# 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  
Through the above study, it is found that the hot jet can form vortexes to accelerate flame propagation and promote DDT in the detonation chamber. However, the formation time of the hot jet is 44.87% of DDT time, which will greatly affect the performance of the detonation engine. In the previous paper, the ignition position inside the detonation chamber affects flame propagation [8]. So, the differences between top ignition and wall ignition are the following focus and research (\(\zeta_{Y}\) = 0 mm as shown in Figure 1b. Figure 10 shows the time and distances to detonation initiation of two ignition positions. Simulation results clearly display that wall ignition can not only effectively reduce the \(t_{HJ}\), but also shorten DDT time and distance. The top ignition \(t_{DDT}\) = 1.575 ms (\(t_{HJ}\)) + 1.935 ms (\(t_{TDC}\)) = 3.51 ms, and \(x_{DDT}\) = 1170 mm. The wall ignition \(t_{DDT}\) = 1.005 ms (\(t_{HJ}\)) + 1.32 ms (\(t_{TDC}\)) = 2.325 ms, and \(x_{DDT}\) = 907 mm, the \(t_{DDT}\) and \(x_{DDT}\) are reduced by 33.76% and 22.48% comparing with top ignition. Figure 10: Time and distance to detonation initiation of top and wall ignition. Figure 9: Variations of pressure and temperature field at detonation transition (DDT). Figure 11 compares the flame propagation speed inside the jet tube of the two ignition positions, which can account for the reason of \(t_{H\!I}\) reduction. In this figure, the distance represents the flame propagation distance in the hot jet tube, the left side is the ignition position, and the right side is the exit of the hot jet. The initial flame development of the two ignition positions is similar, then flame propagation speed of wall ignition is obviously higher than that of top ignition. Finally, the jet flame of wall ignition propagates into the detonation chamber at a velocity of 550m/s, which is about 1.65 times faster than that of top ignition. Base on the \"a\" region of Figure 11, it is found that the flame propagation velocity of wall ignition is more than 2 times of the wall ignition. To investigate this issue, the variations of temperature field of wall ignition are studied as shown in Figure 12. At \(t_{H\!I}=0.3\) ms, the pressure wave reaches right wall and then reflects. The reflected wave propagates to left, and it prevents the flame from contacting the right wall, thus ensuring the contact area between flame and unburned mixture. Comparing with Figure 5, there is more contact area between flame and unburned mixture in the flow field of wall ignition at this moment. More contact area releases more energy to increase the flame propagation speed. Therefore, the flame propagates faster and flame front reaches the exit of the jet tube in only 0.9 ms as shown in Figure 12c, the propagation distance is significantly farther than the flame of Figure 5e. Then flame front transforms from \"fingertip\" to \"planar\" shape. Flame contacting with wall results in reducing the contact area between flame and unburned mixture, thus slowing down the flame propagation speed. However, the flame propagation speed of wall ignition is faster than that of top wall, and wall ignition takes only 1.005 ms to form a hot jet into the detonation chamber. Figure 11: Flame propagation speed in the hot jet tube of two ignition positions. The jet pressure also affects the jet flame propagation into the detonation chamber, so a detailed comparison of the jet pressure changes with time at the center point of the hot jet tube is shown in Figure 13. The first pressure peak appears at 0.5 ms. The pressure peak of wall ignition is 1.35 times that of top ignition. Subsequently, the pressure of wall ignition is always higher than the top ignition. The second pressure peak appears at 0.75 ms and the peak value can reach 0.2 MPa. The jet flame of wall ignition enters detonation chamber with 0.1 MPa at 1.005 ms, which is obviously higher than 0.06 MPa of top ignition.