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

A Lattice Boltzmann model for diffusion of binary gas mixtures

This thesis describes the development of a Lattice Boltzmann (LB) model for a binary gas mixture. Specifically, channel flow driven by a density gradient with diffusion slip occurring at the wall is studied in depth. The first part of this thesis sets the foundation for the multi-component model used in the subsequent chapters. Commonly used single component LB methods use a non-physical equation of state, in which the relationship between pressure and density varies according to the scaling used. This is fundamentally unsuitable for extension to multi-component systems containing gases of differing molecular masses that are modelled with the ideal gas equation of state. Also, existing methods for implementing boundary conditions are unsuitable for extending to novel boundary conditions, such as diffusion slip. Therefore, a new single component LB derivation and a new method for implementing boundary conditions are developed, and validated against Poiseuille flow. However, including a physical equation of state reduces stability and time accuracy, leading to longer computational times, compared with 'incompressible' LB methods. The new method of analysing LB boundary conditions successfully explains observations from other commonly used schemes, such as the slip velocity associated with 'bounce-back'. The new model developed for multi-component gases avoids the pitfalls of some other LB models, a single computational grid is shared by all the species and the diffusivity is independent of the viscosity. The Navier-Stokes equation for the mixture and the Stefan-Maxwell diffusion equation are both recovered by the model. However, the species momentum equations are not recovered correctly and this can lead to instability. Diffusion slip, the non-zero velocity of a gas mixture at a wall parallel to a concentration gradient, is successfully modelled and validated against a simple one-dimensional model for channel flow. To increase the accuracy of the scheme a second order numerical implementation is needed. This can be achieved using a variable transformation method which does not result in an increase in computational time. Simulations were carried out on hydrogen and water diffusion through a narrow channel, with varying total pressure and concentration gradients. For a given value of the species mass flux ratio, the total pressure gradient was dependent on the species concentration gradients. These results may be applicable to fuel cells where the species mass flux ratio is determined by a chemical reaction and the species have opposing velocities. In this case the total pressure gradient is low and the cross-channel average mass flux of hydrogen is independent of the channel width. Finally, solutions for a binary Stefan tube problem were investigated, in which the boundary at one end of a channel is permeable to hydrogen but not water. The water has no total mass flux along the channel but circulates due to the slip velocity at the wall. The cross-channel average mass flux of the hydrogen along the channel increases with larger channel widths. A fuel cell using a mixture of gases, one being inert, will experience similar circulation phenomena and, importantly, the width of the pores will affect performance. This thesis essentially proves the viability of LB models to simulate multi-component gases with diffusion slip boundaries, and identifies the many areas in which improvements could be made.This work was supported by the EPSRC and ROlls ROyce Fuel Cells Ltd. (Grant Number RG47435

Entropic lattice Boltzmann method for simulation of binary mixtures

A new kinetic model for binary mixtures and its lattice Boltzmann (LB) discretization is formulated. In the hydrodynamic limit, the model recovers the Navier-Stokes and the Stefan-Maxwell binary diffusion equations, satisfies the indifferentiability principle, and is thermodynamically consistent. The present model is able to simulate mixtures with different Schmidt numbers and with a large molecular weight ratio of the components