Cross-sectional temperature distributions at different X locations at t = 4.305 s

Figure 6. Cross-sectional temperature distributions at different X locations at t = 4.305 s (front view).

At X = 41.02 mm, 3.6 mm ahead of the arc centre, the base metal at both sides of the groove has already been heated by arc heat. At the bottom of the groove, there is some mass overflow from the weld pool. This part of the metal cooled by the base metal is almost in a solid state. At X = 37.42 mm, which is the arc centre, a new droplet with a temperature of 2500 K and sulfur concentration of 300 ppm appears inside the groove and is ready to impinge onto the weld pool. At this location, melting of the base metal is limited and the liquid layer is thin, as can be seen in figures 7 and 8. The velocity distribution in this thin liquid layer is complicated. The high sulfur concentration near the top portion of the groove is caused by the spatter of the droplets containing the highest sulfur, figure 8.

At X = 34.42 mm, which is 3 mm behind the arc centre, the groove is already filled by the mass of droplets. There are two areas with the highest temperature and sulfur concentration. One is at the surface around the arc centre caused by the outward flow of the impinged droplet fluid, as

8

J. Phys. D: Appl. Phys. 41 (2008) 065202 J Hu and H L Tsai

6

8

X = 37.42 (mm)

0.40 (m/s)

6

8

0.30 (m/s)

X = 34.42 (mm)

6

8

0.20 (m/s)

X = 29.17 (mm)

Y (mm)

Z (m

m )

-6 -4 -2 0 2 4 6

6

8 X = 23.77 (mm)

Full Solidification

6

8 X = 41.02 (mm)

Before Melting

Figure 7. The corresponding velocity distribution as shown in figure 6.

explained in figure 3. The other is at the bottom of the groove due to the flow of droplet liquid along the groove bottom, as again shown in figure 3. As shown in figure 7, the fluid arising from the bottom of the groove comes from the flow along the bottom of the groove. Two vortices, one on each side of the groove, are created. At X = 29.17 mm, the maximum temperature occurs nearly at the centre of the groove, figure 6, as does the maximum sulfur concentration, figure 8. The flow in the groove is very small and is upwards, figure 7. At X = 23.77 mm, the weld pool is completely solidified, and the maximum temperature of the weld pool occurs near its top and in the centre. This is the final shape of the weld bead with the final sulfur distribution. As shown in figure 8, there are sulfur- lean stripes in the weld pool. The final sulfur distribution is not as uniform as compared with the case when there is no groove [15].

4.1.3. Three-dimensional view of the impinging process. Figure 9 is a partial view of the three-dimensional mesh system

4

6

8

X = 41.02 (mm)

4

6

8

X = 37.42 (mm)

4

6

8

X = 34.42 (mm)

4

6

8

X = 29.17 (mm)

Y (mm)

Z (m

m )

-6 -4 -2 0 2 4 6 4

6

8

X = 23.77 (mm)

300 290 280 270 260 250 240 230 220 210 200 180 160 140 120 100 0

C (ppm)

Figure 8. The corresponding sulfur concentration distribution as shown in figure 6.

and velocity vectors at the top surface at t = 4.309 s. Figure 10 shows the corresponding top view of the velocity, temperature and concentration distributions. The weld pool is widest near the arc centre and decreases in width towards the rear part of the weld pool, as the weld pool loses heat to the base metal through conduction and convection and to its surroundings through convection and radiation.

The velocity distribution is very complicated, especially for the areas closest to the arc centre, which is impinged by the droplets. It will be easier to visualize the fluid flow in the entire weld pool by cross-referencing figures 4 (side view), 9 and 10. By comparing figure 4 with figure 10, it is clearly seen that the fluid in the ‘bump’ (figure 4) flows outwards and to the right and then meets with an opposing fluid flow on the left side. This leads to a V-shaped interface at which the fluid sinks to the bottom of the weld pool. The temperature distribution near the arc centre is complicated due to the mixing of droplets and the weld pool. It is noted that in addition to the energy carried by high temperature droplets, there is also an arc heat impacting on the top of the weld pool surface. As a result, the highest

9

J. Phys. D: Appl. Phys. 41 (2008) 065202 J Hu and H L Tsai

X ( mm

)

24 26

28 30

32 34

36 38

40 42

Y (mm)

-6 -4

-2 0

2 4

6

4

5

X Y

Z

0.50 (m/s)

Z (mm)

Figure 9. Partial view of a three-dimensional mesh system, weld bead shape and velocity distribution at t = 4.309 s.

-4

-2

0

2

4 0.50 (m/s)

X (mm)

Y (m

m )

24 26 28 30 32 34 36 38 40 42

-4

-2

0

2

4

300

280

260

240

220

200

160

120

0

C (ppm)

-4

-2

0

2

4 2500

2300

2100

1900

1725

1500

1100

700

290

T (K)

Figure 10. The corresponding top view of velocity, temperature and sulfur concentration distributions as shown in figure 9.

surface temperature occurs near the arc centre. However, the characteristics of surface sulfur distribution shown in figure 10 are quite different from those of the temperature distribution. The surface sulfur concentration distribution in the weld pool is directly related to the mixing between droplets and melted base metal. There are two spots with high sulfur concentration: one at the arc centre corresponding to the droplet and the other (between X = 27 mm and X = 31 mm) related to the ascending flow from the bottom of the groove, as shown in figure 4. The fluid consisting of this ascending flow is mainly from the droplets as discussed previously.

4.2. Effects of groove

Generally, the groove provides a ‘confined channel’ which facilitates the flow of filler metal along the bottom of the channel. The existence of the groove changes the fundamental flow pattern in the weld pool compared with the case without a groove [15]. As the groove tends to ‘smooth’ the fluid flow in the weld pool, it reduces the mixing between filler metal and melted base metal. Hence, in general, the uniformity of sulfur in the weld is not as good when there is a groove as compared with when there is no groove.

5. Conclusions

A mathematical model and associated numerical techniques have been developed to calculate the transient velocity, temperature and sulfur concentration distributions in the weld pool for a three-dimensional GMAW process for a thick plate with a groove. From the results of this study, it was found that the groove provides a confined channel facilitating the flow of filler metal along the bottom of the groove. This flow interacts with the flow caused by the surface tension force and the flow due to droplet impingement, leading to a large vortex in the weld pool. The V groove has a smooth effect so that the flow pattern is simpler than that without a groove. As a result, mixing between the filler metal and the weld pool is not good as compared with the case without a groove.

References

[1] 1983 Welding, Brazing, and Soldering, Metals Handbook vol 6, 9th edn (Metals Park, OH: American Society for Metals) pp 153–81

[2] Tsao M C and Wu C S 1988 Weld. J. 67 70s [3] Wang Y and Tsai H L 2001 Int. J. Heat Mass Transfer 44 2067 [4] Fan H G and Kovacevic R 2004 J. Phys. D: Appl. Phys. [5] Fan H G and Kovacevic R 1999 Metall. Trans. B 30 791 [6] Wang Y and Tsai H L 2001 Metall. Trans. B 32 501 [7] Zhu F L, Tsai H L, Marin S P and Wang P C 2004 Prog

Comput. Fluid Dyn. 4 99 [8] Hu J and Tsai H L 2007 Int. J. Heat Mass Transfer 50 8 [9] Hu J and Tsai H L 2007 Int. J. Heat Mass Transfer 50 8

[10] Hu J and Tsai H L 2006 J. Appl. Phys. 100 053304 [11] Hu J and Tsai H L 2007 ASME J. Heat Transfer 129 102 [12] Kim J W and Na S J 1994 ASME J. Eng. Indus. 116 78 [13] Ushio M and Wu C S 1997 Metall. Trans. B 28 509 [14] Cao Z, Yang Z and Chen X L 2004 Weld. J. 83 169 [15] Hu J, Guo H and Tsai H L 2007 Int. J. Heat Mass Trans

at press, doi:10.1016/j.ijheatmasstransfer.2007.07.04 [16] Kothe D B and Mjolsness R C 1991 Los Alamos Report

LA-UR-91-2818 [17] Diao Q Z and Tsai H L 1993 Metall. Trans. A 24 963 [18] Carman P C 1937 Trans. Inst. Chem. Eng. 15 150 [19] Kubo K and Pehlke R D 1985 Metall. Trans. A 16 823 [20] Beavers G S and Sparrow E M 1969 J. Appl. Mech. 36 7 [21] Sahoo P, DeBroy T and Mcnallan M J 1988 Metall. Tra

19 483 [22] Zacharia T, David S A and Vitek J M 1992 Metall. Tran

233 [23] Welch J E, Harlow F H, Shannon J P and Daly B J 1966

Alamos Report No LA-3425 [24] Patankar S V 1980 Numerical Heat Transfer and Fluid

(New York: McGraw-Hill) [25] Kerhaw D S 1978 J. Comput. Phys. 26 43

10

37 2531

.

33 08

5

fer 2 No

11 ns. B

s. B 22

Los

Flow

  • 1. Introduction
  • 2. Mathematical formulation
    • 2.1. Governing equations
    • 2.2. Tracking of solid–liquid interface
    • 2.3. Tracking of free surfaces
    • 2.4. Boundary conditions
    • 2.5. Top surface
    • 2.6. Electromagnetic force
  • 3. Numerical method
  • 4. Results and discussion
    • 4.1. Interaction between filler droplets and weld pool
    • 4.2. Effects of groove
  • 5. Conclusions
  • References