A numerical investigation of various phase change models on simulation of saturated film boiling heat transfer

There is a great variety of two‐phase models in numerical simulations. The performance of each model complicates the numerical simulation of boiling. The challenge of the right choice of heat and mass transfer models makes this type of problem more complicated. In this research work, the volume of the fluid two‐phase model has been used to simulate the film boiling of saturated liquid. The geo‐reconstruction method also reconstructs the interface of two phases. The models of the sharp interface, Lee and Tanasawa have been employed among the available models for calculating the phase change rate and the source terms of the equations. The Numerical solver of the phase‐change is verified through the Stefan one‐dimensional vaporizing problem. Correct empirical coefficients used in both Lee and Tanasawa models are presented. Bubble detachment time, flow pattern, the periodic Nusselt number, and the bubble form have been investigated in all three phase change models. Two Berenson and Klimenko experimental correlations have been used for verification of Nusselt number derived from simulations. The Nusselt number shows a proper fit with the Klimenko's Nusselt number. Obtained Nusselt number demonstrates the Lee model is more precise than other phase change models in simulating of film boiling on the flat plate.     

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 Analysis of Film Boiling in Liquid Jet Impingement

A numerical approach is presented for computing film boiling in liquid jet impingement on a high-temperature plate. The conservation equations of mass, momentum and energy are numerically solved in the liquid, vapor, and air phases. The sharp-interface level-set formulation is employed to track the liquid-air interface, as well as the liquid-vapor interface with phase change. A simplified analytical model for a thin vapor film, whose thickness is several orders of magnitude smaller than the liquid layer, is incorporated into the level-set formulation. The multiscale approach is tested through the computations of film boiling in a circular water jet.     

Influence of condensation on the stability of a liquid film moving under the effect of gravity and turbulent vapor flow

The linear stability of condensate film flowing on an inclined isothermal plate under action of gravity and turbulent vapor flow was the subject of study. The cases of cocurrent and countercurrent flow of two phases were considered at an arbitrary inclination of the plane. The first part of this work deals with stationary film flow. The impact of vapor flow on the film is described by a given shear stress on the interface with account for the transverse mass flux due to phase transition. The integral method gives the analytical solution for distribution of film thickness along the plane (with and without account for film inertia) at different inclination angles. The second part of paper deals with linear stability of stationary film flow. The fluctuation of shear stress on the surface was calculated using the quasilaminar model. The two-wave equation for film thickness with phase transition and dispersion formulas were derived. The results of effect of condensation on film stability are presented for a wide range of flow parameters.     

Molecular Dynamics Simulation on Rapid Boiling of Thin Water Films on Cone-Shaped Nanostructure Surfaces

Molecular dynamics simulations (MDS) are employed to investigate the effects of the size of a nanocone on rapid boiling of an ultrathin liquid water film that is suddenly heated by a hot aluminum plate. A physically sound thermostat is applied to control the temperature of the aluminum plate and then to heat the water molecules that are placed on the solid surface. The results show that the cone nanostructures drastically enhance heat transfer from the solid aluminum plate to liquid water and the phase change process from liquid water to vapor. They also have significant effects on temperature histories and the density distributions in the system. In all cases studied, the water molecules above the solid surface rapidly boil after contact with an extremely hot aluminum plate and consequently a cluster of liquid water is observed to move upward during the phase change. It is also observed that the separation temperature associated with separation of liquid water film from the solid surface and its final temperature when the system is at equilibrium strongly depend on the height of the nanocone. Furthermore, in all cases, at a specific time after beginning of boiling, a nonvaporized water molecular layer is formed above the surface of the aluminum plate.     

Direct numerical simulations of pool boiling curves including heater's thermal responses and the effect of vapor phase's thermal conductivity

Effects of heater's thermal properties and vapor phase's thermal conductivity on saturated pool boiling above a large horizontal heater are simulated numerically based on an improved pseudo-potential liquid-vapor phase change lattice Boltzmann model. A transient conjugate heat transfer problem is under consideration, where the conjugate thermal boundary condition is imposed and heater's thermal responses during boiling processes are investigated. Saturated pool boiling curves from onset of nucleate boiling to critical heat flux (CHF), to transition boiling regime to stable film boiling regime are obtained numerically. It is found that the simulated critical heat flux (CHF) agrees reasonably well with existing analytical models. Also, the simulated boiling heat fluxes in stable film boiling regime are shown to be in good agreement with the existing analytical solution. Thus, this improved pseudo-potential liquid-vapor phase change lattice Boltzmann model is quantitatively validated. Simulation results demonstrate that there is significant maldistribution in temperature distribution near the top of heater surface in nucleate boiling regime, CHF point and transition boiling regime. As a result, two-dimensional heat conduction can not be ignored when evaluating heat flux closely beneath the heater's top surface. It is also shown that both heater's thermal conductivity and thermal mass (the product of density and specific heat at constant pressure) have no effect on CHF value as well as the boiling curve in nucleate boiling regime and film boiling regime for a thick heater. However, the transition boiling regime of the boiling curve moves to the left with the increasing heater thermal conductivity and heater thermal mass for a thick heater. Increasing the vapor theraml conductivity has no effect on CHF but would increase boiling heat flux in film boiling regime, and hence shortening the transition boiling regime.     

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.     

Condensation heat transfer enhancement in the presence of non-condensable gas using the interfacial effect of dropwise condensation

Heat transfer characteristics of dropwise condensation (DWC) were experimentally studied on a vertical plate for a variety of non-condensable gas (NCG) concentration, saturation pressure, and surface sub-cooling degree. As the heat transfer performance was dominated by the vapor diffusion process near the interface of the gas–liquid within the gas phase, the additional thermal resistance of the coating layer may not be strictly limited, a fluorocarbon coating was applied to promote dropwise condensation mode. Compared with the traditional filmwise condensation (FWC), heat and mass transfer with NCG can be enhanced with the dropwise condensation mode. In the present paper, the effect of condensate liquid resistance should not be regarded as the most vital factor to explain the results, but the vapor diffusion process. This is attributed to the liquid–vapor interfacial perturbation motion caused by coalescence and departure of condensate droplets. The results also demonstrated that the feature of droplets departure is the dominant factor for the steam–air condensation heat transfer enhancement.     

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.     

水平管外TFE/NMP部分膜状冷凝热、质耦合传递过程研究

通过对水平管外双组分(TFE／NMP为三氟乙醇／氮甲基吡咯烷酮)部分膜状冷凝过程特点的分析，建立起部分膜状冷凝过程中热质传递过程的物理模型。以双膜理论为基础，利用部分膜状冷凝的特点，通过对界面传质、液膜内质量平衡、界面相平衡、界面能量平衡和汽膜截面能量平衡的分析计算，得到汽相温度和界面温度分布、汽相及液相NMP质量分数分布，由此进一步计算出冷凝膜厚分布、液膜传热系数分布和热流密度的分布。计算的热流密度与相关实验作了比较，发现与实验能较好的吻合。     

Phase Change Heat Transfer Simulation for Boiling Bubbles Arising from a Vapor Film by the VOSET Method

This article presents a numerical method directed towards the simulation of flows with changes of phase. The volume-of-fluid level set (VOSET) method, which is a new interface capturing method and combines the advantages of both volume-of-fluid (VOF) and level set methods, is used for interface tracking. A difficulty occurs for the problems studied here: the discontinuous velocity field due to the difference between mass-weighted velocity and volume weighted velocity caused by the phase change at the interface. In this article, some special treatment is made to overcome this difficulty. The VOSET method and the developed treatment for the difference between mass-weighted and volume-weighted velocities are adopted to simulate a one-dimensional Stefan problem, two-dimensional horizontal film boiling, and horizontal film boiling of water at near critical pressure. The predicted results in both Nusselt number and flow patterns are agreeable with experimental results available in the literature.     

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.     

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.     

Numerical simulation of condensation for R410A at varying saturation temperatures in mini/micro tubes

ABSTRACT

Heat transfer and pressure drop characteristics of condensation for R410A inside horizontal tubes (d_h = 0.25, 1, and 2 mm) at saturation temperatures Tsat = 310, 320, and 330 K are investigated numerically. The results indicate that local heat transfer coefficients and pressure drop gradients increase with increasing mass flux and vapor quality and with decreasing tube diameter and saturation temperature. Liquid film thickness also increases with increasing saturation temperature because of the lower surface tension at higher saturation temperature. When gravity dominates the condensation process, a vortex with its core lying at the bottom of the tube is found in the vapor phase region. For the annular flow regime, stream traces point from the symmetry plan to the liquid–vapor interface, where the vapor phase becomes the liquid phase. Numerical heat transfer coefficients and pressure drop gradients are compared to available empirical correlations. Two new models for heat transfer coefficients and frictional pressure drop gradients are developed based on the numerical work.     

Analytical modelling of transient phase‐change problems

In this paper, an analytical solution for the temporal location of moving solid–liquid interface of a phase‐change process, occurring in parallel plate channels, is presented. The motion of the solid–liquid interface is governed by the convection from the surface of one of the plates, while constant heat supply is assumed to occur on the surface of the other plate. The steady location of the solid–liquid interface is also determined. The variation of the Biot number versus the Fourier number is investigated. The results of this study indicate that simple analytical solutions for transient phase‐change problems with heat flux and convective boundary conditions that are of practical importance to the people working in the field can be obtained. Copyright © 2000 John Wiley & Sons, Ltd.     

Condensation of organic binary mixtures flowing horizontally in a horizontal tube bundle

Both heat and mass transfer in the gas phase and heat transfer in the liquid phase are examined experimentally for film condensation of organic binary mixtures such as ethanol-water and methanol-water. Experimental results on the average heat flux, vapor-liquid interface temperature and liquid-phase Nusselt number are compared with analytical solutions based on stagnant film theory and heat-transfer relationships for film condensation from a pure vapor. Experimental heat transfer results agree well with the analytical solutions, except that the experimental liquid-phase Nusselt numbers under conditions of low mass fraction of water are considerably higher than predicted by the analytical solutions. This high value of the liquid-phase Nusselt number is considered to be caused by dropwise condensation in the liquid phase. However, its effect on the tube bundle is not so remarkable compared with that in gravity-controlled condensation on a vertical surface. This is considered to be caused by the condensate inundation effect. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25(6): 342–361, 1996     

Numerical Study of the Forced Convective Condensation on a Short Vertical Plate

Numerical investigation was conducted on the effects of gravity, surface tension, and wall adhesion upon condensation on a short vertical plate. The volume of fluid method was applied to model the interaction between the liquid and vapor phases and to capture the interface. The surface tension was implemented by employing the method of continuum surface force model. A modified phase-change model, derived from basic equations related to the kinetic gas theory, was proposed and verified based on the cases of Nusselt film condensation of water vapor on a vertical flat plate, the forced convection film condensation on a horizontal flat plate, and the capillary blocking due to condensation in a horizontal miniature circular tube. The predicted results showed that a laminar capillary wavy flow regime exists and the waves enhance the heat transfer of condensation on the plate. The mean film thickness increases and the heat transfer performance becomes worse with decrease of gravity. A high value of surface tension or contact angle, representing a large surface free energy difference, leads to an enhancement of heat transfer on the plate with large-amplitude waves.     

Plate heat exchangers: Recent advances

This study presents the advances in plate heat exchangers both in theory and application. It dresses the direction of various technical research and developments in the field of energy handling and conservation. The selected areas of heat transfer performance and pressure drop characteristics, general models and calculations change of phase; boiling and condensation, fouling and corrosion, and welded type plate heat exchangers and finally other related areas are highlighted.     

Two-phase modelling of laminar film condensation from vapour–gas mixtures in declining parallel-plate channels

A two-phase model is presented that analyzes laminar film condensation from mixtures of a vapour and a non-condensing gas in parallel-plate channels. The channel is declining (inclined downward from the horizontal) and has an isothermal cooled bottom plate and an insulated upper plate. The model uses a finite volume method to solve the complete two-phase boundary-layer equations including inertia forces, energy convection, interfacial shear, and axial pressure change. Results are presented for steam–air mixtures in terms of axial variation of film thickness and local Nusselt number for various Froude numbers, inlet Reynolds numbers, inlet gas mass fractions, and inlet temperature differences. Profiles of axial velocity, temperature, and gas mass fraction are also presented. Increasing the angle of declination (decreasing the Froude number) produces thinner, faster moving films. The change in local Nusselt number with Froude number was not as substantial as the change in film thickness. The detrimental effect of the noncondensable gas on the heat transfer rate was observed to be more pronounced at higher Froude numbers. An exact analytical solution for the liquid and mixture axial velocity profiles under end of condensation conditions is also presented and compared with the numerical results.     

Subcooled flow boiling heat transfer of R-134a and the associated bubble characteristics in a vertical plate heat exchanger

Subcooled flow boiling heat transfer characteristics of refrigerant R-134a in a vertical plate heat exchanger (PHE) are investigated experimentally in this study. Besides, the associated bubble characteristics are also inspected by visualizing the boiling flow in the vertical PHE. In the experiment two vertical counterflow channels are formed in the exchanger by three plates of commercial geometry with a corrugated sinusoidal shape of a chevron angle of 60°. Upflow boiling of subcooled refrigerant R-134a in one channel receives heat from the downflow of hot water in the other channel. The effects of the boiling heat flux, refrigerant mass flux, system pressure and inlet subcooling of R-134a on the subcooled boiling heat transfer are explored in detail. The results are presented in terms of the boiling curves and heat transfer coefficients. The measured data showed that the slopes of the boiling curves change significantly during the onset of nucleate boiling (ONB) especially at low mass flux and high saturation temperature. Besides, the boiling hysteresis is significant at a low refrigerant mass flux. The subcooled boiling heat transfer coefficient is affected noticeably by the mass flux of the refrigerant. However, increases in the inlet subcooling and saturation temperature only show slight improvement on the boiling heat transfer coefficient.The photos from the flow visualization reveal that at higher imposed heat flux the plate surface is covered with more bubbles and the bubble generation frequency is substantially higher, and the bubbles tend to coalesce to form big bubbles. But these big bubbles are prone to breaking up into small bubbles as they move over the corrugated plate, producing strong agitating flow motion and hence enhancing the boiling heat transfer. We also note that the bubbles nucleated from the plate are suppressed to a larger degree for higher inlet subcooling and mass flux. Finally, empirical correlations are proposed to correlate the present data for the heat transfer coefficient and the bubble departure diameter in terms of boiling, Froude, Reynolds and Jakob numbers.