# Effects of Diverging Nozzle Downstream on Flow Field Parameters of Rotating Detonation Combuster
## 3 Numerical Results and Discussion
### Effect of Different Diverging Nozzles on Temperature Parameters  
The main purpose of the diverging nozzle in this paper is to improve the working environment of the downstream turbine and reduce the thermal stress and aerodynamic load on turbine blades. The pressure parameter distribution under the diverging nozzle was studied above, while, temperature is directly relative to the thermal protection performance and component integration of the RDC-based engine. Under different diverging angles \(\theta\), the outlet temperature fluctuations with time are demonstrated in Figure 17. The curves show that the averaged outlet total temperature of the RDC with different \(\theta\) behaves with similar periodic fluctuations to the total pressure presented in Figure 11.  
Figure 16: Entropy in different axial cross-sections of the RDC at \(t=3980\) μs. Figure 15: The circumferential outlet static pressure distribution of the RDC at \(t=3980\) μs. Obviously, the variation of outlet total temperature with different \(\theta\) still follows the law of isenthalpic process, meaning their values are basically equal, which are about 2593.31 K, 2595.20 K, 2594.34 K, and 2594.77 K, respectively. Figure 18 presents the averaged total temperature distribution along the flow direction at \(t=3980\)\(\upmu\)s. As shown in Figure 18, since the chemical reactions in the RDC are constantly exothermic, the total temperature of the mixture increases continuously, and then reaches the maximum value at about \(X=160\) mm and remains stable afterwards. For the RDC with different \(\theta\), their outlet total temperature changes extremely little. However, in the chemical reaction zone, the increasing rate of total temperature for \(\theta=0^{\circ}\) is gradually slowed down, while this value remains almost unchanged in RDCs with diverging nozzles. The results indicate that the chemical reaction is more uniform and sufficient in RDCs with diverging nozzles, and the total temperature increases almost linearly during the detonation combustion process. Since the static temperature parameter directly affects the thermal load, the following mainly analyzes the changes of static temperature parameters in flow fields. Figure 19 gives the averaged static temperature along the flow path of different RDCs. As can be seen from the curves, the static  
Figure 17: The time-varied outlet total temperature of the RDC with different \(\theta\). Figure 18: The averaged total temperature in different axial cross-sections of the RDC at \(t=3980\)\(\upmu\)s.  
temperatures of \(\theta\) = 15\({}^{\circ}\), 30\({}^{\circ}\), and 45\({}^{\circ}\) are lower than that of \(\theta\) = 0\({}^{\circ}\) from the inlet position, and their value differences reach the maximum at the outlet. In addition, the outlet static temperature values of \(\theta\) = 0\({}^{\circ}\) from \(X\) = 150 mm to \(X\) = 200 mm are relatively close and almost consistently maintained at the highest value. However, for \(\theta\) = 15\({}^{\circ}\), 30\({}^{\circ}\), and 45\({}^{\circ}\), the static temperatures of this region begin to move away from the high temperature region in the RDC, which reduces by 22.91%, 29.45%, and 32.12% compared to the value of \(\theta\) = 0\({}^{\circ}\) at the outlet, respectively. This will greatly improve the working environment at the RDC outlet and reduce the thermal stress and thermodynamic load of the downstream turbine. Figure 20 clearly presents the static temperature contour of the RDC outlet with different \(\theta\) at \(t\) = 3980 \(\upmu\)s. There is a high temperature region after the oblique shock wave in the RDC without a diverging nozzle. Nevertheless, the region of high temperature is decreasing with the increasing of the diverging angle; when \(\theta\) increases to 45\({}^{\circ}\) (as shown in Figure 20d), the high temperature region appears in the location near the inner wall and is relatively insignificant. Moreover, in other regions, the static temperature also has a certain degree decrease under the action of the diverging nozzle.