Second-Order Moment Approach Of Particles And Numerical Simulation Of Dense Gas-Solid Two-Phase Flows

Gas-solid two-phase flows are widespread in chemical industry, electric power, metallurgy, food, pharmarcy and other fields. In-depth understand and grasp of the mechanism of gas-solid flows has important significance. With the development of computational fluid dynamics (CFD), numerical simulation has become one of the most promising tools for researching gas-solid flows. However, due to the complexity of gas-solid system, theoretical models for numerical simulation of gas-solid flows are still needed in great improvement and enchancement.Currently, the commonly used model is based on the kinetic theory of granular flow, in which only the granular temperature is introduced to describe the strength of particle velocity fluctuating. In fact, the fluctuation of particle velocity shows a strong anisotropy from experiments. Therefore, it's necessary to develop a second-order moment model of particles which could take the anisotropic characteristic of particle velocity fluctuating into account.With the basic principles of the kinetic theory, the transport equation for the second-order moment of particle fluctuating velocity is present. The solid phase constitutive model is closed with the kinetic approach, and the third-order moment of particle fluctuating velocity is approximated with the elementary transport theory and linear theory respectively. Then the second-order moment model is established for the simulation of dense gas-solid flows. By using the normal and tangiential restitution coefficients of particle-wall collision, the wall boundary condtions for solid phase velocity and second-order moment are also derived with the kinetic approach.The second-order moment model is applied to simulate the hydrodynamics of gas-solid two-phase flows in bubbling fluidized beds. For the case of freely bubbling fluidized bed with an air distributor, the model predicts the trailing votex type and neighboring type bubble coalescence and trailing votex cut type and flow field stretched type bubble break-up. The time-averaged solid phase velocity and second-order moments of particle velocity are obtained and agree with experimental results. By reducing the restitution coefficient of particle- particle collision, the bubble dynamics in the freely fluidized bed varies a lot, so that the anisotropy of particle velocity fluctuating is strengthed. For the case of the bubbling fluidized bed with a central jet, comparison between anisotripic model and isotropic model shows that both models give similar macroscopic flow structure, but different size of bubble jets, different strength and anisotropic characteristic of particle velocity fluctuating. The anisotropic behaviors of the particle velocity fluctuating is better reflected by using the second-order moment model.The second-order moment model is used to simulate the hydrodynamics of gas-solid two-phase flows in risers. The time-averaged radial distribution of particle concentration and solid mass flux, axial gas pressure drop in a two-dimensional riser are obtained and agree with experimental results. The simulation of one-dimensional"core-annulus"flow in the riser shows that anisotropic models with different third-order moment closures are able to predict the anisotropic fluctuation of particle velocity. Then the parameters in the third-order moment closures, the interphase interactions, the wall parameters as well as the physical parameters of particles are studied using the anisotropic model. It is found that the drag items in the third-order moment closures effect the gas-solid flow structures, but hardly effect the anistropic characterisc of particle velocity fluctuating. The dissipation item of interphase interaction, the physical parmeters of particles effect both the flow strctures and the anisotropic behaviors of particle velocity fluctuating. Considering the dissipation term of interphase interaction, or reducing the particle diameter or decreasing the restitution coefficient of particle-particle collision would increase the anisotropic of particle velocity fluctuating. Simulation results also show that the flow structure is less affeced by the normal restitution coefficient of particle-wall collision, but is greatly affected by the tangential one.The effect of particle fluctuating velocity on interphase drag model is then studied by incorporating it into the second-order moment model. Simulation of the gas-solid flow in a riser shows that the particle fluctuating velocity increases the non-linear characteristics of interphase interaction, and the higher of the granular temperature, the greater impact of the particle fluctuating velocity. It's found that with the contribution of the particle fluctuating velocity, the granular temperature decreases significantly. By increasing the operating gas velocity, the impact of particle fluctuating velocity on interphase interaction becomes more obvious.