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Register a new userFurther investigations on the interface instability between fresh injections and burnt products in 2-D rotating detonation
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Instabilities in rotating detonation are concerned because of their potential influence on the stability of operation. Previous studies on instability of 2-D rotating detonation mainly cared about the one of the contact discontinuity originated from the conjunction of the detonation and oblique shock. Hishida et al. first found the rippled structure existed in the interface between fresh injections and burnt product from the previous cycle (Shock Waves 19, 2009), and a mechanism of Kelvin-Helmholtz instability was suggested as well. Similar structures were observed as well in simulations by current authors, where a fifth-order WENO-type scheme with improved resolution and 7-species-and-8-reaction chemical model were used. In order to achieve a deep understanding on the flow mechanism, more careful simulations are carried out by using three grids with increasing resolution. The results show that besides the previously-mentioned Kelvin-Helmholtz instability, there are two other mechanisms which take effect in the interface instability, i.e., the effect of baroclinic torque and Rayleigh-Taylor instability. Occurrence conditions for two instabilities are checked and testified. Especially, the spike- and bubble-like structures are observed at the interface, which show appearances different from canonical structures by Kelvin-Helmholtz instability.
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In studies on instabilities of flowfield in rotating detonation, one of the most common concerns is the instability at the slip line originating from the conjunction of the detonation wave and oblique shock. Using Euler equations associated with 7-species-and-8-reaction finite-rate chemical reaction model of hydrogen/air mixtures, further studies are performed to simulate the 2-D rotating detonation, and the flow mechanism of instability at the slip line is investigated in depth. The results show that the distinct wake profile exists at the slip line, which is different from the typical mixing layer. Analysis indicates that the generation of wake is caused by the transition shock between the detonation wave and oblique shock. Because of the wake profile, the vorticity distribution therein appears in a double-layer layout, and different evolution exist in different vorticity layers. Based on the velocity profile across the slip line, the analysis by the linear stability theory is made, and two unstable modes which have different shape profiles and phase velocities are found. Discrete Fourier transformation is utilized to analyze the numerical results, and similar shape profiles are obtained. A general coincidence in velocity of vortex movement is also attained between the theoretical predictions and simulations. Investigations show that the wake instability is responsible for the unstable mechanism, and corresponding unstable structures differs from the canonical ones in typical mixing layers.
The present work examines the role of instability and diffusive phenomena in controlling the limits of detonations subject to lateral strain rates. Experiments were conducted in hydrocarbon-oxygen mixtures with varying levels of cellular instability. These detonations were propagated in channels with exponentially enlarging cross-sections, following the recent works of Radulescu & Borzou (2018) and Xiao & Radulescu (2020). Steady detonation waves were obtained at the macro-scale, with the near-limit reaction zone structures characterized by significant unreacted gas pockets. The turbulent flame burning velocity of these pockets was evaluated to be 30 m/s to 70 m/s, which is larger than the theoretical laminar value by a factor of 2 to 7. For all the mixtures tested, the characteristic $D-K$ relationships, relating the detonation mean propagation speed with lateral flow divergence, were obtained directly from experiments and as well from the generalized ZND model with lateral strain rates using detailed chemical kinetics. The results showed that the degree of departure between experiments and the theoretical predictions increases significantly with the detonation instability level. As compared to the laminar ZND wave, the more unstable detonations are much more detonable than the more stable detonations, with substantially larger limiting divergence rates and maximum velocity deficits. Such enhanced detonability with detonation instability can be manifested in the significantly enhanced global rates of energy release with the notably suppressed thermal character of ignition for the more unstable detonations. This globally enhanced burning mechanism is found to be realized by the intensified auto-ignition assisted by the turbulent diffusive burning of the unreacted gas pockets, substantially shortening the characteristic reaction zone lengths.
We present an investigation of rapidly rotating (small Rossby number $Roll 1$) and stratified turbulence where the stratification strength is varied from weak (large Froude number $Frgg1$) to strong ($Frll1$). The investigation is set in the context of a reduced model derived from the Boussinesq equations that efficiently retains anisotropic inertia-gravity waves with order-one frequencies and highlights a regime of wave-eddy interactions. Numerical simulations of the reduced model are performed where energy is injected by a stochastic forcing of vertical velocity, which forces wave modes only. The simulations reveal two regimes characterized by the presence of well-formed, persistent and thin turbulent layers of locally-weakened stratification at small Froude numbers, and by the absence of layers at large Froude numbers. Both regimes are characterized by a large-scale barotropic dipole enclosed by small-scale turbulence. When the Reynolds number is not too large a direct cascade of barotropic kinetic energy is observed, leading to total energy equilibration. We examine net energy exchanges that occur through vortex stretching and vertical buoyancy flux and diagnose the horizontal scales active in these exchanges. We find that the baroclinic motions inject energy directly to the largest scales of the barotropic mode, implying that the large-scale barotropic dipole is not the end result of an inverse cascade within the barotropic mode.
A quasi-one-dimensional analytic model is proposed for the internal fluid of rotating detonation combustors (RDCs). This model uses the shock-tube model that constrains the flow to have only a longitudinal component, while admitting the propagation of the detonation wave in the azimuthal direction. The proposed model is able to compute the thruster performance and two-dimensional distributions of gas properties. The calculation process of the model excludes iterative calculation or space discretization. The case calculations of the hydrogen-air RDC and the ethylene-oxygen RDC are conducted, and the results calculated by the analytic model are compared with those simulated by computational fluid dynamics (CFD). Good agreement has been observed between the results obtained with the proposed model and CFD, in terms of both of the qualitative and quantitative comparisons. The proposed model is simple and fast, and also maintains the fundamental characteristics of RDCs.
The present study addresses the reaction zone structure and burning mechanism of unstable detonations. Experiments investigated mainly two-dimensional methane-oxygen cellular detonations in a thin channel geometry. The sufficiently high temporal resolution permitted to determine the PDF of the shock distribution, a power-law with an exponent of -3, and the burning rate of unreacted pockets from their edges - through surface turbulent flames with a speed approximately 3-7 times larger than the laminar one at the local conditions. Numerical simulations were performed using a novel Large Eddy Simulation method where the reactions due to both auto-ignition and turbulent transport and treated exactly at the sub-grid scale in a reaction-diffusion formulation. The model is an extension of Kerstein & Menons Linear Eddy Model for Large Eddy Simulation to treat flows with shock waves and rapid gasdynamic transients. The two-dimensional simulations recovered well the amplification of the laminar flame speed owing to the turbulence generated mainly by the shear layers originating from the triple points and subsequent Richtmyer-Meshkov instability associated with the internal pressure waves. The simulations clarified how the level of turbulence generated controlled the burning rate of the pockets, the hydrodynamic thickness of the wave, the cellular structure and its distribution. Three-dimensional simulations were found in general good agreement with the two-dimensional ones, in that the sub-grid scale model captured the ensuing turbulent burning once the scales associated with the cellular dynamics, where turbulent kinetic energy is injected, are well resolved.
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