Separation of a vapor bubble and calculation of the critical bubble radius

In this work a statistical model is developed by deriving the probability density function (pdf) of bubble coalescence on boiling surface to describe the distribution of vapor bubble radius. Combining this bubble coalescence model with other existing models in the literature that describe the dynamics of bubble motion and the mechanisms of heat transfer, the surface heat flux in subcooled nucleate boiling can be calculated. By decomposing the surface heat flux into various components due to different heat transfer mechanisms, including forced convection, transient conduction, and evaporation, the effect of the bubble motion is identified and quantified. Predictions of the surface heat flux are validated with R134a data measured in boiling experiments and water data available in the literature, with an overall good agreement observed. Results indicate that there exists a limit of surface heat flux due to the increased bubble coalescence and the reduced vapor bubble lift-off radius as the wall temperature increased. Further investigation confirms the consistency between this limit value and the experimentally measured critical heat flux (CHF), suggesting that a unified mechanistic modeling to predict both the surface heat flux and CHF is possible. In view of the success of this statistical modeling, the authors tend to propose the utilization of probabilistic formulation and stochastic analysis in future modeling attempts on subcooled nucleate boiling.

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The Deflection of an Ice Sheet by a Submerged Gas Source

Journal of Applied Mechanics ◽

10.1115/1.3424038 ◽

1977 ◽

Vol 44 (2) ◽

pp. 279-284 ◽

Cited By ~ 1

Author(s):

D. R. Topham

Keyword(s):

Material Properties ◽

Bubble Radius ◽

Ice Sheet ◽

Large Degree ◽

Ice Thickness ◽

Oil Well ◽

Gas Source ◽

Elastic Thin Plate ◽

Trapped Gas ◽

Critical Bubble

The deflection of an infinite ice sheet by a submerged gas source, as would result from an undersea gas or oil well blowout is analysed utilizing an elastic thin plate model. The results show that fracture may occur either at the bubble center or just beyond the bubble edge, depending upon the bubble depth, the ice thickness, and the material properties assumed for the ice sheet. For ice one meter in thickness and a trapped gas depth greater than 100 mm, fracture at the bubble edge is probable. The critical bubble radius for failure varies rapidly with ice thickness, bubble depth, and the ice properties, which in view of the variability of the latter, makes the prediction of actual bubble radii to cause failure subject to a large degree of uncertainty.

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Growth of Microcellular Foams in Viscoelastic Mediums

Materials ◽

10.1115/imece2004-59490 ◽

2004 ◽

Author(s):

Ki Young Kim ◽

Sung Lin Kang ◽

Ho-Young Kwak

Keyword(s):

Integral Method ◽

Close Agreement ◽

Bubble Radius ◽

Saturation Pressure ◽

Polymer Processing ◽

Governing Equations ◽

Concentration Boundary ◽

First Order ◽

Microcellular Foams ◽

Critical Bubble

The growing of the critical bubble by diffusion process in visco-elastic medium was treated by an integral method for the concentration boundary layer. In this study, we obtained a set of the first order time dependent equations to obtain bubble radius and gas pressure inside the bubble simultaneously. The calculated final cell sizes depending on the initial saturation pressure are in close agreement with the observed ones. The governing equations developed in this study may be used in polymer processing of microcellular foams.

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Growth and Collapse Dynamics of a Vapor Bubble near or at a Wall

Water ◽

10.3390/w13010012 ◽

2020 ◽

Vol 13 (1) ◽

pp. 12

Author(s):

Huigang Wang ◽

Chengyu Zhang ◽

Hongbing Xiong

Keyword(s):

Vapor Bubble ◽

Bubble Growth ◽

Solid Wall ◽

Bubble Radius ◽

Entropy Change ◽

Growth Stages ◽

Change Rate ◽

Bubble Density ◽

Particle Hydrodynamics ◽

Vapor Mass

This study investigated the dynamics of vapor bubble growth and collapse for a laser-induced bubble. The smoothed particle hydrodynamics (SPH) method was utilized, considering the liquid and vapor phases as the van der Waals (VDW) fluid and the solid wall as a boundary. We compared our numerical results with analytical solutions of bubble density distribution and radius curve slope near a wall and the experimental bubble shape at a wall, which all obtained a fairly good agreement. After validation, nine cases with varying heating distances (L2 to L4) or liquid heights (h2 to h10) were simulated to reproduce bubbles near or at a wall. Average bubble radius, density, vapor mass, velocity, pressure, and temperature during growth and collapse were tracked. A new recognition method based on bubble density was recommended to distinguish the three substages of bubble growth: (a) inertia-controlled, (b) transition, and (c) thermally controlled. A new precollapse substage (Stage (d)) was revealed between the three growth stages and collapse stage (Stage (e)). These five stages were explained from the out-sync between the bubble radius change rate and vapor mass change rate. Further discussions focused on the occurrence of secondary bubbles, shockwave impact on the wall, system entropy change, and energy conversion. The main differences between bubbles near and at the wall were finally concluded.

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Vapor bubble growth with a high value of overheating

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2007.1.006 ◽

2007 ◽

Vol 5 ◽

pp. 85-90

Author(s):

S.P. Aktershev ◽

V.V. Ovchinnikov

Keyword(s):

Experimental Data ◽

Numerical Simulation ◽

Satisfactory Agreement ◽

Vapor Bubble ◽

Bubble Growth ◽

Bubble Dynamics ◽

Bubble Radius ◽

Temperature Inhomogeneity ◽

Evaporation Front ◽

Initial Stage

The numerical simulation of the growth of a vapor bubble in inhomogeneously heated liquid is performed; the influence of the temperature inhomogeneity on the bubble dynamics is investigated. The calculations are compared with experimental data for a vapor bubble growing on a cylindrical heater. At high overheating, the results of the calculations are in satisfactory agreement with experimental data for the initial stage of growth of the vapor bubble. In the presence of evaporation fronts, the measured bubble radius values exceed the calculated values. This excess can be explained by the inflow of vapor to the bubble from the evaporation front.

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Approximate Solution for the Heat Transfer Controlled Growth of a Steadily Translating Vapor Bubble

Heat Transfer: Volume 2 ◽

10.1115/ht2008-56204 ◽

2008 ◽

Author(s):

Michael Shusser

Keyword(s):

Heat Transfer ◽

Approximate Solution ◽

Vapor Bubble ◽

Bubble Growth ◽

Constant Velocity ◽

Thermal Boundary Layer ◽

Bubble Radius ◽

Controlled Growth ◽

Flow Models ◽

Rate Comparison

Existing analytical solution for the problem of the heat transfer controlled growth of a spherical vapor bubble moving with a constant velocity under the assumptions of a thin thermal boundary layer and potential flow results in a complicated integral equation for the bubble radius and is too unwieldy to be used in multiphase flow models. The goal of this work is to suggest an approximate solution for this problem that gives correct asymptotic behavior and yields a simpler expression for the bubble growth rate. Comparison with the exact solution showed that this way a good approximation can be obtained.

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Numerical Simulation of Vapor–Bubble Collapse—Heat Transfer and Nonlinear Dynamics Issues

Journal of Heat Transfer ◽

10.1115/1.4045353 ◽

2020 ◽

Vol 142 (3) ◽

Author(s):

Jyoti Bhati ◽

Swapan Paruya ◽

Subhramaniam Pushpavanam

Keyword(s):

Heat Transfer ◽

Nonlinear Dynamics ◽

Steady State ◽

Vapor Bubble ◽

Bubble Radius ◽

Bubble Collapse ◽

Large Contribution ◽

Steady State Analysis ◽

The Stability ◽

State Analysis

Abstract In this work, we compute the dynamics of a spherical vapor-bubble in an infinite pool of subcooled water during bubble collapse using our semi-analytical method. The main contribution of this work is to bring out the dynamics of nonmonotonic bubble collapse describing heat transfer characteristics and nonlinear dynamics. The dynamics shows the variation of radius with time for collapsing vapor bubble at different subcooling ΔTsub of 1.40 K to 35 K. The present approach accurately determines the bubble radius decreasing with time and has been compared with our experimental results, the experiment from literature, the other theories, and correlations. As it is noted that the literature lacks steady-state analysis of oscillating bubble collapse, we also report the steady-state analysis and the bifurcation analysis of bubble collapse at a pressure of 1.0 atm to check the stability of bubble collapse. The effect of ΔTsub and initial bubble radius R0 on dynamics of bubble collapse has been analyzed. The collapse of big bubbles involves with the bubble oscillations because of a large contribution of liquid inertia and the collapse of very small bubbles essentially occurs in heat transfer regime.

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