## 3 Results and Discussion  
### Model Validation and Heat Transfer Characteristics Analysis  
In order to verify the heat transfer characteristics of spray/wall interaction predicted by the numerical model, a simulation case was completed under the typical diesel exhaust flow conditions of 300 \({}^{\circ}\)C and 100 kg/h and compared with the experimental data in Ref. [1]. Figure 6a, b shows the numerical results and the experimental results of the front surface temperature distribution of the plate at different times after the start of injection (SOI), respectively. It can be noticed from both the numerical and experimental results that the spray/wall interaction forms three independent quasi-elliptical cooling regions with a large temperature drop in the thin plate. The three regions are referred to as upstream, midstream, and downstream cooling zones depending on the direction of air flow. In each cooling zone, the simulation and experimental results show a significant temperature drop, and the temperature drop slowly recovers after the injection. There are time differences between the temperature drops in different cooling zones because the distance from each nozzle to the wall surface is not consistent. To quantitatively study the cooling effect of the spray, the wall temperature distributions at different time periods along the centerline of the air flow direction in each cooling zone are shown in Figure 7. The simulation results are in good agreement with the experimental data in Ref. [1], but the numerical results in the upstream and midstream cooling zones show a deeper temperature drop. The maximum relative error of the lowest temperature is about 10%. The main reason for the error may be the numerical model having some error in the characterization of the spray. As shown in Figure 7, the lowest temperature appears at the center of each cooling zone, and the temperature drop  
Figure 5: The initial droplet size distribution at 0.9 MPa. decreases with the increase in the distance from each cooling center. The asymmetry of temperature distribution is attributed to the inclination angle of the spray to the wall and the entrainment effect of air flow. In all three cooling zones, the wall temperature decreases significantly from the spray impingement start, and the temperature gradient drop first increases and then decreases with time. Figure 6: Temperature distribution of the wall surface with time: (**a**) simulation, (**b**) experiment. The significant temperature drop means that the initial wall temperature is below or equal to the critical transition temperature of wall film formation. [PERSON] et al. [23] indicated that the critical transition temperature is characterized by an abrupt change in the gradient of the wall temperature-time curve, as illustrated in Figure 8a. Figure 8b provides a full explanation of the trend of the wall temperature gradient. When the wall temperature is marginally higher than the critical heat flux temperature and continues to decrease, the heat flux first increases and then decreases and reaches the maximum at the critical heat flux temperature (220 \({}^{\circ}\)C) [22,34]. Therefore, the evaporation mode at the liquid/solid interface transitioned from the transition boiling regime to the nucleate boiling regime during the injection cycle. Figure 9 shows the variation of the maximum heat flux of the front surface during an injection cycle. The maximum heat flux of the front surface increases rapidly at 3 ms from the start of injection (SOI) and reaches a critical value at 10 ms from SOI. In this phase, the evaporation mode at the liquid-solid interface of spray impingement is the transition boiling regime. Subsequently, the maximum heat flux shows a relatively gentle  
Figure 8: (**a**) Heat flux—Wall temperature curve; (**b**) Wall temperature—time curve. Figure 7: Temperature curve across the centerline of each cooling zone on the wall surface at different times after SOI: (**a**) upstream, (**b**) midstream, (**c**) downstream.