## 4 Results and Discussion
### Blow-Off Dynamics  
To further investigate the transient blow-off behavior and the impact of hydrogen ratio on the transient flame process, the equivalence ratios for each case were suddenly decreased to 0.2 from the aforementioned stale condition (\(\phi\) = 0.75). Data were collected over 55 ms, about three flow-through times (FTT), defined by the length of the combustor chamber divided by the mean bulk velocity in the chamber. The instance of the equivalence ratio decrease was specified at 0 ms. Figure 9 shows the integrated heat release rate normalized by the maximum value at the stable condition. The flame is considered blown out when the normalized heat release rate decreases below 50%. The resistance of the heat release rate over time for different equivalence ratios can be observed in Figure 9. The extinction process of a bluff-body-stabilized flame can be divided into two stages, as shown in Figure 9. In the first stage, the lean mixture slightly affects the combustion process, and the heat release rate decreases slowly. In the second stage, the heat release rate decreases rapidly due to the effect of the overall equivalence ratio reduction. In the current study, the beginning of the second stage was defined as when the derivative of \(Q/Q_{max}\) with respect to the time was smaller than \(-0.1\). This metric can be employed to identify specific portents that trigger blow-off. It can be seen that 00H2 entered the second stage at 6.4 ms, 30H2 entered the second stage at 6 ms, 60H2 entered the second stage at 5 ms, and 90H2 entered the second stage at 4 ms. Additionally, with an increase in the hydrogen ratio, the duration of the first stage decreased, which corresponded to a faster occurrence of the onset of the second stage. Figure 8: The vortices and the flame location characterized by 10% of the maximum heat release. This phenomenon is due to the reduction in the flame height for higher hydrogen ratios, meaning that the flame is more sensitive to the incoming fresh mixture. The heat release rate along the central plane was collected at different time instances to further analyze the effect of increasing the hydrogen ratio. Figure 10 displays a comparison of the blow-off processes corresponding to the four hydrogen ratios considered in this study. For each operating condition, the heat release rate was normalized by the maximum heat release rate. The first time instance is selected during the stable process. The second instance refers to the initiation of the blow-off stage. The third instance represents the point at which the maximum release rate drops to 75% HRR\({}_{\text{max}}\), and the fourth instance refers to blow-off (blow-off is defined by HRR \(<\) 50% HRR\({}_{\text{max}}\)). Figure 10: Normalized heat release rates of different hydrogen ratios during the blow-off process. (**a**) 00H2; (**b**) 30H2; (**c**) 60H2; (**d**) 90H2. Figure 9: The change in normalized integrated heat release rate over time (ms). Figure 10a shows the blow-off process for the 00H2 case, where the flame shrinkage as a result of flow field influence is evident at the beginning of the second stage (i.e., 6 ms). This is an indication of cool reactants going into the IRZ. The heat release rate at the flame root quickly decreases, and local extinction (local extinction is defined by local HRR \(<\) 50% HRR\({}_{\text{max}}\)) occurs at the flame root at 9 ms. It can be seen that the flame lifts off from the bluff body completely at 12 ms. For 30H2, as shown in Figure 10b, the heat release rate of the flame roots decreased at 8 ms. The flame root detached from the bluff body, and local extinction occurred. Global extinction occurred at 11 ms. For the 60H2 and 90H2 cases, as shown in Figure 10c,d, flames were always anchored at the bluff body's edge until the flame was completely blown out, since hydrogen reinforces the ability of the flame to attach to the bluff body. For 90H2, the flame height rose rapidly when close to extinction. For this case, the flame height rise was twice the flame height in stable conditions.