Computational aspects of temperature-based finite element technique for the phase-change heat conduction problem

Abstract Liquid–solid phase transition is accompanied by a latent heat release, both in isothermal and non-isothermal phase transformations. The latent heat, the discontinuous phase-change function, and the local exchange of field variables during phase-changes increase the difficulties for obtaining a solution for the Fourier heat conduction equation. Celentano et al. [3] (COO) proposed a temperature-based finite element model for solving the multidimensional transient heat conduction problem involving phase-change. The present work addresses the computational aspects of the COO model. The importance of a line-search algorithm for improving the convergence of the Newton–Raphson iterations are explained in detail. While performing the iterations in this kind of fixed domain methods, the phase front moves back and forth fictitiously. The introduced phase-change matrix handles the latent effect efficiently. Three numerical examples including Direct Chill casting are presented, and the benefits and difficulties of the solution technique are elaborately discussed.

[1]  Z. Abdullah,et al.  On the numerical modelling of heat transfer during solidification processes , 1988 .

[2]  T. Belytschko,et al.  The extended finite element method (XFEM) for solidification problems , 2002 .

[3]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[5]  Sergio Oller,et al.  A coupled thermomechanical model for the solidification of cast metals , 1996 .

[6]  Suyitno,et al.  Effects of alloy composition and casting speed on structure formation and hot tearing during direct-chill casting of Al-Cu alloys , 2004 .

[7]  J. Drezet,et al.  Experimental investigation of thermomechanical effects during direct chill and electromagnetic casting of aluminum alloys , 1995 .

[8]  Nicholas Zabaras,et al.  Front tracking thermomechanical model for hypoelastic-viscoplastic behavior in a solidifying body , 1990 .

[9]  J. Drezet,et al.  Thermomechanical Effects in DC Casting of Aluminium Alloy: A Numerical Benchmark Study , 2000 .

[10]  E. Specht,et al.  Estimation of heat flux in array of jets quenching using experimental and inverse finite element method , 2009 .

[11]  D. Knoll,et al.  A NEW NONLINEAR SOLUTION METHOD FOR PHASE-CHANGE PROBLEMS , 1999 .

[12]  D. Mortensen.  A mathematical model of the heat and fluid flows in direct-chill casting of aluminum sheet ingots and billets , 1999 .

[13]  Suyitno,et al.  Hot tearing criteria evaluation for direct-chill casting of an Al-4.5 pct Cu alloy , 2005 .

[14]  S. Cockcroft,et al.  On the development of a three-dimensional transient thermal model to predict ingot cooling behavior during the start-up phase of the direct chill-casting process for an AA5182 aluminum alloy ingot , 2004 .

[15]  Seid Koric,et al.  Efficient thermo‐mechanical model for solidification processes , 2006 .

[16]  Daan M. Maijer,et al.  Quantification of temperature, stress, and strain fields during the start-up phase of direct chill casting process by using a 3D fully coupled thermal and stress model for AA5182 ingots , 2005 .

[17]  Alberto Cardona,et al.  A fast convergent and accurate temperature model for phase‐change heat conduction , 1999 .

[18]  Frank Kreith,et al.  Heat transfer with melting or freezing in a wedge , 1973 .

[19]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[20]  J. Drezet,et al.  Modeling of ingot distortions during direct chill casting of aluminum alloys , 1996 .

[21]  Petr N. Vabishchevich,et al.  Numerical simulation of convection/diffusion phase change problems—a review , 1993 .

[22]  Pil-Ryung Cha,et al.  A phase field model for isothermal solidification of multicomponent alloys , 2001 .

[23]  David J. Browne,et al.  A FIXED GRID FRONT-TRACKING MODEL OF THE GROWTH OF A COLUMNAR FRONT AND AN EQUIAXED GRAIN DURING SOLIDIFICATION OF AN ALLOY , 2004 .

[24]  R. Lewis,et al.  Finite element simulation of metal casting , 2000 .

[25]  Suresh V. Garimella,et al.  FIXED-GRID FRONT-TRACKING ALGORITHM FOR SOLIDIFICATION PROBLEMS, PART I: METHOD AND VALIDATION , 2003 .

[26]  T. N. Croft,et al.  Modeling of ingot development during the start-up phase of direct chill casting , 2003 .

[27]  Kumar K. Tamma,et al.  Recent advances, trends and new perspectives via enthalpy-based finite element formulations for applications to solidification problems , 1990 .

[28]  J. Drezet,et al.  Determination of thermophysical properties and boundary conditions of direct chill-cast aluminum alloys using inverse methods , 2000 .

[29]  Brian G. Thomas,et al.  Fixed grid techniques for phase change problems: A review , 1990 .

[30]  Alfredo Edmundo Huespe,et al.  Phasewise numerical integration of finite element method applied to solidification processes , 2000 .

[31]  B. Nedjar,et al.  An enthalpy-based finite element method for nonlinear heat problems involving phase change , 2002 .

[32]  Suyitno,et al.  Finite element method simulation of mushy zone behavior during direct-chill casting of an Al-4.5 pct Cu alloy , 2004 .

[33]  Sergio Oller,et al.  A temperature‐based formulation for finite element analysis of generalized phase‐change problems , 1994 .

[34]  B. Moon,et al.  Solidification Parameters Dependent on Interfacial Heat Transfer Coefficient between Aluminum Casting and Copper Mold , 2005 .