Reacting Flows

To that end, we formulate a system of kinetic equations for a multicomponent fluid and couple it with another system of kinetic equations for compressible hydrodynamics. The systems being coupled through pressure, momentum, composition and energy, are free of passive scalars and hence thermodynamically consistent. With a focus on practical applications, we develop boundary conditions and optimizations for efficiency and numerical stability. Apart from the LBM, we also explore the feasibility of the Particle-on-Demand (PonD) method, for compressible high Mach reactive flows.

The resulting models are useful for simulation of biological flows such as breathing; combustion in manufacturing processes, energy and transport; electrochemical flows in fuel cells; thermoacoustics etc.

Importance of compressible mixtures is hard to overestimate because they are a prerequisite for combustion applications. However, incorporating the basic mechanism of multicomponent diffusion in gases, the Stefan–Maxwell diffusion, remains an essentially unsolved problem in the LBM context, in spite of the fact that the Stefan–Maxwell diffusion is itself a derivative of Boltzmann's kinetic theory. It is worth recalling that the Stefan–Maxwell diffusion mechanism is well recognized as a fundamental feature of gas mixtures, supported by experiment and molecular dynamics simulations. The Stefan–Maxwell model, accounts for binary interaction between each of the species pairs through pairwise diffusion coefficients and can lead to counter-intuitive effects such as uphill diffusion when a component in a ternary mixture moves from the lower to higher concentration region. We proposed a lattice Boltzmann framework for multicomponent mixtures of ideal gases with a more realistic number of coupled lattice Boltzmann equations. A new LBM system for the Stefan–Maxwell diffusion and barodiffusion comprising M lattice Boltzmann equations was proposed. Then a mean-field description of the mixture momentum and energy using the two-population setting was also presented.