Energy Consumption Analysis Of The EMMS Model And Its Application

As typical non-linear and non-equilibrium systems,complex heterogeneous structures are characteristic of gas-solid two-phase flows.The existence of meso-scale structures,such as bubbles or clusters,distinguish them from single-phase systems in terms of momentum,mass and heat transfer.The analysis and simulation of gas-solid flows have,therefore,long been a hot topic and challenge in chemical engineering science.The Energy Minimization Multi-Scale(EMMS)model considered the multi-scale interactions in gas-solid flows at the single-particle,cluster and system scales,respectively,and proposed a stability condition for the closure of the model.The model can predict and clarify the choking and drag reduction phenomena in these systems.This work aims to analyze the mathematical properties of the EMMS model and clarify its physical meaning,which also validates the more general principle of'compromise in competition' behind the EMMS model.The study also results in an effective simplification of the meso-scale drag model for heterogeneous gas-solid flows.The main contents of this thesis are as follows:Chapter 1 focuses on literature review.First,the local and global heterogeneous structures,as well as the flow regime transitions in gas-solid flows are analyzed.The different drag models are then investigated on this basis.Finally,the EMMS model for gas-solid flows is summarized and the more the general principle behind this model is discussed,aiming at all non-linear and non-equilibrium systems.Chapter 2 examines the extremum tendency of the EMMS model.The expressions of some quantities in the EMMS model are further clarified first.The fractions of different energy consumption terms in the steady state are analyzed,which is shown to be reasonable and consistent with the model assumptions.As the stability conditions in the EMMS model,Nst=min,results from the compromise between Wst = min for gas dominance in the system and eg = min for solids dominance,these two extremum tendencies are also applied as stability conditions to the system individually.It is found that,in this case,they represent the minimization and maximization of energy dissipation,respectively.Other related extremum tendencies are also studied in this way,showing that they either result in structures similar to those for the minimization or maximization of energy dissipation,or structures with characteristic parameters ranging between these two extrema.Moreover,these results are found to be insensitive to the change of the cluster diameter correlations.All these findings suggest that Wst = min and eg = min are indeed the intrinsic competing mechanisms in the system.Based on the foregoing works,Chapter 3 mainly carries out an analysis on the complete spectrum of the flow regimes in gas-solid fluidization systems.As a precondition,a new model for the maximum voidage of heterogeneous structures,the voidage of the dilute phase and the cluster diameter in the EMMS model are proposed,which are shown to be more reasonable and self-consistent.Then,taking the example of typical circulating fluidization beds,the regime transitions from uniform expansion,bubbling fluidization,fast fluidization,dilute transport,and ideal dilute transport are reasonably predicted.The sensitivity of the fitting parameter in the model of maximum voidage is studied,suggesting a reasonable range of its value.Finally,the effect of cluster diameter correlation on choking prediction is investigated,and it can be found that the current correlation in the EMMS model is a good choice in engineering from a practical point of view.Based on the researches above,Chapter 4 proposes a practical drag model for heterogeneous structures in gas-solid flows.The stability conditions and cluster diameter correlations in different drag models are investigated,which indicates that the unreasonable drag coefficient can be avoided if larger diameter is adopted in dense cases,and the transport term in the stability condition has little effect on the drag.On this basis,an effective drag model based on slip velocity is proposed,which avoids recalculating the drag for different operating conditions.This model is also suitable for the downer case.Chapter 5 summarizes the main achievements and conclusions of this work,and prospects on further improvement of the EMMS model.