and carries heat to the pool bottom, thus resulting in a deeper pool. These results are consistent with Heiple's theory [27].
Figure 3.23 Computer modeling showing effect of dγ/dT on fluid flow in weld pool and shape of pool surface: (a) dγ/dT < 0 resulting in a concave pool surface; (b) dγ/dT > 0 resulting in a convex pool surface.
Source: Tsai and Kou [43]. © Wiley.
The effect of dγ/dT on pool‐surface deformation is interesting. With dγ/dT < 0 the fast outward surface flow (~1 m/s) is suddenly decelerated near the pool edge. Bernoulli's principle [21], though not used in the computer modeling, can be applied here as a simple explanation for the pool‐surface shape. The deceleration, according to the principle, causes the liquid pressure to rise and push the pool surface upward near the edge, resulting in a concave pool surface. Likewise, with dγ/dT > 0 the fast inward flow is suddenly decelerated near the pool center. The pool surface is raised by the pressure increase near the center and becomes convex.
Figure 3.24 shows the current‐density distribution in a stationary Al weld pool, the Lorentz force it induces, and the flow pattern the force creates [46]. The electric current converges from the workpiece to the center of the pool surface. The Lorentz force is inward and downward, thus pushing the liquid downward along the pool axis. This causes the liquid metal to fall along the pool axis and rises along the pool boundary. The maximum velocity is about 40 cm/s, much slower than Marangoni flow. The downward axial flow carries heat from the heat source to the pool bottom and causes a deep penetration.
Figure 3.24 Computer modeling showing flow driven by Lorentz force: (a) current density field; (b) Lorentz force field; (c) flow field.
Source: Tsai and Kou [46]. Welding Journal, June 1990, © American Welding Society.
Since liquid has a lower density than solid, e.g. by about 6% for aluminum [47]. The weld pool should expand as it forms, and this results in a convex pool surface. Figure 3.25 shows weld pool surface deformation caused by volume expansion due to melting (and superheating) [48]. The pool surface is convex because of the volume expansion. The flow induced by gravity, i.e. buoyancy flow, is too slow (about 1 cm/s) to cause surface deformation. Furthermore, the convexity is much more significant than that induced by Marangoni flow driven by dγ/dT < 0. This convex pool surface is very stable. Because it is supported by extra volume of liquid instead of by fast fluid flow. The concave pool surface under dγ/dT < 0 (Figure 3.23a) and convex pool surface under dγ/dT > 0 (Figure 3.23b) can be highly unstable because they are supported only by the surface tension effect under fast Marangoni flow.
Figure 3.25 Computer modeling showing significant weld pool surface deformation caused by volume expansion due to melting (and superheating): (a) convex pool surface; (b) slow fluid flow induced by buoyancy force.
Source: Tsai and Kou [48]. © Taylor and Francis.
Choo and Szekely [49] first considered turbulence in GTA weld pools and showed that turbulence can affect the pool depth significantly. Weckman and coworkers [50–52] demonstrated that a fluid flow model based on laminar can overpredict the pool depth, as shown in Figure 3.26 for a GTA weld in a 304 stainless steel. When turbulence is considered, however, the effective viscosity increases (μeff > μ) and convection slows down. Furthermore, the effective thermal conductivity (keff > k) increases and the effect of convection on the pool shape thus decreases. Consequently, the calculated pool depth decreases and agrees better with the observed one.
Figure 3.26 Weld pool shapes and isotherms in a 304 stainless steel with 50 ppm sulfur calculated based on: (a) laminar flow; (b) turbulent flow.
Source: Weckman [50–52]. © Taylor and Francis.
3.5 Flow Oscillation and Ripple Formation
Figure 3.27 shows oscillatory Marangoni flow in a simulate weld pool of NaNO3 using a horizontal light‐cut technique (Fig. 3.21b) [32]. This is believed to be the first demonstration of oscillatory Marangoni flow in a weld‐pool‐like liquid pool [53]. The surface flow is outward toward the pool edge (dγ/dT < 0), so the return flow below the surface is inward as illustrated previously in Figure 3.21b. With the CO2 laser at 4 W and 1.5 mm diameter, the inward return flow is steady and converges to the center. At 6 W and 1.5 mm diameter, however, two inward streams oppose each other, as indicated by the arrows. The directions of the streams keep alternating with time at a period of about 1.4 sec. This indicates the frequency of flow oscillation is about 0.71 Hz (1 ÷ 1.4 sec). Figure 3.28 shows the temperature oscillation detected by a very fine thermocouple immersed in the NaNO3 pool. Fast‐Fourier transform shows a 0.8 Hz frequency of oscillation, which is close to the 0.71 Hz frequency based on the flow patterns in Figure 3.27b. In a separate experiment, a NaNO3 sessile drop on a graphite substrate was heated from above with a CO2 laser beam to induce oscillatory Marangoni flow. The drop shook visibly, indicating surface oscillation induced by flow oscillation [32].
Figure 3.27 Visualization of inward return flow below pool surface (Figure 3.21b): (a) steady flow at CO2 laser power of 4 W; (b) oscillatory flow at 6 W. Two opposing inward‐flowing streams (indicated by arrows) change directions with time at a frequency of about 0.71 Hz (1 ÷ 1.4 seconds).
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