Influence of electromagnetic stirrer position on fluid flow and solidification in continuous casting mold

A computational study of the effect of stirrer position on fluid flow and solidification in a continuous casting billet mold with in-mold electromagnetic stirring has been carried out. The numerical investigation uses a full coupling method in which alternating magnetic field equations are solved simultaneously with the governing equations of fluid flow and heat transfer. An enthalpy-porosity technique is used for the solidification analysis while the magnetohydrodynamics technique is used for studying the fluid flow behavior under the electromagnetic field. The streamline, liquid fraction, and solid shell thickness at the mold wall have been predicted with and without EMS application at different positions along the length of the mold. Recirculation loops are seen to be formed above and below the stirrer position when fluid flow and electromagnetic field equations were solved, without incorporating the solidification model. Application of the solidification model interestingly resulted in the reduction of the size of the recirculation loops formed. The tangential component of velocity of the fluid near the solidification front, stirring intensity and the effective length of stirring below the stirrer decrease as the stirrer position is moved downwards. Significant changes in characteristics of solid shell formation like delay in initiation of solidification at the mold wall and formation of a gap in the re-solidified shell have been observed with change in stirrer position.     

热防护服-空气-皮肤热传导模型及其解析解

建立了高温环境下热防护服-空气-皮肤的热传导模型.利用热传导时,层合界面间温度相等和热流量连续的条件,结合微分思想,用分离变量法推导了微小时间段内模型热传导的解析解,然后通过循环得到整个时域内的解析解.利用求得的解析解分析了在80℃的环境温度下模型各位置温度和热流密度的变化情况,以及在不同环境温度下皮肤表面温度变化和热...     

Thermal resistance of high-viscosity adhesive layers

The buildup of thermal resistance of high-viscosity adhesive layers is discussed. It has been established experimentally that geometry of the substrate surfaces, hardening pressure, and the amount and viscosity of the adhesive used have a significant influence on the thermal resistance of the adhesive layer. In the case of low hardening pressures the thermal resistance of the layer increases sharply with increasing roughness of the substrate surface and adhesive viscosity, due to an increase in layer thickness and the dimensions of gaseous inclusions.     

Determination of heat transfer properties of media with a single-needle probe

Needle probes with a line heater inside are often used in studying the heat transfer properties of loose rocks. The key problem of contact methods of measuring thermal properties of various media consists in finding thermal contact resistance at the probe/medium interface which must be taken into account in determining the thermal diffusivity of the medium. We describe a mathematical model of heating of a long needle probe in the medium under study, taking into account dimensions and thermal properties of the needle source and assuming that thermal contact between the source and the medium is not ideal. Based on the proposed model, we formulate and solve the inverse problem of finding the thermal diffusivity coefficient of the medium and the heat exchange coefficient at the probe/medium interface. The purpose of the article is to create methodology for determining thermal properties of various media in the field.     

On an inverse problem arising in continuous casting of steel billets

In continuous casting of steel, the control of the solidification front by means of the amount of water sprayed onto the strand is of great practical interest. We study the thermal history in a continuously cast cylindrical billet. The mathematical model is a two-dimensional nonlinear heat equation div[k(u)gradu] = ut subject to water-cooling and heat radiation boundary conditions. We establish existence, uniqueness and stability results for both the temperature field and the solidification front. We study the monotonicity behaviour of the temperature field and show that certain technically easy-to-realize cooling-strategies may generate double liquid fingers at the final stage of solidification. The inverse problem of determining the cooling strategy is an ill-posed problem. We therefore use Tikhonov regularization as a stable and convergent methodfor treating this problem.     

Thermoelastic contact of half-spaces with equal thermal distortivities in the presence of a heat-permeable intersurface gap

We consider the interaction of elastic half-spaces with equal thermal distortivities in the presence of a heat-permeable medium in an intercontact gap caused by a recess on the surface of one of the bodies. Outside the gap, a perfect thermal and frictionless mechanical contact takes place between the bodies. Using the method of functions of intercontact gaps, the formulated contact problem is reduced to a singular integral equation for a derivative of the height of the gap, which is solved analytically, and to a Prandtl-type singular integro-differential equation for the difference of temperature of the surfaces in the region of the gap, for the solution of which we propose an analytic-numerical approach. Plots illustrate the influence of load and the thermal conductivity of the filler on the temperature difference between the edges of the gap, contact stresses, heat flows, and longitudinal strains between the half-spaces.     

A finite element method for steady-state conduction-advection phase change problems

A new finite element: technique is developed to solve steady-state conduction-advection problems with a phase change. The energy balance equation at the solid/liquid interface is employed to calculate the velocity of the solid/liquid interface in the Lagrangian frame. The position of the solid/liquid interface in the Eulerian frame is determined based on the composition of the velocity of the solid/liquid interface in the Lagrangian frame and the steady-state velocity of a rigid body. The interface position and the finite element mesh are continuously updated during an incremental process. No artificial diffusion is needed with this new finite element approach. An analytical solution for solidification of a pure material with a radiative boundary condition is also developed in this paper. Numerical experimentation is conducted and the corresponding results are compared with analytical solutions. The numerical results agree well with analytical solutions.     

Frictionless elliptical contact of thin viscoelastic layers bonded to rigid substrates

A three-dimensional unilateral contact problem for thin viscoelastic layers bonded to rigid substrates shaped like elliptic paraboloids is considered. Two cases are studied: (a) Poisson’s ratios of the layer materials are not very close to 0.5 and (b) the layer materials are incompressible with Poisson’s ratio of 0.5. Poisson’s ratios are assumed to be time independent. In the present paper we derive the general solutions to the problems of elliptical contact between thin compressible or incompressible layers of arbitrary viscoelastic materials. The approach is based on the analytical method developed by the authors for the elliptical contact of thin biphasic cartilage layers. The obtained analytical solution is valid for monotonically increasing loading conditions.     

Transient thermal model for the hot chamber injection system in the pressure die casting process

This paper describes a three-dimensional numerical model that is used to predict the transient thermal behaviour of the metal injection system of a hot chamber pressure die casting machine. The behaviour of the injection system is considered in conjunction with that of the die. The Boundary Element Method (BEM) is used to model the transient thermal behaviour of the injection system elements and the die blocks. A perturbation approach is adopted. By adopting this approach, only those surfaces over which a significant transient variation in temperature occurs need be considered. The model assumes that a corresponding steady-state analysis has first been performed so that time-averaged thermal information is available. A finite element based technique is used to model the phase change of the liquid metal in the die cavity and in the injection system. At injection the nozzle and die are assumed to be instantly filled with liquid metal, however, a procedure is presented that attempts to model the heat transfer associated with the flow through the nozzle, gate, and runner regions during injection. Model predictions are compared against thermocouple readings and thermal images obtained from experimental tests. Good agreement is obtained between predicted and measured temperatures. The transient thermal behaviour of an existing hot chamber injection system is investigated in detail and recommendations for improved performance are made. In an attempt to improve the solidification pattern of the casting and the thermal behaviour of the injection system, a redesign of the experimental die is considered. The numerical predictions indicate that the redesign will have a beneficial effect on the solidification pattern of the casting, and on the performance of the injection system.     

Verified reduction of a model for a continuous casting process

The casting of metals is known to involve the complex interaction of turbulent momentum and heat transfer in the presence of solidification, and it is believed that computational fluid dynamical (CFD) techniques are required to model it correctly. Here, using asymptotic methods, we demonstrate that the key quantities obtained in an earlier CFD model for a particular continuous casting process – ostensibly for a pure metal, but equally for an alloy of eutectic composition – can be recovered using a much simpler model that takes into account just the heat transfer, requiring the numerical solution of a two-phase Stefan problem. Combining this with a more recent asymptotic thermomechanical model for the same continuous casting process, we postulate that it should be possible, with the additional help of algebraic manipulation, to reduce a model that takes into account turbulent momentum and heat transfer in the melt and the thermomechanics in the solid shell to one formulated in terms of only heat transfer, without adversely affecting model predictions.     

A finite element approach for modelling hip joint contact

In this contribution a finite element model for the three dimensional investigation of hip joint contact is described. A shell-like interface element with variable thickness is developed for modelling fluid flow in the synovial gap. For this purpose the Taylor-Hood element is extended in order to take a spatial thickness distribution and local thickness changes into account. The interaction between the synovial fluid and the cartilage layers is solved by a staggered iteration using an artificial compressibility method. Cartilage is modelled using the theory of porous media and three dimensional geometries are reconstructed from medical imaging data. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical and numerical solutions of a one-dimensional fractional-in-space diffusion equation in a composite medium

In this paper a one-dimensional space fractional diffusion equation in a composite medium consisting of two layers in contact is studied both analytically and numerically. Since domain decomposition is the only approach available to solve this problem, we at first investigate analytical and numerical strategies for a composite medium with the same fractal dimension in each layer to ascertain which domain decomposition approach is the most accurate and consistent with a global solution methodology, which is available in this case. We utilise a matrix representation of the fractional-in-space operator to generate a system of linear ODEs with the matrix raised to the same fractional exponent. We show that the global and domain decomposition numerical strategies for this problem produce simulation results that are in good agreement with their analytic counterparts and conclude that the domain decomposition that imposes the Neumann condition at the interface produces the most consistent results. Finally, we carry this finding to study the composite problem with different fractal dimensions, where we again favourably compare analytic and numerical solutions. The resulting method can be naturally extended to space fractional diffusion in a composite medium consisting of more than two layers.     

主动冷却点阵夹层防热结构温度响应计算模型北大核心CSCD

针对点阵夹层结构主动热防护问题,建立了夹层结构面板和芯体导热与冷却剂对流耦合的非稳态传热理论模型,利用有限体积法离散控制方程并在MATLAB中进行了迭代求解.模型首次考虑了面板与夹芯杆之间的收缩热阻,并利用分离变量法得到了收缩热阻的近似解析解.基于单胞模型和周期性边界条件,模拟得到了模型所需的表面对流传热系数h_(b)和h_(fin).最后,选取多单胞计算工况进行数值模拟和理论模型对比,并讨论了收缩热阻对模型预测精度的影响.结果表明:理论模型能够准确预测夹层结构及内部流体的温度变化,理论与仿真之间的最大误差不超过1%;随着外加热流密度不断增大,忽略收缩热阻使得计算结果造成的误差不断增大;与数值模拟相比,理论模型可显著地减少计算时间并节省计算资源,尤其适用于非均匀、非稳态复杂热载荷下点阵夹层结构的温度响应计算.     

An analytical solution for conduction-dominated unidirectional solidification of binary mixtures

In this paper, a fully analytical solution technique is established for the solution of unidirectional, conduction-dominated, alloy solidification problems. By devising appropriate averaging techniques for temperature and phase-fraction gradients, governing equations inside the mushy region are made inherently homogeneous. The above formulation enables one to obtain complete analytical solutions for solid, liquid and mushy regions, without resorting to any numerical iterative procedure. Due considerations are given to account for variable properties and different microscopic models of alloy solidification (namely, equilibrium and non-equilibrium models) in the two-phase domain. The results are tested for the problem of solidification of a NH₄Cl–H₂O solution, and compared with those from existing analytical models as well as with the corresponding results from a fully numerical simulation. The effects of different microscopic models on solidification behaviour are illustrated, and transients in temperature and heat flux distribution are also analysed. A good agreement between the present solutions and results from computational simulation is observed.     

A solution methodology for contacting domains in pressure die casting

Multi-domain elastostatic problems can often be efficiently solved using coupled single domain iterative techniques. A particular difficulty however is the decrease in convergence rate associated with the increase in number of solution domains. Further convergence difficulties are encountered for multi-domain problems where contacting domains suffer variable contact conditions. Problems of this type are evident in pressure die casting with die blocks coupled together prior and subsequent to thermal loading. Particular interest in this paper is the development of an efficient solution methodology for prediction of gaps at block interfaces in pressure die casting.     

Numerical modelling of melt-conditioned direct-chill casting

Melt conditioned direct-chill (MC-DC) casting is a novel technology which combines direct-chill (DC) casting with a high shear device directly immersed in the sump for in situ microstructural control. A numerical model of melt-conditioned direct-chill casting (MC-DC) is presented in this paper. This model is based on a finite volume continuum model using a moving reference frame (MRF) to enforce fluid rotation inside the rotor-stator region and is numerically stable within the range of processing conditions. The boundary conditions for the heat transfer include the effects of the hot-top, the aluminium mould, and the direct chill. This model is applied to the casting of two alloys: aluminium-based A6060 and magnesium-based AZ31. Results show that MC-DC casting modifies the temperature profile in the sump, resulting in a larger temperature gradient at the solidification front and a shorter local solidification time. The increased heat extraction rate due to forced convection in the sump is expected to contribute to a finer, more uniform grain structure in the as-cast billet.     

Crack – interface crack interactions in functionally graded/homogeneous composite bimaterials subjected to a heat flux

A bimaterial containing an interface crack and consisting of a homogeneous material and a functionally graded material (FGM) with a system of small internal cracks is considered. The thermal fracture of the biomaterial under the action of a heat flux applied to it at infinity is investigated. The problem is studied in the case where the interface crack is much larger than the internal ones. It is assumed that the thermal properties of the FGM are continuous functions of the thickness coordinate. Asymptotic analytical formulas for the thermal stress intensity factors (TSIFs) at the tips of the interface crack are obtained as series in a small parameter (the ratio between sizes of the internal and interface cracks). Then, the critical heat fluxes and the angles of propagation direction of the interface crack are calculated using the criterion of maximum circumferential stress. A parametric analysis shows that the propagation direction of the interface crack depends on the location and orientation of the system of internal cracks. The parameters of inhomogeneity of the FGM affect the value of TSIFs and, hence, the deflection angle of the interface crack.     

MHD analysis in hydromagnetic casting process of clad steel slabs

A novel continuous casting process for clad steel slabs has been developed by suppressing the mixing of molten steels in the mold pool of continuous casting strand with a level DC magnetic field (LMF) installed in the mold. In this process, two molten steels of different chemical composition are discharged by two nozzles into the upper and the lower pools respectively to solidify in the outer and the inner layers as a clad steel slabs. The mechanism of separation into two layers has been elucidated by using a three dimensional MHD analysis. The numerical prediction employing Maxwell's equation, Ohm's law, and the turbulent flow model shows that the mixing of the different type of steels is suppressed by the electromagnetic dividing of the upper and the lower recirculating flows. The principle of the new process has also been verified by steel casting trials of the stainless-steel clad steel slabs with an 8-ton scale pilot continuous casting machine.     

具有初始层间压力的层合圆筒的热冲击研究

采用一种解析方法求解具有初始层间压力的双层层合圆筒内的动态热应力的瞬态响应·　首先,将由自紧装配双层层合圆筒引起的初始层间压力考虑作为热弹性动力学方程的初始条件·　其次,利用一个简便的数学变换方法求解具有初始应力场的单层圆筒的热弹性动力学解,然后利用层合圆筒的边界条件和连接条件,得到具有初始层间压力的双层层合圆筒的热冲击解·