液固系统和气液固三相系统在自然界和过程工业中十分常见，了解不同多相系统的流动机制有助于多相流反应器的设计优化。实验研究发现，虽然液固流态化通常被认为是固相在液相均匀分布的散式流态化，但是在包含溶胀颗粒的液固体系中有非均匀结构存在，溶胀颗粒由于较强的颗粒间粘附力而发生团聚，团聚行为影响了反应器的操作稳定性，甚至会造成反应器堵塞。而气液固三相系统的非均匀特性更为复杂，以浆态鼓泡塔反应器为例，气泡群在浆液里上升的过程中伴随着变形、聚并、破碎、夹带尾涡等复杂行为，气泡表面的液相滑移、液涡与气泡的相互作用、颗粒与气泡的接触等都会对气泡的聚集形态产生影响，导致气泡呈现不同的粒径分布。溶胀液固系统及浆态鼓泡塔内非均匀结构的存在导致系统的流动机制变得十分复杂，而此类反应器也往往因为非均匀结构的存在导致放大效应。能量最小多尺度方法是近二十年来新兴的一种描述非均匀介尺度结构的模型方法，最早被用来描述稀密两相共存的气固流态化系统，后来在气液鼓泡塔中也得到了广泛应用。该方法的核心在于分析非线性系统的不同控制机制，并以此为根据找到系统的稳定性条件。目前，基于稳定性条件的多尺度模型能够描述气固和气液系统的典型特征，但对于存在非均匀结构的液固体系和更为复杂的气液固系统则鲜有研究。本论文的核心工作是将多尺度模型方法拓展应用到存在非均匀结构的液固系统和浆态鼓泡塔中。多尺度模型的其中一种应用方法是基于多流体模型框架对封闭模型进行修正。以气固模型中相间动量交换为例，能量最小多尺度模型导出的曳力模型可以更为准确的反映出介尺度结构对于相间动量交换的影响，进而使得多流体模型可以更为准确的描述气固系统中稀密相共存等流场特征。借鉴上述研究思路，本论文的第2章首先通过CFD模拟液固均匀体系，考察了一种新型双桨双区的搅拌槽结晶器的流体力学特性。模拟研究发现，两浆的搅拌速度之差影响总功耗以及固相分布。另外，由于结晶过程停留时间较长，计算耗时巨大，本论文提出了一种提高模拟效率的简化模型，以更为高效的为工程应用提供指导。本论文第3章针对包含溶胀颗粒的液固非均匀体系，分析其多尺度行为机制（如微尺度的传质行为、介尺度的团聚行为），把不同尺度的行为通过组分输运、群平衡方程等模型工具耦合到多流体模型中，进而提出了一种描述非均匀体系的新模型策略。新模型捕捉到了不同反应器中溶胀液固体系的典型特征，如环管反应器中堵塞、功率突增以及搅拌槽中功率缓慢增长等现象。基于新模型对不同环管反应器结构的模拟结果，本文进一步提出了一种降低颗粒溶胀风险、缓解颗粒团聚程度的新型反应器结构和操作模式，为工程应用提供借鉴。第4章基于以往文献中气液鼓泡塔的多尺度模型方法，探索低颗粒浓度浆态鼓泡塔的多尺度模拟方法。模拟研究表明，气液多尺度模型耦合三流体模型中可以准确预测气含率分布、固相动力学参数等。在此基础上，第5章进一步探索适用于高颗粒浓度的多尺度模型及模拟方法，并提出了一个考虑颗粒对气泡行为影响的新模型。新模型表征了高浓度浆态鼓泡塔的基本特征，与CFD耦合后对高浓度浆态鼓泡塔中气含率分布的预测也与实验较为吻合。上述研究重点考察了固相为可润湿性颗粒的浆态鼓泡塔体系（如空气-水-玻璃珠体系），文献中以往的实验研究表明，可润湿性颗粒与不可润湿性颗粒对气泡行为有着不同的影响机制，因此本文第5章进一步基于不可润湿性颗粒对气泡的影响机制探索了新的多尺度模型，新模型预测了不可润湿性颗粒导致全局气含率增加的现象，与实验观测吻合。 简而言之，本文通过分析颗粒溶胀系统和气液固浆态鼓泡塔的多尺度行为特性，提出了表征其介尺度结构、描述其多尺度行为的新的模型方法，新模型捕捉到了液固和气液固非均匀系统的典型特征，拓展了欧拉多流体模型对液固和气液固非均匀系统的适用性。;Liquid-solid and gas-liquid-solid systems are ubiquitous in nature and industrial processes. Generally, the flow structure in liquid-solid systems is well recognized as particulate fluidization, characterized by homogeneous bed expansion and phase distribution. However, the structure becomes heterogeneous in practice, e.g., the slurry loop reactors of swollen particles. Swollen particles may aggregate due to adhesive forces, which then causes operation instability and even reactor blockage. More complex mesoscale structure exists in gas-liquid-solid systems. The rise of bubble swarms is accompanied by bubble breakage, coalescence, deformation and bubble wakes. The effects of particles on fluid dynamics, bubble swarms, gas-liquid interaction and bubble breakage and coalescence are important to understanding and modeling, but remain a challenge. The Energy-Minimization Multi-Scale (EMMS) models have been developed for the study of heterogeneous structures of gas-solid and gas-liquid systems in recent two decades. The hallmark of this approach is to analyze the different dominating mechanisms in non-linear non-equilibrium multiphase systems with the so-called stability conditions. Currently, the effect of swollen particles have not been considered in modeling liquid-solid systems and the solid effect on bubble behaviors have not been incorporated into models of gas-liquid- solid systems. Multi-scale simulations or EMMS models provide potential methods to account for above effects. This work then focused on applying the multi-scale method in liquid-solid and gas-liquid-solid systems. Chapter 2 firstly evaluates the traditional two-fluid model in description of homogeneous liquid-solid flows. The hydrodynamics in a novel double-partition and double impeller stirred tank for crystallization process are investigated. Simulations show that differences of the agitation speeds between two impellers are relevant to the total power consumption and solid distribution. On the other hand, the physical time for crystallization process costs several hours, which consumes huge computational cost. A simplified model strategy is thereby proposed in this section to improve the efficiency for engineering application. Chapter 3 develops a swelling-dependent two-fluid model (STFM) for the liquid-solid flows of swelling particles in polyethylene reactors. The microscale mass transfer and mesoscale particle aggregation process are considered into the multi-fluid model through the species transport equation and the population balance equation. Simulations show that only the TFM fails to capture the main features of swelling systems. By contrast, the STFM captures the gradual increase of power consumption due to particle swelling and aggregation, which agrees with the experiments in a stirred tank. The STFM predicts also the slug formation and a sharp increase of power consumption in a slurry loop reactor as well as the solid accumulation behind pump. The difference of model prediction for stirred tanks and loop reactors suggests the potential of reactor optimization by enhancing local mixing while still keeping high solid concentration for productivity. Chapters 4 deals with low-solid-concentration slurry bubble columns. we demonstrate that the Dual-Bubble-Size (DBS) drag model based on the Energy-Minimization Multi-Scale (EMMS) concept, is capable of effectively predicting the distribution of gas holdup in slurry bubble columns. For solid-free or low solid loading systems, a thorough comparison of the DBS-Global and other drag models indicates that, without any fitting parameters, the DBS-Global drag model prediction on the radial distribution of gas holdup and solid hydrodynamics is in conformity with experiments over a wide range of superficial gas velocities. Chapter 5 further explores the multi-scale models for high-solid-concentration slurry bubble column, where the solid effect must be considered and gas-liquid models thus cannot be directly used. We propose a particle-dependent new model in this part. The model well captures the main feature in high solid concentration systems and predicts well of gas distribution when coupled with the three-fluid model. To summarize, this work proposes new models that account for mesoscale structures in heterogeneous liquid-solid and gas-liquid-solid systems. The new model captures typical flow structures in above systems. On the other hand, the new models propose modifications in previous multi-fluid models and the multi-fluid models are thereby extended for description of heterogeneous liquid-solid and gas-liquid-solid systems.