Lattice Boltzmann Simulation Of Thermal Fluid Flow

This thesis mainly covers two parts:first,the fundamental principles of lattice Boltzmann method and the classification of thermal lattice Boltzmann models and thermal boundary treatments as well;second,numerical simulations of lattice Boltzmann method for thermal fluid flows.1 Lattice Boltzmann MethodBoltzmann-BGK equation is written as:The macroscopic density and velocity of the fluid is denoted as:First, the equilibrium distribution function is expanded as Taylor series of velocity up to the second order:And require the selected discretized velocity satisfying the following numerical integrity:In whichωi and ci are weights and integrity points. Applying Gauss numerical integrity scheme with the accuracy of fifth order,we get a new distribution function fα( x , t ) =ωαf ( x , cα, t) ,whose evolution form is: In which Fα=(ξf)αa ?? ,τ=τ0 /δt,andδt is time step.The macroscopic density and velocity of the fluid is computed as:By discretizing the equation along with the charactaristic direction in time and space, and the following differential scheme is obtained: Which is the standard lattice Boltzmann equation.By the Chapmann-Enskog expansion,macroscopic Navier-Stokes equation can be recovered from the standard lattice Boltzmann equation.2 Thermal Boltzmann Models and Thermal Boundary TreatmentsThermal lattice Boltzmann models can be divided into three catalogues:multi-speed model,double distribution model and hybrod model,of which double distribution model is of well numerical stability and be widely used.The TD2G9 double distribution model proposed by Guo in 2002 can be used to solve Boussinesq equations,simple to compute and effective to eliminate compressible errors. Whears the internal energy double distribution model constructed by He etc. in 1998 can include viscous heating and compressible work. However, this model consumes too much calculation time and is likely to introduce extra numerical error associated with gradient computation. Based of the above, in 2007 Guo etc. proposed the total energy distribution model tobe an alternative one.When applying thermal lattice Boltzmann method, one often use bounce-back scheme and non-equilibrium exterpolation scheme to treat boundary conditions, taking constant temperature and no-slip boundary condition as an example:3 Numerical SimulationsWe first simulated natural convection flow in a square cavity. The top and bottom wall of the square cavity is insulted, and the left wall keeps at high temperature while the opposite wall keeps lower temperature. The flow is propelled by the buoyangcy force. The flow field and temperature field is observed at Ra = 10 3 ? 106, and the method is validated by comparing the charactaristic figures obtained with benchmark solutions. Then the mixed convection supplemented with roof driving effect is investigated for different Re and Ri number. Also we investigated thermal fluid flow in porus media which is heated from bottom with finite length of heat source, and simulated the thermal Couette flow in the slip regime, which demonstrate well results of lattice Boltzmann simulation in the field of thermal fluid flow.