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.     

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 simplified numerical model for melting of ice with natural convection

Ice in a rectangular enclosure is melted by heating from the top, while maintained at its melting point at the bottom. The other surfaces are insulated. In the enclosure near the hot region, liquid phase starts forming as temperatures reach values higher than the melting point of ice. This phenomenon is first modeled by ignoring the effect of natural convection in the liquid phase. The resulting equations of conservation of energy are solved in each phase. The motion of melting front is governed by an energy balance at the interface. This conduction model is verified by applying it on a system for which an analytical solution is available. The model is then extended to include convective heat transfer in such a way that the liquid phase is assumed to be a mixed body subjected to natural convection from the top surface and the liquid-solid interface. The flux at the interface is obtained by finding a heat transfer coefficient for natural convection with a cold plate facing upward. Comparison of the results of the numerical work with experiments performed on water/ice system shows a strong effect of natural convection on melting of ice. The model involving natural convection in the liquid phase agrees well with the experimental work.     

Convection film boiling on horizontal cylinders

Free, mixed and forced convection film boiling on a horizontal cylinder in a saturated or subcooled liquid is studied theoretically using a single model based on a two-phase laminar boundary layer integral method. The vapour flow is described accurately by including the inertia and convection terms in the momentum and energy equations, in order to study convection film boiling in the cases of very high superheat. Different film boiling cases are then analysed with this model. The case of high superheat and low subcooling was first analysed by comparing the model with an experiment consisting in the quenching of wires with very high superheat: the model was able to predict the measured heat transfer from the cylinder with errors less than 30%, performing better than previous models or correlations. Additional calculations in other high superheat conditions have also been performed and compared with a model which does not include the inertia and convection terms in order to have a more quantitative idea of their effects on the heat transfers. The case of low superheat and high subcooling is then analysed by comparing the model with other forced convection experiments with cylinders at lower temperatures. By analysing different experiments, it is found that there are in fact two different forced convection film boiling sub-regimes characterised by relatively “low” or “high” heat transfers, and that the existence of these sub-regimes is probably linked with the stability of the vapour film during film boiling. The model results compare quite well with the experimental data which belong to the “stable” sub-regime but, on the other hand, the model largely underestimates the heat transfer for experimental data which belongs to the “unstable” sub-regime. Finally, the model is compared to some free convection experimental data. The model was able to predict the measured heat transfers from the cylinder with errors less than 30% both in saturated and subcooled cases.     

A new generalised model for liquid film cooling in rocket combustion chambers

A one dimensional analytical model of liquid film cooling in rocket combustion chambers operating at subcritical conditions is developed. The approach followed involves the selection of a control volume for mass and energy balance. The coolant evaporation rate per area is obtained from this energy balance. The present model incorporates mass transfer via entrainment by adapting suitable correlations from literature pertaining to annular flow conditions. The model predicted favourably with the experimental data available in open literature and produced superior results compared to all existing models. Results are presented for a mixed gas–water system under different conditions. Results indicate that convection dominates the heat transfer at the gas–liquid interface. Effects of gas Reynolds number, coolant inlet temperature, combustion chamber pressure, mass flow ratio of the liquid coolant to the free stream and the free stream turbulence on the liquid film length are presented in detail.     

Boiling from small cylinders

Heat transfer is observed as a function of temperature on small horizontal wires in water and four organic liquids. When the wire radius is sufficiently small, the hydrodynamic transitions in the boiling curve disappear and the curve becomes monotonie. Three modes of heat removal are identified for the monotonie curve and described analytically: a natural convection mode, a mixed film boiling and natural convection mode, and a pure film boiling mode. Nucleate boiling does not occur on the small wires.     

Statistic analysis of the boiling curve for a droplet

Statistic analysis of the experimentally determined values of a water droplet's evaporation times was made. Measurements were taken from heating surface temperatures characteristic for liquid phase natural convection up to film boiling of a droplet. The results obtained confirm the hypothesis of two boiling curves in the region of transition boiling proposed by Witte and Lienhard. They also allow this concept on the region of nucleate boiling to be expanded.     

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.     

Film boiling from a rotating sphere in forced convection

Film boiling heat transfer fluxes were measured on a 3.84-cm rotating hollow copper sphere in forced convection. Forced convection tests in Freon-113 were run at speeds of 0.5 to 1.0 m/s and for sphere rotation in the range of 0 to 1500 rpm. The tests were conducted in the stable film boiling regime of the boiling curve. The experimental measurements revealed that the rotation of the heated surface enhanced the occurrence of liquid-solid contact in film boiling. A theoretical model for flow film boiling from a spherical heater including the effects of surface rotation is developed. The model does not account for the occurrence of liquid-solid contacts, however, the experimental data and the theoretical formulation show good agreement at low rpm.     

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.     

Cryogenic chilldown process under low flow rates

In this paper, we investigated the chilldown process of a horizontal tube by a liquid nitrogen flow with low mass fluxes. The flow patterns and heat transfer characteristics are studied experimentally. Visualization results illustrate the successive states of liquid–wall interaction with different mass fluxes. For a horizontal tube, the liquid filament–wall interaction is an important contributor to the heat transfer on the bottom wall while the upper wall is cooled by forced convection with superheated vapor. A phenomenological model is developed, in which the heat transfer on the bottom wall is composed of film boiling and forced convection while for the upper wall, forced convection is the only mechanism of heat transfer. A good agreement is achieved between the model prediction and the experimental result.     

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.     

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.     

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 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.     

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.     

Marangoni convection,evaporation and interface deformation in liquid films on heated substrates with non-uniform thermal conductivity

Marangoni convection plays an important role in hydrodynamics of liquid films on heated or cooled substrates. In this paper a model describing Marangoni convection, interface dynamics and evaporation in liquid films on composite substrates or substrates of functionally graded materials is developed. Non-uniform thermal conductivity of the substrate causes non-uniformity of temperature distribution at the liquid–gas interface which leads to appearance of Marangoni stresses, convective vortices and film deformation. The film dynamics is described in the framework of long-wave theory. The substrate thermal conductivity non-uniformity has a pronounced effect on transport processes in the liquid film.     

Non-linear dynamical analyses of transient surface temperature fluctuations during subcooled pool boiling on a horizontal disk

The class of dynamics in pool boiling on a large-size heater is assessed under subcooled pool boiling conditions. Transient surface temperature measurements are obtained using surface micro-machined K-type thin film thermocouples (TFT) in 10 °C subcooled pool boiling experiments on a 62.23 mm diameter silicon wafer using PF-5060 as the test liquid. Surface temperature data is obtained at each steady state condition to generate the boiling curve. The fraction of false-nearest neighbors, recurrence plots and space–time separation plots are obtained using the TISEAN package. The correlation dimension is then estimated from the re-constructed phase space data using a naïve algorithm. The correlation dimension varies from ～11.2 to 11.5 near onset of nucleate boiling (ONB), to ～7–10 in fully developed nucleate boiling (FDNB) ～7–9 near critical heat flux (CHF) condition, and from ～6.6 to 7.7 in film boiling. False-nearest neighbor estimates and recurrence plots show that nucleate boiling may be dominated by statistical processes near ONB and in partial nucleate boiling (PNB). In contrast, FDNB, CHF and film boiling seem chaotic and governed by deterministic processes.     

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.     

Thermophysics of the Interfacial Region and Its Impact on Instability and Rupture of Thin Free Liquid Films

Merging of adjacent bubbles is a particularly important process in nucleate boiling heat transfer, bubbly two-phase flow in small tubes, and the mechanisms that dictate the Leidenfrost transition. The merging process is ultimately associated with the rupture of the liquid film separating two bubbles, and the stability of the liquid film dictates whether coalescence is likely to occur. This paper examines two methods of exploring how the molecular-level features of the thin film and its interfaces affect the stability of the film and its subsequent impact on bubble merging. One method is an extended molecular capillarity model that has been developed for a free liquid film bounded by two liquid–vapor interfacial regions. This model predicts that as film thickness diminishes, a point is reached at which the mean centerline density in the film is between the spinodal limits for the fluid, implying that the film core lacks intrinsic stability. This suggests that loss of intrinsic stability may be the mechanism for film rupture in some cases. The second method examined here is use of molecular dynamics simulations to examine film structure and stability. Simulations using a Lennard–Jones interaction potential for non-polar fluids and the SPC/E potential for water and salt water are examined. Results of these explorations indicate that for water–NaCl solution films, surface tension increases with increasing NaCl concentration. These predictions are shown to be consistent with measured surface-tension data for such solutions. The results also indicate that for pure water and NaCl solutions, below a threshold thickness, the surface tension decreases with film thickness. Wave interface stability theory implies that this tends to make the film less stable. The implications of the results of these investigations for bubble merging in two-phase flow and boiling processes are also examined.