## 5 Results and Discussion  
### Cell Structure  
Comparing Figure 6\(\theta\) = 15\({}^{\circ}\), \(\theta\) = 20\({}^{\circ}\), \(\theta\) = 30\({}^{\circ}\) with \(\theta\) = 40\({}^{\circ}\), \(\theta\) = 45\({}^{\circ}\), \(\theta\) = 60\({}^{\circ}\), a great difference is found between the results of these two groups. In the same pipe distance, the stable cell structure of the first group is destroyed and the size of cell becomes inhomogeneous after being affected by the curvature of the pipe. However, the cellular detonation wave can spread continuously. The second group is so heavily affected by the curvature of the pipe that a wide range of cell seven disappear completely on the surface of the pipe wall. Figure 5: Triple structure comparison results. Figure 6: Cellular structure of different bend angles. Figure 6 shows different propagation characteristics of detonation wave in the bend pipe, which can be explained by the change of cellular structure. The cellular structure plays an important role in the investigation of detonation propagation mechanism. The detonation wave propagation is able to form a regular cellular structure and this is mainly driven by the chemical reaction. The disappearance of cellular structure indicates that the energy supplied by the chemical reaction is insufficient to maintain the structure and the chemical reaction surface is gradually decoupled from the detonation wave front. The increase of cellular structure shows that the driving energy supplied by chemical reaction is less than the requirement of the stable cell and the detonation wave is under driven. The decrease of cellular structure implies that the energy supplied by the chemical reaction is greater than the needs of stable cell and the detonation wave is over driven. The decrease of the chemical energy is generated by the rarefaction wave on the up wall, which causes the pressure and temperature drop behind the detonation, while the increase is due to the compression wave on the lower wall, which causes the pressure and temperature increases behind the detonation. The disappearance of the cellular structure also indicates the detonation is extinguished. The stable structure must have periodic transverse wave structure. However, the rarefaction wave generated in the upper wall makes the transverse wave decay rapidly near the edge of the wall. Thus, the quenching area is generated. A comparison between Figure 6\(\theta\) = 15\({}^{\circ}\), \(\theta\) = 20\({}^{\circ}\) and \(\theta\) = 30\({}^{\circ}\) shows that the whole pipe is divided into A, B and C regions. The structure in A region is regular and the propagation of detonation is stable. Cellular structure in B region becomes irregular, where the cell size increases in the upper half while it decreases in the lower half. The reason is that the detonation wave is diffracted on the upper wall, and the pressure of the detonation wave reduced by the rarefaction makes it instable. This leads to the increasing of cellular structure. However, the Maher reflection happens between the pipe and detonation wave in the lower wall and induces increase of the pressure and temperature correspondingly after the Maher. With the increase of the detonation wave intensity, the cell structure is reduced. In contrast to B region, the cell size in C region decreases in the upper part while it increases in the lower part. The result is that along with the propagation of detonation waves spreading to downstream of the bend, the three wave structure interacts among the others at the same time, the Maher reflection between the detonation and the pipe is stopped. Unlike \(\theta\) = 15\({}^{\circ}\) and \(\theta\) = 20\({}^{\circ}\), the results of \(\theta\) = 30\({}^{\circ}\) show that there is a critical detonation in the B region (the transition curvature between the presence of quenching and absence of quenching). Comparison between Figure 6\(\theta\) = 40\({}^{\circ}\), \(\theta\) = 45\({}^{\circ}\) and \(\theta\) = 60\({}^{\circ}\) shows that a quenching area exists in B region.