# Numerical Simulation of Hot Jet Detonation with Different Ignition Positions
## 3 Results Analysis and Discussion
### The Influence of Ignition Position on the Hot Jet Detonation Initiation
The average pressure of the wall ignition is twice than top ignition due to more intense burning and wave superimposition. On the basis of above discussions of jet velocity, it is found wall ignition brings a faster hot jet with higher pressure. In order to understand flame propagation and detonation wave formation of the two ignition positions. The comparison of flame propagation speed is shown in Figure 14. The trend of these two flame propagations is generally the same due to the same structure, but the flame propagation of wall ignition is substantially faster than that of top ignition. The wall ignition forms a detonation wave first. According to the characteristics of the flame speed, this figure is divided into two regions to study. **(I)** In this region, the vortex entrains the jet flame to increase the flame speed before the first obstacle. **(II)** The flame constantly accelerates because of the obstacles, and eventually forms a detonation wave. Figure 14: Flame propagation speed in the detonation chamber. Figure 13: Pressure changes of two ignition positions at the exit of the hot jet tube. In the first region, the flame propagation speed of wall ignition increases significantly fast and remains at big speed. Except for the area around 0.23 m (the V\({}_{1}\) entrains the flame of top ignition as shown in Figure 8e), the flame speed of wall ignition is always faster than that of top ignition. Figure 15 displays the variations of temperature and \(Q\) criterion field of wall ignition before the first obstacle to investigate why the flame speed of wall ignition is faster. Comparing with Figure 8a, it can be seen that the scale of the vortexes (V\({}_{1}\) and V\({}_{2}\)) is larger at \(t_{TDC}\) = 0.03 ms due to the higher jet pressure and the faster jet velocity. Additionally, the reducing formation time of hot jet results in short moving time of V\({}_{1}\) and V\({}_{2}\), so the vertical distance between the vortexes (V\({}_{1}\) and V\({}_{2}\)) and the flame front is only 14 mm, which is obviously closer than that of top ignition. Base on Figure 15b,c, flame quickly contacts the vortexes (V\({}_{1}\) and V\({}_{2}\)). The two same scale vortexes (V\({}_{1}\) and V\({}_{2}\)) simultaneously entrain the flame. Then flame temperature and wrinkling surface both increase rapidly and a symmetrical \"mushroom-shaped\" flame is produced at \(t_{TDC}\) = 0.24 ms. Subsequently, flame reaches the first obstacle by only 0.66 ms, which is 26.67% less than top ignition. Moreover, a large amount of mixture is burned to release energy, which is more conducive to the next acceleration of the flame. Comparing with Figure 8, vortex entrains flame earlier and the scale of vortex is significantly larger, so the flame propagation speed of wall ignition is faster than that of top ignition. In the second region, as the flame propagation speed of wall ignition is faster than that of top ignition when the flame passes the first obstacle, its flame propagation speed is always faster at the second stage as shown in Figure 14. Subsequently, the wall ignition forms a detonation wave in advance as shown in Figure 16. Wall ignition burns more intensely at the early stage in the detonation chamber, so superposition of pressure waves is more intense. According to Figure 16a, two high-intensity reflected waves have been formed before the third obstacle. Then the reflected waves and leading shock collide at point \"c\", and a hot spot is formed which is significantly ahead of the top ignition. The high temperature and pressure point accelerate energy release to accelerate DDT which precedes than top ignition. The triple point(r) Mach stem, r incident shock, and r transverse shock) is promoted for the case of ignition at the wall because of the higher pressure waves and flame strength than that of top ignition. On the basis of above discussions, it is found that wall ignition forms a fast hot jet with high pressure, shortens the formation time of hot jet, and forms large-scale vortexes.