Numerical Simulation Of The Hydrodynamic Characteristics Of Particles And Liquid Phases In Fluidized Beds Using Kinetic Theory Of Rough Spheres

Liquid-solid two-phase flow widely exists in petrochemical industry.Because of the nonlinearity,structural heterogeneity and polymorphism of the liquid-solid system,the characteristics of liquid-solid two-phase flow in the fluidized bed are more complex.Therefore,it is of great academic significance and engineering application value to deeply study the liquid-solid two-phase flow.The kinetic theory of granular flow（KTGF）model is a tool developed from the kinetic theory of gases to describe the granular media flow and interaction.The theory assumes that particles are smooth and ignores the effects of particles rotation caused by particles surface roughness on the exchange and dissipation of momentum and energy during particles collision.For rough particles,the friction between particles transfers the shear stress,and the extrusion between particles transfers the normal pressure,which makes particles rotate under the action of particles collision and liquid turbulence.Particles rotation not only affects the trajectory of particles,but also the solid phase distribution and the surrounding gas or liquid flow field.Therefore,it is necessary to establish the kinetic theory of rough spheres（KTRS）model considering the particles rotation on the basis of the traditional kinetic theory of granular flow（KTGF）model,so as to further study the liquid-solid two-phase flow in the fluidized bed under different working conditions and reveal the effects of particles rotation on the two-phase flow.Based on the traditional kinetic theory of granular flow（KTGF）model,the tangential restitution coefficientβ,which characterizes the surface friction and tangential inelasticity of rough particles,and the total granular temperature e₀,which synthetically reflects the fluctuating intensity of the translational and rotational motion of particles,are introduced.Combining with the transport theory,the conservation equations of particle phase mass,momentum and total granular temperature considering particles rotation are established.The total granular temperature is used to correlate the parameters such as the pressure,viscosity and energy dissipation of the particle phase.On this basis,the constitutive relations of particle phase are proposed,and the kinetic theory of rough spheres（KTRS）model is obtained.Based on the two-fluid model,the flow characteristics of liquid and particles in a fluidized bed are simulated by combining the kinetic theory of rough spheres（KTRS）model and kinetic theory of granular flow（KTGF）model,respectively.The simulation results show that the liquid volume fraction obtained from the kinetic theory of rough spheres（KTRS）model is more consistent with the measured value by Ehsani et al.The particles rotation gives rise to increments in the solids volume fraction and particles aggregation,and declines in the bed expansion height,particles axial velocity and total granular temperature.After considering the effect of rotation,the maximum agglomerate size increases approximately 2.92 mm.In addition,the effects of the tangential restitution coefficient,normal restitution coefficient,particles size,particles density,liquid viscosity and liquid velocity on the particles rotation are analyzed.Based on the two-fluid model,combined with the kinetic theory of rough spheres（KTRS）model,considering the rheological characteristics of different fluids,a liquid-solid two-phase flow model suitable for non-Newtonian fluid and rough particles is established.Numerical simulations of non-Newtonian fluid and particles flow behaviors in a fluidized bed are built on the experiments of Ehsani et al.The results show that there are obvious non-uniform structure of particles and eddies in the fluidized bed.When the liquid is power-law fluid,the dynamic height of the bed simulated by the kinetic theory of rough spheres（KTRS）model is in good agreement with the experimental data obtained by Broniarz-Press et al.At the same time,the effects of flow index and consistency coefficient of power-law fluid on the bed expansion height and total granular temperature,et al.are analyzed.When the liquid is Bingham fluid,the model is still applicable.In addition,the effects of plastic viscosity and yield stress of Bingham fluid on the bed expansion height and liquid viscosity are analyzed.Compared with the kinetic theory of rough spheres（KTRS）model,the liquid viscosity of different plastic viscosities obtained by the kinetic theory of granular flow（KTGF）model is smaller.Under different yield stresses,the bed expansion height obtained by the kinetic theory of granular flow（KTGF）model is higher.Based on the two-fluid model combined with the kinetic theory of rough spheres（KTRS）model,considering the change of normal restitution coefficient caused by the liquid film between quasi-spherical particles,the kinetic theory of rough spheres（KTRS）model for quasi-spherical wet particles is established.The flow characteristics of quasi-spherical wet particles in a liquid-solid fluidized bed are simulated by this model.The simulation results are verified by the liquid volume fraction measured by Ehsani et al.and the non-spherical particles volume fraction measured by Lu et al.The results show that the variation tendencies of the wet normal restitution coefficient model and modified wet normal restitution coefficient model with the particles sphericity are opposite,and the change in the wet normal restitution coefficient with the particles sphericity predicted by the modified model coincides well with the experimental results from Wang et al.That is,the wet normal restitution coefficient rises with the increase of the particles sphericity.In addition,the effects of particles rotation,particles size and particles sphericity on the parameters such as wet normal restitution coefficient,particles collision velocity,total granular temperature,particle phase pressure and particle phase shear viscosity are analyzed.The results show that the pressure and viscosity of wet particles are higher than that of dry particles,and the shear viscosity of particles is about 20 times higher than that of the spin viscosity of particles.