Non- Fourier Heat Transfer and Fluid Flow Simulation in Keyhole Plasma Arc Welding Process

Authors

Abstract

To obtain the transient temperature in different parts of the body and the welding pool growing, the continuity and momentum equations are solved along with the energy equation. The analysis for a rectangular plate made of AISI 304 Stainless Steel is done by writing a program with Fortran.90. Because the Fourier heat transfer equation at short times and large dimensions does not have sufficient accuracy a non-Fourier form of heat transfer equation is being used. Gaussian heat source is considered as a heat source model. The governing equations for fluid flows are solved by the finite volume method in which the SIMPLE method is used for calculating pressure-velocity coupling in fluid flows, likewise the Power-Law method and the staggered grid can be used for discretization equations. The finite difference method is also used to solve the energy equation. The effect of heat conduction, fluid flows and force actions at the weld pool is considered. Thermo-physical properties such as thermal conductivity, specific heat and dynamic viscosity are a function of temperature. There are two mechanisms, radiation and convection heat transfer, which actively cause heat transfer to the surroundings. The numerical results were compared with experimental data. Finally, the results obtained from the assumed Fourier heat transfer are compared for the same study. The results bear the fact that the weld pool thick in the cross section of keyhole PAW and the time that molten metal reaches to the end of thick metal, are in good agreement compared to experimental measurements.

Keywords


 
[1] T. DebRoy and S. Kou “Heat Flow in Welding”, 9th Edition, Chapter 3, Welding Handbook, vol. 1, American Welding Society, pp. 87-113, (2001).
[2] K. Easterling “Introduction to the Physical Metallurgy of Welding”, 2nd Edition, Butterworth-Heinemann, Oxford, (1992).
[3] S. Kou “Welding Metallurgy”, 2nd Edition, John Wiley & Sons, Hoboken, New Jersey, (2003).
[4] W. H. Giedt, X. C. Wei, and S. R. Wei, “Effect of surface convection on stationary GTA weld zone temperatures”, Welding Journal, vol. 63, no. 12, pp. 376s–383s, (1984).
[5] W. E. Lukens and R. A. Morris, “Infrared temperature sensing of cooling rates for arc welding control”, Welding Journal, vol. 61, no. 1, pp. 27–33, (1982).
[6] R. Kovacevic, Y. M. Zhang, and S. Ruan, “Sensing and control of weld pool geometry for automated GTA welding”, Journal of Engineering for Industry, vol. 117, no. 2, pp. 210–222, (1995).
[7] Y. F. Hsu, B. Rubinsky, “Two-dimensional heat transfer study on the keyhole plasma arc welding process”, Int. J. Heat Mass Trans. 31, 1409–1421, (1988).
[8] R. G. Keanini, B. Rubinsky, “Plasma arc welding under normal and zero gravity”, Weld. J. 69, 41–50, (1990).
[9] A. Nehad, “Enthalpy technique for solution of stefan problems: to the keyhole Plasma arc process involving moving heat source”, Int. Comm. Heat Mass Transfer, Vol. 22, No. 6, pp. 779-790, (1995).
[10] M. H. Sadd, J. E. Didlake, “Non- Fourier Melting of a same infinite solid”, J. Heat Transfer 2 vol 81, PP. 25-28, (2001).
[11] F. M. Jiang, “Non- Fourier heat conduction phenomena in porous material heated by microsecond laser pulse”, Taylor & Francis, vol 6, PP. 331-346, (2002).
[12] BY C. S. WU, H. G. WANG, AND Y. M. ZHANG, “A New Heat Source Model for Keyhole Plasma Arc Welding in FEM Analysis of the Temperature Profile”, Welding Journal, (2006).
[13] T.Q. Li, C.S. Wu, Y.H. Feng, L.C. Zheng, “Modeling of the thermal fluid flow and keyhole shape in stationary plasma arc welding”, International Journal of Heat and Fluid Flow 34, 117–125, (2012).
[14] W. Zhang and G. G. Roy, J. W. Elmer, T. DebRoya, “Modeling of heat transfer and fluid flow during gas tungsten arc spot welding of low carbon steel”, Journal of Applied Physics, Volume 93, Number 5, (2003).
[15] BY R. RAI, T. A. PALMER, J. W. ELMER, AND T. DEBROY, “Heat Transfer and Fluid Flow during Electron Beam Welding of 304L Stainless Steel Alloy”, Welding Journal, VOL. 88, (2009).
[16] V. R. Voller and C. Prakash, “A fixed grid numerical modelling methodology for convection-diffusion mushy region phasechange problems”, International Journal of Heat and Mass Transfer 30: 1709–1720, (1987).
[17] A. D. Brent, V. R. Voller, and K. J. Reid, “Enthalpy-porosity technique for modeling convection-diffusion phase change: Application to the melting of a pure metal”, Numerical Heat Transfer 13: 297–318, (1988).
[18] V.R. Voller, C.R. Swaminathan, B.G. Thomas, “Fixed grid techniques for phase change problems: a review”, Int. J. Numer. Methods Eng. 30, 875–898, (1990).
[19] C.S. Wu, “Welding Thermal Processes and Weld Pool Behaviors”, 1st ed. CRC Press Taylor & Francis Boca Raton, (2010).
[20] K. Mundra, T. DebRoy, and K. M. Kelkar, Numer. Heat Transfer, Part A 29, 115, (1996).
[21] C. Cattaneo, “A Form of conduction Equation Which Eliminates the Paradox of Instantaneous Propagation”, Compt.Rend.,vol.247,PP. 431-442, (1986).
[22] P. Vernotte, “Paradox in the Continuous Theory of Heat Equation”, Compt.Rend.,vol.246,PP. 3154-3159, (1986).
[23] H. K. VERSTEEG and W. MALALASEKERA, “An introduction to computational fluid dynamics: The finite volume method”, John Wiley & Sons, New York, (1995).
[24] N. Ashcroft, N. David, “Solid State Physics”, PP: 10, (1975).