颗粒流体系统广泛存在于自然界并应用于制药、冶金、能源、化工等工业过程。该系统是典型的非线性非平衡复杂体系，不仅存在着颗粒与颗粒间以及颗粒与流体间的复杂作用，并且伴有团聚物等介尺度结构的形成。近年来，由于计算机的快速发展，基于计算流体力学对颗粒流和气固两相流的模拟方法受到了越来越多的关注，并广泛地应用于工业反应器的放大、设计和优化过程中。目前已有的模拟颗粒流和气固两相流的模型主要分为两大类：基于欧拉方法的连续模型和基于拉格朗日追踪法的离散模型。连续模型一般采用连续介质假设并结合颗粒动理论，其优点是计算量较小，因此可以用来模拟大型工业问题。但是，由于连续模型把固相处理成“拟流体”，其精度和普适性都低于基于拉格朗日追踪的离散模型。然而，在离散模型中，每个颗粒的运动轨迹都需要用单独的方程追踪，所以对工业装置的模拟将会产生庞大的计算量，目前的计算能力远无法满足。为解决连续模型精度有限及离散模型效率低的矛盾，本论文开发了一种混合动态多尺度模型（离散-连续跨尺度耦合模型）用以解决连续模型的精度和离散模型的计算效率问题。该模型的核心是在一个模拟体系中同时使用连续和离散两种模型，即只在连续模型不适用的关键区域使用离散模型来捕捉准确的流动细节，而其余大部分区域仍然使用连续模型以降低计算量。离散和连续两种模型在空间尺度和时间尺度上通过合理的物理模型实现动态耦合，从而兼顾离散模型的精度和连续模型的计算经济性。本论文围绕混合多尺度模型的模型建立、算法实现和实际应用展开研究，主要内容安排如下：混合多尺度模型需要同时使用连续模型和离散模型，而目前已有的商业软件难以实现两种模型的扩展和实时交互。因此本论文在第二章叙述了两种模型各自的算法实现过程，并使用程序模拟了一个典型的提升管装置。计算结果显示连续模型和离散模型都与实验结果定性吻合，但由于实验测量及物理模型参数存在不确定因素，模拟的定量分析结果与实验测量仍有一定差别。第三章建立了适用于颗粒流的混合多尺度模型框架，并通过模拟颗粒管流初步验证了所构建的混合多尺度模型的合理性。在该模型中，本文构造了一个重叠区域以使不同模型在此处交换边界条件。重叠区域又可进一步分为三个不同用途的子区域，即连续模型向离散模型提供边界的区域、缓冲区域和离散模型向连续模型提供边界的区域。在进口固相速度为抛物线速度分布的算例中，纯离散模型、纯连续模型及混合多尺度模型三者得到了定性一致的径向固相体积分数分布及速度分布。然而，在进行定量对比时发现纯连续模型同纯离散模型的模拟结果在壁面附近的偏差较大，其中原因是在壁面附近努森数较大使得连续介质假设失效。因此，本文在构造混合多尺度模型模拟区域时，在壁面附近使用离散模型，而在管中心仍然使用连续模型以减少计算量。混合多尺度模型模拟的定量结果同纯离散模型吻合很好。第四章进一步将混合多尺度模型扩展到气固两相流系统，并使用建立的混合多尺度模型模拟了无重力条件下的气体-颗粒管流及Geldart D类粗颗粒的循环流态化。在气体-颗粒管流计算中，双流体模型预测的管壁附近处的固含率、固相速度及气相速度与颗粒轨道模型相差较大，而混合多尺度模型则与颗粒轨道模型吻合较好。在粗颗粒的循环流态化算例中，由于在壁面及进出口附近处的颗粒努森数较大，混合多尺度模型的结果与颗粒轨道模型的一致性比双流体模型更好。工业流化床反应器常使用Geldart A类及B类细颗粒，并且在流化床内存在着团聚物等非均匀结构，因此在模拟这些细颗粒的循环流态化时需要考虑介尺度结构的影响。第五章建立了考虑介尺度结构的混合多尺度模型，其核心是使用了能量最小多尺度（EMMS）模型将气固系统处理为稀密两相结构的思路。该模型将基于EMMS的介尺度双峰速度分布函数应用在连续模型和离散模型的相互边界映射过程中，并引入EMMS稳定性条件来约束新插入颗粒位置的选择。双流体模型轴向时均固相体积分数分布的预测结果同颗粒轨道模型相近，但径向上流场分布的预测与颗粒轨道模型差别较大，而考虑介尺度结构的混合多尺度模型得到的轴向时均固相体积分数分布及径向的时均流场变量都与颗粒轨道模型的模拟结果吻合良好。模拟结果显示本文所开发的混合多尺度模型充分利用了连续模型和离散模型各自的优势，为实现颗粒流体系统的高效、准确地实时模拟及虚拟过程工程提供了相应的理论基础。

Particle-fluid systems are widely found in nature and applied in process engineering, such as pharmaceutical, metallurgical, energy and chemical industries. Particle-fluid systems are typically non-linear and non-equilibrium because meso-scale flow structures such as clusters are formed due to complex particle-particle and particle-fluid interactions inside the system. Thanks to the rapid improvement of computational capacity and performance of computers in recent years, computational fluid dynamics for studying particle-fluid systems has attracted more and more attentions and become a powerful tool for the design and optimization of these industrial reactors. In general, there are two popular approaches to study granular flows and gas-solid flows: the Eulerian based continuum model and the Lagrangian based discrete model. The continuum model treats particle as continuum media and usually combines with kinetic theory of granular flow for closure relations, which is computationally efficient and suitable for large scale industrial problems. However, the drawback of this model is the requirement of complex constitutive relations, which makes the accuracy of continuum model insufficient. On the other hand, discrete model tracks individual particles using Newton’s laws of motion and thus is much more accurate. However, the computational costs are often very demanding in the case of dense suspensions encountered in industrial reactors, which are far beyond the computational capacity of current computers.In order to solve the above dilemma, a hybrid multi-scale model (discrete-continuum trans-scale coupled model) is proposed in this dissertation to compromise the inaccuracy of the continuum model and inefficiency of the discrete model. The strategy is to dynamically link continuum model and discrete model in different domains of studied devices, that is, use continuum model to describe the domain where continuum assumption is valid and use discrete model to simulate the domain where the continuum assumption breaks down. Hybrid multi-scale model could make full of their advantages since continuum model and discrete model are dynamically coupled in both temporal and spatial scales.The hybrid multi-scale model needs dynamical interactions of both continuum model and discrete model, which is difficult to achieve through current commercial software. Therefore, we used an in-house code and the detailed implementations of the program of these two methods were described in chapter two. Then, we used the code to simulate a typical circulating fluidized bed and compared the simulation results with the experimental data. The simulation results indicated that both continuum model and discrete model were in a fair or good agreement with experimental results. However, the simulation results cannot exactly match the experimental results because of some extra factors such as the uncertainty of the experimental measurement and the adjustable parameters in physical models.In the third chapter, we described the framework of the hybrid multi-scale model which was developed for granular flow, and then a granular channel flow was simulated to verify the validity and advantage of the proposed model. In the hybrid multi-scale model, an overlap region was constructed in order to make different models exchange their boundary conditions. The overlap region was further divided into three sub-regions according to their usages, i.e. a sub-region with boundary condition provided from continuum model to discrete model, a buffer sub-region and a sub-region with boundary condition provided from discrete model to continuum model. When the distribution of inlet particle velocity was parabolic, the simulation results of pure continuum model had a relative large deviation with pure discrete model in the near wall region and at the center of the channel. However, the simulation results of hybrid multi-scale model were in good agreement with pure discrete model.The hybrid multi-scale mode was further extended to gas-solid flows in the fourth chapter, and then a gas-solid channel flow without gravity and a circulation fluidized bed with coarse particles were simulated. In the coarse particle circulating fluidized bed example, the simulation results of hybrid multi-scale model was also in good agreement with discrete particle model. On the other hand, because the particle Knudsen number in the near wall and inlet region was relatively large, the performance of two-fluid model was not good enough.Heterogeneous structures such as clusters are prevalent in circulating fluidized bed and thus the model needs to consider the influence of these heterogeneous structures in the simulation of the Geldart A and Geldart B type of particles. Therefore, in the fifth chapter, we developed a hybrid multi-scale model considering the effects of meso-scale structures. The idea was to derive a meso-scale bimodal particle velocity distribution function based on the EMMS model which assumed there existed a dilute phase and a dense phase structure inside the simulated coarse grid. The stability condition in EMMS model was also used to constrain the degree of the location of the newly inserted particles during the boundary mapping process from continuum model to discrete model. Although the axial solid volume fraction predicted by two-fluid model showed a good agreement with discrete particle model, the radial solid volume fraction and velocity predicted by two-fluid model still had a relative large deviation. On the other hand, the simulation results of hybrid multi-scale model considering the meso-scale structures were in good agreement with discrete particle model both in the axial and radial solid volume fraction distribution. All the simulations showed that the hybrid multi-scale model takes advantage of both two-fluid model and discrete model, which provides the potential possibility for efficient and accurate real-time simulation and virtual process engineering.