| Granular fluid systems are common in nature and have important applications in indus-try.Although granular fluid systems have been studied for many years,the understanding of its complexity is not much comprehensive.In recent years,computational fluid dynamics has been widely used to study the hydrodynamics of granular fluid systems.Two-fluid mod-el,discrete particle method and direct numerical simulation are the most popular methods.Two-fluid model has a more extensive application especially in the industrial-scale sim-ulation.It treats the gas phase and the solid phase as continuous phases and these two phases can be mixed with each other.The mass,momentum and energy conservation equations are obtained via proper averaging.The constitutive relation of the solid-phase stress is usual-ly closed by kinetic theory.From the thermodynamic point of view,the continuum model under Navier-Stokes order is based on the assumption of local thermodynamic equilibri-um(LTE).If the state of the system is far from the equilibrium,the local thermodynamic equilibrium hypothesis does not valid,that is to say,the N-S order continuum model does not valid anymore.Discrete particle model(DPM)only treats the gas phase as a continuous flow.The mo-tion of the particles is tracked by Newton’s second law.The model only needs the interphase coupling force to close the governing equation.Under the same drag model,the feasibility of the continuous assumption of solid phase in two-flow model can be studied by discrete particle model.In order to find out under what conditions the N-S order continuum model or the local thermodynamic equilibrium hypothesis is valid,the main work of this thesis is to quantify the non-equilibrium gas-solid flow by using discrete particle model.The first chapter of this thesis introduces the TFM model and reviews the state-of-the-art in using the Knudsen numbers and the entropy criterion to judge the local non-equilibrium hypothesis.In the second chapter,the discrete particle model is elaborated to calculate the entropy criterion and the Knudsen numbers in the bubbling,turbulent and circulating fluidization of Geldart A,B and D particles.The conclusions obtained are as follows:(i)The local equilibrium hypothesis is valid in most region under bubbling flu-idization no matter which criterion is chose while the local equilibrium hypothesis fails with low solid concentrations in bubble center.(ii)For turbulent and circulate fluidization,the validity of the local equilibrium hypothesis depends on the criteria used.The entropy cri-terion describes the non-equilibrium characteristics with particle velocity gradient,particletemperature gradient and particle inelastic collision.By quantifying the entropy criterion,we find that the local equilibrium hypothesis applies to all tested particle-fluid system,so the assumption of continuous process for solid phase is not the major reason for the inaccuracy of continuum model.According to the kinetic theory,the particle velocity distribution in the equilibrium s-tate can be described as the Maxwellian distribution.However,when the system is in the non-equilibrium state which is far from the thermodynamic equilibrium,the particle ve-locity distribution exhibits a non-Maxwellian with an overpopulated high-energy tail or the bimodal distribution.Therefore,the third chapter discusses the form of the particle velocity distribution function(PVDF)in the gas-solid flow.The statistic results of PVDF calculat-ed by DPM is regressed by the functions of Maxwell distribution,exponential distribution,t-distribution and bimodal distribution.It is found that the exponential or t-distribution fits the numerical results well in the horizontal direction,while the bimodal distribution based on EMMS is much closer to the statistic results in the gas-flow direction.The forth chap-ter summarizes the main conclusions and innovations of this thesis,and puts forward the prospect of this research. |
PDF Full Text Request