An Enthalpy Control Volume Method for Transient Mass and Heat Transport with Solidification

A single domain enthalpy control volume method is developed for solving the coupled fluid flow and heat transfer with solidification problem arising from the continuous casting process. The governing equations consist of the continuity equation, the Navier–Stokes equations and the convection–diffusion equation. The formulation of the method is cast into the framework of the Petrov–Galerkin finite element method with a step test function across the control volume and locally constant approximation to the fluxes of heat and fluid. The use of the step test function and the constant flux approximation leads to the derivation of the exponential interpolating functions for the velocity and temperature fields within each control volume. The exponential fitting makes it possible to capture the sharp boundary layers around the solidification front. The method is then applied to investigate the effect of various casting parameters on the solidification profile and flow pattern of fluids in the casting process.     

A note on a derivative scheme for the finite volume method applied to incompressible viscous fluid

In the last two decades, there have been significant advances in application of the finite volume method to a wide spectrum of physical phenomena, ranging from heat transfer and compressible/incompressible fluid flow to solid mechanics. The finite volume method requires for different applications similar approximations of derivatives at the control surface. Within this framework, this study discusses a derivative scheme used in the finite volume method for incompressible viscous fluids. The numerical scheme is based on an implicit technique associated with the SIMPLE method to attain pressure–velocity coupling. The present work addresses simulation of two-dimensional flows in plane channels with and without contractions. The results show velocities and pressure fields with good agreement when compared to analytical results.     

Direct Numerical Simulation of Flow in a Ribbed Channel

The issue of turbine lifetime is an important one, particularly for modern turbines operating at high temperature regimes. A cooling design such as ribs may achieve an improved lifetime and complex mechanisms of heat transfer need to be well studied. In this paper, a Direct Numerical Simulation (DNS) is presented for a 3-D channel flow with two square ribs on the lower wall. The full unsteady compressible Navier-Stokes equations are solved with an original hybrid finite difference/finite element scheme. The Reynolds number of the simulation is 7 000 based on the bulk velocity at the inlet and the channel height. The present study is mainly devoted to understand the mechanism of heat transfer at the wall through the topological analysis of the flow and the temperature flux. Results show that the large-scale structures generated by obstacles splash onto the lower surface and induce longitudinal vortices which enhance heat transfer at the wall. A comprehensive data base including 56 correlations was set up for testing and improving turbulence models for this complex, separated flow.     

基于特征分裂有限元准隐格式的共轭传热整体耦合数值模拟方法

共轭传热现象在科学和工程领域中大量存在. 随着计算能力的发展, 对共轭传热现象进行准确有效的数值模拟, 成为科学研究和工程设计上的重要挑战.共轭传热数值模拟的方法可以分为两大类: 分区耦合和整体耦合.本文采用有限元法对共轭传热问题进行整体耦合模拟. 固体传热求解采用标准的伽辽金有限元方法.流动求解采用基于特征分裂的有限元方法. 该方法是一种重要的求解流动问题的有限元方法, 可以使用等阶有限元. 该方法的准隐格式与其他格式相比, 具有时间步长大的特点. 将稳定项中的时间步长与全局时间步长分开, 改进了准隐格式的稳定性. 基于改进的特征分裂有限元方法的准隐格式, 发展了一种层流共轭传热数值模拟的整体耦合方法. 采用这种方法可以将流体计算域和固体计算域作为一个整体划分有限元网格, 并且所有变量都可以采用相同的插值函数, 从而有利于程序的实现. 通过对典型问题的模拟, 验证了这种方法的准确性. 本工作还研究了固体区域时间步长对定常共轭传热问题数值模拟收敛性的影响.      

Streamline upwind finite element method for conjugate heat transfer problems

This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method. The English text was polished byYunming Chen.     

轴对称热传导有限元格式

分析了目前一些有限元专著中轴对称热传导有限元方法推导中的问题,给出了轴对称热传导有限元格式的正确表达形式。     

RTM充模过程数值模拟的隐式有限元算法

建立了基于欧拉方法描述树脂传递模塑(RTM)工艺充模过程的基本数学方程,并采用有限元隐式时间积分方法对基本方程进行了数值求解．编制了基于隐式有限元算法及传统有限元控制体算法的程序,通过具体算例比较了这两种算法的优缺点．与传统的有限元控制体法相比,该文提出的隐式有限元算法能节省计算时间,特别适合于单元、节点数目多的情况．隐式有限元算法是一种纯有限元方法,不需要使用控制体积技术,采用该算法计算出的流动前沿与时间步长无关。     

Investigation of Coulomb force effects on ethylene glycol based nanofluid laminar flow in a porous enclosure

Forced convection heat transfer of ethylene glycol based nanofluid with Fe_3O_4 inside a porous medium is studied using the electric field. The control volume based finite element method(CVFEM) is selected for numerical simulation. The impact of the radiation parameter(R_d), the supplied voltage(?φ), the volume fraction of nanofluid(?), the Darcy number(Da), and the Reynolds number(Re) on nanofluid treatment is demonstrated. Results prove that thermal radiation increases the temperature gradient near the positive electrode. Distortion of isotherms increases with the enhance of the Darcy number and the Coulomb force.     

Two numerical modelings of free convection heat transfer using nanofluids inside a square enclosure

This work describes the numerical simulation of natural convection heat transfer of Cu–water nanofluids in a square enclosure for Rayleigh numbers varying from 10³ up to 10⁵. Two different numerical approaches were used: the finite volume method and the finite element method. The nanofluids were assumed to be single-phase fluids with modified thermal properties obtained from experimental results and theoretical models. The results showed that the Nusselt number for nanofluids was basically the same as that obtained for the base fluid. Therefore, the enhancement observed in the heat transfer coefficient was significant due to the augmentation in the thermal conductivity.     

Stabilized finite element solution to handle complex heat and fluid flows in industrial furnaces using the immersed volume method

We consider the numerical simulation of conjugate heat transfer, incompressible turbulent flows for multicomponents systems using a stabilized finite element method. We present an immersed volume approach for thermal coupling between fluids and solids for heating high‐alloy steel inside industrial furnaces. It consists in considering a single 3D grid of the furnace and solving one set of equations with different thermal properties. A distance function enables to define precisely the position and the interface of any objects inside the volume and to provide homogeneous physical and thermodynamic properties for each subdomain. An anisotropic mesh adaptation algorithm based on the variations of the distance function is then applied to ensure an accurate capture of the discontinuities that characterize the highly heterogeneous domain. The proposed method demonstrates the capability of the model to simulate an unsteady three‐dimensional heat transfers and turbulent flows in an industrial furnace with the presence of three conducting solid bodies. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical simulation of glass fogging and defogging

A numerical procedure for the prediction of fogging and defogging phenomena is presented. The simulation involves the solution of an air flow field along a cold solid surface, the evaluation of the unsteady conduction through the solid itself, and a model for the heat and mass transfer within the thin water layer on the fogged surface. A suite of routines for the unsteady simulation of the water layer evolution is coupled with an equal order finite element Navier Stokes solver and a finite volume conduction code. The procedure is fully independent of the numerical details of the solid and fluid domain solvers. Two different coupling approaches may be followed: A loose one, where the Navier Stokes solution is used only for a steady state estimate of the heat transfer coefficient, or a close one, where the Navier Stokes, conduction and water layer codes are iterated simultaneously. The latter is required for the problem of natural convection, where temperature (and thus the energy balance of the water layer) and flow field are coupled. The water layer is modelled as a collection of closely packed tiny droplets, leaving a portion of dry area among them. The effect of the contact angle is taken into account, and physical assumptions allow to define the local ratio between wet and dry surface for both the fogging and defogging process. As a case study, a comparison with experimental data for a complete fogging and defogging cycle of a glass lens in natural convection is presented.     

Numerical simulation of flow and heat transfer in a random packed bed

Random packed beds have more complex interior structure than structured beds and are widely used in industry and engineering.CFD simulation was carried out to investigate and analyze the local flow and heat transfer in a 120-sphere random packed bed.3D Navier-Stokes equation was solved with a finite volume formulation based on the Chimera meshing technique.Investigation was focused on low Reynolds number flow(Re=4.6-56.2),which typically occurs in packed bed reactors in bio-chemical fields.Detailed temperature field information was obtained.Inhomogeneity of flow and heat transfer due to the non-uniform distribution of void fraction was discussed and analyzed.     

Finite element analysis of multicomponent two-phase flows with interphase mass and momentum transport

The application of the finite element method to multiphase flow problems with interphase mass and heat transfer is described. A general forinulation is used that determines the position of the interfacial boundary and allows for multiple solvents, differential volatilities and concentration- and temperature-dependent thermophysical properties. Species phase change and the dramatic volume change that acompanies interphase mass transfer make implementation of the theory challening, since these events lead to discontinuous velocities and concentrations at phase boundaries. These discontinuities are especially large in processes involving rapid evaporation or condensation. As examples we examine the effects of rapid drying on film and fibre formation of sol--gel materials, which are often laden with volatile species.     

具有非线性表面换热系数半圆柱薄壳在快速冷却过程中的热分析

用实验和数值计算相结合的方法，得到半圆柱壳体快速冷却过程中内外表面的非线性表面换热系数。在此基础上，用有限单元法对半圆柱壳体的热应力和变形进行了分析。在数值计算中，模拟钢的CCT图，计算了奥氏体、珠光体、贝氏体和马氏体的体积百分比，并将热物理性质和力学性能处理为相变体积百分比和温度的函数。所得结果表明，在半圆柱壳体快速冷却过程中的热应力和变形计算中，有必要考虑非线性表面换热系数、相变等非线性效应。     

Finite Element Modeling of Liquid Deuterium Flow and Heat Transfer in a Cold-neutron Source

A finite element simulation of flow and heat transfer in the moderator cell of a cold-neutron source (CNS), in which liquid deuterium subject to internal heat generation is flowing, is reported. The numerical scheme consists of a stabilized equal-order method. A time-accurate approach is adopted to resolve the large-scale eddies of the flow, with a Smagorinsky's model for the subgrid-scale effects. The thermal coupling follows a staggered strategy, with SUPG-type upwinding. A specific wall-law is developed that accounts for the correct partition of the heat deposited at the wall by radiation between the liquid deuterium and the helium gas flowing at the outer side of the wall. The average flow and thermal structure are presented. The turbulent fluctuations are both illustrated in physical space and decomposed into spectral components. The wavenumber spectrum suggests that adequate resolution of the large-scale eddies has been attained with just 200,000 nodes, while a DNS analysis would have required at least 1010 nodes. Usefulness of the approach in the design process of the CNS is highlighted.     

注塑成型充填／后充填过程统一的可压缩流动分析

注塑成型是重要的塑料成型工艺,成型过程中熔体在模腔中的流动和传热对最终制品的性能和质量有重要的影响,因此,精确预测注塑过程的流动及传热历史,并进一步预测注塑制品的收缩、翘曲和机械性能等性能和质量指标具有重要意义。为了精确地描述成型过程中材料的流动及传热行为,本文针对注塑成型过程的工艺特点,将充填后充填过程作为一个统一的过程,考虑材料可压缩性及相变对充填和后充填过程的影响,建立了充填后充填过程的统一数学模型。采用有限元/有限差分/控制体积混合数值方法,实现了注塑成型充填后充填一体化模拟。数值模拟结果与实验结果的对比,验证了本文模型和算法。     

Coupled heat transfer and viscous flow,and magnetic effects in weld pool analysis

A finite element formulation and analysis is developed to study coupled heat transfer and viscous flow in a weld pool. The thermal effects generate not only buoyancy forces but also a variation in the surface tension which acts to drive the viscous flow in the molten weld pool. A moving phase boundary separates molten and solid material. Numerical experiments reveal the nature of the highly convective flow in the weld pool and the associated thermal profiles. The relative importance of buoyancy, surface tension, phase change, convection, etc. are examined. We also consider the sensitivity of the solution to the finite element mesh and related non-linear numerical instabilities. Of particular interest is the coupling of the thermal and viscous flow fields for the case when radial flow is inward or outward.     

Use of experiment and an inverse method to study interface heat transfer during solidification in the investment casting process

A technique to determine the thermal boundary conditions existing during the solidification of metallic alloys in the investment casting process is presented. Quantitative information about these conditions is needed so that numerical models of heat transfer in this process produce accurate results. In particular, the variation of the boundary conditions both spatially and temporally must be known. The method used involves the application of a new inverse heat conduction method to thermal data recorded during laboratory experiments of aluminium alloy solidification in investment casting shell moulds. The resultant heat transfer coefficient for the alloy/mould interface is calculated. An experimental programme to determine requisite mould thermal properties was also undertaken. It was observed that there is significant variation of the alloy/mould heat transfer coefficient during solidification. It is found to be highly dependent on the alloy type and on the vertical position below the initial free surface of the liquid metal. The aluminium casting alloys used in this study were 413, A356, 319 (Aluminum Association designations), and commercially pure aluminium. These alloys have significantly different freezing ranges. In particular, it was found that alloys with a high freezing range solidify with rates of heat transfer to the mould which are very sensitive to metallostatic head.     

Numerical simulation of MHD stagnation point flow and heat transfer of a micropolar fluid towards a heated shrinking sheet

A comprehensive study of magneto hydrodynamics two‐dimensional stagnation flow with heat transfer characteristics towards a heated shrinking sheet immersed in an electrically conducting incompressible micropolar fluid in the presence of a transverse magnetic field is analyzed numerically. The governing continuity, momentum, angular momentum and heat equations together with the associated boundary conditions are first reduced to a set of self similar nonlinear ordinary differential equations using a similarity transformation and are then solved by a method based on finite difference discretization. Some important features of the flow and heat transfer in terms of normal and streamwise velocities, microrotation and temperature distributions for different values of the governing parameters are analyzed, discussed and presented through tables and graphs. The results indicate that the reverse flow caused due to shrinking of the sheet can be stopped by applying a strong magnetic field. The magnetic field enhances the shear stresses and decreases the thermal boundary layer thickness. The heat loss per unit area from the sheet decreases with an increase in the shrinking parameter. Micropolar fluids exhibit reduction in shear stresses and heat transfer rate as compared with Newtonian fluids, which may be beneficial in the flow and thermal control of polymeric processing. Copyright © 2011 John Wiley & Sons, Ltd.     

A finite element model for numerical simulation of thermo-mechanical frictional contact problems

Two kinds of variational principles for numerical simulation of heat transfer and contact analysis are respectively presented. A finite element model for numerical simulation of the thermal contact problems is developed with a pressure dependent heat transfer constitutive model across the contact surface. The numerical algorithm for the finite element analysis of the thermomechanical contact problems is thus developed. Numerical examples are computed and the results demonstrate the validity of the model and algorithm developed. The project supported by the National Key Basic Research Special Foundation (G1999032805), the National Natural Science Foundation of China (50178016, 10225212) and the Foundation for University Key Teacher by the Ministry of Education of China