DSMC Modeling of the Detonation Wave Structure in Narrow Channels

Abstract

RANSITIONAL and near-continuum flows are important for numerous promising applications, in particular, in the development of microand nanoelectromechanical systems (MEMS and NEMS) and low-thrust engines for aerospace applications. A more profound understanding of the nature of flows in such engineering systems is an urgent problem of today’s fluid mechanics and also molecular physics [1, 2]. A principally novel aspect of this field is the development of micro-devices capable of performing mechanical work with the use of chemically induced heat release. As the efficiency of conventional devices, such as internal combustion engines, rapidly decreases with a decrease in their size because of higher heat loss, a reasonable direction of MEMS and NEMS evolution seems to be the use of detonation waves at the microscopic scale for accelerating combustion processes and increasing the heat-release rate [3, 4]. This requires better understanding of physical and chemical processes associated with propagation of detonation waves at small scales. There is a significant current effort in this direction; in particular, the beginning of activities aimed at creating a microscopic test facility (shock tube 10 μm in diameter) was announced [4]. Some recent publications also deal with microdetonics – processes that occur during detonation of microscopic amounts of explosives. Interesting results were obtained in experimental research of propagation of detonation waves in capillary tubes (V.I. Manzhalei, Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 1992-1999); in particular, Manzhalei found that detonation waves under such conditions can propagate with velocities that are only 0.45-0.6 of the Chapman-Jouguet velocity. It should be noted that propagation of detonation waves in thin capillary tubes is important for explosion safety problems. Numerical simulations can become a really indispensable tool for solving problems of detonation at small scales. There are two different approaches, kinetic and continuum, to the gas flow modeling. In the first approach, the gas is considered at a level of the molecular velocity distribution function which can be determined as the solution of the kinetic Boltzmann equation; in the second approach, the gas or liquid is presented as a continuum whose motion is determined by the laws of conservation of mass, momentum, and energy. Flows whose geometric scales are typical of MEMS are near-continuum or transitional, which necessitates allowance for rarefaction effects, because the mean free path of molecules λ cannot be considered as negligibly small, as compared with the characteristic length scale L of the flow. Though the kinetic approach can be used to describe gas flows in all regimes, its application in practice for modeling a rather dense gas is impossible because of tremendous computational resources needed for that. The most effective numerical method for solving the Boltzmann equation is currently the Direct Simulation Monte Carlo (DSMC) method [5]. It allows computations of steady flows with Knudsen numbers Kn=λ /L=0.001 for twodimensional problems and Kn=0.005 for three-dimensional problems, i.e., up to the continuum flow regime [6, 7]. The DSMC method is well suited for modeling flows with nonequilibrium chemical reactions. Collision models of various chemical processes (vibrational and electron excitation and relaxation, dissociation, recombination, ionization, etc.) can be implemented directly into the collision algorithm. Nevertheless, the DSMC method can be hardly applied to compute unsteady flows because of considerable statistical fluctuations arising if averaging over a sufficiently large time period cannot be performed, which is the case with unsteady flows. Solving such problems is impossible without parallel computational technologies and without using advanced multiprocessor computers. The continuum approach is usually much less expensive, which is a strong argument for using the latter. It is applicable, however, for low Knudsen numbers only. For Knudsen numbers Kn ~ 10 -2 and higher, the continuum approach has