EMMS-Based Drag Model And Extremum Analysis Of Energy Dissipation Rate For Fluidized Beds

Multi-scale heterogeneous structures have significant effects on the hydrodynamics,heat transfer,mass transfer and chemical reactions in fluidized beds.Traditional two-fluid model(TFM),integrated with homogeneous drag force,fails to predict the hydrodynamic characteristics,reaction and transport behaviors in fluidized beds,because it neglects sub-grid heterogeneous structures.In order to improve the numerical simulation of fluidized beds,it is necessary to take into account the sub-grid heterogeneous structures in the drag model.The energy-minimization multi-scale(EMMS)model,which is based on the multiscale resolution of structure and closed with a stability condition,enables effective solving the dense-and-dilute two-phase distribution in fluidized beds and predicting the regime transitions in circulating fluidized beds.Meanwhile,the EMMS-based drag model can effectively quantify the sub-grid drag reduction induced by heterogeneous structures,and hence has been widely applied in numerical simulations of fluidized beds.The previous versions of EMMS drag models introduced the particle acceleration terms to account for the unsteady state behavior.However,the consistency between these extra dynamic variables and the stability conditions of the steady-state EMMS model has not been proven.Moreover,the validity of various extremum principles,including nonequilibrium thermodynamics,needs to be analyzed in the field of fluidization.Further,as to algorithm and solution,current EMMS drag models heavily depend on the operating conditions(Ug.Gs),thus need case-specific regression and calculation,with extra expense of computation,and lack universality in application.To resolve the above issues,firstly,this thesis aims to develop a drag model suitable for more flow regimes based on the steady-state EMMS framework.Secondly,to understand the applicability of stability conditions,the extremum analysis of energy dissipation rate is carried out for fluidized beds,indicating the advantage of the EMMS stability condition and the problem of using the minimum energy dissipation rate principle.Further,a new model for cluster diameter is proposed based on the analysis of two-phase fluctuation energy and dissipation,and thereby enables prediction of the minimum bubbling state beside the choking transition.The application of EMMS method is thus extended.In Chapter 2,an EMMS-based heterogeneous drag model is proposed based on steady state EMMS model.The new drag model without tunable parameters is suitable for multiple flow regimes,such as bubbling fluidized beds,turbulent fluidized beds and circulating fluidized beds.Compared with the previous versions of EMMS-based drag model,the constitutive relations of this new drag model is independent of regimes or operating conditions.Two-fluid modeling,integrated with the new drag model,indicates that it can reasonably predict the hydrodynamic characteristics of bubbling fluidized beds,turbulent fluidized beds and circulating fluidized beds.Then,based on the assumption of dense-and-dilute two-phase distribution in fluidized beds,the mass,momentum,energy and entropy balance equations of the structure-dependent multi-fluid model(SFM)are derived by applying the volume averaging method in Chapter 3.The mass and momentum balance equations of SFM help clarify the relationships among SFM,TFM and EMMS balance equations.The energy and entropy balance equations pave the way for analyzing the process of energy transport and dissipation,and the extremum behavior of energy dissipation rate in fluidized beds.In Chapter 4,the structure-dependent entropy production and energy dissipation rate of SFM are derived from the balance equations of SFM,and further,the extremum analysis of energy dissipation rate is carried out.The results show that the minimization principle of energy dissipation rate is applicable to ideally dilute pneumatic conveying.The result predicted by the maximization principle of energy dissipation rate is consistent with that predicted by EMMS stability condition in the dense flow region.Specifically,the EMMS stability condition predicts the choking transition phenomenon.In Chapter 5,the mesoscale fluctuation energy between the dense and dilute phases is derived based on SFM balance equations.The length scale of clusters is correlated with mesoscale fluctuation energy and its dissipation rate by applying the dimensional analysis method.By substituting this new correlation into EMMS model,it effectively predicts the bed expansions in bubbling fluidized bed and the different regime transition phenomena near the minimum bubbling of both Geldart groups A and B particles.Finally conclusions and perspectives are given.