Numerical simulation of hydrodynamic characteristics of particles and power-law fluid in fluidized beds using kinetic theory of rough spheres

doi:10.11949/0438-1157.20191207

Abstract

Abstract:

On the basis of the traditional kinetic theory of granular flow (KTGF), the tangential restitution coefficient β, 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 particle rotation are established. Under the condition of solving the parameters of energy dissipation and particle phase stress with both translational and rotational motions, the constitutive relations of solids pressure, shear viscosity and energy dissipation, as well as the boundary conditions, are proposed. Finally, the kinetic theory of rough spheres (KTRS) is obtained. By changing the fluid rheological properties, the effects of flow index n and consistency coefficient K_l in the power-law rheology model on the hydrodynamic characteristics in a fluidized bed are studied respectively. The simulation results show that with the increase of the flow index and the consistency coefficient, the energy dissipation rate of the liquid phase turbulence gradually increases, while the particle phase pressure gradually decreases, and the particle rotation increases first and then decreases.

Key words: particle rotation, kinetic theory of rough spheres, non-Newtonian fluid, fluidized bed, two-phase flow, numerical simulation

摘要：

在颗粒动理学理论（KTGF）的基础上，通过引入表征粗糙颗粒摩擦和切向非弹性的切向弹性恢复系数β，以及综合反映颗粒平动和旋转运动脉动强度的颗粒拟总温e₀，结合输运理论建立了考虑颗粒旋转作用的颗粒相质量、动量和颗粒拟总温守恒方程。并在求解了同时具有平动和旋转运动的能量耗散和颗粒相应力等参数的前提下提出了颗粒相压力、剪切黏度和能量耗散等本构关系式以及边界条件，最终得出了粗糙颗粒动理学理论（KTRS）。通过改变液相的流变特性，分析了幂律流变模型中流动指数n和稠度系数K_l对流化床内流固两相流动特性的影响，模拟结果表明：随着流动指数和稠度系数的增大，液相湍动能耗散率逐渐增大，而颗粒相压力逐渐减小，颗粒旋转先增大后减小。

关键词: 颗粒旋转, 粗糙颗粒动理学, 非牛顿流体, 流化床, 两相流, 数值模拟

CLC Number:

TQ 018

Ruichao TIAN, Shuyan WANG, Baoli SHAO, Haoting LI, Yulin WANG. Numerical simulation of hydrodynamic characteristics of particles and power-law fluid in fluidized beds using kinetic theory of rough spheres[J]. CIESC Journal, 2020, 71(4): 1528-1539.

田瑞超, 王淑彦, 邵宝力, 李好婷, 王玉琳. 基于粗糙颗粒动理学流化床内颗粒与幂律流体两相流动特性的数值模拟研究[J]. 化工学报, 2020, 71(4): 1528-1539.

Figures/Tables 14

Table 1 Parameters used in simulations and experiments by Broniarz-Press et al.[32] and Ehsani et al.[33]

参数	文献[32] 实验值	本文对应的模拟值	文献[33] 实验值	本文对应的模拟值
颗粒密度/(kg/m³)	2258	2258	8030	8030
颗粒直径/m	0.004~0.005	0.0046	0.003	0.003
液体密度/(kg/m³)	—	1001	—	1000
液体流动指数	0.82	0.82	1	1
液体稠度系数/(Pa·sⁿ)	0.013	0.013	—	1×10^-3
床高/m	2.0	2.0	0.6	0.6
床宽/m	0.09	0.09	0.08	0.08
初始颗粒浓度	0.578	0.578	0.6	0.6
初始床层高度/m	0.12	0.12	0.24	0.24
恢复系数	—	0.95	—	0.95
壁面恢复系数	—	0.9	—	0.9
切向恢复系数	—	-0.2	—	-0.2
壁面摩擦系数	—	0.2	—	0.2

Fig.1 Distributions of bed dynamic height as a function of superficial liquid velocity

Fig.2 Instantaneous liquid viscosity in bed with KTGF and KTRS models

Fig.3 Instantaneous liquid volume fraction as a function of time in bed with KTGF and KTRS models

Fig.4 Distributions of particle concentration and velocity in fluidized bed at different flow indexes

Fig.5 Profile of cluster size along bed height at different flow indexes

Fig.6 Time-averaged granular temperature as a function of particle concentration at different flow indexes

Fig.7 Time-averaged solids pressure as a function of particle concentration at different flow indexes

Fig.8 Distributions of turbulence dissipation as a function of particle concentration at different flow indexes

Fig.9 Distributions of particle concentration and particle velocity in fluidized bed at different consistency coefficients

Fig.10 Profile of cluster size along bed height at different consistency coefficients

Fig.11 Time-averaged granular temperature as a function of particle concentration at different consistency coefficients

Fig.12 Time-averaged solid pressure as a function of particle concentration at different consistency coefficients

Fig.13 Time-averaged turbulence dissipation as a function of particle concentration at different consistency coefficients

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