Evolution of distortions of the spherical shape of a cavitation bubble in acoustic supercompression

The evolution of small perturbations of the spherical shape of a vapor bubble in the process of its single strong expansion and compression in deuterated acetone is studied. In the mathematical model used the motion of vapor and liquid is broken down into the spherical component and its small nonspherical perturbation. The spherical component is described by the fluid dynamics equations with account for time-dependent heat conduction and evaporation and condensation on the liquid-vapor interface using equations of state constructed from experimental data. In describing the nonspherical component the liquid viscosity and the surface tension are taken into account, while the effect of the bubble content is disregarded. Certain simple analytical formulas are presented which describe the bubble radius at the moment of maximum expansion, its variation in the compression stage, and the evolution of the bubble sphericity distortion in compression.     

Direct-contact heat transfer to a spherical liquid/vapor two-phase bubble trailing a wake

The paper deals with the heat transfer causing evaporation of liquid drops in a medium of an immiscible, less volatile liquid. Each drop turns into a two-phase bubble, consisting of a growing vapor phase and a reducing liquid phase, which continues to buoy up in the medium. The bubble is modeled as a sphere in which the yet-to-be vaporized liquid spreads over the rear surface while the rest is occupied by the heat-insulating vapor phase. The rear surface to serve as the effective heat transfer area is assumed to be covered with an axisymmetric wake instead of a boundary layer flow. The quasi-steady, overall heat transfer through the wake in the medium and the layer of the yet-to-be vaporized liquid in the bubble is predicted and compared with relevant experimental results.Die Untersuchung befaßt sich mit der durch die Verdampfung von Flüssigkeitstropfen in einem aus unvermischbarer, flüchtiger Flüssigkeit bestehendem, Medium verursachten Wärmeübertragung. Aus jedem Tropfen entsteht eine Zweiphasenblase, bestehend aus einer wachsenden Dampfphase und einer abnehmenden Flüssigkeitsphase, die in das Medium aufsteigt. Die Blase wird anhand eines Kugelmodells betrachtet, an dem sich die noch nicht verdampfte Flüssigkeit über die Rückseite verteilt und die restliche Fläche mit der wärmeisolierenden Dampfphase behaftet ist. Es wird angenommen, daß sich an der Rückseite als wirksamer Wärmeübergangsbereich ein achsensymmetrischer Nachlauf bildet. Es werden die quasi-gleichförmige Wärmeübertragung durch den Nachlauf in das Medium und durch die Schicht Lage der nicht verdampften Flüssigkeit in der Blase mathematisch berechnet und mit relevanten Versuchsergebnissen verglichen.     

Instability of a spherical gas bubble in a variable-pressure field

Only a few studies, of which we mention [1–5], have been addressed to the problem of the stability of the accelerated motion of a spherical interface of two fluids. In the present paper we consider the problem of the stability of radial motion of the spherical boundary of a gas bubble in an incompressible inviscid liquid under the action of variable external pressure. Surface tension is not taken into account. We study the possibility of the existence of stable motions for broad classes of time dependence of the external pressure, namely for monotonic and periodic dependences. It is shown that stability is possible only for infinitely large bubble radii or for very specific assumptions concerning the initial conditions and the pressure-time dependence law.     

Modeling the motion of a vapor bubble in a tube in an ascending flow

The steady rise of a vapor bubble in a liquid moving in a vertical tube is modeled by means of the Navier-Stokes equations. The shape of the vapor bubble (drop) and the structure of the flow are determined by numerically solving the equations inside and outside the drop. The calculations are made on the interval of intermediate values of the dimensionless parameters and describe the transition to piston-type motion. The solutions obtained are compared with the existing experimental and approximate data for creeping flows. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 76–86, July–August, 1994.     

Influence of physical parameters on the collapse of a spherical bubble

This paper examines the influence of physical parameters on the collapse dynamics of a spherical bubble filled with diatomic gas ($\kappa =7/5$). The problem is formulated by the Rayleigh–Plesset dynamical equation, whose numerical solutions are carried out by Maple. Our studies show that each physical parameter affects the bubble collapse dynamics in different degree, which reveals that bubble collapse dynamics must considers all the parameters including liquid viscosity, surface tension, etc, else the outcome cannot be trusted.     

Shape of the vapor bubble upon explosive boiling

A relation for the shape of a vapor bubble forming during propagation of a vaporization front is proposed. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 122–123, March–April, 2000.     

An initially spherical bubble rising near a vertical wall

The dynamics of a single rising bubble in the vicinity of a vertical wall is explored via three-dimensional numerical simulations. A finite volume method is used to solve the incompressible Navier–Stokes equations. The gas–liquid interface is reconstructed by volume-of-fraction (VOF) method. The trajectory, velocity, shape and vorticity of the bubble are analyzed in detail. The numerical results show that the presence of the wall imposes a repulsion on the bubble and that the bubble migrates away from the wall upon release. The onset of bubble path oscillation is found to occur earlier than for a freely rise counterpart and also at a lower Galilei number. Interestingly, we find that the vertical wall serves as a destabilizing factor in the wall-normal direction but a stabilizing factor in the spanwise direction. The increase of bubble inertia is discovered to enhance the influence of the wall. Furthermore, the bubble oscillations seem insensitive to the variation of the initial bubble-wall distance.     

On the particle inertia-free collision with a partially contaminated spherical bubble

The collision between a contaminated spherical bubble and fine particles in suspension is considered for r_p/r_b ? 1 (r_p being the radius of the particles in suspension and r_b the radius of the bubble). The collision probability or efficiency is defined as the number of particles colliding the bubble surface to the number of particles initially present in the volume swept out by the bubble. In this note we show that the collision probability can be expressed as P_c(r_p/r_b,Re) = g(r_p/r_b)f(Re) for both mobile and immobile interfaces. For partially contaminated bubbles a linear or quadratic dependency in r_p/r_b is found depending on the level of contamination and the value of r_p/r_b. These behaviors are given by the flux of particles near the surface which is controlled by the tangential velocity for mobile interfaces and by the velocity gradient for immobile interfaces. The threshold value (r_p/r_b)_th between the r_p/r_b and (r_p/r_b)² evolution is shown to vary as sin^n(Re)(θ_clean/n(Re))sin(3θ_clean/4), θ_clean being the angle describing the front clean part of the bubble and n(Re) varying from n = 2 to n = 1 from small to large Reynolds number.     

Forced oscillations of a gas bubble in a spherical volume of a compressible liquid

A spherically symmetric problem of oscillations of a single gas bubble at the center of a spherical flask filled with a compressible liquid under the action of pressure oscillations on the flask wall is considered. A system of differential-difference equations is obtained that extends the Rayleigh-Plesset equation to the case of a compressible liquid and takes into account the pressure-wave reflection from the bubble and the flask wall. A linear analysis of solutions of this system of equations is performed for the case of harmonic oscillations of the bubble. Nonlinear resonance oscillations and nearly resonance nonharmonic oscillations of the bubble caused by harmonic pressure oscillations on the flask wall are analyzed. Ufa Scientific Center, Russian Academy of Sciences, Ufa 450000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 111–118, March–April, 1999.     

The behavior of a spherical bubble near a solid wall in a compressible liquid

Summary The behavior of a spherical bubble near a solid wall is analysed by considering the liquid compressibility. The equation of motion of the bubble with first order correction for the effects of liquid compressibility and solid wall is derived. The equation obtained here coincides with the known result in case of L or C . Further experimental study is made on the motion of bubbles produced by a spark discharge in water. The theoretical results are in good agreement with the experiments.

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Das Verhalten einer kugelförmigen Blase in einer kompressiblen Flüssigkeit in der Nähe einer festen Wand

Übersicht Bei Berücksichtigung der Flüssigkeitskompressibilität wird das Verhalten einer kugelförmigen Blase in der Nähe einer festen Wand analysiert. Die Gleichung der Bewegung der Blase wird mit der Korrektur erster Ordnung für den Einfluß der Flüssigkeitskompressibilität und der festen Wand angegeben. Aus der erhaltenen Gleichung wird für L oder C das bekannte Ergebnis hergeleitet. Darüber hinaus wird eine experimentelle Untersuchung der Blasenbewegung durchgeführt. Die Blase wird mit Hilfe von Funkendurchschlägen zwischen Elektroden in Wasser erzeugt. Die theoretischen Ergebnisse stimmen gut mit den Experimenten überein.

     

Experimental investigation of vapor bubble growth during flow boiling in a microchannel

Experiments were conducted to analyze flow boiling characteristics of water in a single brass microchannel of 25 mm length, 201 μm width, and 266 μm depth. Different heat flux conditions were tested for each of two different mass flow rates over three different values of inlet fluid temperature. Temporal and spatial surface temperature profiles were analyzed to show the relative effect of axial heat conduction on temperature rise along the channel length and the effect of flow regime transition on local surface temperature oscillation. Vapor bubble growth rate increased with increasing wall superheat. The slower a bubble grew, the further it was carried downstream by the moving liquid. Bubble growth was suppressed for increased mass flux while the vapor bubble was less than the channel diameter. The pressure spike of an elongating vapor bubble was shown to suppress the growth of a neighboring bubble by more than 50% of its volume. An upstream progression of the Onset of Bubble Elongation (OBE) was observed that began at the channel exit and progressed upstream. The effects of conjugate heat transfer were observed when different flow regime transitions produced different rates of progression for the elongation sequence. Instability was observed at lower heat fluxes for this single channel experiment than for similar studies with multiple channels.     

Interfacial mass transfer around a vapor bubble during nucleate boiling

Interfacial mass transfer from vapor bubbles affects markedly the heat transfer efficiency of nucleate boiling. The position of the interfacial zone that exhibits zero net mass flux, namely, the zero-flux zone, represents an essential parameter in detailed modeling works on nucleate boiling. Assuming a linear temperature profile in the superheated liquid adjacent to the heating wall, our previous work (Li et al. [10]) demonstrated the zero-flux angle as a function of wall superheat, solid-liquid- vapor contact angle, and bubble growth rate. To make a more realistic framework, we refined in this paper the proposed mass flux model by taking into account the role of thermocapillary flow that is induced by the temperature gradient around the vapor bubble, and that of non-condensable gas presented in the boiling liquid. The Hertz-Kundsen-Schrage equation describes the interfacial mass flux distribution along the vapor bubble surface. Owing to the flattened temperature distribution produced by thermocapillary flow, which significantly reduces the interfacial area to evaporation, the zero-flux zone shifts to the bubble base with most of the cap regime to condense vapor at the interface and to produce the thermal jet. This occurrence also weakens the dependence of bubble growth rate and of the contact angle on the location of zero-flux zone, and yields early occurrence of the non-condensation limit at which the entire bubble surface is subjected to evaporation. Sensitivity analysis demonstrated the significance of process parameters on the evaluation of zero-flux angle using the HKS equation.