Detonation Propagation and Quenching in Gas-Particle Mixtures

Propagation and quenching of curved detonation waves in particle-laden mixtures were investigated analytically and numerically. The present analysis employs the square wave model and quasi-steady state assumption. An analytical expression describing the combined effects of heat and momentum losses due to the interaction between the particle and gas phases, as well as the wave curvature on detonation velocity, was obtained. Detonation quenching and multiple detonation regimes were examined. Numerical simulation of the detonation wave structure was also conducted. The results showed that the particle heat loss, momentum loss and wave curvature considerably reduce the detonation speed and cause detonation quenching. It is also shown that, for fixed particle volume fractions, small particles cause a larger heat loss from the gas phase and result in a lower detonation velocity and narrow detonation limit. Introduction Recent interest in the development of high speed propulsion systems such as the pulse detonation engine and the ram-accelerator has led to renewed interest in the study of the ^Research Staff, Department of Mechanical and Aerospace Engineering. tRobert H. Goddard Professor, Department of Mechanical and Aerospace Engineering. Fellow, AIAA. Copyright © 2001 by the authors. Published by the American Institute of Aeronatics and Astronautics, Inc., with permission. fundamental mechanisms of detonation initiation, propagation, and quenching. Studies of detonation propagation in tube experiments were complicated by turbulent transition, near wall inhomogeneity, tube resistance, wall heat loss and phase interactions. Earlier experimental and theoretical investigations on the effects of the tube resistance and viscous boundary layer were studied by Shchelkin, Fay and Dabora et al. The results showed that wall resistance results in a lower wave speeds than the Chapmann-Jouguet (CJ) detonation velocity. In addition, based on the Shchelkin's spin instability criterion, Dabora et al. defined an empirical detonation quenching limit for mixture concentrations. Systematic investigations on the tube friction and wall inhomogeneity were later conducted by Lee, Knystautas and Freiman, and Lyamin and Pinaev. The results showed that there exist multiple propagation regimes, the quasi-detonation regime and the low velocity detonation regime. The first attempt to interpret the reduction of the wave speed and the existence of multiple detonation regimes was conducted by Zeldovich et al. by introducing the momentum and heat losses due to wall friction and cooling with a quasi-one-dimensional formulation. The numerical results with one-step chemistry successfully demonstrated the reduction of detonation velocity and the existence of the detonation limit. In addition, it was also shown that compared to wall friction, wall heat loss only exerts weak influence on the detonation velocity near the detonation limit. By extending 1 American Institute of Aeronautics and Astronautics (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. this model to detailed chemistry, Kusharin et al. numerically calculated the detonation velocity of H2/CO/CO2 mixture in the detonation tube and showed good agreement with the experimental data. Recently, by employing the Zeldovich model, Brailovsky and Sivashinsky numerically identified the high velocity sub-CJ quasi-detonation and the supersonic choking regimes. The dynamics of detonation waves in unconfined flow fields was theoretically analyzed by Klein and Stewart and He and Clavin. Their results showed that wave curvature can also dramatically reduce the wave speed and even quench the detonation wave. For various practical reasons, liquid fuels are preferred in pulse detonation engines. The employment of liquid fuel substantially enriches the detonation phenomena due to momentum and energy exchange between the two phases. Particularly, heat loss from the gas mixture to the droplets may have a profound effect in affecting the detonation velocity. In addition, most of the detonation waves in practical detonation engine are curved, particularly during the initiation process. Therefore, the coupling between the curvature effect and the loss mechanisms in two-phase media may aggravate the reduction of detonation speed. Detonation propagation in gas mixtures in the presence of evaporating and/or inert particles were numerically studied by Fan and Sichel, Gelfand et al.,12 Uphoef, Hanel and Roth13 and Eidelman and Yang. The results demonstrated significant effect of particle drag on the detonation speed and initiation energy. Recently, numerical simulations of the multi-dimensional diesel-air and kerosene-liquid oxygen were conducted respectively by Smirnov et al. and Navaz and Berg. However, emphasis and theoretical description of the combined effects of particle drag, heat loss and curvature on detonation propagation have not been made. The purpose of the present work is to analytically and numerically study the above effects on the detonation velocity and quenching limit in particle-laden mixtures, using the quasi-one-dimensional formulation. In the next section the governing equations are formulated, which is followed by asymptotic and numerical analyses of these effects on the detonation velocity. Governing Equations In the coordinate of the moving front with curvature Rc and speed £>, the one-dimensional governing equations for mass, momentum, energy and species conservations for a particle-laden mixture can be written as