Hybrid Multi-scale Model For Particle-fluid Systems

Particle-fluid systems are widely found in nature and applied in process engineering, such as pharmaceutical, metallurgical, energy and chemical industries. 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. This thesis focuses on the development, numerical implementation and application of the hybrid multi-scale model to particle-fluid systems. The content of this thesis is as follows,(1) The first chapter of thesis firstly introduces the background and significance of the research topic and then the simulation methods for particle-fluid systems are outlined. Furthermore, the literature of hybrid multi-scale simulation model for single phase flows is reviewed. Finally, the research route of this thesis is proposed.(2) 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.(3) 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.(4) 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 Geldart D type of 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.(5) 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. 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.