A sharp-interface level-set method for compressible bubble growth with phase change

A sharp-interface level-set method is presented for simulating the growth and collapse of a compressible vapor bubble. The interface tracking method is extended to include the effects of bubble compressibility and liquid-vapor phase change by incorporating the ghost fluid method to efficiently implement the matching conditions of velocity, stress and temperature at the interface. The numerical results for one-dimensional compressible flows and spherical bubble growth show good agreement with the exact solutions. The level-set method is applied to investigate the effects of phase change, ambient temperature and wall on the compressible bubble growth and collapse.     

A phase change processor method for solving a one-dimensional phase change problem with convection boundary

A simple yet accurate iterative method for solving a one-dimensional phase change problem with convection boundary is described. The one-dimensional model takes into account the variation in the wall temperature along the direction of the flow as well as the sensible heat during preheating/pre-cooling of the phase change material (PCM). The mathematical derivation of convective boundary conditions has been integrated into a phase change processor (PCP) algorithm that solves the liquid fraction and temperature of the nodes. The algorithm is based on the heat balance at each node as it undergoes heating or cooling which inevitably involves phase change. The paper presents the model and its experimental validation.     

A level-set based adaptive-grid method for premixed combustion

A numerical method to simulate premixed combustion is analyzed. It consists of a Cartesian cut-cell flow solver for compressible viscous flows coupled with a level-set method which solves the G-equation to describe the kinematics of the premixed flame. The coupling of the two solvers is achieved via a dual hierarchical dynamic adaptive-mesh framework. Both solvers operate on different Cartesian hierarchical meshes sharing a common background grid level through which they are connected. For the flow solver, feature- and G-based adaptive mesh refinement is taken advantage of, while a uniform high-resolution grid is used for the level-set solver. The heat release due to combustion is described by a source-term formulation by which the reaction rate profile of the premixed flame can be attached to the flame front, the motion of which is governed by the G-equation. A flame–vortex interaction problem is discussed in detail to validate the proposed methodology and to demonstrate the benefits of solution-adaptive mesh refinement in the context of the level-set approach for premixed combustion. After a forced laminar Bunsen flame is considered as an example for attached flames, the coalescence of two spherical flame kernels is simulated to assess the performance of the method and the potential savings in terms of computational costs for three-dimensional problems. The results of the test problems show the artificial thickening of the flame and numerical errors in the level-set solution on coarser grids to possess a comparatively small impact on the overall accuracy. The best findings in the sense of efficiency and physical quality are achieved by the combined feature-/G-based adaptation method.     

The effects of liquid motion induced by phase change and thermocapillarity on the thermal equilibrium of a vapour bubble

A theoretical estimate is made of the liquid motion induced in the vicinity of a vapour bubble on a heated solid surface by evaporation and condensation at the bubble surface and by thermocapillarity effects. These results are used to examine the thermal equilibrium of the vapour bubble.     

Direct contact heat transfer with change of phase: Condensation of a bubble train

Solution of the coupled velocity and temperature fields associated with the condensation of a single or two-phase bubble train is used to obtain the bubbles' radii as a function of time (or height), frequency, temperature driving force and inerts concentration.The reliability of the solution procedure is demonstrated by its convergence at zero frequency to other solutions of single bubble condensation and by the good agreement of the calculated results with experimental data.     

Direct contact heat transfer with phase change: Theoretical expression for instantaneous velocity of a two-phase bubble

An analytical expression for instantaneous velocity of two-phase bubble evaporating through immiscible liquid, has been developed. This expression, predicts very well, the experimental data for n-pentane and furan drops evaporating through high viscosity aqueous glycerol.     

A sharp-interface level-set method for analysis of Marangoni effect on microdroplet evaporation

A level-set method is presented for computation of microdroplet evaporation including not only the effects of heat and mass transfer, phase change and contact line dynamics but also the Marangoni effect, which is a key parameter affecting the internal flow of the droplet and the particle deposition pattern. A sharp-interface formulation of the Marangoni force is derived and tested for two-phase Marangoni convection in a cavity. The computed results show good convergence in both the liquid and gas regions and are in excellent agreement with the analytical solutions. The level-set formulation is applied to microdroplet evaporation on a solid surface to investigate the Marangoni effect.     

A multi-zonal integral method for problems involving unsteady one-dimensional heat conduction with change of phase

A method is presented for calculating the temperature in a solidifying slab of molten material with greatly differing cooling rates on the inner and outer surfaces. For the purposes of analysis the slab is divided into a number of zones having time-varying boundaries, e.g. solidification or conduction fronts. Appropriate approximations are made for the temperature profile and the heat-balance integral equation applied separately in each zone. This leads to systems of first-order ordinary differential equations which can be integrated numerically by using simple standard methods. Results are presented which correspond to the industrial casting of polypropylene film.     

A non-parametric method for estimating enthalpy-temperature functions of shape-stabilized phase change materials

A method for thermodynamic characterization of shape-stabilized phase change materials (PCM) based on one-single sample and one-single experiment has been proposed. The simplicity of the experimental device is comparable to that of the T-History method. However, instead of simple energy balances as in T-History method, a numerical heat transfer model is used to retrieve the whole set of parameters/functions characterizing the PCM from temperature measurements at one-single point within the PCM. An efficient inversion technique has been proposed for that. Its most striking feature is that it allows non-parametric identification of the enthalpy-temperature function in an easy way. Such a function is retrieved by solving a problem of nonhomogeneous heat source term estimation by inversion of a linear heat conduction model.     

Coupled level-set and volume-of-fluid method for two-phase flow calculations

In simulating two-phase flows, the volume-of-fluid (VOF) method has the advantage of mass conservation while with the level-set (LS) method, the surface tension force can be calculated more accurately. In this study, we present a coupling method which combines the advantages of both methods. The volume-of-fluid (VOF) method adopted in the calculation is the conservative interpolation scheme for interface tracking method proposed recently by the authors. Based on the location of the interface calculated from the VOF, the LS function is obtained by solving the equation used in the LS method for re-initialization without needing to solve its advection equation. A high-resolution-bounded scheme within the frame of finite-volume methods is used to solve the re-initialization equation. This scheme is verified by considering a variety of interface geometries. A circular bubble at equilibrium is used to assess the coupled LS and VOF method by examining the spurious currents generated in the bubble. Three-dimensional calculations are conducted to study the rising of a bubble in the quiescent water.     

Collapse of one-component vapor bubble with translatory motion

Theoretical analysis of one-component vapor bubble collapse with translatory motion in uniformly subcooled liquid has been carried out. The bubble is spherical and flow in the region surrounding the bubble is potential. General solution is obtained in which the function R = R(τ) is defined implicitly by integral equation. General solution is reduced to the quasi steady state and quasi linear problem. Quasi steady state solution is used to obtain a set of simple and explicit expressions by which the bubble radius is determined in function of time. The results of theoretical analysis are compared with those given by other authors and available experimental data. The agreement between compared experimental data and theoretical results is very good.     

A modular phase change heat exchanger for a solar oven

A modular energy storing heat exchanger designed to use pentaerythritol for thermal storage (solid-solid phase change at 182°C) is tested in an oven by circulating heat transfer oil which is electrically heated in a manner to simulate a concentrating solar collector. Three efficiencies for heating the system under controlled and measured power input are determined—the heat exchanger efficiency, the efficiency of the heater with distribution lines, and the total system efficiency. Thermal energy retention times and cooking extraction times are determined, and along with the efficiencies, are compared with the results previously reported for a nonmodular heat exchanger. The modular configuration provides a highly improved extraction rate for cooking due to its wrap-around character and its increased surface-to-volume ratio. A full scale glass model of the copper tubing of the system is described and flow observations reported demonstrating how uniformly the parallel pumping branches perform and how trapped air pockets affect pumping power. A technique for measuring pumping power is described and its application to our system is quantified to show that less than 1 watt is required to circulate the heat transfer oil even when the system includes the solar collector and its longer connecting tubes.     

A phase density based enthalpy model for laser assisted phase change process

Diffusion dominated laser assisted phase change process in a pure metal is numerically investigated using the enthalpy based fixed-grid approach. The single equation based on the total enthalpy (sensible and latent heat) is used in the whole domain (solid, liquid and vapor) to describe the transport processes in individual phases. To simulate in line with the experiment for laser drilled cavity in a cylinder, density variation due to change of phase has been taken into account in the proposed axisymmetric model. The proposed model also includes temperature dependent thermal properties. An iterative enthalpy update equation is developed to capture the evolution of the complicated melt as well as vapor front. To resemble a true laser beam, a Gaussian laser pulse is irradiated on the substrate surface. The drilled cavity depth predicted using the proposed model is compared with the available experimental results and a good agreement is found.     

变速运动相变胶囊强化传热实验研究

为了研究变速运动对相变胶囊的强化传热效果,选用十六烷为相变材料,黄铜为壳制备圆柱形相变胶囊,利用曲柄摇杆往复装置实现变速运动并搭建实验平台;实验设计相变胶囊在蓄、放热过程中温度的变化范围为10~30 ℃,变速运动的方向为沿胶囊轴向或径向往复运动,振幅为6~12.5 mm,频率为1.55~3.78 Hz,通过测量均匀分布在胶囊内部轴线上8个测点的温度数据分析变速运动的方向、振幅和频率对胶囊蓄、放热效果的影响。实验结果表明：变速运动显著增强了相变胶囊的换热效果,在实验范围内,相比于静止状态,换热系数最大可增加35.6%;胶囊沿径向运动比沿轴向运动强化换热效果更好,沿径向运动时换热时间最多可缩短26.7%;不同工况下胶囊的放热时间均高于蓄热时间,增加振幅和频率可以有效提高蓄、放热效率且对蓄热过程的影响更加显著。     

Performance indicators for solar pipes with phase change storage

Performance indicators for a solar pipe system in which solar radiation is stored as latent heat of a phase changing material are proposed. These performance indicators are aimed at serving as a yardstick by which such multivariables systems are evaluated. The indicators are the melt and solidification times obtained for standardized systems and conditions. These indicator enable the comparison between the suitability of systems with different materials and configurations to store and release thermal energy. The indicators are obtained from numerical solutions of the nonlinear heat conduction problem of the axisymmetric liquid-solid interface motion within the solar pipe. Longitudinal dimension required for the determination of the solidification time is added by an axial superposition of axisymmetric sections. This simplified approach enables a simple numerical solution for an otherwise complicated problem. Estimates of performance characteristics that are based on a simplified model and realistic materials point to the practical potential of solar pipe utilization.     

CLSVOF as a fast and mass-conserving extension of the level-set method for the simulation of two-phase flow problems

The modeling of two-phase flows in computational fluid dynamics is still an area of active research. One popular method is the coupling of level-set and volume-of-fluid (CLSVOF), which benefits from the advantages of both approaches and results in improved mass conservation while retaining the straightforward computation of the curvature and the surface normal. Despite its popularity, details on the involved complex computational algorithms are hard to find and if found, they are mostly fragmented and inaccurate. In contrast, this article can be used as a comprehensive guide for an implementation of CLSVOF into the existing level-set Navier–Stokes solvers on Cartesian grids in three dimensions.