Simulation of heat transfer with the growth and collapse of a cavitation bubble near the heated wall

The growth and collapse behaviors of a single cavitation bubble near a heated wall and its effect on the heat transfer are numerically investigated. The present study is designed to reveal the mechanism of cavitation enhanced heat transfer from a microscopic perspective. In the simulation, the time-dependent Navier-Stokes equations are solved in an axisymmetric two-dimensional domain. The volume of fluid (VOF) method is employed to track the liquid-gas interface. It is assumed that the gas inside the bubble is compressible vapor, and the surrounding liquid is incompressible water. Mass transfer between two phases is ignored. The calculated bubble profiles were compared to the available experimental data, and a good agreement was obtained. Then, the relationship among bubble motion, flow field and surface heat transfer coefficient was analyzed. On this basis, the effects of such factors as the initial distance between the bubble and the wall, the initial vapor pressure and the initial bubble nucleus size on the heat transfer enhancement are discussed. The present study is helpful to understand the heat transfer phenomenon in presence of cavitation bubble in liquid.     

Bubble induced heat transfer in two phase gas-liquid flow

The influence of gas bubbles on heat transfer in two phase gas-liquid systems has been investigated. Platinum wires have been used as heat-transfer probes and the two phase flow has been simulated by generating a single continuous stream of discrete gas bubbles into a stationary liquid. The contribution of various modes of heat transfer has been determined. It has been found that transient conduction into the liquid is the predominant mode of the bubble induced heat transfer and is responsible for about 75 per cent of heat transfer. Convection contributes the remainder. A theoretical model of the bubble induced heat transfer based on the surface renewal and penetration theory has been developed.     

Numerical simulation on enhancement of natural convection heat transfer by acoustic cavitation in a square enclosure

Natural convection heat transfer of liquid in a square enclosure with and without acoustic cavitation is numerically investigated. In order to model the effect of sound field, a prescribed periodic change pressure is imposed on liquid in the region with ultrasonic beam. The cavitation model which takes into consideration such effects as phase change, bubble dynamics, and noncondensable gases is established. In order to capture the cavitation phenomenon and obtain a realistic pressure field and cavitation zones, the time step is set to quarter period of sound pressure and a relatively small relaxation factor for momentum equation and near zero relaxation factors for vaporization mass and density are used. The simulation results show that both liquid temperature uniformity and heat transfer coefficient of heating surface are greatly improved by means of acoustic cavitation. This phenomenon can be explained by jet-flow bundle formed by the asymmetry collapse of cavitation bubbles on the heating surface. The jet-flow bundle cannot only enhance fluid mixing around the heating surface and thus improve the uniformity of liquid temperature in the square enclosure, but also directly impact the heating surface and thus make thermal boundary layer become thin. The field synergy principle is introduced to analyze the heat transfer enhancement by acoustic cavitation.     

The effect of liquid film evaporation on flow boiling heat transfer in a micro tube

Flow boiling in micro channels is attracting large attention since it leads to large heat transfer area per unit volume. Generated vapor bubbles in micro channels are elongated due to the restriction of channel wall, and thus slug flow becomes one of the main flow regimes. In slug flow, sequential bubbles are confined by the liquid slugs, and thin liquid film is formed between tube wall and bubble. Liquid film evaporation is one of the main heat transfer mechanisms in micro channels and liquid film thickness is a very important parameter which determines heat transfer coefficient. In the present study, liquid film thickness is measured by laser focus displacement meter under flow boiling condition and compared with the correlation proposed for an adiabatic flow. The relationship between liquid film thickness and heat transfer coefficient is also investigated. Initial liquid film thickness under flow boiling condition can be predicted well by the correlation proposed under adiabatic condition. Under flow boiling condition, liquid film surface fluctuates due to high vapor velocity and shows periodic pattern against time. Frequency of periodic pattern increases with heat flux. At low quality, heat transfer coefficients calculated from measured liquid film thickness show good accordance with heat transfer coefficients obtained directly from wall temperature measurements.     

Lattice-Boltzmann simulation of induced cavitation in protruding structure

Pressure induced cavitation is a promising heat dissipation technology since it enables phase-change heat transfer at relatively low temperature. In this study, the sustainability properties of induced cavitation in protruding structure are studied by the Lattice Boltzmann Method. The simulation results suggest that a typical cavitation process is composed of four stages: 1st: cavitation appears in front of inflow liquid, 2nd: bubble shedding, 3rd: cavitation area gradually stretches towards downstream, 4th: cavitation area reaches equilibrium steady state. The flow pattern varies as the increase of inlet velocity. Only inlet velocity greater than “critical inlet velocity” can cavitation bubbles exist perpetually in protruding structure. The value of the critical inlet velocity decreases as the increase of width ratio and the resulting cavitation number falls to 1.8–2.1. The main mechanism for cavitation in protruding structure is pressure drop, rather than shear force.     

On the transition from partial to fully developed subcooled flow boiling

The subject of the present study is to relate the boiling heat transfer process with experimentally observed bubble behaviour during subcooled flow boiling of water in a vertical heated annulus. It presents an attempt to explain the transition from partial to fully developed flow boiling with regard to bubble growth rates and to the time that individual bubbles spend attached to the heater surface.Within the partial nucleate boiling region bubbles barely change in size and shape while sliding a long distance on the heater surface. Such behaviour indicates an important contribution of the microlayer evaporation mechanism in the overall heat transfer rate. With increasing heat flux, or reducing flow rate at constant heat flux, bubble growth rates increase significantly. Bubbles grow while sliding, detach from the heater, and subsequently collapse in the bulk fluid within a distance of 1-2 diameters parallel to the heater surface. This confirms that bubble agitation becomes a leading heat transfer mode with increasing heat flux. There is however, a sharp transition between the two observed bubble behaviours that can be taken as the transition from partial to fully developed boiling. Hence, this information is used to develop a new model for the transition from partial to fully developed subcooled flow boiling.     

Bubble growth and horizontal coalescence in saturated pool boiling on a titanium foil,investigated by high-speed IR thermography

Growth of an isolated bubble and horizontal coalescence events between bubbles of dissimilar size were examined during pool nucleate boiling of water on a horizontal, electrically-heated titanium foil 25 μm thick. Wall temperature measurements on the back of the foil by high-speed IR camera, synchronized with high-speed video camera recordings of the bubble motion, improved the temporal and spatial resolution of previous observations by high-speed liquid crystal thermography to 1 ms and 40 μm, respectively, leading to better detailed maps of the transient distributions of wall heat flux. The observations revealed complex behaviour that disagreed with some other observations and current modelling assumptions for the mechanisms of heat transfer over the wall contact areas of bubbles and interactions between bubbles. Heat transfer occurred from the entire contact area and was not confined to a narrow peripheral triple-contact zone. There was evidence of an asymmetrical interaction between bubbles before coalescence. It was hypothesised that a fast-growing bubble pushed superheated liquid under a slow-growing bubble. Contact of this liquid with regions of the wall that had been pre-cooled during bubble growth caused local reductions in the wall heat flux. During coalescence, movement of liquid under both bubbles caused further changes in the wall heat flux that also depended on pre-cooling. Contraction of the contact area caused a peripheral reduction in the heat flux and there was no evidence of a large increase in heat flux during detachment. Boiling on very thin foils imposes special conditions. Sensitivity to the thermal history of the wall must be taken into account when applying the observations and hypotheses to other conditions.     

Similarities and Differences Between Flow Boiling in Microchannels and Pool Boiling

Recent literature indicates that under certain conditions the heat transfer coefficient during flow boiling in microchannels is quite similar to that under pool boiling conditions. This is rather unexpected, as microchannels are believed to provide significant heat transfer enhancement under single-phase as well as flow boiling conditions. This article explores the underlying heat transfer mechanisms and illustrates the similarities and differences between the two processes. Formation of elongated bubbles and their passage over the microchannel walls have similarities to the bubble ebullition cycle in pool boiling. During the passage of elongated bubbles, the longer duration between two successive liquid slugs leads to wall dryout and a critical heat flux that may be lower than that under pool boiling conditions. A clear understanding of these phenomena will help in overcoming these limiting factors and in developing strategies for enhancing heat transfer during flow boiling in microchannels.     

Influence of convective heat transfer modeling on the estimation of thermal effects in cryogenic cavitating flows

The accuracy of numerical simulations for the prediction of cavitation in cryogenic fluids is of critical importance for the efficient design and performance of turbopumps in rocket propulsion systems. One of the main remaining challenges is efficiency in modeling of the physics, handling the multi-scale properties involved and developing robust numerical methodologies. Such flows involve thermodynamic phase transitions and cavitation bubbles that are on a smaller scale than the global flow structure. Cryogenic fluids are thermo-sensitive, and therefore, thermal effects and strong variations in fluid properties can alter the cavitation properties. The aim of this work is to address the challenge posed by thermal effects. The Rayleigh–Plesset equation is modified by the addition of a term for convective heat transfer at the interface between the liquid and the bubble coupled with a bubbly flow model to assess the prediction of thermal effects. We perform a parametric study by considering several values of and models for the convective heat transfer coefficient, h_b, and we compare the resulting temperature and pressure profiles with the experimental data. Finally, the results of a 2D simulation with a commercial CFD code are presented and compared with the previous results. We note the importance of the choice of h_b for the correct prediction of the temperature drop in the cavitating region, and we assess the most efficient models, underlining that the choice of h_b estimation model in a cryogenic cavitating flow is more important in the bubble growth phase than in the bubble collapse phase.     

Heat transfer in subcooled jet impingement boiling at high wall temperatures

An analytical approach for heat transfer modelling of jet impingement boiling is presented. High heat fluxes with values larger than 10 MW/m² can be observed in the stagnation region of an impinging jet on a red hot steel plate with wall temperatures normally being associated with film boiling. However, sufficiently high degrees of subcooling and jet velocity prevent the formation of a vapor film, even if the wall superheat is large. Heat transfer is governed by turbulent diffusion caused by the rapid growth and condensation of vapor bubbles. Due to the high population of bubbles at high heat fluxes it has to be assumed that a laminar sublayer cannot exist in the immediate vicinity of a red hot heating surface. A mechanistic model is proposed which is based on the assumption that due to bubble growth and collapse the maximum turbulence intensity is located at the wall/liquid interface and that eddy diffusivity decreases with increasing wall distance.     

Convective heat transfer to water containing bubbles: Enhancement not dependent on thermocapillarity

Upstream injection of small gas bubbles causes increases of up to 50 per cent in heat-transfer coefficient for water flowing upward in a channel of rectangular cross-section. The increase depends on gas flow rate and liquid phase Reynolds number but not on heat flux, indicating that thermocapillary flows do not contribute to the heat transfer. A possible mechanism for the increase is secondary flow production by the interaction of bubbles with the shear flow near the wall.     

Investigation of heat transfer and bubble dynamics in a boiling thin liquid film flowing over a rotating disk

Nucleate boiling heat transfer and bubble dynamics in a thin liquid film on a horizontal rotating disk were studied. A series of experiments were conducted to determine the heat transfer coefficient on the disk. At low rotation and flow rates, vigorous boiling increased the heat transfer coefficients above those without boiling. Higher rotational speeds and higher flow rates increased the heat transfer coefficient and suppressed boiling by decreasing the superheat in the liquid film. The flow field on the disk, which included supercritical (thin film) flow upstream of a hydraulic jump, and subcritical (thick film) flow downstream of a hydraulic jump, affected the type of bubble growth. Three types of bubble growth were identified. Vigorous boiling with large, stationary bubbles were observed in the subcritical flow. Supercritical flow produced small bubbles that remained attached to the disk and acted as local obstacles to the flow. At low rotational rates, the hydraulic jump that separated the supercritical and subcritical regions produced hemispherical bubbles that protruded out of the water film surface and detached from the disk, allowing them to slide radially outward. A model of the velocity and temperature of the microlayer of water underneath these sliding bubbles indicated that the microlayer thickness was approximately 1/25th of that of the surrounding water film. This microlayer is believed to greatly enhance the heat transfer rate underneath the sliding bubbles.     

On the dynamics and heat transfer of bubble train in micro-channel flow boiling

The dynamics and heat transfer characteristics of flow boiling bubble train moving in a micro channel is studied numerically. The coupled level set and volume of fluid (CLSVOF) is utilized to track interface and a non-equilibrium phase change model is applied to calculate the interface temperature as well as heat flux jump. The working fluid is R134a and the wall material is aluminum. The fluid enters the channel with a constant mass flux (335 kg/m² 1 s), and the boundary wall is heated with constant heat flux (14 kW/m²). The growth of bubbles and the transition of flow regime are compared to an experimental visualization. Moreover, the bubble evaporation rate and wall heat transfer coefficient have been examined, respectively. Local heat transfer is significantly enhanced by evaporation occurring vicinity of interface of the bubbles. The local wall temperature is found to be dependent on the thickness of the liquid film between the bubble train and the wall.     

Numerical investigation of the bubble growth in horizontal rectangular microchannels

To explore the mechanism of flow boiling in microchannels, the processes of a single-vapor bubble evaporating and two lateral bubbles merging in a 2D microchannel are investigated. The temperature recovery model based on volume of fluid method is adopted to perform the flow boiling phenomena. The effects of wall superheat, Reynolds number, contact angle, surface tension, and two-bubble merger on heat transfer are discussed. Wall superheat dominates the bubble growth and is roughly proportional to wall heat flux. The update of velocity and temperature fields’ distribution in the channel increases with increasing inflow Reynolds number, which improves the wall heat flux markedly. Besides, the area of thin liquid film between the wall and the bubble is enlarged by reducing the contact angle, thus, expanding the wall heat flux several times compared with the single-phase cross section. However, variation of surface tension (0.0589, 0.1?N/m) is found to be insignificant.     

Subcooled flow boiling heat transfer and associated bubble characteristics of R-134a in a narrow annular duct

Experiments are conducted here to investigate how the channel size affects the subcooled flow boiling heat transfer and associated bubble characteristics of refrigerant R-134a in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm in this study. From the measured boiling curves, the temperature undershoot at ONB is found to be relatively significant for the subcooled flow boiling of R-134a in the duct. The R-134a subcooled flow boiling heat transfer coefficient increases with a reduction in the gap size, but decreases with an increase in the inlet liquid subcooling. Besides, raising the imposed heat flux can cause a substantial increase in the subcooled boiling heat transfer coefficient. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are small in the narrow duct. Visualization of the subcooled flow boiling processes reveals that the bubbles are suppressed to become smaller and less dense by raising the refrigerant mass flux and inlet subcooling. Moreover, raising the imposed heat flux significantly increases the bubble population, coalescence and departure frequency. The increase in the bubble departure frequency by reducing the duct size is due to the rising wall shear stress of the liquid flow, and at a high imposed heat flux many bubbles generated from the cavities on the heating surface tend to merge together to form big bubbles. Correlation for the present subcooled flow boiling heat transfer data of R-134a in the narrow annular duct is proposed. Additionally, the present data for some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density are also correlated.     

Numerical Simulation of Bubbles Deformation,Flow, and Coalescence in a Microchannel Under Pseudo-Nucleation Conditions

This paper reports the results of numerical study on bubbles deformation, flow, and coalescence under pseudo-nucleate boiling conditions in horizontal mini-/microchannels. The numerical simulation, which is based on the multiphase model of volume of fluid method, aims to study the corresponding flow behaviors of nucleate bubbles generated from the tube walls in mini-/microchannels so as to understand the effect of confined surfaces/walls on nucleate bubbles and heat transfer. Under the pseudo- or quasi-nucleate boiling condition, superheated small vapor bubbles are injected at the wall to ensure that the bubbles generation is under a similar condition of real nucleation. The numerical study examined the fluid mechanics of bubble motion with heat transfer, but the mass transfer across the bubble–liquid interface is not simulated in the present work.     

Phase-field modeling of bubble growth and flow in a Hele–Shaw cell

A phase-field model is presented for gas bubble growth and flow in a supersaturated liquid inside a Hele–Shaw cell. The flows in the gas and liquid are solved using a two-phase diffuse interface model that accounts for surface tension, interfacial mass transfer, and density and viscosity differences between the phases. This model is coupled with a phase-field equation for interface motion and a diffuse interface conservation equation for gas species transport. The model is first validated for a planar gas layer and a spherical bubble growing in a supersaturated liquid. It is shown that the results converge to the solution of the corresponding sharp interface model in the thin-interface limit. The model capabilities are demonstrated in several examples involving the growth and flow of multiple bubbles, including bubble coarsening and coalescence.     

Interfacial heat transfer of condensing bubble in subcooled boiling flow at low pressure

The interfacial heat transfer coefficient is an important parameter for the analysis of multi-phase flow. In subcooled boiling flow, bubbles condense through the interface of phases and the interfacial heat transfer determines the condensation rate which affects the two-phase parameters such as void fraction and local liquid temperature. Thus, the present experiments are conducted to correlate the interfacial heat transfer coefficient at low pressure in the subcooled boiling flow. The local liquid temperature is measured by microthermocouple and the bubble condensation rate is estimated by orthogonal, two-image processing. The condensate Nusselt number, which is a function of bubble Reynolds number, local liquid Prandtl number, and local Jacob number, is obtained from the experimental results. The bubble history is derived from the newly proposed correlation and the condensate Nusselt number is compared with the previous models.     

Numerical investigation of subcooled flow boiling in segmented finned microchannels

Bubble growth behavior and heat transfer characteristics during subcooled flow boiling in segmented finned microchannels have been numerically investigated. Simulations have been performed for a single row of segmented finned microchannel and predicted results are compared with experimental investigations. Onset of nucleation, formation of bubbles, their growth and movements have been investigated for different values of applied heat flux. Mechanism of bubble expansion without clogging resulting in enhanced heat transfer in segmented finned microchannels has been explained. Temperature and pressure fluctuations during subcooled flow boiling condition have been investigated. It is observed that at high heat flux, thin liquid film trapped between the bubble and channel wall is evaporated leading to localized heating effect. Predicted flow patterns are similar to experimental results. However, simulations over predict the bubble growth rate and heat transfer coefficient.     

Diffusion and reaction controlled dissolution of oxygen microbubbles in blood

A model for the dissolution of a bubble in blood is presented in this paper. The gas inside the bubble is oxygen and the collapse of the bubble is controlled by the diffusion of the gas from the bubble surface into the surrounding blood. The diffusion is facilitated by the oxygen uptake reaction between the dissolved gas and the hemoglobin, which is described using the Hill saturation curve. The model consists of a system of coupled differential equations describing the related mass transfer physics in an expanding computational domain, which follows the moving interface between the shrinking bubble and the surrounding blood. The main findings regarding the important collapse time of microbubbles in blood indicate that this time may vary from 10 s to 2 or 3 h depending on the size of the bubbles and on the parameters which specify the blood conditions.