Method for calculating the dynamics of vapor bubbles when a liquid boils in a centrifugal force field

The specific feature of the study of the dynamics of vapor bubbles during boiling of a liquid in a centrifugal force field is the fact that the velocity of a bubble is much greater than the rate of change of its radius, and its movement occurs in fields of variable pressure and underheating that have to be determined in the solution of the problem. In addition, when investigating processes occurring when liquid helium boils in a centrifugal force field, its thermodynamic parameters may be close to the critical values, and the dependences of the thermophysical properties of the liquid and vapor on the temperature and pressure must be taken into consideration. The equation of state of a substance close to its critical thermodynamic point cannot be an approximation to the equation of state of an ideal gas, as has been suggested in a series of articles. The nonequilibrium nature of the phase transition must be taken into consideration in the case of substances existing at near-critical parameters and substances with a low coefficient of accommodation. A marked deformation of the bubbles, which also has to be taken into account, will be observed in strong centrifugal force fields. Such studies have not appeared in the specialist journals. Equations of the two-temperature and two-velocity hydrodynamics of two-phase media in a one-dimensional form for substances obeying the equation of state for an ideal gas were discussed in [1, 2] with allowance for the dependence of the thermophysical properties on the temperature and pressure. In strong centrifugal force fields the one-dimensional approach is unacceptable and the flow of liquid around a buoyant bubble must be taken into account. A joint examination of the change in the temperature field with time in the vicinity of a vapor bubble with changes in its dimensions and position was made for the first time in [3–8]. The present article is an extension of the latter work and takes the aforementioned factors into account.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 66–71, July–August, 1984.     

Gas content of a foam bed at reduced pressures

The gas content of a foam bed has been experimentally investigated using a 50 × 80 mm² column at the following parameters: pressure P=0.1–1.0 bar, W=0.5-2.0 m/sec, H = 140–180 mm. In all cases the gas phase was air and the liquid phase was water and aqueous solutions of ethanol and glycerol. It has been established that reducing the pressure causes a considerable decrease in gas content, leading to an increase in the depth of the starting layer of liquid h₀. A formula that conforms with the experimental data to within ± 10% is obtained for the gas content.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 2, pp. 166–169, March–April, 1970.     

Modeling of retrograde condensation in the process of steady radial flow through a porous medium

The problem of the steady axisymmetric two-phase flow of a multicomponent mixture through a porous medium with phase transitions is considered. It is shown that the system of equations for the two-phase multicomponent flow process, together with the equations of phase equilibrium, reduces to a system of two ordinary differential equations for the pressures in the gas and liquid phases. A family of numerical solutions is found under certain assumptions concerning the pressure dependence of the molar fraction of the liquid phase.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 92–97, November–December, 1994.     

Influence of the structure of a porous medium on the residual gas saturation in the case of capillary displacement by a liquid

A model of a porous medium consisting of randomly branching conical pores is used to investigate the quasistatic displacement of gas by a wetting liquid without application of an external pressure. Allowance is made for the circumstance that in the capillary process all the pores have at least one-sided permeability for the liquid phase. An expression is obtained that relates the residual gas saturation to the parameters which characterize the structure of the pores and the wetting properties of the system. Two new characteristics of the pore space are introduced — the branching parameter and the opening angle of the pores — and the influence of these parameters on the residual saturation is investigated. It is shown that for individual classes of natural media the residual gas saturation depends only on the porosity and the contact angle of wetting.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 128–133, September–October, 1981.     

Concentration jump on the plane surface in a binary gas mixture

From the solution of linearized Boltzmann equations with the collision operators in the Gross and Krook form the authors have obtained an expression for the concentration jump of a vapor evaporating from a plane liquid surface into a stationary gas, for which the liquid surface is impermeable. Langmuir [1] was the first to point out that at the surface of an evaporating liquid the vapor pressure differs from saturated vapor pressure, i.e., a jump occurs in vapor concentration. An expression was obtained by Brock [2] for the concentration jump at the plane surface in the binary gas mixture with identical molecular masses of components by gas kinetic analysis. No solution has yet been obtained to the problem at different molecular masses of components.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 119–122, March–April, 1972.     

Wave dynamics of mixed,periodically nonstationary flows of a spontaneously condensing vapor

A study is made of the dynamics of mixed flows of a condensing vapor with nonequilibrium phase transitions and gas-dynamic discontinuities in channels of variable area in the presence of periodically nonstationary boundary conditions at the entrance. The results are given of a numerical investigation of the flows of superheated and spontaneously condensing water vapor in a supersonic nozzle. It is shown that the periodic nonstationarity of the flow at the entrance can lead to a qualitative rearrangement of the flow structure in the presence of spontaneous condensation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 116–121, November–December, 1980.     

Kinetic theory of disperse systems

A kinetic equation for the motion of solid particles in a liquid or gas is derived on the basis of the Fokker-Planck-Kolmogorov diffusion equation for the N particle distribution function. It is shown that, under appropriate assumptions, Bogolyubov's method can also be applied to equations of diffusion type. The obtained kinetic equation is a generalization of the one proposed earlier in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 128–132, January–February, 1980.I thank V. P. Myasnikov for suggesting the problem and for helpful discussions.     

Dynamics of soluble gas bubbles

The problem of the mass, thermal and dynamic interaction between a bubble containing a soluble gas and a liquid is considered. It is shown that this problem can be reduced to the problem of the behavior of a vapor bubble with phase transitions investigated in detail in [1–3]. Expressions are obtained for the rate of decay of the radially symmetric oscillations of the bubbles due to the solubility of the gas in the liquid. The effective coefficients of mass transfer between the radially pulsating bubbles and the liquid are determined. A numerical solution is obtained for the problem of the radial motion of a bubble created by a sudden change of pressure in the liquid which, in particular, corresponds to the behavior of the bubbles behind the shock front when a shock wave enters a bubble screen.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 52–59, November–December, 1985.     

Phase Interaction in a Vapor-Liquid Medium in Transient Flow Regimes

A mathematical model and a numerical method are developed for studying nonlinear wave processes in two-phase liquids with gas or vapor bubbles under conditions of impact interaction with deformable media. On the basis of the proposed approach to the numerical modeling of the dynamics of the transient processes in the two-phase vapor-liquid and deformable media, the basic features of the phase behavior, the phase transitions, and the interphase heat and mass transfer, typical of liquids containing vapor bubbles, are analyzed. The results of solving problems of the dynamics of different vapor-liquid media are presented.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 88–102.Original Russian Text Copyright © 2005 by Petushkov.     

On the modeling and simulation of a laser‐induced cavitation bubble

Single cavitation bubbles exhibit severe modeling and simulation difficulties. This is due to the small scales of time and space as well as due to the involvement of different phenomena in the dynamics of the bubble. For example, the compressibility, phase transition, and the existence of a noncondensable gas inside the bubble have strong effects on the dynamics of the bubble. Moreover, the collapse of the bubble involves the occurrence of critical conditions for the pressure and temperature. This adds extra difficulties to the choice of equations of state. Even though several models and simulations have been used to study the dynamics of the cavitation bubbles, many details are still not clearly accounted for. Here, we present a numerical investigation for the collapse and rebound of a laser‐induced cavitation bubble in liquid water. The compressibility of the liquid and vapor are involved. In addition, great focus is devoted to study the effects of phase transition and the existence of a noncondensable gas on the dynamics of the collapsing bubble. If the bubble contains vapor only, we use the six‐equation model for two‐phase flows that was modified in our previous work [A. Zein, M. Hantke, and G. Warnecke, J. Comput. Phys., 229(8):2964‐2998, 2010]. This model is an extension to the six‐equation model with a single velocity of Kapila et al. (Phys. Fluid, 13:3002‐3024, 2001) taking into account the heat and mass transfer. To study the effect of a noncondensable gas inside the bubble, we add a third phase to the original model. In this case, the phase transition is considered only at interfaces that separate the liquid and its vapor. The stiffened gas equations of state are used as closure relations. We use our own method to determine the parameters to obtain reasonable equations of state for a wide range of temperatures and make them suitable for the phase transition effects. We compare our results with experimental ones. Also our results confirm some expected physical phenomena. Copyright © 2013 John Wiley & Sons, Ltd.     

Charging of disperse particles in two-phase media with unipolar charge

Charging of disperse particles with good conduction in two-phase media with unipolar charge is considered in the case when the volume concentration of the particles is low. For this, in the framework of electrohydro-dynamics [1, 2], a study is made of the charge of one perfectly conducting liquid particle in a gas (or liquid) with unipolar charge in a fairly strong electric field. The influence of the inertial and electric forces on the motion of the gas is ignored, and the velocities are found by solving the Hadamard—Rybczynski problem. We consider the axisymmetric case when the gas velocity and electric field intensity far from the particle are parallel to a straight line. The analogous problem for a solid spherical particle was solved in [3–6] (in [3], the relative motion of the gas was ignored, while in [4–6] Stokes flow around the particle was considered). The two-dimensional problem of the charge of a solid circular, perfectly conducting cylinder in an irrotational flow of gas with unipolar charge was studied in [7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 108–115, November–December, 1980.We thank L. I. Sedov and V. V. Gogosov for a helpful discussion of the present work.     

Two-phase couette flow

A study is made of plane laminar Couette flow, in which foreign particles are injected through the upper boundary. The effect of the particles on friction and heat transfer is analyzed on the basis of the equations of two-fluid theory. A two-phase boundary layer on a plate has been considered in [1, 2] with the effect of the particles on the gas flow field neglected. A solution has been obtained in [3] for a laminar boundary layer on a plate with allowance for the dynamic and thermal effects of the particles on the gas parameters. There are also solutions for the case of the impulsive motion of a plate in a two-phase medium [4–6], and local rotation of the particles is taken into account in [5, 6]. The simplest model accounting for the effect of the particles on friction and heat transfer for the general case, when the particles are not in equilibrium with the gas at the outer edge of the boundary layer, is Couette flow. This type of flow with particle injection and a fixed surface has been considered in [7] under the assumptions of constant gas viscosity and the simplest drag and heat-transfer law. A solution for an accelerated Couette flow without particle injection and with a wall has been obtained in [6]. In the present paper fairly general assumptions are used to obtain a numerical solution of the problem of two-phase Couette flow with particle injection, and simple formulas useful for estimating the effect of the particles on friction and heat transfer are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–46, May–June, 1976.     

Investigation of turbulent vapor-air jets in the presence of condensation and the injection of foreign particles

A study is made of flow in turbulent jets when there is condensation of the water vapor contained in them. A necessary condition for condensation in vapor-air jets is formulated. Relations are obtained for the regime of equilibrium condensation. An experimental investigation was made of the local characteristics of an isobaric turbulent vapor jet exhausting into air at rest when condensation develops in the jet and foreign condensation nuclei (smoke particles) and charged particles (ions produced in a corona discharge) are introduced into the flow. Measurements were made of the local characteristics of the condensed disperse phase — the Sauter diameter d₃₂ of the drops and their volume concentration c_s — using the optical method of an integrating diaphragm. It is shown that d₃₂ and₃₂ c_s increase downstream in the main section of the jet. Specific features of temperature measurements using an end-type microthermocouple were established. Quantitative data were obtained about the influence on the condensation of the thermal conditions and the presence of the foreign particles. The conditions under which there is an intensification of the condensation in vapor-air jets in the presence of ions were determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 53–61, May–June, 1984.     

Radial oscillations of vapor bubbles in solutions

The dynamics and heat and mass transfer of vapor bubbles in binary systems are investigated. An anomalous effect of the component composition on the bubble dynamics in boiling nonideal solutions is established. It is shown that in some binary systems the value of the logarithmic decay rate for small free radial oscillations does not lie within the limiting values calculated for the pure components, which is associated with the cardinal importance of the effect of diffusion in the liquid phase on the intensity of the phase transitions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 108–113, May–June, 1989.     

Heat transfer in a thin layer of a viscous heavy noncompressible liquid under wavy flow conditions

The article describes a method for calculating the flow of heat through a wavy boundary separating a layer of liquid from a layer of gas, under the assumption that the viscosity and heat-transfer coefficients are constant, and that a constant temperature of the fixed wall and a constant temperature of the gas flow are given. A study is made of the equations of motion and thermal conductivity (without taking the dissipation energy into account) in the approximations of the theory of the boundary layer; the left-hand sides of these equations are replaced by their averaged values over the layer. These equations, after linearization, are used to determine the velocity and temperature distributions. The qualitative aspect of heat transfer in a thin layer of viscous liquid, under regular-wavy flow conditions, is examined. Particular attention is paid to the effect of the surface tension coefficient on the flow of heat through the interface.Notation x, y coordinates of a liquid particle - t time - v and u coordinates of the velocity vector of the liquid - p pressure in the liquid - c_v, , T,, andv heat capacity, thermal conductivity coefficient, temperature, density, and viscosity of the liquid, respectively - g acceleration due to gravity - surface-tension coefficient - c phase velocity of the waves at the interface - T_w wall temperature - h₀ thickness of the liquid layer - u₀ velocity of the liquid over the layer Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 147–151, July–August, 1970.     

Influence of the viscous boundary layer on the deposition of particles from a gas suspension flowing past a sphere

The flow of incompressible gas containing particles past bodies of simple shapes at moderate and high velocities is investigated in [1–5], in which the flow of the carrier medium is assumed to be irrotational. The estimates made in [3] for the neighborhood of the stagnation point show that it is necessary to take into account the viscous boundary layer in the case of fine particles. In the present paper, the viscous flow of a gas suspension over the front surface of a sphere at Reynolds numbers R = 10³–10⁷ is considered. It is assumed that the carrier gas is incompressible and the particle concentra ion negligibly small. The influence of the boundary layer on the particle trajectories and the deposition of the disperse phase on the surface of the sphere is investigated. It is shown that there is a wide range of flow parameters for the gas suspension in which the influence of the boundary layer is important. The limits of this range are established.Translated from Izvestiya Akademli Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 59–66, January–February, 1982.I thank Yu. P. Savel'ev for a helpful discussion of the work.     

Use of an electric field to keep bubbles and drops in a given shape and position in a liquid dielectric

A study is made of the problem of finding an electric field that keeps a spherical gas bubble in a fixed position in a dielectric liquid in a gravity field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 101–105, November–December, 1982.We thank I. E. Tarapov for helpful advice and discussion of the results.     

Collapse of vapor bubbles in a liquid

The effect of nonequilibrium phase transitions on the vibrations of a vapor bubble in a liquid caused by a suddenly applied pressure drop is considered. This problem is of interest in the study of mixed liquid and vapor flows with a discrete vapor phase. Results are presented of a numerical solution of this problem in the form of dimensionless radius-time curves for various values of the parameter which characterizes the kinetics of the phase transitions. The case of equilibrium phase transitions has been considered in [1, 2]. The thermal and dynamic interactions of a gaseous bubble with the surrounding fluid are the subject of [3, 4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 50–54, November–December, 1973.The author thanks R. I. Nigmatulin for advice and interest in this work and V. Sh. Shagapov for useful discussions.     

Bubble generation and transport in a microfluidic device with high aspect ratio

Bubble generation and transport in a micro-device composed of a micro-T-junction and a following serpentine micro-channel was experimentally investigated. It has a rectangular cross-sectional with an aspect ratio of 7.425. Air and water were used as gas and liquid, respectively. Mixtures of water–glycerol and water–Tween-20 were used to study the effects of liquid viscosity and surface tension. Compared with previous T-junction bubble generation, the liquid and gas inlets orientation was switched in this work. The continuous flow was driven from the perpendicular channel and the dispersion flow was from the main channel. It shows that the break-up process has three periodic steps under certain operating conditions. The dimensionless bubble length L/w in the micro-channel with high aspect ratio is much larger than that in square microchannels. A correlation is proposed to correlate L/w with liquid flow rate J_L, gas flow rate J_G, and liquid viscosity μ_L. Surface tension σ can change the bubble shape but almost does not affect the bubble length in this fast break-up process. Additionally, a long bubble may be broken up at the corners at the same time because the locations of gas and liquid are exchanged relative to the concave and convex portions of an elbow after a turn which may result in the change of fluid velocities and gas–liquid pressure drop.     

Dynamics of a vapor shell around a heated particle in a liquid

The dynamics and heat and mass exchange of a vapor bubble containing a heated particle is studied in relation to the problem of vapor explosions. It is shown that the process involves two stages: dynamic stage and thermal stage. The dynamic stage is characterized by pressure fluctuations and a rapid increase in the thickness of the vapor layer. It is shown that the simplifying assumptions of the constancy of assumptions of constant heat conductivity of the vapor and linear temperature profile in the vapor layer lead to qualitatively incorrect results. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 69–78, July–August, 2007