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

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.

Numerical Analysis of Vapor Bubble Growth and Wall Heat Transfer During Flow Boiling of Water in a Microchannel

2005 ◽  
Author(s):  
Abhijit Mukherjee ◽  
Satish G. Kandlikar
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Vapor Bubble ◽  
Bubble Growth ◽  
Stokes Equations ◽  
Flow Boiling ◽  
Navier Stokes ◽  
Channel Cross Section ◽  
Wall Heat Transfer ◽  
Wall Superheat

The present study is performed to analyze the wall heat transfer mechanisms during growth of a vapor bubble inside a microchannel. The microchannel is of 200 μm square cross section and a vapor bubble begins to grow at one of the walls, with liquid coming in through the channel inlet. The complete Navier-Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid vapor interface is captured using the level set technique. The bubble grows rapidly due to heat transfer from the walls and soon turns into a plug filling the entire channel cross section. The average wall heat transfer at the channel walls is studied for different values of wall superheat and incoming liquid mass flux. The results show that the wall heat transfer increases with wall superheat but is almost unaffected by the liquid flow rate. The bubble growth is found to be the primary mechanism of increasing wall heat transfer as it pushes the liquid against the walls thereby influencing the thermal boundary layer development.

A New Method for Estimating Bubble Diameter At Different Gravity Levels for Nucleate Pool Boiling

2021 ◽  
Author(s):  
Sandipan Banerjee ◽  
Yongsheng Lian ◽  
Yang Liu ◽  
Mark Sussman
Keyword(s):  
Heat Transfer ◽  
Growth Rate ◽  
Vapor Bubble ◽  
Bubble Growth ◽  
Bubble Diameter ◽  
Nucleate Boiling ◽  
New Method ◽  
Space Applications ◽  
Earth Gravity ◽  
Micro Gravity

Abstract Nucleate boiling has significant applications in earth gravity( in industrial cooling applications) and micro-gravity conditions (in space exploration, specifically in making space applications more compact). However, the effect of gravity on the growth rate and bubble size is not yet well understood. We perform numerical simulations of nucleate boiling using an adaptive Moment-of-Fluid (MoF) method for a single vapor bubble (water or Perfluoro-n-hexane) in saturated liquid for different gravity levels. Results concerning the growth rate of the bubble, specifically the departure diameter and departure time have been provided. The MoF method has been first validated by comparing results with a theoretical solution of vapor bubble growth in super-heated liquid without any heat-transfer from the wall. Next, bubble growth rate, bubble shape and heat transfer results under earth gravity, reduced gravity and micro-gravity conditions are reported and they are in good agreement with experiments. Finally, a new method is proposed for estimating the bubble diameter at different gravity levels. This method is based on an analysis of empirical data at different gravity values and using power-series curve fitting to obtain a generalized bubble growth curve irrespective of the gravity value. This method is shown to provide a good estimate of the bubble diameter for a specific gravity value and time.

A Statistical Model of Bubble Coalescence and Its Application to Boiling Heat Flux Prediction—Part I: Model Development

2009 ◽  
Vol 131 (12) ◽  
Author(s):  
Wen Wu ◽  
Barclay G. Jones ◽  
Ty A. Newell
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Statistical Model ◽  
Vapor Bubble ◽  
Surface Heat Flux ◽  
Bubble Radius ◽  
Nucleate Boiling ◽  
Surface Heat ◽  
Bubble Coalescence ◽  
Bubble Motion

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.

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

Water ◽  
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.

Vapor bubble growth with a high value of overheating

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.

Numerical Study of the Effect of Surface Tension on Vapor Bubble Growth During Flow Boiling in Microchannels

2006 ◽  
Author(s):  
Abhijit Mukherjee ◽  
Satish G. Kandlikar
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Vapor Bubble ◽  
Bubble Growth ◽  
Stokes Equations ◽  
Numerical Study ◽  
Flow Boiling ◽  
Navier Stokes ◽  
Wall Heat Transfer ◽  
Effect Of Surface

Microchannel heat sinks typically consist of parallel channels connected through a common header. During flow boiling random temporal and spatial formation of vapor bubbles may lead to reversed flow in certain channels which causing an early CHF condition. Inside the microchannels the liquid surface tension forces is expected to play an important role and impact the vapor bubble growth and corresponding wall heat transfer. In the present study growth of a vapor bubble inside a microchannel during flow boiling is numerically studied by varying the surface tension but keeping the value of contact angle constant. The complete Navier-Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid-vapor interface is captured using the level set technique. The fluid properties used are of water but the surface tension value is varied systematically. The effect of surface tension on bubble growth rate and wall heat transfer is quantified. The results indicate that for the range of parameters investigated surface tension has little influence on bubble growth and wall heat transfer.

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