EMMS-based Simplified Two-fluid Model And Its Application In Simulations Of Gas-solid Flows

Gas-solid two-phase flow systems are significantly influenced by meso-scale structures involved such as particle clusters and gas bubbles.Numerical methods for gas-solid two-phase flows can be classified into three categories:direct numerical simulation(DNS),discrete particle model(DPM),and two-fluid model(TFM).For numerical simulations of industrial devices,the computational costs required by both DNS and DPM are formidable,and thus TFM is currently the most frequently used method.However,the accuracy of TFM closely depends on the accuracies of sub-models,such as drag models which measure the forces between gas and solid phases,and solid stress models which considers the interactions between solid particles.The most widely used two-fluid model considers the interactions between particles via the kinetic theory of granular flow(KTGF)based solid stress model,in which additional computational cost is required to solve the transport equation of granular temperature,and numerical stabilities decrease because of those highly nonlinear equations.For the calculation of inter-phase drag force,one consensus is that the effects of meso-scale structures has to be considered.In addition,many results show that drag force model is much more influential than solid stress model for the simulations of gas-solid two-phase flows.Therefore,a combination of EMMS drag,which considers the effects of meso-scale structures,with simplified solid stress model is potentially to form a simplified two-fluid model with improved accuracy but lower computational cost.Meanwhile,with reasonable numerical discretization schemes,the numerical instability of the simplified model can be further improved.In chapter 2,a simplified two-fluid model(STFM)was proposed,which simplifies the formula of solid stress model and incorporates EMMS drag.In addition,to circumvent singularity in the momentum equation of solid phase,the momentum-equations of both phases are reformulated to separate phase volume fraction from phase velocity.Chapter 3 introduced the foundations of finite volume method,and then details of the implementation of STFM in the framework of OpenFOAM.Furthermore,the principle of MULES algorithm for the continuity equation of solid phase was elaborated.Chapter 4 validated the proposed STFM with three simulation case with different complexities.Both STFM coupled with EMMS drag and full two-fluid model(FTFM)coupled with EMMS drag showed good accuracy,but the computational cost of STFM is less than half of that of FTFM.However,for complex industrial devices,several flow regimes can coexist.Different regimes may exhibit completely different flow behaviors,no single model could be suitable for all the regimes.Therefore,in chapter 5,a multi-region simplified two-fluid model was proposed,in which the whole device can be divided into several regions,and different sub-models were chosen for different regions according to their flow characteristics.In the framework of two-fluid model,two main categories of sub-models are drag models and solid stress models.The frictional stress has important influence on the simulation of very dense gas-solid flows,and this effect was investigated in the simulation of particle packing and dense bubbling fluidized beds.Then the effect of drag models in different flow regimes was studied.Based on these investigations,a multi-region simplified two-fluid model was implemented,which can choose different drag and frictional stress models in different regions.In addition,to improve numerical stability,a deferred correction scheme for the convection term was implemented,which preserves both the stability of upwind scheme and accuracy of second order scheme.Afterwards,a lab-scale full loop circulating fluidized bed was simulated with the proposed multi-region STFM,and the numerical results were compared with predictions of the previous single region STFM.It was showed that with multi-region STFM the accuracy was improved notably.Finally,Chapter 6 gives a summary of this study,and perspectives of the STFM is also presented.