AN IMPROVED μ(I) RHEOLOGY MODEL FOR DENSE GRANULAR FLOW IN MOVING BEDS AND ITS APPLICATIONS
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摘要: 颗粒移动床在工业领域应用广泛, 发展实用可靠的颗粒移动床模型具有理论和应用价值. 本文基于颗粒流μ(I)模型, 补充局部颗粒体积分数与颗粒局部压力和局部颗粒流密度的关系式, 将移动床内密集颗粒处理成可压缩拟流体, 建立了颗粒流单相可压缩流μ(I)模型, 并建立了颗粒流−壁面摩擦条件, 在计算中对颗粒流拟黏度和拟压力项进行正则化处理. 采用上述模型与方法对3种典型散料在移动床缩口料仓内的流动进行模拟, 与实验对比, 得到了玻璃珠、刚玉球和粗沙的μ(I)模型参数, 分析了3种不同散料在料仓内的颗粒速度、体积分数等分布特性, 模拟结果较好地揭示了料仓内不同物料的整体流和漏斗流特性; 进而以玻璃珠为例, 对移动床颗粒单管绕流流动进行了模拟, 所得结果合理揭示了管流附近的流动特性. 计算结果表明, 对于本文的计算工况, 颗粒体积分数变化最大范围为0.510 ~ 0.461, 绝大部分区域流动惯性数小于0.1, 改进的单相μ(I)模型能合理预测出密集颗粒流移动床内的流动特性, 方法可行且较多相流算法能明显减小计算量.Abstract: Moving bed technology of dense granular flow has been widely applied in industrial processes. A practical simulation method and detailed studies on the characteristics of granular flow in moving bed are of great significance for its design and operation. In this paper, an improved μ(I) rheology model for dense granular flow in moving beds is presented. Specifically, the relationship among local particle volume fraction, local granular pressure and granular flow density, is proposed, based on which the governing equations by treating the dense granular flow as a compressible pseudo-fluid are established. The particle-wall shear slip boundary condition, together with the regularisation method in the calculation of pseudo-fluid viscosity and granular pressure are presented as well. Firstly, the proposed model is validated and the rheological parameters involved in μ(I) model are determined by the experimental results of velocity distributions for 3 kinds of typical granular materials, namely, glass beads, corundum beads, and coarse sand in a silo. Detailed results regarding the particle velocity, solid volume fraction, velocity shear rate and inertial number of the 3 different granular flow in the silo are obtained. The two typical different flow modes, i.e. the funnel flow for coarse sand and the mass flow for glass beads in silos, are well predicted. Secondly, the granular flow of glass beads passing through a moving bed with an inbuilt pipe is studied as well. Reasonable results including particle velocity, solid volume fraction and granular pressure around the pipe are revealed and analyzed. The typical solid volume fraction of the studied cases ranges from 0.510 ~ 0.461, and the inertial numbers in most region of the beds are less than 0.1. The simulated results show that the proposed model is feasible for dense granular flow in moving beds and the calculation amount is significantly reduced compared with that of the multi-phase simulation method.
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Key words:
- moving bed /
- μ(I) rheology model /
- granular flow /
- particle volume fraction /
- granular pressure
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图 5 不同散料的惯性数分布 (0 ~ 0.001)
Figure 5. Inertial number distribution of different granular materials (0 ~ 0.001)
图 7 不同散料的体积分数分布
Figure 7. Volume fraction distribution of different granular materials
图 10 颗粒流绕管固相拟压力分布
Figure 10. Particle pressure distribution of granular flow around a pipe
图 11 颗粒流绕管颗粒体积分数分布
Figure 11. Particle volume fraction distribution of granular flow around a pipe
表 1 模拟参数
Table 1. Simulation parameters
Glass beads Corundum beads Coarse sand μs 0.32 0.37 0.42 μ2 0.64 0.7 0.88 μw,s 0.22 0.27 0.37 μw,2 0.26 0.30 0.40 I0 0.279 0.279 0.279 I0,w 0.279 0.279 0.279 αs,max 0.55 0.55 0.55 αs,min 0.45 0.45 0.45 ρs/(kg·m−3) 2600 1800 2650 d/mm 3 2 1 
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