Combustion mode and wave multiplicity in rotating detonative combustion with separate reactant injection
Introduction
The efficiency of detonation engine cycles can be up to 19% higher than that of engine cycles based on deflagrative combustion [1]. Compared to pulse detonation engines, the Rotating Detonation Engine (RDE) concept has numerous advantages, including its compact configuration, the continuous existence of Rotating Detonation Waves (RDW's) and avoidance of cyclic deflagration-to-detonation transitions, high frequency and high specific power [1,2]. The fundamental physics of Rotating Detonation Combustion (RDC) relevant to RDE configurations has been studied through theoretical analysis, experimental measurements and numerical simulations, and the latest research progress is summarized in several detailed reviews, for instance, by Anand and Gutmark [1], Wolanski [2], Kailasanath [3], Lu and Braun [4], and Zhou et al. [5]. Although the first successful RDE operation [6] used premixed propellant injection, separate injection of fuel and oxidant is more desirable due to the inherent safety advantages [1].
RDC with separate reactant injection has been achieved with varying degrees of success for different combustor configurations, fuel types and operating conditions [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. However, there are still significant challenges that must be tackled before such RDE's can be commercialized. Chief among these challenges is the need to rapidly mix the propellant in the fuel refill zone of the combustor to within detonable limits ahead of the encroaching, highly unsteady RDW [1]. In practical RDE's with non-premixed reactant supply, it is possible that detonation waves could first be established in a homogeneous premixture with the expectation that stable detonation would then be sustained in the heterogeneously mixed fuel and oxidant. However, the thermal and/or compositional non-uniformity in the fuel refill zone are likely to cause a range of unstable propagation phenomena, including quenching and initiation of multiple, new detonation waves [8,17]. Moreover, the quality of reactant mixing can also result in various RDC modes even in the same run of the RDE, i.e., under stoichiometric and off-stoichiometric conditions, or under locally premixed, non-premixed or partially premixed conditions. These phenomena are only partially understood due to the difficulty of both experimental observation and numerical simulation. Fundamental questions yet to be answered include: Can RDC proceed only through locally premixed mixtures? What fractions of the fuel are burnt by detonative and deflagrative regions of the combustor? Are locally fuel-lean or fuel-rich conditions more favorable for RDC?
Another aspect of RDC dynamics deserving of research focus is bifurcation and multiplicity of RDW's, which has been experimentally observed, and is found to be sensitive to mixture reactivity, propellant injector configuration and manifold stagnation pressure (or mass flow rate) [1]. A series of numerical simulations have been conducted to clarify the underlying mechanisms. For instance, Wang et al. [18], [19], [20] demonstrate that new RDW's are generated from shock waves surviving from the collisions between two counter-rotating detonative waves and also the interactions between the detonation and oppositely travelling shock waves. In the simulations of H2/air RDEs by Schwer and Kailasanath [21], the new detonation wave is caused by the ignition of the unburned reactant compressed by the shock waves, which are reflected from the nozzle exit. Through modeling H2/air RDE's with detailed chemistry and real injection nozzles, Sun et al. [22] highlight that the combustion along the contact interface between the fresh premixture and the burnt gas from the last RDW cycle may interact with reflected shocks to induce a new detonation wave. Multiple (up to four) RDW's of CH4/air mixtures were seen in the experimental and numerical work by Frovol et al. [23]. The initiation of new RDW's is attributed to the interactions of shocks reflected from the downstream outer nozzle and the upstream refilling gas close to the head end.
Moreover, Deng et al. explore the feasibility of mode control (i.e., number and direction of RDW's) in non-premixed H2/air RDC, through changing oxidizer mass flow rate, chamber length and exit blockage ratio [15]. They find that increased propellant reactivity leads to pre-combustion ahead of the detonation front, which may develop into a new detonation via shock wave amplification, known as the coherent energy release mechanism. More recently, Zhao and Zhang predict RDW multiplicity for an injection configuration consisting of discrete premixed jets of hydrogen and air separated by wall sections [24], and the results indicate that new RDW's evolve from chemically reactive hot spots that are enhanced by sweeping shocks. This process is observed to always follow an extended period of chaotic RDW propagation. However, the above-mentioned simulation studies, except [15], are focused on RDC in premixed propellants, and therefore bifurcation and wave multiplicity under practically relevant, non-premixed propellent injection conditions is still in need of thorough investigations.
The aims of the present paper are to study the combustion modes and mechanisms for detonation wave multiplicity in a simplified model RDE configuration with separate injection of fuel and oxidizer. A series of two-dimensional CFD simulations will be conducted, with varying global equivalence ratios and mixing levels. The effects of variation in inlet pressure and temperature are investigated, along with exploration of the sensitivity of RDC modes to the inlet configuration (specifically, the number of injection ports). In Sections 2 and 3 the computational method and the physical model are introduced. Results are presented in Section 4 and conclusions are in Section 5.
Section snippets
Governing equation
The governing equations of mass, momentum, energy, and species mass fraction, together with the ideal gas equation of state, are solved. They are written asHere t is time, is divergence operator, is the density, is the velocity vector, is the pressure, is the mass fraction of m-th species and is the total species number. Only () equations are solved
Physical model
Figure 1 shows the two-dimensional rectangular domain which is used here as a simplified model of an annular RDE combustor. Because the annular RDE chamber width (typically several millimeters) is very small compared to its diameter, the computational domain of RDE can generally be “unrolled” into a two-dimensional one due to the limited radial variation within the flow field. It permits a wide range of conditions to be modeled with affordable computational effort. While it neglects
Combustion mode
Figure 2 shows instantaneous mixture fraction, flame index (FI) and heat release rate (HRR) for Case 1 when the RDW runs stably. The corresponding temperature distribution is already shown in Fig. 1. Note that the mixture fraction is computed from a transport equation which is similar to the species mass fraction equation (i.e., Eq. (4)) without the chemical source term. Similar to premixed RDC studies [30,43,45,46], the present computational modeling captures the main flow structures including
Conclusions
Simulations of two-dimensional rotating denative combustion with separately injected hydrogen and air are performed using detailed chemical kinetics in this work. Four cases are investigated with various fuel and oxidant compositions and the emphasis is laid on their influences on combustion mode and detonation wave bifurcation.
The results show that the reactant in the refill zone is highly imhomogeneous due to the insufficient mixing before the detonation wave arrives. Also, fuel-rich and
Declaration of Competing Interest
None.
Acknowledgment
This work used the computational resources in National Supercomputing Center, Singapore (https://www.nscc.sg/), and is partially supported by USyd–NUS Partnership Collaboration Awards.
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