Numerical Simulation Of Fluidized Bed Using Coupled Euler Gas Phase-Euler Solid Phase-Lagrangian Discrete Particles Model

The Euler-Euler method and Euler-Lagrangian method are two main methods for the simulations of fluidized beds.In the Euler-Euler method,the conservation equation of the solid phase is closed by the kinetic theory of granular flow,in which the determination of solid pressure,viscosity and other parameters depend on the elastic restitution coefficient.However,in the Euler-Lagrangian method,the gassolid phase momentum transfer is achieved by the collision between particles,and the effect of gas-solid turbulent kinetic energy transfer on the motion of discrete particles is ignored.Therefore,it is of great significance to develop a reasonable gas-solid two-phase flow model to describe particle collision and gas-solid turbulent kinetic energy transfer accurately.Based on this,the influence of the elastic restitution coefficient on the collision process of the solid phase and the influence of turbulent kinetic energy transfer between gas and solid phase on the motion of discrete particles have been considered.Thus,a coupled Euler gas phase-Euler solid phase-Lagrangian discrete particle model(CEEL)is established.Discrete particle motion follows Newton's law and all the particle information can be obtained by tracking the trajectory of particles.The average elastic restitution coefficient in grid is obtained from the impact velocity of particle during collisions,which is introduced into solid phase constitutive equation in the kinetic theory of granular flow(KTGF)to predict the transport coefficient and collision energy dissipation of Euler solid phase.Thus,the constitutive equations of transport coefficient and collisional energy dissipation of Euler solid phase in KTGF are improved.Euler gas phase and Euler solid phase exist as continuous phases,and the turbulent kinetic energy transfer between gas and solid phase is considered by k-? turbulence model.By coupling the gas-solid turbulent kinetic energy transfer of the Euler gas phase and Euler solid phase with discrete particle dynamics theory,the calculation model of discrete particle motion is established,and the energy transfer between Euler gas phase and discrete particle phase is modified.The gas-solid flow behaviors in bubbling beds are numerically simulated by the CEEL model.Compared with the simulation results of the two-fluid model(TFM)and Discrete element model(DEM),the simulated porosity distribution via CEEL model is closer to the experimental value.The distribution of elastic restitution coefficient in the bed is also analyzed and it is shown that the elastic restitution coefficient is related to the dynamics characteristics of the gas-solid phase,and the distribution is non-uniform in the bed.Moreover,it is found that the velocity of Euler solid phase is consistent with the average velocity of Lagrangian discrete particles in the grid by analyzing the dynamic gas-solid flow characteristics of Euler solid and discrete particles in the system.The numerical simulation shows that the CEEL model can well reproduce the internal circulation process of particles that rise in the center and decrease near the wall in the bubbling bed.The flow characteristics of gas-solid two-phase flow in a spouted bed are numerically simulated,the gas and solid movement in a spouted zone and an annular zone is analyzed.The simulated velocity distributions of the Euler solid phase and Lagrangian discrete particles agree well with the experimental values.The relationship between granular temperature and solid concentration is given.According to the particle position,the dispersion coefficient distribution of discrete particles is obtained.The results show that the diffusion in the axial direction of discrete particles is the most obvious and the instantaneous energy dissipationis obtained by energy analysis.The results show that the impact energy dissipation between discrete particles and beween discrete particles and walls is the largest.In the particle collision energy dissipation of spouted bed,the impact energy dissipation is dominant.Based on the CEEL model,the gas-solid two phase flow characteristics in an internal circulating fluidized bed are simulaed.The velocity and volume fraction of the Euler gas phase,Euler solid phase and Lagrangian discrete particles are statistically analyzed.It is found that the Euler solid concentration and velocity are consistent with those of Lagrangian discrete particles.The solid circulation mass flow rate predicted by the Euler solid phase is consistent with that of discrete particles in the internal circulating fluidized bed.However,the solid circulation flow rate using the TFM and DEM is clearly different.The elastic restitution coefficient in the internal circulating fluidized bed is obtained.In general,the elastic restitution coefficient in the low-velocity chamber is larger than that in high-velocity chamber.Numerical simulations further indicate that the elastic restitution coefficient is not only related to the impact velocity,but also related to the solid concentration.With the increase of the solid concentration and the impact velocity of Lagrangian discrete particles,the elastic restitution coefficient decreases.The results show that the CEEL model can reproduce the elastic restitution coefficient in the bed and modify the calculation of the collision between particles.