724 research outputs found
Double-distribution-function discrete Boltzmann model for combustion
A 2-dimensional discrete Boltzmann model for combustion is presented.
Mathematically, the model is composed of two coupled discrete Boltzmann
equations for two species and a phenomenological equation for chemical reaction
process. Physically, the model is equivalent to a reactive Navier-Stokes model
supplemented by a coarse-grained model for the thermodynamic nonequilibrium
behaviours. This model adopts 16 discrete velocities. It works for both
subsonic and supersonic combustion phenomena with flexible specific heat ratio.
To discuss the physical accuracy of the coarse-grained model for nonequilibrium
behaviours, three other discrete velocity models are used for comparisons.
Numerical results are compared with analytical solutions based on both the
first-order and second-order truncations of the distribution function. It is
confirmed that the physical accuracy increases with the increasing moment
relations needed by nonequlibrium manifestations. Furthermore, compared with
the single distribution function model, this model can simulate more details of
combustion.Comment: Accepted for publication in Combustion and Flam
Multiple-Relaxation-Time Lattice Boltzmann Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number
A new multiple-relaxation-time lattice Boltzmann scheme for compressible
flows with arbitrary specific heat ratio and Prandtl number is presented. In
the new scheme, which is based on a two-dimensional 16-discrete-velocity model,
the moment space and the corresponding transformation matrix are constructed
according to the seven-moment relations associated with the local equilibrium
distribution function. In the continuum limit, the model recovers the
compressible Navier-Stokes equations with flexible specific-heat ratio and
Prandtl number. Numerical experiments show that compressible flows with strong
shocks can be simulated by the present model up to Mach numbers .Comment: Accepted for publication in EP
Prandtl number effects in MRT Lattice Boltzmann models for shocked and unshocked compressible fluids
For compressible fluids under shock wave reaction, we have proposed two
Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) models [F. Chen, et al,
EPL \textbf{90} (2010) 54003; Phys. Lett. A \textbf{375} (2011) 2129.]. In this
paper, we construct a new MRT Lattice Boltzmann model which is not only for the
shocked compressible fluids, but also for the unshocked compressible fluids. To
make the model work for unshocked compressible fluids, a key step is to modify
the collision operators of energy flux so that the viscous coefficient in
momentum equation is consistent with that in energy equation even in the
unshocked system. The unnecessity of the modification for systems under strong
shock is analyzed. The model is validated by some well-known benchmark tests,
including (i) thermal Couette flow, (ii) Riemann problem, (iii)
Richtmyer-Meshkov instability. The first system is unshocked and the latter two
are shocked. In all the three systems, the Prandtl numbers effects are checked.
Satisfying agreements are obtained between new model results and analytical
ones or other numerical results.Comment: 17 pages, 8 figure
Multiple-relaxation-time lattice Boltzmann kinetic model for combustion
To probe both the Hydrodynamic Non-Equilibrium (HNE) and Thermodynamic
Non-Equilibrium (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.Comment: 32 pages, 11 figure
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