Numerical Analysis of Bubble Growth and Departure from a Microcavity

A numerical approach is presented for analysis of bubble growth and departure from a microcavity during nucleate boiling. The level-set formulation for tracking the phase interfaces is modified to include the effect of phase change on the liquid–vapor interface and to treat the no-slip and contact angle conditions on the immersed (or irregularly shaped) solid surface of the microcavity. Also, the formulation is coupled with a simple and efficient model for predicting the evaporative heat flux from the liquid microlayer on an immersed solid surface. The effects of cavity size and geometry on the bubble growth and departure in nucleate boiling are investigated.     

Numerical simulation of the quenching process in liquid jet impingement

Direct numerical simulation is performed for quenching of a hot plate in liquid jet impingement. The flow and thermal characteristics associated with the quenching process, which includes film boiling in the fluid region as well as transient conduction in the solid region, are investigated by solving the conservation equations of mass, momentum and energy in the liquid, gas and solid phases. The liquid–vapor and liquid–air interfaces are tracked by the sharp-interface level-set method modified to treat the effect of phase change. The computations demonstrate that the boiling curve of wall heat flux versus temperature does not depend on the transient or steady-state heating conditions. The effects of initial solid temperature and solid properties on the quenching characteristics are quantified.     

Three-dimensional simulation of saturated film boiling on a horizontal cylinder

Three-dimensional simulations of film boiling on a horizontal cylinder have been performed. A finite difference method is used to solve the equations governing the conservation of mass, momentum and energy in vapor and liquid phases. A level set formulation for tracking the liquid–vapor interface 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. From the numerical simulations, the effects of cylinder diameter and gravity on the interfacial motion and heat transfer in film boiling are quantified. The heat transfer coefficients obtained from numerical analysis are found to compare well with those predicted from empirical correlations reported in the literature.     

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.     

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.     

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.     

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.     

Oscillation of a liquid-vapor interface: experimental observations

The effects of liquid subcooling, velocity, and vapor superheat on the wavy nature of film boiling from a sphere in Freon-113 were studied. Experiments for both pool and flow film boiling were performed for a heater surface superheat of around 100 to 300°C, liquid velocity from 0- to 2.10 m/s, and Freon-113 subcooling from 0 to 25°C. Photographs taken in the film boiling regime show that the nature of the liquid-vapor interface is a function of the above-mentioned parameters. For low liquid subcooling ripples were present on the liquid-vapor interface. At greater subcooling these ripples disappear. For very large vapor superheat and liquid velocity ripples are always present on the liquid-vapor interface.     

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.     

A Level-Set Method for the Direct Numerical Simulation of Particle Motion in Droplet Evaporation

A sharp-interface level-set (LS) method is presented for direct numerical simulation (DNS) of particle motion in droplet evaporation. The LS formulation for liquid–gas flows is extended to liquid–gas–solid flows by treating the moving solid region as a high-viscosity fluid phase. The evaporation effect is accurately implemented by imposing the coupled temperature and vapor fraction conditions at the interface. The LS method is tested through computations of particle sedimentation in single-phase and two-phase fluids. The DNS of particle motion in droplet evaporation demonstrates the pinning phenomena of the liquid–gas–solid contact line.     

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.     

Examination of minimum-heat-flux-point condition for film boiling on a sphere in terms of the limiting liquid superheat and the critical vapor film thickness

Previously proposed theories of the minimum-heat-flux-point (MHF-point) condition were examined using available experimental data obtained from the immersion cooling of spheres in water. The sphere diameter ranged from 9.5 to 30 mm and the liquid subcooling from 0 to 85 K. The limiting liquid superheat predicted by the Lienhard equation was compared with the liquid–solid interface superheat at the instant of liquid–solid contact at the MHF-point. The results showed that the liquid–solid interface superheat was not limited by the limiting liquid superheat and its value was connected with the collapse mode of vapor film. The collapse mode was a coherent collapse at a low interface superheat and the mode changed to a propagative collapse as the interface superheat increased. The critical vapor film thickness obtained from the linear stability analysis of vapor film was compared with the calculated value of average vapor film thickness at the MHF-point. For all data, the ratio of the average vapor film thickness to the critical vapor film thickness was correlated well as a function of liquid subcooling. The ratio decreased with increasing liquid subcooling and tended to about 0.8 to 1 depending on the experiments. This indicated that the MHF-point at a high liquid subcooling was determined by the critical vapor film thickness. A physical consideration was given to the effect of liquid–solid contact that occurred in the film boiling region on the calculated value of the vapor film thickness and the stability of vapor film.     

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.     

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.     

Numerical study of single bubbles with dynamic contact angle during nucleate pool boiling

Nucleate pool boiling is typically characterized by cyclic growth and departure of vapor bubbles from a heated wall. It has been experimentally observed that the contact angle at the bubble base varies during the ebullition cycle. In the present numerical study, a static contact angle model and dynamic contact angle models based on the contact line velocity and the sign of the contact line velocity have been used at the base of a vapor bubble growing on a heated wall. The complete Navier–Stokes equations are solved and the liquid–vapor interface is captured using the level-set technique. The effect of dynamic contact angle on bubble dynamics and vapor volume growth rate is compared with results obtained with the static contact angle model.     

Numerical and analytical study of laminar film condensation in upward and downward vapor flows

Abstract

Laminar film condensation in upward and downward vapor flows is numerically investigated by using a sharp-interface level-set method to track the condensate film surface and accurately calculating the phase-change mass flux under the saturation temperature condition at the interface. An analytical model for steady laminar film condensation in upward as well as downward vapor flows is developed to validate the present numerical results. As the vapor velocity increases, the condensation rate is observed to decrease in upward vapor flows whereas it increases in downward vapor flows. The effects of vapor velocity and wall temperature on laminar film condensation in upward and downward vapor flows are investigated.     

A level-set method for ultrasound-driven bubble motion with a phase change

A level-set (LS) method is presented for computation of ultrasound-driven bubble motion including the effect of liquid and vapor compressibility as well as the effect of liquid–vapor phase change. The semi-implicit pressure correction formulation is implemented into the LS method to avoid the serous time-step restriction in low Mach number (or near incompressible) flows. The numerical results for one-dimensional compressible flows and spherical bubble motion in a periodic acoustic field show good agreement with the analytical solutions. The effects of phase change and ambient temperature on the ultrasound-driven bubble motion are quantified.     

Dynamics of a vapor bubble on a heated substrate

The dynamics of a vapor bubble between its liquid phase and a heated plate is studied in relation to the breakdown and recovery of the film boiling. By examining the expansion and the contraction of the vapor bubble the film boiling and transition boiling states are predicted. Conservation laws in the vapor, solid, and liquid phases are invoked along with fully nonlinear, coupled, free boundary conditions. These coupled system of equations are reduced to a single evolution equation for the local thickness of the vapor bubble by using a long-wave asymptotics, which is then solved numerically to yield the transient motion of the vapor bubble. Of the numerous parameters involved in this complex phenomenon we focus on the effects of the degree of superheat from the solid plate, that of the supercooling through the liquid, and the wetting/dewetting characteristics of the liquid on the solid plate. A material property of the substrate thus is incorporated into the criteria for the film boiling based on hydrodynamic models.     

Generalized stability theory of vapor film in subcooled film boiling on a sphere

The previously proposed stability theory of vapor film in subcooled film boiling on a sphere was generalized to take account of interaction between base flow and perturbed components. A disturbance of standing wave type was assumed to be superimposed on the base flows of surrounding liquid and vapor film. For the surrounding liquid, the wave equation was applied to the whole region including the boundary layer and the energy equation was solved analytically by introducing a simplifying assumption. For the vapor film, the basic equations were solved by an integral method. By use of compatibility conditions at the liquid–vapor interface, the solutions for the surrounding liquid and the vapor film were combined to yield an algebraic relation among the vapor film thickness, the order of disturbance and the complex amplification factor of disturbance. The numerical solutions of critical vapor film thickness at which the real part of complex amplification factor was equal to zero were obtained for the disturbances of the zeroth, first and second orders. The numerical results indicated that the vapor film was most unstable for the disturbance of the zeroth order (i.e., uniform disturbance). The calculated value of the critical vapor film thickness for the uniform disturbance compared well with the average vapor film thickness at the minimum-heat-flux point obtained from the immersion cooling experiments of spheres in water at high liquid subcoolings.     

Confined Boiling Heat Transfer,Two-Phase Flow Patterns,and Jet Impingement in a Hele-Shaw Cell

ABSTRACT

Experiments were carried out to study heat transfer and two-phase flow patterns during boiling in a Hele-Shaw cell filled with pure water vapor at atmospheric pressure and with a central inlet of a liquid jet. The Hele-Shaw cell was based on a circular copper rod surface and a polycarbonate plate permitting optical access and thus high-speed cinematography. The diameter of the heated copper rod was 10 mm, the jet diameters were 0.5 and 1 mm, and spacing was varied between 50, 100, and 200 μm. The heat was applied through 4 cartridge heaters with a maximum heat flux of 327 W/cm². Results showed how high-volume flow rates for the liquid jet led to jet impingement heat transfer while low flow rates led to a Hele-Shaw flow boiling system. The relationship between the volume flow rate and the temperature difference differed significantly between these two regimes. Different flow patterns and evaporation fronts were observed using high-speed cinematography. They strongly depended on jet properties, applied heat flux, and gap spacing. The efficiency of the Hele-Shaw flow boiling system during high heat flux levels was attributed to high interface velocities, combined with viscous fingering at the interface. This combination led to high wetting rates with substantial microlayer evaporation. Good results regarding the heat transfer and the pressure drop were obtained with the final configuration of a 10-mm copper rod diameter, a jet diameter of 1 mm, and a spacing of 0.1 mm. A rather surprising observation was the existence of a stable rotation of an evaporating liquid jet in the Hele-Shaw boiling chamber. The driving mechanism for the rotation with a frequency of 105 Hz was the rapid microlayer evaporation at the rear side of the rotating liquid jet.