# Numerical Simulation of Hot Jet Detonation with Different Ignition Positions
## 3 Results Analysis and Discussion
### Optimization of Ignition Position  
Through the above study, it is found that wall ignition is more conducive to the acceleration of DDT. To further study the performance advantage of wall ignition, the effect of different wall ignition positions on DDT is studied in this section. The ignition positions of \(\zeta_{Y}\) = 30 mm, 60 mm, 90 mm, 120 mm, and 150 mm are simulated as well. Figure 17 displays the jet velocity and pressure of different ignition positions when jet flame front enters into the detonation chamber. Since too big \(\zeta_{Y}\) results in less mixture combustion in the jet tube, thus weakening the jet velocity and pressure. When \(\zeta_{Y}\) is large, the jet velocity and pressure are both relatively small. As \(\zeta_{Y}\) increases, the jet velocity maintains at about 550 m/s and then an obvious reduction occurs. The jet pressure increases firstly and then weakens with increase of \(\zeta_{Y}\), and the highest peak is observed \(\zeta_{Y}\) = 30 mm. The pressure wave is reflected not only on the left and right walls but also on the top of jet tube [46]. Therefore, it is more advantageous to obtain larger jet pressure when \(\zeta_{Y}\) = 30 mm.  
Figure 16: Variations of pressure and temperature field at deflagration-to-detonation transition (DDT) of wall ignition.  
Figure 17: Jet velocity and pressure of different ignition positions.  
Then jet flame propagates into the detonation chamber, flame wrinkling surface area and propagation speed both increase by vortexes and obstacles. In order to compare the flame propagation in the detonation chamber for different ignition positions, distributions of pressure and temperature on the axis at different ignition positions at \(t_{TDC}\) = 1.44 ms are shown in Figure 18 (\(\zeta_{Y}\leq\) 60 mm) and Figure 19 (\(\zeta_{Y}\geq\) 90 mm). Since the fast hot jet, flame and pressure propagate farther in Figure 18 than those of Figure 19. The propagation distances of flame and pressure are farthest when \(\zeta_{Y}\) = 30 mm. The values of leading shock already meet the detonation parameter in Figure 18, and flame front couple with the leading shock, so the detonation wave has been formed in the detonation chamber.  
Base on Figure 19, the propagation distance of pressure wave and flame decrease as \(\zeta_{Y}\) increasing, and the pressure wave propagate slightly further than flame front. It is clearly seen that the pressure of deflagration wave is weak at this time, and value of pressure wave decreases as \(\zeta_{Y}\) increasing. The pressure of \(\zeta_{Y}\) = 150 mm is obviously lower than other ignition positions, which does not form the leading shock.  
Figure 18: Distributions of (**a**) pressure and (**b**) temperature of \(\zeta_{Y}\leq\) 60 mm at \(t_{TDC}\) = 1.44 ms.  
Figure 20 shows the DDT distance and time of different ignition positions. The \(t_{DDT}\) (\(t_{H\!I}+t_{T\!DC}\)) and \(x_{DDT}\) both decrease firstly and then increase with \(\zeta_{Y}\) increasing. The ignition position is near the exit of the hot jet tube when the \(\zeta_{Y}\) is big, so the \(t_{H\!I}\) is small. However, the reduction of jet intensity leads to a long time and distance to complete DDT. As the jet velocity and pressure are the largest at \(\zeta_{Y}\) = 30 mm, the shortest \(x_{DDT}\) is 810 mm and the fastest \(t_{DDT}\) is 2.055 ms at this time.  
Figure 19: Distributions of (**a**) pressure and (**b**) temperature of \(\zeta_{Y}\geq\) 90 mm at \(t_{T\!DC}\) = 1.44 ms.  
Figure 20: DDT distance and time of different ignition positions.