Multiple-relaxation-time lattice Boltzmann kinetic model for combustion

Abstract

To probe both the Hydrodynamic Non-Equilibrium (HNE) and Thermodynamic NonEquilibrium (TNE) in the combustion process, a two-dimensional Multiple-Relaxation-Time (MRT) version of Lattice Boltzmann Kinetic Model(LBKM) for combustion phenomena is presented. The chemical energy released in the progress of combustion is dynamically coupled into the system by adding a chemical term to the LB kinetic equation. Beside describing the evolutions of the conserved quantities, the density, momentum and energy, which are what the Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained description on the evolutions of some non-conserved quantities. The current model works for both subsonic and supersonic flows with or without chemical reaction. In this model both the specific-heat ratio and the Prandtl number are flexible, the TNE effects are naturally presented in each simulation step. The model is verified and validated via well-known benchmark tests. As an initial application, various non-equilibrium behaviours, including the complex interplays between various HNEs, between various TNEs and between the HNE and TNE, around the detonation wave in the unsteady and steady one-dimensional detonation processes are preliminarily probed. It is found that the system viscosity (or heat conductivity) decreases the local TNE, but increase the global TNE around the detonation wave, that even locally, the system viscosity (or heat conductivity) results in two kinds of competing trends, to increase and to decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses.

Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows

“…Generally, the nonequilibrium state is too complex to be described. Fortunately, the DBM provides an effective tool to investigate the nonequilibrium manifestations [10,11,[46][47][48][49]. It is noteworthy that f (5)- (7) according to the conservation of mass, momentum and energy.…”

“…7 (not shown here). Furthermore, the nonequilibrium quantities are not susceptible to numerical errors in the discretization and evolution of the DBM [47,49] differences are 4% and 13% , respectively. This is satisfactory.…”

“…In addition to a better characterization of nonequilibrium flow state, the study on the TNE is helpful for understanding the nonlinear constitutive relation which significantly influences the physical accuracy of the hydrodynamic model. To this end, we resort to a variant of the traditional LBM which is named the discrete Boltzmann model (DBM) [10,11,[46][47][48][49][50]. The DBM has been used to investigate various complex flows.…”

Diameter Effect on the Propagation of Curved Detonation Waves in Micro‐Channel Charges Within a Strong Confinement

“…When x f = d/2, q = 0, f = p/2, and y f ' = 0 which, when combined with Eqs. (7), (8), and (9), yield:…”

“…Tran [6] et al found that a detonation wave is closely related to charge diameter and density through experiment and the confinement material can affect the detonation velocity and shock front curvature. In recent years a discrete Boltzmann model, or lattice Boltzmann kinetic model, was proposed to investigate the nonequilibrium effects in combustion systems, especially in micro-channel explosion systems [7][8][9][10]. Further, much numerical simulation work has been done on detonation wave propagation to study the diameter effect.…”