A Level Set Method for Analysis of Film Boiling on an Immersed Solid Surface

A numerical method is presented for simulating film boiling on an immersed (or irregularly shaped) solid surface. The level set formulation for tracking the phase interfaces is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip condition at the fluid–solid interface. The boundary or matching conditions at the phase interfaces are accurately imposed by incorporating the ghost fluid approach based on a sharp-interface representation. The numerical method is tested through computations of bubble rise in a stationary liquid, single-phase fluid flow past a circular cylinder, and film boiling on a horizontal cylinder.     

A Novel Approach for Modeling Mixed Convection Film Boiling for a Vertical Flat Plate

A numerical model is developed to study mixed convection film boiling over a vertical flat plate. The integral form of conservation equations for each phase along with the appropriate interface conditions due to phase change is transformed into ordinary differential equation (ODE)-form. The length scale used in the model is based on Rayleigh–Taylor instability wave at the liquid–vapor interface. The heat transfer associated in the process is assessed and results are validated successfully for different available experimental results for natural convection and mixed convection film boiling. The mixed convection film boiling is characterized in terms of relevant nondimensional parameters for each phase.     

Forced Convection Film Boiling Heat Transfer Over a Vertical Cylinder

The knowledge of subcooled film boiling heat transfer is important as the basis of understanding the reflooding phenomenon during emergency cooling in a nuclear reactor under a loss-of-coolant accident. In this study, forced convection film boiling heat transfer from a vertical cylinder in Freon-113 flowing upward along the cylinder was measured for the flow velocities ranging from 0 to 1.3 m/s, and liquid subcoolings ranging from 0 to 20 K at pressures near atmospheric. A platinum heater with a diameter of 3 mm was heated by electric current. The heat transfer coefficients obtained are almost independent of vertical positions on the cylinder. The heat transfer coefficients are almost independent of velocity for the velocities lower than about 1 m/s and become higher for the velocities higher than 1 m/s. The heat transfer coefficients at each velocity are higher for higher liquid subcoolings. Improvement of film boiling heat transfer from the vertical cylinder with the increase in flow velocity is much less than that of horizontal cylinder in cross flow previously reported by the authors. This is mainly due to the difference of heat transfer enhancement mechanism; the former is the drag force on vapor flow acted by a liquid flow, and the latter is the pressure gradient near the front stagnation point caused by external potential flow.     

Numerical Simulation of Bubble Growth and Heat Transfer During Flow Boiling in a Surface-Modified Microchannel

Flow boiling in a microchannel without or with surface modifications, such as fins, grooves, and cavities, has received significant attention as an effective cooling method for high-power microelectronic devices. However, a general predictive approach for the boiling process has not yet been developed because of its complexity involving the bubble dynamics coupled with boiling heat transfer in a microscale channel. In this study, direct numerical simulations for flow boiling in a surface-modified microchannel are performed by solving the conservation equations of mass, momentum, and energy in the liquid and vapor phases. The bubble surfaces are determined by a sharp-interface level-set method, which is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip and contact-angle conditions on immersed solid surface of microstructures. This computation demonstrates that the surface-modified microchannel enhances boiling heat transfer significantly compared to a plain microchannel. The effects of various surface modifications on the bubble growth and heat transfer are investigated to find better conditions for boiling enhancement.     

Numerical simulation of nucleate boiling on a horizontal surface at high heat fluxes

Nucleate boiling at high heat fluxes has been studied numerically by solving the equations governing conservation of mass, momentum and energy in the liquid and vapor phases. The interface is captured by using the level set method based on a sharp-interface representation. The evaporative heat flux from the liquid microlayer is incorporated in the analysis. The effects of wall superheat, number density of nucleation sites and waiting period on the bubble dynamics and heat transfer in nucleate boiling are investigated. The heat fluxes obtained from the present numerical simulations are compared with the experimental data reported in the literature.     

Direct numerical simulation of flow boiling in a finned microchannel

Direct numerical simulations of bubble growth and heat transfer associated with flow boiling in a finned microchannel are performed by solving the conservation equations of mass, momentum and energy in the liquid and vapor phases. The phase interfaces are determined by a sharp-interface level-set method which is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip and contact-angle conditions on the immersed solid surface of fins. The effects of fin height, spacing, and length on the flow boiling in a microchannel are investigated to find the better conditions for heat transfer enhancement.     

Effect of surface wettability and electric field on transition of film boiling to nucleate boiling

Abstract

The phenomena of liquid–solid contact during film boiling due to the effect of surface-wettability have been focused in the present study. The numerical simulations during film boiling exhibit the collapse of vapor layer when the surface-wettability is sufficiently high, that is, for the hydrophilic surface. Vapor film collapse results in contact of liquid with the heated surface, which transforms the boiling mode more toward the nucleate regime. The contact area of liquid increases with time. However, such transition is not observed in the case of hydrophobic surface or the surface with higher contact angles. When a sufficiently strong electric field is applied across the liquid-vapor interface, the vapor film collapses and results in similar transition from film boiling to nucleate boiling. The required intensity of electric field at which the vapor film collapses increases with the increase in surface-superheat.     

Theoretical analysis of the stability of vapor film in subcooled film boiling on a horizontal wire

Linear stability analysis of a thin vapor film in subcooled film boiling on a horizontal cylinder is reported. The effects of liquid inertia, vapor viscosity and compressibility, and heat transfer were taken into account. Theoretical predictions of the heat transfer coefficient at the neutral stability point were compared with experimental data at the minimum-heat-flux point that was obtained during rapid quenching of thin horizontal wires in water and ethanol. At high liquid subcooling, the experimental value was 60% of the theoretical prediction irrespective of the wire diameter and quenching liquid. This difference was considered to be due to the nonuniformity of the vapor film which was neglected in the theoretical analysis. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(4): 219–235, 1997     

3D heat transfer analysis in a loop heat pipe evaporator with a fully saturated wick

A practical quasi three-dimensional numerical model is developed to investigate the heat and mass transfer in a square flat evaporator of a loop heat pipe with a fully saturated wicking structure. The conjugate heat transfer problem is coupled with a detailed mass transfer in the wick structure, and incorporated with the phase change occurring at the liquid–vapor interface. The three-dimensional governing equations for the heat and mass transfer (continuity, Darcy and energy) are developed, with specific attention given to the wick region. By comparing the results of the numerical simulations and the experimental tests, the local heat transfer mechanisms are revealed, through the obtained temperature distribution and the further derived evaporation rates along the liquid–vapor interface. The results indicate that the model developed herein can provide an insight in understanding the thermal characteristics of loop heat pipes during steady-state operation, especially at low heat loads.     

Film boiling heat transfer around a vertical finite‐length cylinder with a convex hemispherical bottom

The film boiling heat transfer around a vertical silver cylinder with a convex hemispherical bottom was investigated experimentally in quiescent water at atmospheric pressure. The experiments have been carried out using a quenching method. The diameter and length of the test cylinder are 32 mm and 48 mm, respectively. The test cylinder was heated to about 600 °C in an electric furnace and then cooled in saturated or subcooled water with an immersion depth of about 100 mm. The degree of liquid subcooling was varied from 0 K to 30 K. The analytical solutions for saturated and subcooled boiling are obtained by applying a two‐phase boundary layer theory for vapor film with a smooth interface. The experimental data correlates within ±15% based on the proposed prediction method. Also, the lower limit of film boiling was examined in terms of wall heat flux and degree of superheating. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20289     

Bubble Dynamics,Flow, and Heat Transfer during Flow Boiling in Parallel Microchannels

Significant efforts have recently been made to investigate flow boiling in microchannels, which is considered an effective cooling method for high-power microelectronic devices. However, a fundamental understanding of the bubble motion and flow reversal observed during flow boiling in parallel microchannels is lacking in the literature. In this study, complete numerical simulations are performed to further clarify the boiling process by using the level-set method for tracking the liquid–vapor interface which is modified to treat an immersed solid surface. The effects of contact angle, wall superheat, and the number of channels on the bubble growth, reverse flow, and heat transfer are analyzed.     

The effect of three-phase contact line speed on local evaporative heat transfer: Experimental and numerical investigations

In pool boiling or flow boiling devices or e.g. during meniscus evaporation within capillary structures the local heat flux and evaporation rate at the position where the liquid–vapor interface meets the solid wall can be extremely high. This three-phase contact line region is characterized by a thin liquid film with a very low heat resistance. Depending on the application the contact line can move with velocities of several meters per second, either in receding (dewetting) or in advancing (wetting) direction. In this paper, experimental and numerical results on the influence of three-phase contact line speed on the local heat transfer in the contact line region during pool boiling and during meniscus evaporation are presented and analyzed. It is shown that the local heat flux can be one or more orders of magnitude higher than the mean heat flux supplied to the system. This local heat transfer peak is almost independent of the contact line speed in the case of a receding contact line while it significantly increases with contact line speed for an advancing contact line. This behavior could be observed in different evaporation configurations and with different fluids. Experimental and numerical results agree well and allow a characterization of the transient heat transfer phenomena in the contact line region during evaporation.     

NUMERICAL COMPUTATION OF FILM BOILING INCLUDING CONJUGATE HEAT TRANSFER

This article presents a numerical method and simulations of film boiling including conjugate heat transfer. A volume-of-fluid (VOF) interface tracking method is augmented with a mass transfer model and a model for surface tension. The bulk fluids are viscous, conducting, and incompressible. We explore film boiling on a horizontal surface and we consider the effect of the energy exchange between a solid wall and the boiling fluid during saturated horizontal film boiling.     

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.     

Numerical simulation of film boiling on a sphere with a volume of fluid interface tracking method

This paper presents a numerical method for the simulation of boiling flows on non-orthogonal body-fitted coordinates. The volume-of-fluid (VOF) method based on piecewise linear interface construction (PLIC) is used to track liquid–vapor interface and is extended to body-fitted coordinates. Some special treatment is taken to deal with the discontinuous velocity field due to phase change at the interface. A double staggered grid with the SIMPLE method is adopted to solve the flow field. This method is used to simulate natural convection film boiling and forced convection film boiling on a sphere at saturated conditions. The simulation results are compared with analytical correlations and experimental data.     

Extensive study on laminar free film condensation from vapor–gas mixture

The dimensionless velocity component method was successfully applied in a depth investigation of laminar free film condensation from a vapor–gas mixture, and the complete similarity transformation of its system of governing partial differential equations was conducted. The set of dimensionless variables of the transformed mathematical model greatly facilitates the analysis and calculation of the velocity, temperature and concentration fields, and heat and mass transfer of the film condensation from the vapor–gas mixture. Meanwhile, three difficult points of analysis related to the reliable analysis and calculation of heat and mass transfer for the film condensation from the vapor–gas mixture were overcome. They include: (i) correct determination of the interfacial vapor condensate saturated temperature; (ii) reliable treatment of the concentration-dependent densities of vapor–gas mixture, and (iii) rigorously satisfying the whole set of physical matching conditions at the liquid–vapor interface. Furthermore, the critical bulk vapor mass fraction for condensation was proposed, and evaluated for the film condensation from the water vapor–air mixture, and the useful methods in treatment of temperature-dependent physical properties of liquids and gases were applied. With these elements in place, the reliable results on analysis and calculation of heat and mass transfer of the film condensation from the vapor–gas mixture were achieved.The laminar free film condensation of water vapor in the presence of air was taken as an example for the numerical calculation. It was confirmed that the presence of the non-condensable gas is a decisive factor in decreasing the heat and mass transfer of the film condensation. It was demonstrated that an increase of the bulk gas mass fraction has the following impacts: an expedited decline in the interfacial vapor condensate saturation temperature; an expedited decrease in the condensate liquid film thickness, the condensate liquid velocity, and the condensate heat and mass transfer. It was found that an increase of the wall temperature will increase the negative effect of the non-condensable gas on heat and mass transfer of the film condensation from the vapor–gas mixture.     

Computations of film boiling. Part I: numerical method

A numerical method for direct simulations of boiling flows is presented. The method is similar to the front tracking/finite difference technique of Juric and Tryggvason [Int. J. Multiphase Flow 24 (1998) 387], where one set of conservation equations is used to represent the mass transfer, heat transfer, and fluid flow in the liquid and the vapor, but improves on their numerical technique by elimination of their iterative algorithm. The justification of the mathematical formulation is presented and the numerical method and the code is validated by comparison of the results with the exact solutions of a few analytical problems. A grid refinement test for film boiling on a horizontal surface shows the convergence of results.     

A microscale model for thin-film evaporation in capillary wick structures

A numerical model is developed for the evaporating liquid meniscus in wick microstructures under saturated vapor conditions. Four different wick geometries representing common wicks used in heat pipes, viz., wire mesh, rectangular grooves, sintered wicks and vertical microwires, are modeled and compared for evaporative performance. The solid–liquid combination considered is copper–water. Steady evaporation is modeled and the liquid–vapor interface shape is assumed to be static during evaporation. Liquid–vapor interface shapes in different geometries are obtained by solving the Young–Laplace equation using Surface Evolver. Mass, momentum and energy equations are solved numerically in the liquid domain, with the vapor assumed to be saturated. Evaporation at the interface is modeled by using heat and mass transfer rates obtained from kinetic theory. Thermocapillary convection due to non-isothermal conditions at the interface is modeled for all geometries and its role in heat transfer enhancement from the interface is quantified for both low and high superheats. More than 80% of the evaporation heat transfer is noted to occur from the thin-film region of the liquid meniscus. The very small Capillary and Weber numbers resulting from the small fluid velocities near the interface for low superheats validate the assumption of a static liquid meniscus shape during evaporation. Solid–liquid contact angle, wick porosity, solid–vapor superheat and liquid level in the wick pore are varied to study their effects on evaporation from the liquid meniscus.     

The experimental and numerical investigation of a grooved vapor chamber

An effective thermal spreader can achieve more uniform heat flux distribution and thus enhance heat dissipation of heat sinks. Vapor chamber is one of highly effective thermal spreaders. In this paper, a novel grooved vapor chamber was designed. The grooved structure of the vapor chamber can improve its axial and radial heat transfer and also can form the capillary loop between condensation and evaporation surfaces. The effect of heat flux, filling amount and gravity to the performance of this vapor chamber is studied by experiment. From experiment, we also obtained the best filling amount of this grooved vapor chamber. By comparing the thermal resistance of a solid copper plate with that of the vapor chamber, it is suggested that the critical heat flux condition should be maintained to use vapor chamber as efficient thermal spreaders for electronics cooling. A two-dimensional heat and mass transfer model for the grooved vapor chamber is developed. The numerical simulation results show the thickness distribution of liquid film in the grooves is not uniform. The temperature and velocity field in vapor chamber are obtained. The thickness of the liquid film in groove is mainly influenced by pressure of vapor and liquid beside liquid–vapor interface. The thin liquid film in heat source region can enhance the performance of vapor chamber, but if the starting point of liquid film is backward beyond the heat source region, the vapor chamber will dry out easily. The optimal filling ratio should maintain steady thin liquid film in heat source region of vapor chamber. The vapor condenses on whole condensation surface, so that the condensation surface achieves great uniform temperature distribution. By comparing the experimental results with numerical simulation results, the reliability of the numerical model can be verified.     

Numerical investigation on subcooled pool film boiling of liquid hydrogen in different gravities

A clear understanding of bubble dynamics and heat transfer characteristics of hydrogen boiling in microgravity is significant for achieving safe and high-efficiency utilization of liquid hydrogen in space. In the present paper, a numerical simulation model is developed to predict the subcooled pool film boiling for liquid hydrogen in different gravities. The computations are based on the volume of fluid method combined with Lee's phase change model. The results show that the bubble released from the wavy gas-liquid interface might grow to a larger size before departure with the decrease of gravity, and poor heat transfer performance is observed in reduced gravity. However, once the gravity level is low enough or the subcooling of liquid is sufficiently large, instead of bubble formation and release at the vapor-liquid interface, a thin gas film layer is almost observed and maintained in the surface of horizontal flat or wire heater.