Lattice Boltzmann Simulations Of Electro-Thermo-Hydrodynamic Flows And Its Stability Analysis

Electro-thermo-hydrodynamics(ETHD)is an interdisciplinary field dealing with the interactions between heat transfer,fluid flow,and electrohydrodynamics.Single phase dielectric liquid exhibits a rich flow structure and unique heat transfer characteristics under the simultaneous effects of a unipolar injection of ions and a thermal gradient,and flow is driven by the resultant of Coulomb force and buoyancy force.The complex physics involved in electro-thermo-convective phenomena together with the promising applications in the active enhancement of heat transfer with electric field draw a wide attention to this field.The complex mathematical model as well as the strong nonlinear couplings between multi-physics is the main reason for the lacking of theoretical analysis a nd experimental studies on this field.A unified lattice Boltzmann model(LBM)is developed in this work to solve the electro-thermo-convection,and an extension application to convection melting is also investigated.The main topics studied in this thesis are as follows:Based on the same discrete velocity model(D2Q9),a unified LB model is constructed to solve the coupling between the charge density distribution,electric field,temperature field and flow field.In the charge transport equation,ion drif t velocity and flow velocity is combined as a general velocity,and the charge potential equation is transferred to be a transient form.By this manner,the coupled equations,including the Navier–Stokes equations,the conservation equation of charge density,the Poisson's equation for electric potential and the energy equation,can be unified to be a general convection-diffusion type equation.Besides,different time and velocity scales are analyzed,and the relaxation time in LBEs are updating in evolution process to ensure the stability of the model.The electro-convection induced by unipolar charge injection is numerically studied by coupling LBM.Results show that the LBM can accurately reproduce the subcritical bifurcations of the problem,including the linear and nonlinear critical values,the basic flow structures with charge void regions,as well as the route to chaos in weak injection regimes.Besides,take advantages of LBM in complex boundary treatment,the electro-convection between concentric and eccentric annulus electrodes are simulated,and the effects of geometrical parameters on the flow pattern and bifurcation behavior are investigated.When compared with FVM code,the efficiency of LBM is much higher(up to six times)in the same condition s.The electro-thermo-convection driven by the simultaneous action of Coulomb force and buoyancy force is further studied.The coupling interaction between electro-convection and classical Rayleigh-Bernard convection is analyzed.The neutral stability curve is drawn and is found to be consistent with existing linear stability results.Also,the application of unified LBM is extended to the electro-thermo-convection in complex electrode configurations.It is found that the augmentation of heat transfer is significant when the Coulomb force is large enough to cause the radial flow.Moreover,in the case of Coulomb force to be dominant,heat transfer no longer depend on the buoyancy force.Finally,the effects of charge injection strength,fluid physical parameters and electrode geometrical parameters on heat transfer are investigated.The cellular flow pattern in three-dimensional electro-convection is one of the basic phenomena of electro-hydrodynamics,but unfortunately none numerical verification exists due to its difficult.In this paper,using the unified LBM,the typical honeycomb flow structure reported in experiment studies is well reproduced numerically.And the linear and nonlinear bifurcation critical points predicted by LBM is high consistent with those obtained by the stability analysis.Besides,the effects of initial disturbance and boundary conditions on steady flow patterns are discussed.The subcritical bifurcation diagrams of the rolls,hexagons and squares flow patterns are provided.As an extended application,the multi-field coupling unified LB model is used to solve the problem of solid-liquid phase change in complex heat storage system,and the effect of electro-convection on phase change enhancement is studied.Numerical results shows that the enthalpy-based lattice Boltzmann model with basic evolution variable of enthalpy(HLBM)for thermal field avoids the sink(melting)term in the collision step,and the multiple relaxation time(MRT)model for flow field overcomes numerical instability and inaccurate boundary.Besides,the efficiency of phase change heat transfer under different geometrical shapes and different phase change materials are analyzed.Finally,under the consideration of electro-convection effects,phase change efficiency can be increased by about 40% in numerical simulations.