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Unsteady marangoni flow in a molten pool when welding dissimilar metals

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Abstract

The unsteady variations of transport processes in molten pools when welding dissimilar metals are systematically investigated. Convection is driven by Marangoni forces with different directions and magnitudes on a flat free surface. For a clear description without loss of generality, three-dimensional quasi-steady welding is stimulated by an unsteady two-dimensional process. Applying the volume of fluid (VOF) and enthalpy methods to determine the interfaces between the immiscible dissimilar metals and between solid and liquid, the computed results show in detail the unsteady variations in the velocity and temperature fields, the solute concentration on the free surface, and the shapes of the molten regions affected by varying the signs and magnitudes of the surface-tension coefficients. The predicted shapes of the fusion-zone and solute distributions agree with the available experimental results in welding iron to aluminum, copper and iron, and copper to nickle.

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Abbreviations

Bi:

Biot number, hH/k 1l

c :

specific heat

c σ :

surface tension coefficient, c *σ =(c σ H(T m1−T ∞)(μ 1 α 1l )

D :

depth of fusion zone, D*=D/H, as illustrated in Fig. 1(b)

f :

liquid-to-solid volumetric fraction

F :

metal 1-to-2 volumetric fraction

g :

gravitational acceleration

G :

H 3 g/α /21l

h :

heat-transfer coefficient

H :

metal thickness, as illustrated in Fig. 1(a)

l :

sensible heat, I*=I/[c ls (T m1−α 1l)]

k :

thermal conductivity, k*=k/k 1l

p :

pressure, p*=pH 2/(ϱ 1 α 21l

Pr:

Prandtl number, μ 1 c 1l /k 1l

Q :

beam power, Q*=Q/[Hk 1l (T m1−T m1−T ∞)]

r :

radial coordinate, r*=r/H

St:

Stefan number=[c 1s (T m1−T m1−T ∞)]/h s/l

t :

time, t*=tα 1l /H 2

T :

temperature, T*=(T−T T−T ∞)/(T m1−T ∞)

u :

velocity component in x direction, u*=uH/α 1l

U :

welding speed

v :

velocity component in y direction, ν*=νH/α 1l

W :

surface width of pool, W*=W/H, as illustrated in Fig. 1(b)

x, y, z :

coordinates, (x*, y*, z*)=(x, y, z)/H, as illustrated in Fig. 1(a)

α 1l :

thermal diffusivity=k 1l /(ϱ 1 c 1l )

β :

expansion coefficient, β*=β/β 1

μ :

viscosity, μ*=μ/μ 1

ϱ :

density, ϱ*=ϱ/ϱ 1

σ :

surface tension=σ m+c σ (T−T m)

σ q :

energy distribution parameter, σ* q =σ q/H

*:

dimensionless quantity

l :

liquid

m :

melting

s :

solid

0:

initial

1, 2:

dissimilar metals, as illustrated in Fig. 1(a)

∞:

ambient

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Author notes

  1. F. K. Chung (Graduate Student, Associate Professor)

    Present address: the Mechanical Engineering Department, National Sun Yat-Sen University, Kaohsiung, Taiwan, Republic of China

Authors and Affiliations

  1. the Mechanical Engineering Department, National Sun Yat-Sen University, Kaohsiung, Taiwan, Republic of China

    P. S. Wei (Professor)

  2. Department of Mold and Die Engineering, National Kaohsiung University of Applied Science, Kaohsiung, Taiwan, Republic of China

    F. K. Chung (Graduate Student, Associate Professor)

Authors
  1. P. S. Wei
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  2. F. K. Chung
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Wei, P.S., Chung, F.K. Unsteady marangoni flow in a molten pool when welding dissimilar metals. Metall Mater Trans B 31, 1387–1403 (2000). https://doi.org/10.1007/s11663-000-0024-0

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  • DOI: https://doi.org/10.1007/s11663-000-0024-0

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