Pressure effects in the planar solidification of a finite slab: convective cooling and prescribed heat flux boundary conditions

Summary The classical Stefan problem assumes a fixed melting temperature. However, when the solid phase is the one with lower density (e.g., water) the solidification of the system causes an overall volume increase that is often contrasted by the container walls. In that case the growing pressure determines a continuous lowering of the freezing point, and the temperature field as well as the interface motion are strongly affected. This paper is concerned with these aspects of the problem; the planar solidification of a slab of finite thickness, contrasted by an opposing elastic force, is numerically simulated. The effects of two different boundary conditions are analysed. When the solidification is driven by convective cooling, the continuous advancement of the melting front is replaced by an asymptotic behaviour, until thermal equilibrium is attained. When the boundary condition is specified in terms of a prescribed heat flow, the melting front velocity is slowed down by a growing adverse temperature gradient. The influence of various parameters on the process is presented and discussed.     

Heat transfer and diffusion-controlled kinetics of liquid–solid phase in titanium matrix composite during selective laser melting

This study describes a self-consistent theoretical model of simulating diffusion-controlled kinetics on the liquid–solid phase boundary during high-speed solidification in the melt pool after the selective laser melting (SLM) process for titanium matrix composite based on Ti–TiC system. The model includes the heat transfer equation to estimate the temperature distribution in the melt pool and during crystallization process for some deposited layers. The temperature field is used in a micro region next to solid–liquid boundary, where solute micro segregation and dendrite growth are calculated by special approach based on transient liquid phase bonding. The effect of the SLM process parameters (laser power, scanning velocity, layer thickness and substrate size) on the microstructure solidification is being discussed.     

相变储热体释热强度研究

对相变储热体以导热为主的释热过程,可以应用一维相变导热模型描述。当进一步简化,认为散热表面的温度低于相变温度且保持不变,不考虑液相区的自然对流和固液两相有明确的分界面,利用Neuman解法求解出释热过程的热强度,并通过实验进行研究。理论与实验结果比较表明,其相对误差不大于5％,从而证明这种方法可作为这类储热体的设计基础。     

相变微胶囊功能流体融化状态的数值模拟

本文用双流体模型模拟相变微胶囊(MCPCM)功能流体在大通道层流流动中的融化状态.MCPCM功能流体的入口条件和边界条件类型是影响MCPCM在管道中沿程融化率和融化速率的两个重要的决定因素.本文给出了恒壁温和恒热流两类边界条件下,不同入口条件时,MCPCM截面平均融化率和融化速率沿管道方向的变化趋势.提出了利用MCPCM的融化率与温度场的关系,通过管道截面的平均温度和截面温度场估算MCPCM截面平均融化率的思路.     

Experimental Investigations on Latent Heat Storage Unit using Paraffin Wax as Phase Change Material

Thermal performance of a latent heat storage unit is evaluated experimentally. The latent heat thermal energy storage system analyzed in this work is a shell-and-tube type of heat exchanger using paraffin wax (melting point between 58°C and 60°C) as the phase change material. The temperature distribution in the phase change material is measured with time. The influence of mass flow rate and inlet temperature of the heat transfer fluid on heat fraction is examined for both the melting and solidification processes. The mass flow rate of heat transfer fluid (water) is varied in the range of 0.0167 kg/s to 0.0833 kg/s (1 kg/min to 5 kg/min), and the fluid inlet temperature is varied between 75°C and 85°C. The experimental results indicate that the total melting time of the phase change material increases as the mass flow rate and inlet temperature of heat transfer fluid decrease. The fluid inlet temperature influences the heat fraction considerably as compared to the mass flow rate of heat transfer fluid during the melting process of the phase change material.     

声悬浮条件下环己烷液滴的蒸发凝固

采用单轴式声悬浮方法研究了环己烷液滴的蒸发过程,发现环己烷液滴的蒸发可以使自身温度降至熔点以下并发生凝固.高速摄像实时观测表明,环己烷晶核开始形成于液滴赤道附近,并以枝晶方式长大,平均生长速度为12.5-160.4 mm/s.进一步研究发现,声悬浮条件下平均Sherwood数与平均Nusselt数的比值Sh/Nu是在自然对流条件下的1.3倍,这表明声流边界层有效提高了环己烷液滴的蒸发速率而对传热的促进作用相对较小,因而可以使液滴降至更低温度,进而发生凝固.据此,提出了挥发性液体在声悬浮条件下发生蒸发凝固的必要条件. 关键词： 声悬浮 声流 环己烷 蒸发凝固     

Grain Boundary Phase Transitions and their Influence on Properties of Polycrystals

Grain boundary (GB) phase transitions can change drastically the properties of polycrystals. The GB wetting phase transition can occur in the two-phase area of the bulk phase diagram where the liquid (L) and solid (S) phases are in equlibrium. Above the temperature of the GB wetting phase transition a GB cannot exist in equlibrium contact with the liquid phase. The experimental data on GB wetting phase transitions in numerous systems are analysed. The GB wetting tie-line can continue in the one-phase area of the bulk phase diagram as a GB solidus line. This line represents the GB premelting or prewetting phase transitions. The GB properties change drastically when GB solidus line is crossed by a change in the temperature or concentration. The experimental data on GB segregation, energy, mobility and diffusivity obtained in various systems both in polycrystals and bicrystals are analysed. In case if two solid phases are in equilibrium, the GB “solid state wetting” can occur. In this case the layer of the solid phase 2 has to substitute GBs in the solid phase 1. Such GB phase transition occurs if the energy of two interphase boundaries is lower than the GB energy in the phase 1.     

The development and investigation of a strongly non-equilibrium model of heat transfer in fluid with allowance for the spatial and temporal non-locality and energy dissipation

The differential equation of heat transfer with allowance for energy dissipation and spatial and temporal nonlocality has been derived by the relaxation of heat flux and temperature gradient in the Fourier law formula for the heat flux at the use of the heat balance equation. An investigation of the numerical solution of the heat-transfer problem at a laminar fluid flow in a plane duct has shown the impossibility of an instantaneous acceptance of the boundary condition of the first kind — the process of its settling at small values of relaxation coefficients takes a finite time interval the duration of which is determined by the thermophysical and relaxation properties of the fluid. At large values of relaxation coefficients, the use of the boundary condition of the first kind is possible only at Fo → ∞. The friction heat consideration leads to the alteration of temperature profiles, which is due to the rise of the intervals of elevated temperatures in the zone of the maximal velocity gradients. With increasing relaxation coefficients, the smoothing of temperature profiles occurs, and at their certain high values, the fluid cooling occurs at a gradientless temperature variation along the transverse spatial variable and, consequently, the temperature proves to be dependent only on time and on longitudinal coordinate.     

Effect of boundary heat flux on solidification in a forced liquid metal flow: a phase-field simulation

A phase-field model coupling with velocity field is employed to study the effect of boundary heat flux on the microstructure formation of a Ni-40.8%Cu alloy with liquid flow during the solidification, and an anti-trapping current is introduced to suppress the solute trapping due to the larger interface width used in simulations than a real solidifying material. The effect of the flow field coupling with boundary heat extractions on the microstructure formation as well as distributions of concentration and temperature fields are analyzed and discussed. The forced liquid flow can significantly affect the heat and solute diffusions, thus influencing morphology formation, concentration and temperature distributions during the solidification. The solute segregation and concentration diffusion are changed by boundary heat extractions, and the morphology, concentration and temperature distributions are significantly influenced by increasing the heat extraction, which relatively makes the effect of liquid flow constrained. By increasing the initial velocity of liquid flow, the lopsided rate of the primary dendrite arm is enlarged and the growth manner of dendrite arms gets changed, and the transition of the microstructure from dendrite to cellular moves to the large heat extraction direction. Therefore, there exists the competition between the heat flux, temperature gradient and forced liquid flow that finally determines the microstructure formation during directional solidification.     

圆管内自由固体相变材料定热流接触熔化

针对水平圆管内自由固体相变材料储能时的吸热熔化,运用接触熔化理论建立定热流圆管热源接触熔化模型.运用Nusselt液膜理论,建立熔化控制方程,并求解得到无量纲熔化方程组.分析讨论不同工况下熔化速度、液膜层厚度和压力分布等熔化参数的变化规律,探讨各影响因素对熔化的影响,并与温差熔化结果进行比较,研究第二类热边界条件下的接触熔化规律.发现,熔化过程中随着固体高度的减小,接触熔化液膜厚度逐渐增大,使熔化速度降低;热流密度较小时,其变化对熔化影响显著.     

Experimental determination of interfacial energies for Ag2Al solid solution in the CuAl2--Ag2Al system

The equilibrated grain boundary groove shapes of solid solution Ag2Al in equilibrium with an Al-Cu-Ag liquid were observed from a quenched sample with a radial heat flow apparatus.The Gibbs-Thomson coefficient,solid-liquid interfacial energy and grain boundary energy of the solid solution Ag2Al have been determined from the observed grain boundary groove shapes.The thermal conductivity of the solid phase and the thermal conductivity ratio of the liquid phase to solid phase for Ag2Al-28.3 at the %CuAl2 alloy at the melting temperature have also been measured with a radial heat flow apparatus and Bridgman type growth apparatus,separately.     

振荡流共轭换热格子-Boltzmann模拟

振荡流共轭换热现象广泛存在于热声热机等工程应用中.基于双分布格子-Boltzmann模型,对平行平板间振荡流共轭换热进行了数值模拟.通过假定共轭界面处流体和固体的未知内能分布函数均为对应的平衡态滑移修正格式,提出了一种处理共轭换热边界的新方法.模拟结果表明,该方法可以保证共轭界面上温度连续和热流连续.分析了不同流体与固体导热系数比情况下振荡流共轭换热的速度场、温度场以及热流分布的特点.     

Effect of melting on the excitation of surface acoustic wave pulses by UV nanosecond laser pulses in silicon

The influence of melting on the excitation of Surface Acoustic Wave (SAW) pulses in silicon is studied both theoretically and experimentally. The developed theory of Rayleigh-type SAW laser-induced thermoelastic excitation in a structure composed of a liquid layer on a solid substrate predicts that the SAW is predominantly generated in the solid phase due to the absence of shear rigidity in a liquid. The characteristic changes in the SAW pulse shape as well as the saturation and even the decrease of the SAW pulse amplitude observed above the melting threshold are explained theoretically to be a result of the decrease of the heat flux into the solid phase as well as due to the decrease of the volume of the solid phase caused by melting. Although the heat flux into the solid phase is decreased both as a consequence of the reflectivity increase and the additional energy losses (latent heat of melting) at the phase transition, it is demonstrated that the influence of reflectivity changes on the SAW pulse is negligible in comparison with the effect of melt-front motion. For laser pulses of 7 ns duration at 355 nm, the threshold value of laser fluence for meltingF _m=0.23±0.04 J/cm² and for the ablationF _a=1.3±0.2 J/cm² were determined experimentally as the points of characteristic changes in the observed SAW pulses.     

铸件在凝固过程中的传热和自然对流计算

论文中以流函数、涡度和温度为基本变量,建立了铸件凝固时的传热和自然对流的数学模型。控制方程采用半隐式有限差分在固定网格上求解。在模型建立过程中,着重讨论了潜热的处理和固液相区(界面)速度条件。对于潜热处理,采用了基于合金平衡相图的比热焓法;对于固液相区(界面)速度条件,提出了一种新的、基于固相率进行修正的处理方法。另外还探讨了将本文提出的解法应用于复杂几何条件的可能性。最后,通过对一个典型例子进行计算,对自然对流对铸件凝固的影响作了深入的讨论。     

Opposed-flow ignition and flame spread over melting polymers with Navier-Stokes gas flow

A numerical model is constructed to predict transient opposed-flow flame spread behaviour in a channel flow over a melting polymer. The transient flame is established by initially applying a high external radiation heat flux to the surface. This is followed by ignition, transition and finally steady opposed-flow flame spread. The physical phenomena under consideration include the following: gas phase: channel flow, thermal expansion and injection flow from the pyrolyzed fuel; condensed phase: heat conduction, melting, and discontinuous thermal properties (heat capacity and thermal conductivity) across the phase boundary; gas-condensed phase interface: radiation loss. There is no in-depth gas radiation absorption in the gas phase. It is necessary to solve the momentum, species, energy and continuity equations in the gas along with the energy equation(s) in the liquid and solid. Agreement is obtained between the numerical spread rate and a flame spread formula. The influence of the gas flow is explored by comparing the Navier-Stokes (NS) and Oseen (OS) models. An energy balance analysis describes the flame-spread mechanism in terms of participating heat transfer mechanisms.     

Effect of Heating Position on Thermal Energy Storage in Cavity With/Without Open-cell Metallic Foams

Thermal energy storage systems inherently store heat at different heating positions. In other words, the heat storage performance changes depending on the heating positions. In this study, the effects of the heating surface position and reinforcement of the open-cell metal foam on the phase change material melting fraction were experimentally investigated. For this purpose, a small-scale rectangular cube was made of plexiglass having a volume of 274 cm³. One of the surfaces of the cube was heated with a constant heat flux, whereas other surfaces were isolated from the room temperature in the environment. Three different constant heat fluxes were applied on the bottom, top, and side surfaces of the cube in the experiments. Paraffin (n-heptacosane), with a phase change point at 59°C–61°C and as phase change material with a rapid heat charge/discharge, was used in the thermal energy storage system. Depending on the heating position and surface heat flux, it was observed that the effect of natural convection significantly increased within the liquid phase change material. Additionally, the results indicate that the presence of metal foams can enhance the heat transfer rate of phase change materials. According to the sensitivity analysis, the effect of independent parameters on the melting ratio of the phase change material was listed in order of importance as time, surface heat flux, heating position, and metallic foam.     

New theory of undercooling during rapid solidification: application to pulsed laser heated silicon

A new theory of undercooling has been developed based on the Fickian form of heat flux expressed in terms of a gradient in enthalpy density. It is shown that heat diffusion is more fundamental than Fourier’s law of heat conduction. During the solid–liquid phase change, diffusion requires continuity of the enthalpy density across the phase-change boundary, which has two important consequences. First, the calculated melt-depth during rapid heating is reduced, and second, during cooling the rate of loss of heat is independent of both the rate of release of latent heat and the temperature of the interphase layer. The cause of undercooling is diffusive heat loss without recrystallisation, which simply causes the temperature of the liquid to drop. Both the nature of melting and classical nucleation have been examined and shown to support diffusion over conduction. In particular, it is established that the literature supports a model of melting in which phase fluctuations at the melting point occur, and that these phase fluctuations must inevitably lead to thermal transport at uniform temperature. Hitherto unrecognized inconsistencies in classical nucleation theory also support the diffusive framework. The model is applied to pulsed laser melting and amorphisation of (111) silicon. PACS  64.70.Dv; 66.30.Xj; 68.18.Jk     

石墨烯气凝胶复合相变材料的热物性研究

相变材料利用其相变潜热能力可吸收储存和释放利用热量,同时在相变过程中其温度浮动小,能够实现温度控制从而用于热管理.但是其低热导率和易泄露问题严重制约了其性能.石墨烯气凝胶因其丰富的多孔结构而具有较大的比表面积,可吸附相变材料解决其泄露问题,同时石墨烯的高导热系数可提高相变材料的热导率.这里选取正十八烷为相变材料,制备了不同质量分数的石墨烯气凝胶复合相变材料.测得石墨烯气凝胶含量为13.99 wt%的样品,其导热系数比纯正十八烷高出306.2%,熔化潜热和凝固潜热分别下降了13.8%和10.8%.分子动力学模拟结果表明,石墨烯气凝胶的引入会在一定程度上增强正十八烷分子的有序性和一致性,即在同一温度下复合相变材料中的正十八烷分子比纯正十八烷分子拥有更集中分布的末端距和扭转角,径向分布函数和自扩散系数都相对较低,说明石墨烯材料的引入可以提升正十八烷的导热系数.     

Melting and resolidification of gold film irradiated by nano- to femtosecond lasers

Rapid melting and resolidification of a free-standing gold film subject to nano- to femtosecond laser pulses are investigated using the two-temperature model in conjunction with an interfacial tracking method. The interfacial velocity, as well as elevated melting temperature and depressed solidification temperature, in the ultra-fast phase-change process are obtained by considering the interfacial energy balance and nucleation dynamics. A nonlinear electron heat capacity and a temperature-dependent electron–lattice coupling factor for the rapid phase change are taken into account. Effects of laser pulse width and fluence on melting and resolidification are also studied. PACS 42.62.Eh; 63.20.Kr; 64.70.Dv     

分析金属熔滴快速凝固过程的双倒易边界元方法

本文发展了非线性边界条件相变传热过程的轴对称双倒易边界元方法,数值模拟了金属熔滴在快速冷却条件下的快速凝固过程。分别研究了在微重力落管和落塔中及喷射成形过程中金属熔滴的快速凝固过程,得到了过冷度,再辉时间,温度变化及相变界面随时间的变化等数值结果。