## 4 Results and Analysis
### Analysis of the Pedestrian Evucuation Strategy with the Thermal Radiation Field of the EV Fire
#### 4.2.2 Analysis of the Influence of the Direction of the Pedestrians Fleeing the EV Fire  
The increase in the pedestrian evacuation speed can ensure a greater distance from the flame source in unit time. An analysis of the numerical results of the pedestrian cumulative thermal radiation with invariant \(v_{x}\) variant \(v_{y}\) and invariant \(v_{y}\) variant \(v_{x}\), is shown in Figure 16. It was found that an increase in \(v_{y}\) can quickly reduce the thermal radiation accumulation of the pedestrians in this situation, which was related to the method of calculating the view factor of the radiation heat transfer. Since the flame surface was limited, the reduction rate of the view factor in the normal direction outside the flame surface was slower than that in the direction parallel to the flame surface. This was also consistent with the results of the accumulated thermal radiation and the basic idea of avoiding the flame center to reduce the thermal radiation damage. Therefore, considering the pedestrian evacuation speed directions \(v_{x}\) and \(v_{y}\) separately, the limited evacuation speed should be distributed in the y\({}^{\prime}\) direction parallel to the flame surface as much as possible to increase the speed along \(v_{y}\). Figure 15: (**a**) Distribution of the thermal radiation field at different heights (1.7 m, 1.4 m and 1.1 m) in the pedestrian evacuation area without airflow; (**b**) Distribution of the pedestrian radiation accumulation at different heights (1.7 m, 1.4 m and 1.1 m) in the pedestrian evacuation area without airflow. 2.3 Analysis of the Pedestrian Evacuation Scenario Considering the Fixed Initiation Position and the Free-Fleeing Direction  
Considering the strategy of a pedestrian fleeing from danger in the fire radiation field, and the most adverse situation of the fire for a pedestrian, the boundary range of the safety threshold calculation was taken as z = 1.15 m at the midpoint of the height of the #2 flame surface. According to Equation (10), the incident thermal radiation Q received by the pedestrian was related to its location. In the O\({}^{\prime}\)-x\({}^{\prime}\)-y\({}^{\prime}\) coordinate system, \(q=f(x,y,z)\). The pedestrians avoided danger from the fire and moved at a constant speed along a certain direction until they reached the boundary of the safety threshold. The accumulated incident thermal radiation of the pedestrian was \(Q_{in}=\int_{x=0}^{x=x_{i}}\int_{y=0}^{y=y_{k}}\int_{z=0}^{z=H}q~{}dxdydz\), where \((x_{i},y_{k})\) is the coordinate value of the safety threshold boundary in the O\({}^{\prime}\)-x\({}^{\prime}\)-y\({}^{\prime}\) coordinate system and H is the height of the pedestrian. To obtain the minimum value of \(Q_{in}\), complex calculus was used in the mathematical equation and it was difficult to obtain an analytical solution. Therefore, a computer program was used to obtain the numerical solution of the minimum value of \(Q_{in}\) by gridding the incident thermal radiation field of the fire in the pedestrian movement area. (1) Scenario without airflow  
For the pedestrian evacuation strategy in the thermal radiation field, we formed a grid in the static thermal radiation field in the pedestrian movement area with a side length of 0.02 m, as shown in Figure 17. The incident thermal radiation flux in the grid was considered uniform. According to the assumption of the pedestrian's straight-line risk avoidance behavior while moving away from the flame and the threshold that divided the thermal radiation intensity as high-risk and low-risk, the threshold curve \(f\) (4.5) for a 4.5 kW/m\({}^{2}\) thermal radiation flux was calculated, as shown in Figure 18. We combined \(f\) (4.5) with the grid radiation field to obtain the discrete set \(F\)\(\{x_{i},~{}y_{k}\}\), as a fleeing target set for the pedestrian evacuation strategies.