# Smoke Back-Layering Phenomenon under the Combined External Wind and Stack Effects in a Staircase
## 3 Results and Discussion
### Wind Effect on the Smoke Movement with Open Stair Door below the Fire Source  
Smoke behaviors with different open stair door location under wind condition are similar at the simulation in the current work, taking cases with open stair door on the first floor as examples. Figure 6 presents time history of vertical temperature profiles at the centerline of the staircase with open stair door on the first floor. At 0-3 m/s, as shown in Figure 6a, temperatures at different height above the fire floor increase with time sequentially and fluctuates around a constant value at the steady state. Temperatures at the height below the fire floor keep the ambient temperature all the time. At 3.5 m/s, as shown in Figure 6b, most of the temperatures at different height increase with time. However, for the thermocouple at the height of at 21.65 m, there is a sudden temperature increment at about 20 s, which reaches a peak value of 50 \({}^{\circ}\)C approximately at 50 s and then decays rapidly. Figure 7 shows the velocity vector graphs inside the staircase at 3.5 m/s. Combining Figures 6b and 7a, it can be concluded that, when the smoke begins to enter the staircase, some smoke moves upward, and some moves downward. The longest back-layering distance occurred at about 50 s. Combining Figures 6b and 7b, we can see that the smoke and the airflow from the open stair door on the first floor move upward, driven by the stack effect eventually. This is because the thermal buoyancy of the smoke is too low to overcome the wind force when it is starts to enter the staircase. Some of the smoke is pushed to move downward, and the smoke back-layering phenomenon occurs. Then, the thermal buoyancy of the smoke and HIRR of the fire increase with time and overcome the wind force. The smoke and airflow from the open stair door move upward, driven by the stack effect finally. Figure 8 presents temperature distributions in the atrium and fire compartment at 3.5 m/s. It can be seen that the flame tilts to the door D1 at 30 s and stands vertically at 52 s, then tilts to the door D3 at 70 s. Combining Figures 7b and 8b, it can be concluded that the time when the longest back-layering distance appears is consistent with the critical transition time of the flame tilting direction. At 4 m/s, as shown in Figure 6c, temperatures keep the ambient temperature all the time at the height above the fire floor. However, temperatures increase sequentially first, then decay to a low value at the height below the fire floor. Figure 9 presents velocity vector graphs inside the staircase at 4 m/s. Combining Figures 6c and 9, it can be concluded that some smoke flows into the staircase and is pushed to move downward by the external wind. There will be a sudden temperature rise when the downward moving smoke front  
Figure 5: Pressure difference distributions in the staircase at 0 m/s. (**a**) Stair door opened on the first floor. (**b**) Stair doors closed. reaches the thermocouple at a given height. The smoke flows out from the open stair door below the fire floor after a sudden temperature rise at 1.85 m. Additionally, Figure 10 shows temperature distributions in the atrium and fire compartment. The flame tilts to the door D3 at 120 s when the smoke moves downward. It is indicated that the flame tilting direction keeps toward the door D3 as the smoke flows out from the open stair door. Smoke behavior is directly related to the flame tilt direction. The theoretical model to determine the flame tilting direction established by [PERSON] et al. (2014) is also valid to predict the smoke behavior. At 4.5 m/s, as shown in Figure 6d, temperatures inside the staircase always keep the ambient temperature. The thermal buoyancy of the smoke cannot overcome the wind force. The whole staircase is smoke-free and safe.