## 4 Results and Discussion
### Parameter Analysis of Flow Path in CRD Combustors
From the inlet direction, the working fluid from region III passed through the detonation wave initially, then through the oblique shock wave. The working fluid from region IV passed through the mixing and deflagration regions. Considering the complexity and non-determinacy of the mixing, there was no further analysis done for this part in this study. From Figure 10b, the following phenomena can be seen. Firstly, the entropy of working fluid increased abruptly after passing through the detonation wave. Secondly, the second entropy generation occurred when the working fluid passed though the oblique shock wave. Thirdly, there was a deflagration area around the discontinuity region between the fresh premikture and product. However, due to the incomplete reaction, the entropy in this region increased slowly. Finally, the mixing region of the detonation product and deflagration product was the highest entropy region. Figure 11 shows the variation in pressure and temperature along the three typical streamlines 1, 2, and 3. The results showed that when the working fluid passed through the detonation wave, there was only one jump in pressure and temperature along streamlines 1 and 3. After that, the values of pressure and temperature decreased abruptly and, finally, were stable. However, along streamline 2, there are two jumps due to the combined effects of the detonation wave and the oblique shock wave. The maximum value of total pressure of the working fluid along streamline 1 reached 4.3316 MPa, which was over fourteen times higher than the inlet total pressure. For the working  
Figure 10: (**a**) Temperature and (**b**) entropy shadowgraphs of the CRD combustor at a time of 6920 \(\upmu\)s.  
fluid along the other two streamlines, maximum total pressure was only 3.6304 MPa and 2.4374 MPa, respectively. In addition, it was discovered that the maximum total temperature of the working fluid along the three streamlines was very close (potentially over 3000 K), which aligns with the C] theory. Figure 12 also shows variations in \(\Delta S\) along the three typical streamlines outlined above. Because there was little effect on potential power in the circumferential changing of entropy generation, change in entropy generation is only presented in the axial direction. Using the same pressure and temperature analysis as above, there was only one jump in entropy generation along streamline 1 and streamline 5 and there were two jumps of entropy generation along streamline 2. At the position of the detonation wave, entropy generation was about 2050.0 J/kg\(\cdot\)K along the three streamlines. However, at the position of the oblique shock wave, the change in entropy generation was only 187.8 J/kg\(\cdot\)K along streamline 2. The major entropy generation roots in the detonation region and the second entropy generation was about 9.2% of that at the position of detonation wave. As the entropy generation of the detonation was smallest in the combustion modes of this study, the major part of entropy generation could not be decreased. Figure 13 shows variations in \(\Delta G\) along the three typical streamlines in the axial direction. There were large losses in Gibbs free energy at the position of the detonation wave and the oblique shock wave. Along streamline 2, Gibbs free energy loss reached 922.8 kJ/kg at the position of oblique shock wave (20.9% of that at the position of detonation wave). Compared to streamline 1 and streamline 5, there was, respectively, about a 20.9% and 12.9% increase in \(\Delta G\) along streamline 2. This means that the oblique shock wave led to extra available energy loss and had a negative influence on pressure gain characteristics. Figure 11: Variations of (a) pressure and (b) temperature along the three typical streamlines. Figure 12: Variations in \(\Delta S\) along the three typical streamlines in an axial direction.