# Numerical Simulation of Hot Jet Detonation with Different Ignition Positions
## 3 Results Analysis and Discussion
### Mechanism of Hot Jet Detonation Initiation
The V\({}_{1}\) and V\({}_{2}\) continue to expand and move downstream in the detonation chamber with time. Comparing the \(Q\) criterion and turbulent kinetic energy at \(t_{HJ}\) = 1.575 ms (Figure 7c) and the \(T\!K\)E filed as shown in Figure 6, it is found that the vortex will form local turbulence. The vortexes have formed before flame enters into the detonation chamber, so they inevitably affect the propagation of hot jet when flame propagates into the detonation chamber. Figure 8 shows the variations of temperature and \(Q\) criterion field, which reflects the interaction of vortex and jet flame. The O indicates the obstacle in the figure, and the O\({}_{i}\) represents the _ith_ obstacle. The gray area represents the vortex. At \(t_{TDC}\) = 0.03 ms, the jet flame propagates into the detonation chamber, the vertical distance between the largest scale vortexes (V\({}_{1}\) and V\({}_{2}\)) and the flame front is 70 mm. From 0.03 ms to 0.24 ms, the flame surface area increases accordingly because of the sudden expansion of flow field structure and the small-scale vortexes. As the influence of the left wall, the jet flame propagates to the right in the detonation chamber. Flame reaches the down wall of the detonation chamber as shown in Figure 8d, and the V\({}_{1}\) and V\({}_{2}\) move to the sides by the hot reaction products. Subsequently, the V\({}_{2}\) enhances the local turbulent fluctuation and entrains flame when \(t_{TDC}\) = 0.66 ms. Then V\({}_{2}\) accelerates the mixing between hot reaction products and cold unburned mixture [47], which is beneficial to promote the chemical reaction rate and diffusion rate of mass and heat. As a result, the vortex-flame interaction increases flame wrinkle surface area and accelerates the flame propagation. Since V\({}_{2}\) entrains the flame surface and V\({}_{1}\) does not touch the flame yet, the right flame surface increases more. Such actions lead to the formation of a \"hook-type\" flame as shown in Figure 8e. In addition, the vortex enhances the superposition between the pressure waves. The increasing pressure wave results in the stronger internal energy of unburned mixture, thus improving the flame propagation. According to Figure 8f, the right flame front propagates to the  
Figure 6: Temperature field and turbulent kinetic energy field at 1.575 ms.  
Figure 7: Variations of \(Q\) criterion field. first obstacle, and the V\({}_{1}\) begins to entrain the left flame. The unburned mixture propagates with the promotion of the high-temperature products and creates vortexes in the boundary layer of obstacle as the Kelvin-Helmholtz (K-H) instability [48]. As flame passes through the obstacles, the flame surface area, and flame propagation velocity both increase due to the Rayleigh-Taylor (RT) and K-H instabilities [49; 50]. The flame becomes fast flame as shown in Figure 9 (a) [51], just arrives at the O\({}_{4}\). Figure 9 describes the formation of detonation wave by the variations of pressure and temperature field in detail. Obviously, a high-pressure zone occurs near the fourth obstacle at this moment. Pressure waves superimpose to form a shock in the leading edge of flame front. Since the leading shock compresses unburned mixture at front of flame to raises the temperature surrounding it, the chemical reaction and combustion are both promoted. Then plenty energies released from rapid combustion will strengthen the leading shock. This creates a positive feedback effect. Figure 8: Interaction of jet flame and vortex in the detonation chamber. Figure 4:0 _Cont._  
According to Figure 9b, the leading shock and flame pass the O\({}_{4}\), and the leading shock reflects from the wall. Then the leading and reflected waves collide at point \"c\" as shown in Figure 9c, the maximum pressure of \"c\" is over 6 MPa. From the temperature field at this time, a hot spot is formed at the point \"c\". At \(t_{TDC}\) = 1.935 ms, the flame surface is coupled to the front shock, the hot spot develops to detonation wave at 1170 mm.