## 4 Comparison of Pressure Drop and Flow Field Distribution between the Basic and Modified Models
### Boundary Conditions for Turbulent Combustion
The Reynolds number is calculated based on the LPG/air mixture gases at the jet hole outlet of the torch:  
\[\text{Re}=\frac{\rho_{\text{mix}}\
u_{\text{mix}}d}{\mu_{\text{mix}}} \tag{20}\]  
The equivalence ratio is defined as follows:  
\[\phi=\frac{\left(F/A\right)_{actual}}{\left(F/A\right)_{\text{{\it{static}}}}} \tag{21}\]  
Due to the uniform flow and almost the same velocity magnitude at the outlets of the modified torches in Figures 9 and 10, model 3 was selected to carry out the simulation and experiment and then compared with the basic model. Figure 12 shows the temperature contour of a combustion flame zone at the center line view in the steel preheating zone for the basic and modified model with an LPG/air mixture as a fuel. The highest temperature for the basic model approached 1877 \({}^{\circ}\)C at an equivalence ratio (\(\Phi\)) of 1.0 and steel-plate distance of 0.1 m. This temperature was slightly higher than that of 1869 \({}^{\circ}\)C for the modified model. This was due to the fact that higher flame temperature in a narrow center region could be obtained from a higher Reynolds number. Thus, the basic model had a longer flame structure near the center region than the modified model. The ambient air near the jet holes was entrained to the flame zone due to the high-speed jet stream. The entrained air also participated in the combustion process. The primary jet line at the center line of the torch was associated with the main combustion process, and the combustion flame of the primary jetline made a major contribution to the steel-plate heating. Figure 13 shows the species mole fraction and temperature variations of the stoichiometric of the LPG/air mixture as a function of the jet flow direction at the center region for the basic model, modified model, and Akram experiment model [25]. For the basic model, before the combustion happened, the mole fractions of C\({}_{3}\)H\({}_{8}\), C\({}_{4}\)H\({}_{10}\), and O\({}_{2}\) were approximately 0.01, 0.02, and 0.2, respectively. The temperature of the unburned mixture was 27 \({}^{\circ}\)C (300 K). After the combustion happened, the reactant mole fractions decreased quickly and CO\({}_{2}\) and H\({}_{2}\)O were generated. Thus, the products and their mole fractions increased quickly. The flame temperature increased very fast in a short distance when the combustion happened. For the modified model, because of the smaller Reynolds number than the basic model, the turbulent combustion had higher temperature and higher product mole fractions in all positions except the starting position (Y = 0 mm) and the last position (Y = 12 mm) than the basic model case. The trends of the species mole fraction and temperature variations of the stoichiometric LPG/air mixture for the basic and modified models coincided well with those of [PERSON] et al. [25], who performed a study on laminar combustion. The present turbulent combustion showed the trends in a longer y-distance of 12 mm, while the trends of [PERSON] et al. 's laminar combustion showed the trends in a shorter distance of 3 mm due to lower momentum. Figure 12: The temperature contours of a combustion flame zone at the center-line view during the steel-plate preheating process: (**a**) basic model; (**b**) modified model. Figure 13: The species mole fraction and temperature variations of the stoichiometric LPG/air mixture for the basic model, modified model, and [PERSON]’s results [25]. Comparison of the Temperature Distribution at the Back Side of a Steel Plate between the Experiment and Simulation  
An experiment was conducted to obtain validation for the numerical simulation results by ANSYS FLUENT 18.2 software. An experimental apparatus was designed for the basic and modified models in the steel preheating process, as shown in Figure 14. The uniformity of the three modified torches was nearly the same, as revealed in Figures 9 and 10, so model 3 was selected to carry out the experiment and compared with the basic model.