## 1 Introduction  
Detonation is a supersonic combustion process relating to pressure gain from reactants to products and has lower emission of the nitrogen oxides (NO\({}_{\mathrm{x}}\)), which becomes the major motivation for researchers to actively investigate the detonation-based propulsion device [1]. Detonation theoretically consists of the leading shock wave and a reaction zone compactly following it [2, 3]. Compared with deflagration, detonation has faster reactive rate, lower entropy production and nitrogen oxides (NO\({}_{\mathrm{x}}\)) emission [4, 5]. Besides, the method to optimize the deflagration-based combistor seems to encounter its limit in recent years. In view of the above considerations, developing detonation-based combistor is a reasonable approach to promote propulsion device entering a new stage. In the past 20 years, a considerable number of investigations were carried out on detonation-based combistor using different formations of detonation wave. The main detonation-based engines include rotating detonation engine (RDE) [6, 7, 8], pulsed detonation engine (PDE) [9, 10, 11] and standing oblique detonation engine (ODE) [12, 13]. In recent years, PDE and RDE is more competitive compared to ODE and capture more researchers' attention consequently. Regarded as a potential pressure gain propulsive device, PDE has been deeply investigated in the past few decades and achieve a lot of promising progress. However, the expectation of using PDE to replace traditional deflagration-based engine has to be diminished due to the complex operational process of PDE. The working process of PDE refers to periodic gas inflation,repeating ignition, and exhaustion, which results in its working frequency is limited on the order of approximately hundreds of Hertz. On the contrary to PDE, the reactant in RDE is injected into the combustor continuously and this can negate the disadvantages of complicated working process such as PDE. After once ignition, the rotating detonation wave (RDW) propagates ceaselessly in rotating detonation combustor (RDC) consuming fresh reactant injected from the head-end inlet simultaneously. Therefore, the working frequency of RDE reaches on the order of thousands of Hertz far higher than PDE. Such high frequency and continuous propagation of detonation wave guarantee the stable thrust output on the outlet. Even though RDE avoids the gas inflation and exhaustion process, proper injection condition and inlet structure are key factors of stable propagation for RDW. The formation and stable propagation of RDW are strongly dependent on the injection condition. Local reactant injected from the plenum will be blocked by RDW due to its high pressure behind the leading shock wave [14; 15; 16]. The reactant intake depends on the local pressure in combustor and the inflow cannot recover until RDW skims over. If the blocking time of reactant is too long, RDW might extinguish in the next period due to lack of enough fresh reactant supporting the energy for RDW. To avoid the extinguishment phenomenon occurring in combustor, high injection pressure is preferred because it can recover reactant intake earlier and provide fresh reactant in time for RDW. However, over high injection pressure will increase the injection velocity of reactant, which may cause the RDW transform into standing detonation wave [17]. The injection scheme of RDC can be divided into two types, namely premixed injection, and non-premixed injection. To gain stable and well-organized RDW, the premixed injection scheme is employed in most of numerical simulations. Nevertheless, the premixed injection scheme cannot describe and capture the mixing process of fuel and oxidizer during the operation of RDC, which deviates from the real process of the experiment. Besides, the premixed injection scheme has the risk of flashback because of the high activity of premixed reactant in inlet holes or slot. On this account, the non-premixed injection scheme is applied to the majority of experiments.