# Effects of Diverging Nozzle Downstream on Flow Field Parameters of Rotating Detonation Combuster
## 1 Introduction  
The gas turbine is one of the power devices widely used in aerospace, marine, electricity generation, and other fields. With the increasing demands for energy conservation and emissions reduction, how to achieve efficient use of fuel in gas turbines has become a popular research direction [1; 2]. Therefore, it is urgent for researchers to develop advanced technologies on combustors of gas turbines. As one kind of pressure gain combustion, detonation theoretically can enhance the cycle performance of many conventional engines, including gas turbines [3; 4]. Among the current mainstream detonation combustion propulsion devices, the rotating detonation engine has been recognized as the most promising one in recent years due to its unparalleled advantages in compact structure, one-time detonation initiation, better controllability, and steadier exhaust. Since supersonic combustion in the rotating detonation combuster (RDC) involves complex chemical reactions, wave collisions,and combustion instability [5; 6], the coupling of the RDC and downstream components face severe aerodynamic, thermodynamic, and structural challenges in applications, which poses a potential hazard to the design of RDC and the evaluation of RDC-based engine performance. Outlet parameters of RDC, mainly including temperature, pressure, and Mach number, directly determine the thrust [7; 8], thermal efficiency [9; 10; 11], and combustor-turbine integration [12; 13; 14] of RDC-based engines. Therefore, the unsteady outlet flow field control of the RDC with different nozzles is one focus of current research. [PERSON] et al. [15] measured the RDC by using time-resolved particle image velocimetry (TR-PIV). Their research results show the non-uniform characteristics of the RDC outlet flow field. [PERSON] et al. [16] experimentally and numerically studied the time-dependent static pressure distributions along the outlet nozzle of the RDC. Their results showed that combining the conical center body and converging-diverging nozzle could effectively control or eliminate the unsteady periodic exhaust flow. [PERSON] [17] investigated the operating performance of an RDC with an aerospike nozzle and turbine. He indicated that outlet structure had no obvious impact on the propagation mode and speed of rotating detonation waves and pressure gain of the RDC. Considering the application of RDCs in gas turbines, [PERSON] et al. [18; 19] experimentally analyzed the effect of a turbine guide vane on the propagation characteristic of a hydrogen-air rotating detonation wave and found that the addition of a turbine guide vane increased detonation wave speed and narrowed the stable operation scope. However, the detailed information related to RDC exhaust was not shown in their research results. [PERSON] et al. [20] measured the propulsive performance of RDCs with four types of outlet configurations (even bluff body, recessed bluff body, open aerospike, and choked aerospike). From their test results, it can be observed that outlet configurations played a significant effect on thrust and specific impulse of the RDC and choked aerospike outlet behaved with better performance. [PERSON] et al. [21; 22] experimentally tested the effect of RDC unsteady exhaust flow on the axial turbine performance in a T63 gas turbine engine. They mainly observed that RDC unsteadiness did not significantly affect turbine efficiency, while they did not discuss the response of the turbine to the RDC. Using particle image velocimetry (PIV) measurement, [PERSON] et al. [23] investigated the velocity field distribution at the outlet of the RDC and indicated that the exhaust velocity profiles were better at smaller outlet nozzle diameter and higher pressure conditions. [PERSON] et al. [24] explored the effects of different outlet structures on RDC performance and operation. From their experimental results, it was clearly seen that the outlet played an important role in controlling the detonation wave speed and pressure gain performance, which was different from that of [PERSON] [17].