## 1 Introduction  
Arc welding is widely used in the manufacturing of industrial equipment, buildings, bridges, vehicles, turbines and pressure vessels. However, good groove preparation, proper filler wire and multi-pass welding are usually necessary with traditional arc welding technologies. More efficient and advanced welding technologies are demanded for modern equipment and sophisticated equipment. Recently, high-power welding technologies have attracted a lot of attention because they are available to produce qualified weld beads with a single pass, and even need no groove preparation. As one of the high-power welding technologies, plasma arc welding (PAW) is superior to others due to lower equipment costs, convenient operation and higher tolerance to joint gaps [1]. The arc is concentrated by a nozzle in PAW, so the heat flux and arc pressure are much higher than that in ordinary arc welding. As a consequence, it can quickly produce a weld pool and then penetrate through the pool, developing into a complete keyhole full of arc. Figure 1 displays a keyhole-mode PAW process. As the arc temperature is very high, much heat can be directly transported to the lower part through the keyhole, which improves the welding penetration. In this way, it can avoid groove preparation and weld thicker pieces with a single pass. In view of the above advantages, researchers have carried out tremendous experimental research about PAW [2; 3; 4] to acquire the keyhole mode welding technology. Up to now, the formation and development of both weld pool and keyhole during the welding process were successfully detected [5; 6]. However, PAW also has some disadvantages. For example, PAW does not use the AC power, and welding thickness is generally no more than 15 mm at the keyhole mode. The tungsten electrode and nozzle are easily burned due to the hot arc. Especially, multiple welding parameters have an important effect on the PAW, and proper welding specifications are required to guarantee the weld quality. Experimental research just displays limited information about the welding process, while numerical calculations can help reveal full and detailed physical mechanism. Therefore, researchers developed a lot of arc welding models in recent years to simulate heat transfer, liquid metal flow and weld pool. For simplicity, some researchers neglected plasma arc in calculations but just constructed an equivalent heat source model [7; 8] in workpiece to predict the temperature development and weld pool morphology. [PERSON] et al. [9; 10] developed a heat source model with a Lattice Boltzmann method (LBM) to study the weld pool behaviors in PAW. In order to reveal the keyhole effect between plasma arc and liquid metal, some researchers apply a two-phase flow model to calculate their interaction. Volume of Fluid (VOF) method, which can locate the phase interface of two or more fluids [11], is widely used to simulate the keyhole welding process. [PERSON] et al. [12; 13] used the VOF method to construct a keyhole-related heat source model, arc pressure model and shear stress model to study the formation mechanism of the weld pool and keyhole. They showed the molten flow patterns in the weld pool and indicated arc pressure and shear stress take the main responsibility for keyhole formation. [PERSON] et al. [14; 15] also established an arc heat model and arc pressure model with VOF to describe heat transfer, liquid metal flow and keyhole surface evolution in PAW. They found liquid metal in the front flows bypass the keyhole wall to the back, and the keyhole channel is crocked because of the movement. Up to now, most of models need the VOF method to simulate the dynamic evolution with respect to the keyhole [16; 17; 18; 19]. However, there is no plasma arc in all the above models, and they only take the workpiece into account so that they all rely on a reasonably designed heat source model and arc pressure model.