Lattice Boltzmann model for combustion and detonation

TL;DR

This paper introduces a lattice Boltzmann model for simulating combustion and detonation, coupling fluid dynamics with chemical reactions, validated through benchmark tests, and used to analyze non-equilibrium effects in detonation phenomena.

Contribution

The paper develops a novel lattice Boltzmann model that integrates chemical reactions with fluid flow using operator-splitting, enabling detailed study of non-equilibrium effects in detonation.

Findings

System nearly in thermodynamic equilibrium at von Neumann peak

Deviations from equilibrium occur on either side of the peak

Chemical energy release causes thermal expansion and non-equilibrium deviations

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, defined in this paper, one can understand more on the macroscopic effects of the system due to the deviation from its thermodynamic equilibrium.