Non-equilibrium Statistical Mechanics Analysis Of Heterogeneous Gas-solid Flow

Particle-fluid systems exits widely in nature and in engineering.The dissipative particle-particle collisions and nonlinear interactions between gas and particles at microcale,the compromise in competition between gas-dominated and particle-dominated mechanisms and the constraints of boundary conditions all result in the formation of multiscale spatio-temporal heterogeneous structures.These complex structures have a significant influence on mass,momentum,energy transport and chemical reaction in the system.With the rapid development of computer technology,computational fluid dynamics(CFD)has been exten-sively used to study gas-solid flow.Continuum model has been chosen frequently for industrial applications.However,solid concentration gradient,velocity gradient and granular temperature gradient are usually high at the boundaries of heterogeneous structures.Hence,it’s necessary to assess whether the Navier-Stokes order continuum model on the basic of the local thermodynamics equilib-rium hypothesis is suitable for the system or not;moreover,different dominant mechanisms have to compromise in competition with each other at mesoscale,resulting in the forma-tion of dynamic mesoscale structures and the coexistence of dilute phase and dense phase.Therefore,the issue about the effect of different dominant mechanisms need to be explored deeply.Chapter 1 introduces the analysis of kinetic theory,and the development of various kinetic theories has been reviewed in detail.In chapter 2,kinetic theory has been used to analyse the entropy of gas-solid systems,it was shown that local thermodynamic equilibrium postulate is only valid for linear non-equilibrium regime,furthermore,an entropy criterion for the boundary of the validity of Navier-Stokes order continuum models,which is the ratio of the second order correction of the entropy density to the equilibrium one and is the indication of the effect of non-linearity,can be obtained from the analysis.The formulation of entropy equation of gas-solid flow has been derived in chapter 2,but the constitutive relations have not been obtained yet.In chapter 3,The classic cluster expansion method is introduced to consider the correlation of granular positions,then the modified Enskog equation is established by introducting a modified pair correlation function into the Enskog equation.Furthermore,a more reasonable entropy equation and constitutive relation are deduced using the Chapman-Enskog expansion method.It was found that there is no H-theorem in dissipative granular gases and gas-solid flow,therefore,the instability will results in the formation of mesocale structures.In response to the heterogeneous gas-solid flow,an EMMS-based two fluid model has been developed from the viewpoint of continuum mechanics.In chapter 4,in case of particle phase,the generalized Boltzmann kinetic theory considering the spatio-temporal variation of the volume,density and velocity of clusters was firstly derived,which launches a solid mi-croscopic foundation of EMMS-based two-fluid model;with respect to the gas phase,a new method was developed by considering the fluctuations at different scales simultaneously,with which we can for the first time derive the governing equations of gas phase via kinetic theory,in the sense that both the molecular stress and the Reynolds(or pseudo-Reynolds)stress can be obtained simultaneously,whereas all previous kinetic theory analyses failed to predict the appearance of Reynolds(or pseudo-Reynolds)stress in the momentum con-servation equation of gas phase due to the assumption of uniform structure.Finally,CFD simulations have been carried out to validate the EMMS-based two-fluid model and to study the effect of gas phase pseudo-turbulence.In chapter 5,the EMMS-based TFM is used to systematically investigate the effect of exit geometry of high-density CFB risers,fully taking the advantage that bed geometry can be easily modified in computational fluid dynamics study.It is shown that(ⅰ)the type of exit has a significant effect on hydrodynamics,the use of abrupt exit results in an increased solids concentration,not only in the immediate vicinity of the exit but also for a considerable distance down to the riser;(ⅱ)the cavity height of abrupt exit,the curvature diameter of smooth exit and the length of the horizontal tube connecting the exit and the primary cyclone only have a minor effect or have no influence on the bed hydrodynamics of the studied risers;(ⅲ)more importantly,the decrease of the diameter of abrupt exit tube results in a remarkable increase of solids holdup,the symmetry of radial solids concentration near the exit can also be enhanced significantly.However,in case of smooth exit,the diameter of the exit tube has no effect on the bed hydrodynamics at all.All of those results are in agreement with conclusions obtained from previous experimental studies,thus offering further validation of the EMMS-based two-fluid model for modelling heterogeneous gas-solid flow.Finally,the main conclusions and innovations of the dissertation have been summarized in chapter 6,moreover,the perspective of future research are also presented.