An experimental-numerical method for estimating heat transfer in a Bridgman furnace

Abstract Direct measurement of heat flux and heat transfer coefficients in a Bridgman furnace is not always possible using traditional methods. This study characterised a vertical tubular Bridgman furnace using experimental data so that the estimated heat flux and heat transfer coefficients may be used in simulations of future experiments using the same furnace. An experimental–numerical method is presented where a discrete proportional integral derivative controller manipulates the radial heat flux in a front tracking solidification model so that the output temperature profile matches experimental data. The method is applicable for other experimentalists and modellers and its usefulness is demonstrated by example.

[1]  S. Seetharaman,et al.  Thermophysical Properties of γ-Titanium Aluminide: The European IMPRESS Project , 2007 .

[2]  A Front Tracking Model for Transient Solidification of Al–7wt%Si in a Bridgman Furnace , 2012, Transactions of the Indian Institute of Metals.

[3]  W. Herfs,et al.  The Development of a Microgravity Experiment Involving Columnar to Equiaxed Transition for Solidification of a Ti-Al Based Alloy , 2010 .

[4]  B. Blackwell,et al.  Inverse Heat Conduction: Ill-Posed Problems , 1985 .

[5]  C. Gandin.  FROM CONSTRAINED TO UNCONSTRAINED GROWTH DURING DIRECTIONAL SOLIDIFICATION , 2000 .

[6]  J. M. Coulson,et al.  Heat Transfer , 2018, Finite Element Method for Solids and Structures.

[7]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[8]  H. R. N. Jones,et al.  Radiation Heat Transfer , 2000 .

[9]  D. Stefanescu.  Fundamentals of Solidification , 2004 .

[10]  William R. Wilcox,et al.  Control of interface shape in the vertical bridgman-stockbarger technique , 1974 .

[11]  Jie Liu,et al.  Numerical investigation of the interfacial characteristics during Bridgman growth of compound crystals , 2007 .

[12]  C. Gandin,et al.  A Comparison of Columnar-to-Equiaxed Transition Prediction Methods Using Simulation of the Growing Columnar Front , 2009 .

[13]  M. Mohammadzadeh,et al.  Directional solidification of Ni base superalloy IN738LC to improve creep properties , 2000 .

[14]  D. Browne,et al.  A front-tracking model to predict solidification macrostructures and columnar to equiaxed transitions in alloy castings , 2009 .

[15]  W. Wilcox,et al.  Influence of crucible on interface shape, position and sensitivity in the vertical Bridgman-Stockbarger technique , 1975 .

[16]  W. Wilcox,et al.  An experimental approach to determine the heat transfer coefficient in directional solidification furnaces , 1991 .

[17]  J. Lapin,et al.  Solidification behaviour of TiAl-based alloys studied by directional solidification technique , 2011 .

[18]  P. W. Bridgman.  Certain Physical Properties of Single Crystals of Tungsten, Antimony, Bismuth, Tellurium, Cadmium, Zinc, and Tin , 1925 .

[19]  Bo Sundman,et al.  Computation of Partial Equilibrium Solidification with Complete Interstitial and Negligible Substitutional Solute Back Diffusion , 2002 .

[20]  W. Wilcox,et al.  Rate change transients in Bridgman-Stockbarger growth of MnBi-Bi eutectic , 1982 .

[21]  A. G. Quarrell.  Solidification , 1965, Nature.

[22]  P. J. Moss,et al.  Fluid Mechanics and Transfer Processes , 1985 .

[23]  H. S. Carslow,et al.  Conduction of Heat in Solids, Second Edition , 1986 .

[24]  A. Hellawell,et al.  Changes of growth conditions in the vertical Bridgman-Stockbarger method for the solidification of aluminum , 1980 .

[25]  Thomas F. Edgar,et al.  Process Dynamics and Control , 1989 .

[26]  David John Jarvis,et al.  IMPRESS Integrated Project : An overview paper , 2005 .

[27]  A technique for measuring the heat transfer coefficient inside a Bridgman furnace , 1993 .

[28]  O. M. Alifanov,et al.  Solution of an inverse problem of heat conduction by iteration methods , 1974 .

[29]  J. G. Ziegler,et al.  Optimum Settings for Automatic Controllers , 1942, Journal of Fluids Engineering.

[30]  M. N. Özişik,et al.  Finite Difference Methods in Heat Transfer , 2017 .

[31]  Y. S. Touloukian.  Thermophysical properties of matter , 1970 .

[32]  D. M. Anderson,et al.  Convective instabilities during the solidification of an ideal ternary alloy in a mushy layer , 2010, Journal of Fluid Mechanics.

[33]  P. Sukanek.  Deviation of freezing rate from translation rate in the Bridgman-Stockbarger technique I. Very low translation rates , 1982 .

[34]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[35]  A. Abdel-azim.  Fundamentals of Heat and Mass Transfer , 2011 .

[36]  M. N. Özişik,et al.  Inverse Heat Transfer: Fundamentals and Applications , 2000 .

[37]  D. C. Stockbarger.  The Production of Large Single Crystals of Lithium Fluoride , 1936 .

[39]  Y. S. Touloukian,et al.  Thermal conductivity: nonmetallic solids , 1970 .