## 4 Results and Discussion  
Figure 5 displays temperature field in the mobile PAW process. Arc is restricted by the nozzle and isotherms are very dense within it. The arc then spreads outwards into a bell shape and impacts vertically on the workpiece. A high-temperature area appears below the electrode, which is like an arc column located in the center of the arc. The highest temperature is above 27,000 K adjacent to the electrode tip, while the lowest temperature is 15,000 K at the edge of the arc column. Workpiece beneath the welding torch absorbs more heat from the plasma arc and quickly melts into a small weld pool at the center. The pool grows in width and depth during the welding process until it finally penetrates the whole workpiece. Due to the relative movement, the weld pool is not symmetrical along the welding direction. It shows that the pool is wide and deep in the front, while it is long and shallow in the rear. It is found that isotherms near the front pool edge are dense while those near the rear edge are distributed, which means the front pool edge absorbs more thermal energy and when it moves backwards the heat dissipates gradually. The torch axis is almost identical with the pool center line at first. However, a deviation appears with the relative movement, and it increases during the welding process. At 3.2 s, the deviation of the two central line reaches to 3.5 mm. Figure 6 displays dynamic evolution of weld pool in the mobile PAW process. At first, a chestnut-like pool appears. However, there is a small corner at the rear. The pool grows continually, and the rear corner also increase simultaneously. However, it mainly spreads along the negative welding direction but has a small depth which is no more than 2 mm. Finally, the front pool penetrates the whole workpiece at 3.2 s. The upper pool is long and wide, but it gradually shrinks along the z direction, forming a boot-shape weld pool. Figure 5: _Cont._  
Figure 5: Temperature field in the mobile PAW process. (**a**) \(t=0.4\) s; (**b**) \(t=0.9\) s; (**c**) \(t=2.1\) s; (**d**) \(t=3.2\) s.  
Figure 6: _Cont._  
Figure 7 shows arc flow and liquid metal flow in the computational domain. The top displays arc velocity, where higher velocities are near the central line, and they are highly concentrated. The arc with velocity above 200 m/s almost gathers within a column of diameter of 3 mm, and that below 200 m/s diffuses at the top of workpiece, and the diameter reaches to about 10 mm. Stream traces of plasma gas show that the gas enters from top inlet, is ionized within the torch, and finally flows out around the bottom column. There is a maximum velocity zone just out of the torch, which is long and narrow, and the velocity is above 1100 m/s. Such high arc velocity brings forth very high pressure, so it promotes the liquid metal to flow downward. Then it is blocked by the front pool edge and flows backward and upward to the rear. The metal velocity is about \(10^{-1}\) m/s, and the maximum velocity may reach to 0.43 m/s. References [33; 34] reveal the measured average velocity of liquid metal is approximately 0.24-0.42 m/s in the keyhole-mode PAW, which basically coincides with the calculated result. Figure 8 displays weld pool and temperature field on the transverse cross-section (_yoz_ plane) at 3.2 s. The temperature field shows the closer to the weld pool, the higher the temperature gradient. There is a maximum weld pool at \(x=-3\) mm, and the whole workpiece is fused from top to bottom. While weld pool decreases quickly in front of the cross-section. The depth reduces to 5.2 mm at \(x=-2\) mm and 0.75 mm at \(x=1\) mm. On the contrary, the pool decreases relatively smoothly at the rear. There is still a full-penetrated weld pool at \(x=-4\) mm. Furthermore, although the depth gradually  
Figure 6: Dynamic evolution of weld pool in the mobile PAW process. (**a**) \(t=0.4\) s; (**b**) \(t=0.9\) s; (**c**) \(t=2.1\) s; (**d**) \(t=3.2\) s.  
Figure 7: Flow distribution in the arc and weld pool.