A Sphericosymmetric VOF Approach for Investigating Immiscible Two-Phase Systems with One Liquid Phase

A numerical model based on the volume-of-fluid (VOF) method in sphericosymmetric geometry containing two immiscible phases is developed. The model is successfully validated using a wide class of available results. These include the inward and outward solidification problems and growth of vapor film in a saturated and metastable liquid. The model is also used to simulate the very rapid collapse phenomenon of vapor film around a hot metal in subcooled water. In each case, the results indicate that the numerical simulation successfully captures the essential physics, even at small length and time scales. It is established that the proposed numerical scheme correctly predicts the advection within the VOF framework in situations with pronounced curvature.     

Interface temperature and heat transfer in forced convection laminar film condensation of binary mixtures

Based on numerical solutions of the balance equations accurate empirical correlations for filmwise condensation in forced convection flow over a horizontal flat plate are presented. The correlations are designed to be also correct for the limiting case of zero and infinite condensation rate. They are applied to determine the interface temperature between liquid and vapour phase and hence the condensation rate and heat flux. The results are in excellent agreement with those from numerical solutions of the balance equations. It turns out that the usually adopted film theory for the vapour-phase mass transfer overestimates the size of a heat exchanger.     

Three-Dimensional Modelling of Density Variation Due to Phase Change in Complex Free Surface Flows

A three-dimensional model of droplet impact and solidification has been modified to include the effects of density variation during phase change. The governing equations for conservation of mass, momentum, and energy, and a volume-of-fluid (VOF) equation are derived by assuming different but constant solid and liquid densities. The equations are solved numerically using a control-volume approach. The model is validated against the Stefan and planar solidification problems. It is then applied to simulate the effects of density variation during solidification of molten tin in a mold and also of an impacting tin droplet on a substrate.     

Effect of salt additives on film boiling heat transfer and mechanism of quenching temperature rise

A high‐temperature stainless‐steel sphere was immersed into various salt solutions to investigate the film boiling behavior at vapor film collapse. The film boiling behavior around the sphere was observed with a digital video camera. Both surface temperature of the sphere and solid–liquid contact behavior were measured. Results of the experiment showed that salt additives enhanced condensation heat transfer, and the observed vapor film was thinner. Furthermore, the frequency of direct contact between the sphere surface and coolant increased. The quenching temperature increased with increased salt concentration, and was highly correlated with ion molar concentration, which represents the density of ions regardless of the type of salt. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20327     

Influence of dispersion forces on phase equilibria between thin liquid films and their vapour

Heat transfer and nucleation processes in nucleate boiling strongly depend on the phase equilibrium at the liquid-vapour interface. In a certain region between heated wall and a vapour bubble where a thin liquid film is adsorbed, phase equilibria are considerably influenced by dispersion forces acting on the liquid film. As shown in the paper in such systems the chemical potential, decisive for phase equilibria between liquid films and their vapour, contains an additional term for the action of dispersion forces, and differs from the chemical potential of dispersion-free systems, though their chemical potential is usually taken in the literature for systems with dispersion forces. With the aid of the chemical potential the Kelvin equations for the pressures at the liquid-vapour interface were derived. It turned out that the Gibbs assumption of a geometrical interface between extremely thin liquid films in equilibrium with its vapour does not hold. Instead, following the ideas of van der Waals junior, the small but finite transition interlayer between both phases had to be introduced.As numerical examples illustrate, the dispersion forces considerably influence the pressures at the liquid-vapour interface. In nucleate boiling processes the driving pressure difference for evaporation undergoes a maximum within a tiny area underneath vapour bubbles. As could be shown the maximum driving pressure difference between gas-side interface and gas-core is a considerable fraction of the vapour pressure itself and contributes significantly to the high heat fluxes in nucleate boiling.     

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.     

波纹管降膜蒸发器传热性能数值模拟

为了理解波纹管降膜蒸发过程中涉及的液膜传热过程,本文采用VOF法建立了二维气-液两相分层流动CFD模型,考虑了液相流量,传热温差,蒸发温度,液相粘度等参数对传热效果的影响,根据模拟结果给出了波纹管降膜蒸发器的流量可操作范围。模拟结果和实验数据比较吻合。     

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.     

沿垂直壁面气-液降膜流动传质过程的数值研究

在考虑气-液两相间质量源项和能量源项的条件下,基于VOF算法,建立了水和空气沿竖直平板壁面两相降膜流动传热传质的CFD模型。利用该模型研究了水和空气两相间的传质特性,分析了液膜波动、进气进液速度以及温度对传质的影响,计算结果表明:一定程度的液膜波动、进气速度和进液速度的提高、气-液之间的温差的增加,都能强化气-液之间的传质过程。     

Heat transfer in an evaporating thin liquid film moving slowly along the walls of an inclined microchannel

A theoretical study has been undertaken to determine the rate of heat transfer in a thin evaporating liquid film flowing along the walls of a microchannel under the combined action of surface tension and gravity. Analytical solutions of conservation equations, in both liquid and vapour phases, have been obtained, in considerations with coupled heat and mass transfer boundary conditions at the interface. It has been recognized that while the local Nusselt number is influenced solely by the liquid film thickness, the average Nusselt number depends both on liquid film thickness and a dimensionless number ρgsinθ, as obtained from the scale of characteristic velocity for both gravity and surface tension.     

Direct numerical simulation of mass transfer from Taylor bubble flow through a circular capillary

In this work mass transfer during a Taylor bubble flow regime has been investigated by a volume of fluid (VOF) based numerical method. The hydrodynamics of Taylor bubble flow through a circular capillary has been simulated in a single unit cell by a moving reference frame. The validity of Taylor bubble hydrodynamics simulation has been checked by comparing the liquid film thickness and the relative bubble velocity obtained from computational fluid dynamics (CFD) simulations with reported empirical correlations and experimental results. The conservation equation of tracer has been solved in whole of flow domain for simulating mass transfer from Taylor bubble to surrounding liquid. The tracer concentrations in the cells that are either completely or partially filled with the gas phase are assigned the equilibrium concentration by employing the concept of internal boundary condition. By this concept an artificial diffusion of tracer has been appeared in the simulations. In order to eliminate this artificial diffusion, the advection scheme in the tracer conservation equation has been modified by using the two film mass transfer model. The simulation of mass transfer from a single bubble has been validated by comparing the CFD results with reported experimental data. Afterwards, the effects of capillary number, unit cell length and capillary diameter variation on mass transfer from Taylor bubble has been investigated.     

The evaluation of the diffuse interface method for phase change simulations using OpenFOAM

In the present study, a new solver named phaseChangeHeatFoam is implemented on the OpenFOAM cfd package to simulate boiling and condensation. The solver is capturing the interface between two immiscible phases with a color function volume of fluid (CF‐VOF) method. The two fluids (vapor and liquid) are assumed Newtonian and incompressible. The surface tension is modeled with continuous surface force (CSF) which is improved with a Lafaurie filter to suppress the spurious current. The mass flux across the interface in the phase change process is determined by either Lee or Tanasawa mass transfer models. Additionally, the slight variation of saturation temperature with local pressure is considered with the simplified Clausius–Clapeyron relation. The coupled velocity pressure equation is solved using the PIMPLE algorithm. The new solver is validated and examined with (i) Stefan problem, (ii) two‐dimensional film boiling, (iii) the film condensation on a horizontal plate, (iv) the laminar film condensation over a vertical plate, and (v) bubble condensation in subcooled boiling. The present study shows the capability of a diffuse interface method in accurate simulation of the phase change process and it is expected to be instructive for further numerical studies in this area.     

Effect of density change on the stability of a planar phase interface

A simple model of the controlled growth of a one-component solid material into a thermally undercooled liquid bath is presented. The model takes the density jump across the phase interface into account. Using the classical Mullins-Sekerka method, we investigate the stability of the planar phase interface and evaluate the effect of including the density jump on the critical wavelength for several metal and semiconductor elements. We show that the changes of the critical wavelength due to density difference between the solid and liquid phases are not negligible.     

Simulation of droplet impact on liquid film with CLSVOF

A two dimensional simulation is carried on to simulate the droplet evolution after impacting on liquid film by CLSVOF (combined level set and VOF). At different parameters the droplet evolutions are obtained and the phenomenon of bubble entrainment is caught successfully. The effects of impact velocity and the liquid film thickness on the crown diameter are analyzed. The results indicate that the bubble entrainment can be captured by CLSVOF method. Also it can be concluded that the bigger the impact velocity is, the earlier the splash emerges. The spreading diameter decreases with the rise of liquid film thickness.     

CFD simulation of the two-phase flow for a falling film microreactor

Falling film microreactors, which provide very high specific interfacial area, have become a promising solution to the fast and strongly exothermic/endothermic gas–liquid reaction systems. A computational fluid dynamic simulation of the two-phase flow for a falling film microreactor is presented using the volume of fluid (VOF) model. The hydrodynamic characteristics, from both 2-D and 3-D simulations, including liquid film thickness, velocity, pressure and shear stress profiles, are analyzed. 2-D simulation is adopted for the study of the relationship of liquid flow rate and film thickness, as well as the effects of gas flow rate, surface tension, liquid viscosity and pressure difference on the liquid flow rate. 3-D simulation is necessary to provide the comprehensive flow profiles. Although the system is in the laminar flow regime, the liquid film features a wavy structure and the velocity profiles are complex.     

横管降膜过程中液膜内流动和传热特性分析

横管降膜流动过程中,液膜速度和温度及其分布是影响传热传质的关键因素,由于实验研究方法的局限性,实验研究结果一般只是液膜内各参数的平均值,而液膜内部的速度和温度具体分布特性却很难得到。借助FLUENT软件,利用VOF模型研究了橫管外液膜速度和温度及其分布特性。通过建立三维数理模型,模拟研究了常温常压下,橫管外液膜无相变条件下横管液膜的传热过程,并从边界层的角度解释了液膜波动对传热过程的影响。     

The importance of turbulence during condensation in a horizontal circular minichannel

Three-dimensional simulations of condensation of refrigerant R134a in a horizontal minichannel are presented. Mass fluxes ranging from 50 kg m^?2 s^?1 up to 1000 kg m^?2 s^?1 are considered in a circular minichannel of 1 mm diameter, and uniform wall and vapour–liquid interface temperatures are imposed as boundary conditions. The Volume of Fluid (VOF) method is used to track the vapour–liquid interface; the effects of interfacial shear stress, gravity and surface tension are taken into account. The influence of turbulence in the condensate film is analysed and compared against the assumption of laminar condensate flow by employing different computational approaches and validating the results against experimental data. Under the assumption of laminar condensate flow, experimental heat transfer coefficient values at low mass fluxes can be predicted, but the computed heat transfer coefficient is found to be almost independent of mass flux and vapour quality. Only when turbulence in the condensate film is taken into account does the numerical model capture the influence of mass flux that is observed in the experimental measurements.     

A numerical investigation on multi-phase transport phenomena in a proton exchange membrane fuel cell stack

In this study, the simulation of a fuel cell stack is performed by applying a general numerical model with VOF method that has been successfully applied to single PEMFC model to investigate the fluid dynamics, mass transport, flooding phenomenon and the effects of liquid water on the stack performance. The performance of three single cells in series connection in the fuel cell stack is examined according to the presence of liquid water in different single cells. The distributions of fluid flow, species concentration and the current density are presented to illustrate the effects of liquid water on the performance of each single cell. The numerical results locate that the low distributions of species in the flooding cell certainly degrade the performance of this cell. Moreover, it can be seen that the performance of the flooding cell will significantly affect the whole stack performance since the values of average current density must be identical in all single cells.     

A Numerical Study of Combined Heat and Mass Transfer in an Inclined Channel Using the VOF Multiphase Model

A numerical study has been performed to determine heat and mass transfer from the surface of liquid ethanol flowing in an inclined channel. The Volume-of-fluid (VOF) multiphase model was used to track the liquid and gas phases. An algorithm has been implemented to determine interfacial heat and mass transfer characteristics. A parametric study was done to determine the effect of gas-phase inlet velocity, temperature, and vapor mass fraction.     

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.