helium

The method is described and the results are presented for numerical calculations of a system of equations of nonsteady gasdynamics, radiation transfer in the continuous spectrum, and the kinetics of collisional ionization and ionization by radiation, which describe the dispersion and cooling of a spherical volume of He. A comparison is made with calculations performed on the assumption of thermodynamic equilibrium.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 36–41, March–April, 1976.     

Analysis of multicomponent gas mixture flows with partial chemical equilibrium

Diffusion equations and the corresponding transfer equations with effective transfer coefficients are derived using new unknown functions (linear combinations of diffusion fluxes and of concentrations) for reactive gas mixture flows with partial chemical equilibrium. The diffusion differential equations for rapid independent reactions degenerate into algebraic equations of detailed chemical equilibrium. The component formation sources on the right-hand sides of the remaining diffusion equations contain no rapid stages. It is shown that the assumption of partial chemical equilibrium is valid for hypersonic flow past blunt bodies with a nose radius of approx. 1 m on portions of their gliding reentry paths in the Earth's and Martian atmospheres.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 114–124, January–February, 1996.     

Development of hydrodynamic instability in film condensation on a cylindrical tube in weightlessness

In the process of film condensation on an heat exchanger tube in weightlessness the evolution of small perturbations of the free surface is determined not only by capillary forces but also by the nature of the heat and mass exchange in the liquid-vapor system. In the present paper it is shown that simultaneously taking all these factors into account, even within the framework of a very simple model, leads to results which differ qualitatively from the known formulas for the case of thermal equilibrium. Under the assumption that the velocity profile is quasi-steady, both analytic formulas and corrections to these formulas associated with the unsteady term in the equation of motion are obtained.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 106–110, November–December, 1995.     

Shock wave in a gas-liquid medium

The propagation of weak shock waves and the conditions for their existence in a gas-liquid medium are studied in [1]. The article [2] is devoted to an examination of powerful shock waves in liquids containing gas bubbles. The possibility of the existence in such a medium of a shock wave having an oscillatory pressure profile at the front is demonstrated in [3] based on the general results of nonlinear wave dynamics. It is shown in [4, 5] that a shock wave in a gas-liquid mixture actually has a profile having an oscillating pressure. The drawback of [3–5] is the necessity of postulating the existence of the shock waves. This is connected with the absence of a direct calculation of the dissipative effects in the fundamental equations. The present article is devoted to the theoretical and experimental study of the structure of a shock wave in a gas-liquid medium. It is shown, within the framework of a homogeneous biphasic model, that the structure of the shock wave can be studied on the basis of the Burgers-Korteweg-de Vries equation. The results of piezoelectric measurements of the pressure profile along the shock wave front agree qualitatively with the theoretical representations of the structure of the shock wave.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 65–69, May–June, 1973.     

Use of additional relations to solve the problem of separation of a laminar boundary layer by the integral method

Under the assumption of the fulfillment of local similarity, the boundary-layer equations are used to derive relationships between integral quantities. The obtained dependences can be used as additional relationships in the solution of the system of integral relationships of general form. The use of these additional relations is demonstrated in the example of the problem of the separation zone in front of a planar screen in the presence of heat transfer; this problem is solved by the integral method. In the calculation of the separation zone on cold surfaces, to eliminate a number of difficulties Curie's universal pressure curve is used upstream of the separation point. The calculations are compared with experimental data, revealing satisfactory agreement.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 62–69, July–August, 1979.     

Effect of external turbulence on the development of a turbulent jet

The effect of external turbulent agitation on jet development has been investigated in [1–3]. The difference of the method employed in the present work lies in the assumption that the turbulence scale of the external flow is substantially larger than the turbulence scales in either the jet or the mixing layer. Utilizing this assumption, it becomes possible to solve separately the energy equations for the turbulence of the external flow and of the jet. Solutions obtained on the basis of this assumption are found to be in qualitative agreement with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 24–29, January–February, 1977.     

A theory of hydroshock in a two-phase gas-liquid mixture

A hydroshock in a two-phase gas-liquid mixture is usually calculated by an analog of the Zhukovskii formula for a mixture (see, for example, [1, 2]) which establishes the relation of the hydro-shock intensity to the velocity of sound in the mixture. However, as the experimental data [1] show, the hydroshock intensity in the mixture can significantly exceed the calculated values, a fact which is explained by the increase in the propagation velocity of the perturbation wave in comparison to the velocity of sound in the mixture [3, 4]. In the present paper, an equilibrium model of shock transition, similar to [5, 6], is used to calculate the attenuation of the hydroshock as the gas content of the mixture increases in a bubble flow regime. It is shown that owing to the high compressibility of the mixture the effect of the elasticity of the pipe-line walls is small, and the dependence of the propagation velocity of the perturbation wave on the intensity and gas content becomes the main effect. A simple dependence of the hydroshock intensity on the gas content and two similarity parameters is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 202–204, September–October, 1984.     

Intrapore convection when the average temperature gradient is vertical

The heat conduction of a porous medium saturated with a fluid is usually regarded as being purely molecular [1]. The assumption here is that in the case of heating from below the local temperature gradient within each of the pores, like the averaged gradient in the complete layer, is strictly vertical, and, since the pores are as a rule small, this local gradient is less than the critical. It is therefore assumed that in the absence of large-scale convection the fluid in the pores is in equilibrium. However, for different thermal conductivities of the fluid and the porous skeleton surrounding it a vertical temperature gradient in the fluid and, accordingly, equilibrium of the fluid are possible only if a cavity is a sphere or an ellipsoid with a definite orientation [1]. Since the pores do not have such shapes, the convective motion that arises in each of the pores or in several communicating pores can lead to an increase in the effective thermal conductivity of the fluid and, accordingly, the effective thermal conductivity of the complete medium. The present paper is devoted to study of this effect.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 93–98, January–February, 1984.     

Nonlinear waves on the surface of a charged liquid. Instability,bifurcation, and nonequilibrium shapes of the charged surface

Plane nonlinear waves in shallow water are described by the Kortewegde Vries equation [1–3]. The present paper contains theoretical investigations of nonlinear waves and nonlinear equilibrium shapes on the surface of a charged liquid. The influence of the field on the velocity and shape of a hydrodynamic soliton is considered. The bifurcation of the equilibrium shapes is investigated. Problems of the equilibrium shapes of a charged liquid are solved in the nonlinear formulation of the dynamics of nonlinear solitary forms (lunes, trenches) on the surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 94–102, May–June, 1984.     

Stability of a stationary front of an exothermic reaction in the gas phase

The influence of the diffusion coefficient on the stability of a stationary front is investigated in the present piper on the assumption that the dependence of the reaction rate on the temperature is piecewise constant.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 14–16, July–August, 1987.     

Comparison of Kinetic and Hybrid-Equilibrium Models Simulating Colloid-Facilitated Contaminant Transport in Porous Media

The presence of colloidal particles in groundwater can enhance contaminant transport by reducing retardation effects and carrying them to distances further than predicted by a conventional advective/dispersive equation with normal retardation values. When colloids exist in porous media and affect contaminant migration, the system can best be simulated as a three-phase medium. Mechanisms of mass transfer from one phase to another by colloids and contaminants can be kinetic or equilibrium-based, depending on the sorption–desorption reaction rate between the aqueous and solid phases. When the rate of sorption between the water phase and the solid phase(s) is not much greater than the rate of change in contaminant concentration in the water phase, kinetic sorption models may better describe the phenomenon. In some cases of modeling one or more mass transfer processes, a useful simplification may be to introduce the local equilibrium assumption. In this study, the local equilibrium assumption for sorption processes on colloidal surfaces (hybrid equilibrium model) was compared with kinetic-based models. Sensitivity analyses were conducted to deduce the effect of major parameters on contaminant transport. The results obtained from the hybrid equilibrium model in predicting the transport of colloid-facilitated groundwater contaminant are very similar to those of the kinetic model, when the point of interest is not at contaminant and colloid source vicinities and the time of interest is sufficiently long for imposed sources.     

Selective drift of gas bubbles in a vibrating liquid in relation to their size

The problem of the motion of a gas-liquid mixture in a vessel placed on a vibrating base is examined. As distinct from investigations [1–8], the surface tension and the finiteness of the rate of propagation of disturbances are taken into account. This provided an explanation of some qualitative features of the effect in question.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 4, pp. 138–140, July–August, 1978.     

Cylindrical equilibrium surfaces of a capillary liquid and their stability

We consider the plane problem of the equilibrium of a capillary surface. We study the stability of a two-dimensional surface with respect to plane and spatial disturbances. We give data which can be used for deciding the question of the stability of any symmetric equilibrium surface in a field of gravitational forces and in conditions of weightlessness. We solve the problems of the stability of a liquid in a rectangular and a sectorial channel and also the problem of the separation of a plane drop from a horizontal wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 57–68, January–February, 1976.The authors are grateful to A. D. Myshkis and A. D. Tyuptsov for their evaluation and their useful comments.     

Analysis of Displacement Variances in Stochastic Nonuniform Flows by Means of a First Order Analytical Model and Comparison with Monte-Carlo Simulations

Flow, particle displacement and particle arrival time statistics in 2D nonuniform flows, without microdispersion, are studied both theoretically, in the framework of stochastic modelling, and numerically by means of Monte-Carlo simulations.Turning, radial convergent and dipolar flow fields are considered. These three types of flow are numerically investigated in heterogeneous media with different levels of heterogeneity. Monte-Carlo simulations show (1) that the scale separation hypothesis, frequently used in fluid mechanics, is justified for one-point flow statistics; and (2) how displacement variances, and consequently the dispersivities defined as their spatial derivatives, depend on the type and the amplitude of flow nonuniformity: in none of the investigated cases does the assumption of scale separation hold for displacement, except in the turning flow when the spatial scale associated to the nonuniformity is much greater than the correlation scale of transmissivity.The theoretical approach of displacement and arrival time statistics relies on the analysis of particle trajectory. Displacement variances expressions are derived by the perturbation method for each type of flow and for different approximation orders. The proposed expressions of displacement variances are, on the whole, in good agreement with the numerical results. On the other hand, the uniform flow approximation – commonly used for the interpretation of tracer experiments – chosen such as to satisfy the mean arrival time to the pumping well, gives the best prediction of the breakthrough curves.     

Molecular gas dynamics applied to phase change processes at a vapor–liquid interface: shock-tube experiment and MGD computation for methanol

This paper deals with a molecular gas-dynamics method applied to the accurate determination of the condensation coefficient of methanol vapor. The method consisted of an experiment using a shock tube and computations using a molecular gas-dynamics equation. The experiments were performed in such situations where the shift from a vapor–liquid equilibrium state to a nonequilibrium one is realized by a shock wave in a scale of molecular mean free time of vapor molecules. The temporal evolution in thickness of a liquid film formed on the shock-tube endwall behind a reflected shock wave is measured by an optical interferometer. By comparing the measured liquid-film thickness with numerical solutions for a polyatomic version of the Gaussian–BGK model of the Boltzmann equation, the condensation coefficient of methanol vapor is accurately determined in vapor–liquid nonequilibrium states. As a result, it is clear that the condensation coefficient is just unity very near to an equilibrium state, but is smaller far from the equilibrium state.     

Propagation of modulated nonlinear waves in a relaxing gas-liquid mixture

The propagation of nonstationary weak shock waves in a chemically active medium is essentially dispersive and dissipative. The equations for short-wavelength waves for such media were obtained and investigated in [1–4]. It is of interest to study quasimonochromatic waves with slowly varying amplitude and phase. A general method for obtaining the equations for modulated oscillations in nonlinear dispersive media without dissipation was proposed in [5–8]. In the present paper, for a dispersive, weakly nonlinear and weakly dissipative medium we derive in the three-dimensional formulation equations for waves of short wavelength and a Schrödinger equation, which describes slow modulations of the amplitude and phase of an arbitrary wave. The coefficients of the equations are particularized for the considered gas-liquid mixture. Solutions are obtained for narrow beams in a given defocusing medium as well as linear and nonlinear solutions in the neighborhood of a diffraction beam. A solution near a caustic for quasimonochromatic waves was found in [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 133–143, January–February, 1980.     

Amplification of tkiangular shock waves in a flammable two-phase medium

In [1, 2] values are established for the parameters of a compression wave with a triangular pressure variation such that when the wave interacts with a two-phase gas-liquid medium it can produce nonstationary combustion. More complicated to study, but of greater practical interest, is the interaction of longitudinal compression waves with a burning two-phase medium.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 119–122, January–February, 1972.