# Effects of Diverging Nozzle Downstream on Flow Field Parameters of Rotating Detonation Combuster
## 3 Numerical Results and Discussion
### Effect of Different Diverging Nozzles on Pressure Parameters
Figure 13 gives the averaged static pressure distribution in different axial cross-sections of the RDC at the time of 3980 \(\upmu\)s. The static pressure distribution in the RDC can be decreased overall by the diverging nozzle. Except the region near the outlet, the variation laws of the static pressure are basically similar to those of the total pressure. Moreover, in the diverging section of the RDC, the static pressure continues to decrease more obviously under the action of larger \(\theta\). At the outlet, the corresponding values are 0.839 MPa, 0.206 MPa, 0.124 MPa, and 0.098 MPa. Compared to the value of \(\theta=0^{\circ}\), the outlet static pressure of the RDC with \(\theta=15^{\circ}\), \(30^{\circ}\), and \(45^{\circ}\) drops 75.45%, 85.22%, and 88.32%, respectively. This indicates that the diverging nozzle can greatly improve the working environment of RDC outlet and reduces the aerodynamic load of the turbine blades. Besides, for the results of \(\theta=30^{\circ}\) and \(45^{\circ}\), their static pressure curves are almost coincident, which indicates that when \(\theta\) reaches a certain value, the effects of \(\theta\) on the RDC outlet static pressure is not so obvious. In order to investigate the specific changes of outlet aerodynamic load, Figure 14 shows the outlet static pressure contour of the RDC with different \(\theta\) at \(t=3980\)\(\upmu\)s. It can be observed that there is a large high pressure region after the oblique shock for \(\theta=0^{\circ}\), and with the increasing of \(\theta\), the high pressure region decreases significantly. It is because the bending of the wall near outlet makes the expansion space of the oblique shock wave larger, and the pressure after it is significantly reduced, which causes the pressure attenuation to increase. To better understand the static temperature distribution at the RDC outlet, we assume that \"\(l\)\" represents the value of the width between the inner wall and outer wall of outlet, and the inner wall is 0% height (\(l=0\%\)) and the outer wall is 100% height (\(l=100\%\)), which are given in Figure 13a. Figure 14: _Cont._  
Figure 13: The averaged static pressure in different axial cross-sections of the RDC at \(t=3980\)\(\upmu\)s.  
Figure 15 gives the circumferential static pressure distribution at three typical heights of \(l=1\%\), \(l=50\%\), and \(l=99\%\), which represent the position near the inner wall, in the middle of the width, and near the outer wall, respectively. It is found that the outlet pressure reduces for different nozzle angles, and the fluctuation of circumferential pressure also becomes gradual, which means the diverging nozzle improves the uniformity of outlet static pressure distribution in different heights. Specifically, for the 1% height, the peak static pressure is reduced from 1.547 MPa to 0.232 MPa. For the 50% height, it is reduced from 1.628 MPa to 0.133 MPa, and for the 99% height, it is reduced from 1.744 MPa to 0.079 MPa. Among them, the static pressure variation of 99% height is the most significant, whose peak value is reduced by 95.5%. In addition, the static pressure distribution of the 1% height is less sensitive to the diverging angle \(\theta\) than the 50% and 99% height. It is mainly because the pressure produced by the oblique shock wave expansion does not have enough space to spread and get relief, making the pressure drop of the inner wall not obvious. In summary, the changes in the outlet pressure of the RDC fully demonstrate that the diverging nozzle has considerable potential in improving the non-uniform characteristics of the outlet pressure and reducing the aerodynamic loads of the turbine. Moreover, the larger the diverging angle, the lower the outlet static pressure is; thus the pressure distribution is more uniform. Figure 14: The outlet static pressure contour of the RDC with different \(\theta\) at \(t=3980\) μs. Figure 15: _Cont._  
The improvement of the pressure distribution at the RDC outlet is due to the adoption of the diverging nozzle.