## 4 Comparison of Pressure Drop and Flow Field Distribution between the Basic and Modified Models  
Figure 6a shows the pressure contours at the mid-plane, and Figure 6b shows the streamlines and velocity vectors of the basic gas torch. The flow tended to concentrate in the center region, and two corner sides of the gas torch had very low velocity. Hence, the exit velocity was high in the center region and low in the right and left side regions, as shown in Figure 6b. Consequently, the flow distribution at the outlet was nonuniform. Figure 5: Grid independence check for velocity at the outlets along the lengthwise (x) direction. Figure 6: _Cont._  
Figure 7 shows the pressure contours at the mid-plane of the three new models. Due to the flow impinging on the guide vanes at the center of the three modified models, the highest pressure was observed at the top on the guide vanes. The pressure then decreased as the central flow spread towards the right and left side regions. Compared with the basic model, all three new models had uniform pressure at the outlets of the gas torches. This led to enhanced uniformity of the flow velocity at the outlet. Figure 6: (**a**) Basic gas torch pressure contours; (**b**) inner streamlines and velocity vectors at the outlets. Figure 7: _Cont._  
The inner streamlines and velocity vectors at the outlets of the three new gas torches are shown in Figure 8. The highest velocity of all three models was around 11.1 m/s, which was less than velocity of 12.7 m/s of the basic model. In model 1, with a long perforated plate, one part of the flow passed through the perforated plate directly, and the rest spread to the two sides. In model 2, the main flow went through the diffuser with many holes, and the two split flows went through the two smaller pipes to produce uniform exit flow. Model 3 was expected to operate with combined characteristics of model 1 and model 2 because it had combined structures from the inner strip from model 1 and the enlarged inlet and corner cuts at both sides from model 2. It was clear that there was a uniform velocity distribution at the outlets of the three new models. In these cases, the high velocity at the center was reduced, and the two side velocities were increased. Thus, the velocity uniformity along the x-direction was remarkably improved. Figure 8: _Cont._  
Figure 7: Pressure contours at the middle plane of the three new gas torches: (**a**) model 1; (**b**) model 2; (**c**) model 3. The exit velocity distribution along the lengthwise x-direction of the basic torch and new torches is shown in Figure 9. The flow velocity from the left side to the right side of the basic gas torch was around 11 to 12.7 m/s. The highest velocity was concentrated in the center region of the torch. Therefore, the flow distribution at the outlet of the basic torch was nonuniform. All three modified models had similar shapes of the velocity distribution from the left to the right of the torch. By modifying the inner and outer shapes of the torches, the flow field distribution along the x-direction became uniform from the left to the right side. This uniform flow at the outlets of the torches led to a uniform temperature distribution of the steel plate during the preheating process. Figure 8: **Figure 8.** Inner streamlines and velocity vectors at the outlet of the three new gas torches: (a) model 1; (b) model 2; (c) model 3. To evaluate the uniformity of the flow fields at the outlet of the torches, the velocity uniformity index was utilized as follows:  
Figure 6:0  
where  
Figure 6:1  
Here, \(\gamma\) is the velocity uniformity index, and n is the total number of outlet positions. \(u_{m}\) is the velocity at the \(m\)th position, and \(\overline{u_{a}}\) is the mean of all the velocities. The value of \(\gamma\) is between 0 and 1, and \(\gamma\) = 1 indicates a perfectly uniform distribution [21]. Figure 10 shows a comparison of the velocity uniformity index at the outlets between the basic torch and the three new torches as a function of the pressure drop.