Abstract
In this paper we present a lattice Boltzmann model for combustion and detonation. In this model the fluid behavior is described by a finite-difference lattice Boltzmann model by Gan et al. [Physica A, 2008, 387: 1721]. The chemical reaction is described by the Lee-Tarver model [Phys. Fluids, 1980, 23: 2362]. The reaction heat is naturally coupled with the flow behavior. Due to the separation of time scales in the chemical and thermodynamic processes, a key technique for a successful simulation is to use the operator-splitting scheme. The new model is verified and validated by well-known benchmark tests. As a specific application of the new model, we studied the simple steady detonation phenomenon. To show the merit of LB model over the traditional ones, we focus on the reaction zone to study the non-equilibrium effects. It is interesting to find that, at the von Neumann peak, the system is nearly in its thermodynamic equilibrium. At the two sides of the von Neumann peak, the system deviates from its equilibrium in opposite directions. In the front of von Neumann peak, due to the strong compression from the reaction product behind the von Neumann peak, the system experiences a sudden deviation from thermodynamic equilibrium. Behind the von Neumann peak, the release of chemical energy results in thermal expansion of the matter within the reaction zone, which drives the system to deviate the thermodynamic equilibrium in the opposite direction. From the deviation from thermodynamic equilibrium, Δ m *, defined in this paper, one can understand more on the macroscopic effects of the system due to the deviation from its thermodynamic equilibrium.
Highlights
In recent two decades the Lattice Boltzmann (LB) method has been becoming a powerful tool for simulating complex systems [1,2,3,4,5]
In previous LB studies [57,58,59,60], it was assumed that the chemical reaction does not affect the flow fields, which is a lethal flaw for simulating detonation and most of combustion problems
The λ-V /V0 phase diagram for the viscous detonation obtained by our LB model is showed in Figure 8(b), see the solid circles, where the line is for the integral curve solved by Mathematica 8.0
Summary
In recent two decades the Lattice Boltzmann (LB) method has been becoming a powerful tool for simulating complex systems [1,2,3,4,5]. The Zeldovich-von Neumann-Doering (ZND) model [38,39,40] presented in 1940s treats detonation front as a shock wave in which no chemical reaction occurs. Lee et al [60] proposed a quasi-incompressible model for the laminar jet diffusion flame All those LB models mentioned above are for nearly incompressible systems which are not appropriate for detonation phenomena. They assumed that the chemical reaction does not affect the flow fields, which is a lethal flaw for simulating detonation and most of combustion problems. A novel model for combustion and detonation is proposed It couples the Finite-Difference (FD) LB model by Gan, Xu, Zhang et al [19] for fluid with the Lee-Tarver [61] model for chemical reaction.
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