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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

*Ioan Sorin Leoveanu, ** Gheorghe Zgura *Transylvania University Brasov, Romania. **Polytechnic University Bucharest, Romania

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

The paper proposes a numerical method for analyzing the complexes phenomena’s that appear in the case of keyholes welded pool geometry. Present model consist in a succession of analyses steps, needed to solve the interaction between the liquid/solid, liquid/protection gaze and liquid/MHD welded arc for arc welding or electrons or electromagnetically waves. The liquid/solid geometry result by dissipation the welding power source in a matrix of many point sources. This process gives a first approximation of temperature fields and a good approximation of the digit 3D position and information about the vaporization area.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

1. Introduction. The welding by fusion is an important manufacturing technique that is using more and more frequent in the modern manufacturing of various areas. In the last decade, the knowledge about fusion welding processes has attained the level of maturity that imposes a special attention. The physical processes that take place during fusion welding, are in the field of: Magneto Hydro Dynamics for the Welding Arc Modeling Heat transfer Melting Fluid Flow with Marangoni convection effects and electromagnetic and buoyancy forces for the welded pool in the fluid state. The primary solidification and solid-state transformations give the properties of the weldments and finally the properties of all the structure.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

Several computational studies have also successfully shown insights into the physical processes that occur during welding.[1],[6] Convection in the weld pool is recognized as one of the important processes that determine weld pool characteristics such as size and shape.[1][2][5]. Experimental verification of computational models and prediction of weld pool characteristics as a function of processing conditions have also been relatively successful. Recent advances in manufacturing industry require the powerful welded sources that drive to complexes welded pool geometry, and the estimation made with classical computation [1, 2] give errors not only for dissimilar metals alloys joined but even for similar joins.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

The studies in the area of that type of sources are limited. That new shape is known in literature as keyholes and his mathematical estimation with classical methods give errors unacceptable. Studies of those types of sources are made in the last time using numerical methods. The analyze of that type of sources need the consideration of heat and fluid flows to get the temperature and speed gradients in the fusion and solidification areas. Other aspects of that phenomenon consist in the droplet input of added metal/alloy in the welded pool and in chemical differences between droplet and base material. That gives rice to the necessity of species transfer analysis in a fluid flow with a free boundary transient process and to the complexes crystallization processes.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

The Marangoni condition takes a great complexity, given by gradients of temperature and concentration too. In the current paper, we use matrix-distributed point sources to establish the heat flow and give the key-hole formation. The heat flow is given in a three-dimensional approach and the temperature field obtained in the melt is used to establish the heat and fluid advection in addition with a Gaussian distribution of arc pressure and shield gazes pressure on the face of the free surface. The pressures of arc and gazes are considerate stationary and have not variations in the process analyzing. Based on MAC techniques, the shape of free surface is obtain from longitudinal section of weld and in the transverse section positioned in the arc-welded source

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

2. Numerical Analysis. Figure 1 shows the model for the present study. The inlet position is located at welding arc point in the section where the droplets arrive in the welded melt pool. The staggered grid is adopted in the finite volume approach, which forms the basis of the MAC method.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

b) c) Figure 1. The geometry and limits conditions of the simulation’s process .a) The aspect of the welded pool, b) the transversal key-hole shape, c) geometrical distribution of the point sources.

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**2.1. Governing Equations. a) The liquid phase equations.**

Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources 2.1. Governing Equations. a) The liquid phase equations. To analyze the fluid flow and thermal characteristics of molten metal in the welded pool formed process, are following the hypothesis: l) The flow is 2-D, incompressible, and laminar. 2) Each thermal property of molten metal is constant. 3) The heat dissipation and the turbulent indices are calculated only in the fluid control volumes. Then the general differential equation for conservative lows can be give as followings.

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**F G S Continuity 1 Moment m Energy**

Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources F G S Continuity 1 Moment Vi velocity on xi direction m Vj velocity on xj direction Energy T temperature

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**b) The solid state phase governing equation.**

Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources The fmxi ,fmxj represent the electromagnetic acceleration induced by the electric arc and the ascension buoyancy forces and in the analysis are induced by the arc pressure term: b) The solid state phase governing equation.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

2.2. Boundary Conditions. Heating and cooling is supposed to arise by convection and radiations on the entire internal and external boundary. For fluid flow analysis either the slip wall condition or the no-slip wall condition is adopted [9,19] according to the size of a cell and the magnitude of velocity. It's because, only when the width or the height of a cell is small enough considering low velocity and high viscosity, no-slip wall condition gives reasonable fluid motion. When the alloy is melted, the convection coefficient between melt and solid boundary alloy is calculate based on Rex and Pr numbers by solving with Modified Cellular Automata Method the fluid flow and heat flows system of equations in the neighboring of the surface. The system, in dimensionless form, and under consideration that:

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**Mass x- momentum Heat Solution shape**

Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources Table 2 Mass x- momentum Heat Solution shape

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**2.3. Free Surface and Phase Change**

Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources 2.3. Free Surface and Phase Change On free surface, the sum of tangential stresses must be balanced by the stress given by the gradients of the surface tension with the temperature gradients and concentrations gradients. The sum of normal stresses must be equal to the applied stresses or pressures.

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**gT is the surface tension function of temperature,**

Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources Where: vi, vj are the xi, xj component of velocity m, n are the unit vectors which refer to the local tangential and normal direction of the surface. ja = (pext)/r + gTRm, m represents kinematics viscosity, gT is the surface tension function of temperature, pext is the pressure of welding arc in the area of contact between arc and welded pool and the protection gas pressure for the rest of surface pool geometry, Rm the mean radius of the free surface.

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**2.4. Weld Pool Shape Estimation from Initial heat flow conditions.**

Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources 2.4. Weld Pool Shape Estimation from Initial heat flow conditions. The heat source model is bas on the Myhr–Grong method [1],[5]. The heat source is divided in many horizontal and vertical points sources that are included in the welded area. This method makes possible the modeling of different welded geometry (like key-hole) without using the heat flux distribution. The establish of the points heat sources, in agreement with the welded pool geometry coordinates, consist in mathematical shape, in the solving of the optimization problem.

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**Algorithm for established the key-hole geometry.**

Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources Algorithm for established the key-hole geometry. Scope function conditions: Heat Flow Points Sources. (Fig1.c) Temperatures on fusion boundary

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

Where: The value of temperature at weld boundary The coordonates of boundary points. The coordonates vector of source points The unknown vector of sources point intensity The expresion of the imposed boundary points

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**3. Results. Heat flow estimation sources.**

Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources 3. Results. Heat flow estimation sources.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

Heat Flow, Temperature Distribution.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

The Vx speed in the longitudinal section

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

Instant Vy speed of the fluid flow in the longitudinal section.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

Instant heat added by viscous effect in the longitudinal welded pool section.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

Stream distribution in the transverse welded pool.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

Estimation of the Vy speed of the fluid in the transverse section in the moment of welding.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

Time estimation of turbulence factor in the transverse section of weld.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

3D Temperature distribution on the weld section

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

4. Conclusions. The paper develops an algorithm for solving the fluid and heat flow with FVM to analyze most general welding process. 1. The algorithm consists in solving the heat flow induced by a multipoint approximation of the weld arc sources. The aim of that multipoint approximation consist in generate a welded pool shape and temperature distribution most closely with the reality. After that step the fluid flow and heat dissipation was calculated used the MAC method for solve the N-S equations in the conditions of free upper boundary for two perpendicular sections. Based on the free boundary known aspect and the fluid momentum known in that two sectionals, an Cellular Automata Method was used to generate the 3D analyze of the weld. 2. The convection heat fluxes on the control surfaces is calculated using an more accurate method function of the local Reynolds number and the approximations of that fluxes is avoid. 3. The results based on considering the proposed method can be more reasonable than the results of conventional analysis based on approximation of temperature based on models of semi-infinite body or infinite plate, or in the approximation of heat fluxes based on analyze of MHD physics of the welded arc sources.

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**Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources**

5. References. [1] O. Grong. Metallurgical Modelling of Welding. Second Edition. The Institute of Materials [2] H.S. Carslaw and J.C. Jaeger: Conduction of Heat in Solids; 1959, Oxford, Oxford University Press. [3] R. Hultgren, R.L. Orr, RD. Anderson and K.K. Kelly: Selected Values of Thermodynamic Properties of Metals and Alloys; 1963, New York, J. Wiley & Sons. [4] N.N. Rykalin, A.I. Pugin and V.A. Vasil'eva: Weld. Prod., 1959, 6, [5] O.R. Myhr and 0. Grong: Acta Metall. Mater., 1990, 38, [6] N. Christensen: Welding Metallurgy Compendium, 1985, University of Trondheim, The Norwegian Institute of Technology. [7] CE. Jackson: Weld. J., 1960, 39, 226s-230s. [8] O.M. Akselsen and G. Sagmo: Technical Report STF34 A89147, 1989, Trondheim (Norway), [9] A. A. Amsdenand F. H. Harlow: Report L.A. 4370, Los Alamos Scientific Lab., (1970). [10] B. D. Nichols and C. W. Hirt: J. Computational Physics, 8 (197 l), 434. [11] B. D. Nichols, C. W. Hirt and R. S. Hotchkiss: Tech. Report L.A. 8355, Los Alamos Scientific Lab., (1980). [12] M. Heinlein. S. Mukherjee, and O. Richmond: Acta Mech., 59 (1986), 59. [13] N. Zabaras, Y. Ruan, and O, Richmond: J. Appl. Mech., 58 (1991), ) [14] B. H. Kangand Y. Jaluria: J. Thermophys. Heat Transfer, 7 (1 993), No. 1, 139. [15] M. J. M. Krane and F. P. Incropera: ASME, HDT Vol.284/AMD-Vol.182 (1994), 13. [16] J. Lee and K. Y. Hwang: Int. J. Eng. Sci., 34, (1996), No. 8, 901. [17] J. LeeandK. Y. Hwang:J. Mater. Process. Technol., 57 (1 996), 85. [18] S. V. Patankar: Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, (1980), 79. [19] A. F. Mills: Basic Heat and Mass Transfer, IRWIN, Concord, (1995), 22. [20] Mizika, E. A.: Trans. ASME,239 (1967), 1747. [21] Jin-hoo Lee, Jin-hoo Mok, C.P. Hong.: Straightforward Numerical Analysis of Casting Process In a Rectangular Mold: From Filling to Solidification. ISIJ International, Vol 38, (1999).

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