气固两相流由于其非线性非平衡特性，往往呈现出复杂的多尺度非均匀结构。诸如气泡或团聚物等介尺度结构的产生，使得气固两相流中的传递过程与单相系统差别很大，其分析与模拟一直是两相流研究的热点之一。能量最小多尺度（Energy Minimization Multi-Scale, EMMS）模型考虑了气固两相流中单颗粒、团聚物及系统间的多尺度相互作用，并且从物理机制出发建立了稳定性条件，成功复现并阐释了实验中的噎塞与曳力减小等现象。本论文在EMMS模型的框架下，进一步分析了模型的数学性质和物理意义，特别是对其稳定性条件中包括的不同极值趋势的详细定量对比进一步验证了该模型中蕴含的竞争中协调的原理，改进了非均匀结构曳力的表达。本论文各章内容安排如下：第一章作为文献综述，首先阐述了气固系统中的局部和整体非均匀结构以及流域转变过程，并在此基础上调研了各种曳力模型。最后概述了研究气固两相流这类非线性非平衡系统的EMMS模型及其原理。第二章主要考察了EMMS模型中蕴含的不同控制机制的极值趋势。首先进一步明确了EMMS模型中各物理量的定量表达，并分析了在稳态条件下不同能耗占比的合理性。由于EMMS模型中的稳定性条件Nst = min是由气相占主导的Wst = min与固相占主导的εg = min相互协调产生的，因此考察了它们单独作用于系统时所能产生的结构，发现这两个极值趋势分别代表了非线性非平衡系统的耗散最小与耗散最大。接着研究了其他的极值趋势单独作用时所表现的行为，发现除了一些极值趋势也能反映耗散最大或最小之外，其余的极值趋势对应的结构特征参数均处于两者之间。最后考察了团聚物直径方程对于极值趋势的影响，得到了极值趋势是EMMS模型固有性质的推论。第三章基于第二章的研究结果进行了气固流态化系统的全流域分析。作为其准备工作，对最大非均匀空隙率、稀相空隙率、团聚物直径方程等进行了理论分析，获得了更自洽的表达。然后以典型的循环流化床为例，完整复现了从均匀膨胀、鼓泡、快速流化、稀相输送到理想稀相输送等一系列流域的转变。对于最大非均匀空隙率建模时遗留的待定参数进行了敏感性分析，给出了合理的取值建议。最后还考察了不同的团聚物直径方程对于噎塞预测的影响，发现目前EMMS模型中采用的方程实用性较好。第四章，根据上述研究，从工程实用的角度提出了一种简便而通用的非均匀结构曳力的表达。通过考察不同的团聚物直径方程以及不同的稳定性条件，发现网格内颗粒浓度较高时采用较大的团聚物尺寸可以避免出现不合理的曳力系数，且稳定性条件中的输送部分对于曳力影响不大。由此可以提出基于滑移速度的曳力模型，避免对于不同的操作条件重新计算曳力模型的相关参数，该模型同样适用于下行床体系。第五章总结了本论文工作的主要成果与结论，并展望了EMMS模型进一步发展的几个重要课题。;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 εg = 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 εg = 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.