plasma torch under conditions of pulsed laser stimulation of metal targets are performed to confirm the obtained results. INTRODUCTION. In the case of laser-arc ...
High Temperature. Vol. 44, No. 5, 2006, pp. 647–655. Translated from Teplofizika Vysokikh Temperatur, Vol. 44, No. 5, 2006, pp. 655–663. Original Russian Text Copyright © 2006 by G. A. Turichin, A. M. Grigor’ev, E. V. Zemlyakov, E. A. Valdaitseva,U. Dilthey, and A. Gumeniuk.
PLASMA INVESTIGATIONS
Special Features of Formation of Plasma Torch under Conditions of Hybrid Laser-Arc Welding G. A. Turichin1, A. M. Grigor’ev1, E. V. Zemlyakov1, E. A. Valdaitseva1, 2 2 U. Dilthey , and A. Gumeniuk 1
Institute for Laser and Welding Technologies, St. Petersburg State Polytechnical University, St. Petersburg, 195251 Russia 2 Institute for Welding and Joining of Materials, Rhein–Westfalische Technische Hochschule, Aachen, Germany Received November 15, 2005
Abstract—This paper is devoted to analytical description of processes occurring in hybrid discharge plasma under conditions of laser-arc welding with deep melting. The axially symmetric boundary layer approximation is used to solve the problem on the outflow of a jet of hot metal vapor into an atmosphere of cold protective helium gas in view of the compressibility of gas mixture and of the bulk heat release during absorption of laser radiation in plasma. In so doing, the degree of ionization of plasma is determined from the solution of kinetic problem in the approximation of constant collision frequencies for a helium-iron mixture without the assumption of local thermal equilibrium. A series of experiments in the interferometry of plasma torch under conditions of pulsed laser stimulation of metal targets are performed to confirm the obtained results.
INTRODUCTION In the case of laser-arc welding, optical discharge plasma which forms a plasma torch has a significant effect on the welding process. As distinct from the case of laser welding, in the process of which the formation of plasma leads only to the absorption and refraction of laser radiation during its passage through the torch [1], the plasma torch in the case of laser-arc welding is a region defining the interference between the laser and arc heating sources; it is the presence of this interference that is usually used to explain [2, 3] the increasing efficiency of the heating of metal under combined effect of laser beam and electric arc. In this case, the structure and properties of plasma torch depend both on the parameters of laser radiation [4] and composition and flow rate of protective gas [5] and on the parameters of electric arc [6]. From the gasdynamic standpoint, the plasma torch is a subsonic submerged jet [7] of metal vapor in protective gas with bulk heating owing to absorption of laser radiation and heat release in the electric arc. Both wellknown analytical solutions for incompressible jets [8]
and numerical schemes [9] are used for the calculation of such flows. The bulk heat release in a plasma torch depends in the final analysis on the density of free electrons which defines both the conductivity of plasma and the laser-radiation absorption coefficient [10]. The theoretical description of both laser-induced and arc plasma is usually based on the assumption of local thermal equilibrium. In this case, the temperature of plasma defines its degree of ionization and, accordingly, all of the related parameters [11]. However, under conditions of laser welding, optical discharge plasma is not equilibrium [12], and the description of hybrid laserarc discharge plasma must be based on the solution of the kinetic equation for the electron energy spectrum [13] in view of the chemical composition and gas dynamics of plasma torch; these in turn depend on the density of bulk heat release defined by the degree of ionization of plasma. This paper deals with the construction of a self-consistent analytical description of plasma torch under conditions of mixing a jet of metal vapors with protective gas in view of bulk heat release, thermal conductivity, diffusion, viscosity, and
0018-151X/06/4405-0647 © 2006 Russian Academy of Sciences and Springer Science + Business Media, Inc.
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compressibility of vapor-gas mixture under conditions of laser-arc welding.
FORMULATION OF GASDYNAMIC PROBLEM
where u and v denote the axial and radial components of velocity of flow of mixture in the torch, respectively, and write the set of equations (1)–(3) as 1 ∂ μ ∂u ∂u ∂u u ------ + v˜ ------ = --- ------ ⎛ ------ y ------⎞ , y ∂y ⎝ ρ ∞ ∂y⎠ ∂x ∂y
Let C denote the concentration of iron vapors in a mixture; then the protective gas density is ρg =
ρ ∂C 1∂ ∂C ∂C u ------- + v˜ ------- = --- ------ ⎛ D ------ y -------⎞ , ⎝ y ∂y ρ ∞ ∂y ⎠ ∂y ∂x
= (1 – C)ρ and the density of iron vapors is ρV = Cρ,
1 ∂ λ T ∂h ∂h ∂h q u ------ + v˜ ------ = --- ------ ⎛ ------------ y ------⎞ + --- . y ∂y ⎝ ρ ∞ c p ∂y⎠ ρ ∂y ∂x
where ρ is the total density of the mixture. We will use the approximation of axially symmetric boundary layer for formulation of the problem [7] and represent the equations for flow velocity V, concentration of the mixture, and its enthalpy h as follows: ∂V z ∂V z ∂ ∂V z μ ∂V z ρ ⎛ V z --------- + V r ---------⎞ = ----- ⎛ μ ---------⎞ + --- --------- , (1) ⎝ ∂z ∂r ⎝ ∂r ⎠ r ∂r ∂r ⎠ ∂C 1∂ ∂C ∂C ρV r ------- + ρV z ------- = --- ----- ⎛ rρD -------⎞ , ∂r ⎠ r ∂r ⎝ ∂r ∂z
(2)
∂h ∂h ∂p 1 ∂ ∂T ρV r ------ + ρV z ------ = V z ------ + --- ----- ⎛ ρλ T ------⎞ + q , (3) ⎝ ∂r ∂z ∂x r ∂r ∂r ⎠ where q is the density of heat sources, μ is the coefficient of dynamic viscosity, D is the diffusion coefficient, and λT is the thermal conductivity coefficient. Along with the equation of state
In so doing, the kinetic coefficients of mixture μ, D, and λT are functions of enthalpy and concentration of the mixture.
THE PROPERTIES OF GAS MIXTURE We designate the free path as λ and, according to [14], can write the following for the diffusion coefficient of the mixture components: ρ1 1 ρ2 D = --- ⎛ ----- λ 1 V 1 + ----- λ 2 V 2⎞ . ⎝ ⎠ 3 ρ ρ m 2 V 22 m 1 V 12 3 In view of the fact that --- kT = ------------- = ------------- , 2 2 2 C1 ⎞ ⎛ C2 1 we have D ≈ --- λ 3kT ⎜ ----------- + -----------⎟ . 3 ⎝ m1 m 2⎠ The coefficient of dynamic viscosity of mixture is defined by the expression
ρi C 1–C p = ∑ ---- RT = ⎛ ------ + -------------⎞ ρRT , ⎝ μg ⎠ μV μi Eqs. (1)–(3) fully describe the problem on the outflow of a jet of metal vapor into protective gas. In order to simplify the set of equations, we introduce the Howarth–Dorodnitsyn variables x and y, ydy = (ρ/ρ∞)rdr,
(4)
x = x.
In view of the fact that, in the case of laser welding, a “heavy” but hot metal vapor flows out into an atmosphere of light but “cold” protective gas (He), and the pressure in submerged jet is equal to external pressure, we assume that the function ρ(r) is a weakly 2
varying function of its argument r and introduce r ≈
Ci 1 1 μ = --- λ ∑ m i n i V i = --- λρ 3kT ∑ ---------. 3 3 m i
i
Because the surrounding gas is the main component of mixture in submerged jet, we can assume that C
