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The hydrodynamics of single- and multi-particle fluidized beds: Steady and time-dependent flow regimes.

机译：单颗粒流化床和多颗粒流化床的流体动力学：稳定且随时间变化的流态。

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A mathematical framework for modeling the steady state and dynamic behavior of multi-particle fluidized beds was developed using a continuum approach. Constitutive relations were adopted for closing the multi-phase equations using an excluded volume approach. The hydrodynamics of various fluidized beds of binary particles (having different diameters and densities) was examined, and steady state solutions were found for a system of (small & heavy) glass beads and (large & light) carbon char in water. Solutions characterize the composition and expansion behavior of mixing states, and provide a description of the observed phenomenon of “layer inversion”. Comparison with experimental data suggested that the hydrodynamic mechanism of fluid-particle interaction is not fully captured with an excluded volume assumption. Thus, we showed how experimental data can be used to derive functional forms for expressing complex hydrodynamic behavior within the framework of the model. Steady state results suggest that fluidized particles might exhibit different patterns of behavior if the direction of fluid flow was reversed. We thus examined the stability of single-component systems, operating in inverse and normal mode, and computed one-dimensional traveling wave solutions. Beds having reciprocal fluid to solid density ratios δ were compared to investigate how δ and the dimensionless Froude (Fr) number affect stability behavior and bifurcation structure. The Fr number appeared to be a good indicator of the strength of primary instabilities, and δ appeared to control the onset of the instability. High amplitude, one-dimensional traveling wave solutions exhibited reversed asymmetry of wave structure, and vertically traveling waves always propagated in the direction of fluid flow. The hydrodynamic stability of binary mixtures was examined to determine if mixtures are inherently more stable than their segregated counterparts. In a linear stability analysis, mixed beds of glass and carbon were always more stable than a (single-component) bed of glass, and always less stable than a (single-component) bed of carbon. Moreover, an increase in fluid velocity corresponded to an increase in carbon content in the mixture, resulting in a more stable mixture. These results suggest that the presence of the larger & lighter species serves to stabilize the mixed bed.
机译：使用连续方法开发了用于建模多颗粒流化床的稳态和动态行为的数学框架。本构关系采用排除体积法来封闭多相方程。研究了二元颗粒（具有不同的直径和密度）的各种流化床的流体力学，并发现了（小和重）玻璃珠和（大和轻）碳炭在水中的稳态溶液。解决方案表征混合态的组成和膨胀行为，并提供对“层反转”现象的描述。与实验数据的比较表明，在排除体积的前提下，无法完全捕获流体-颗粒相互作用的流体力学机理。因此，我们展示了如何在模型的框架内利用实验数据得出表达复杂水动力行为的功能形式。稳态结果表明，如果流体流动方向相反，则流化颗粒可能表现出不同的行为模式。因此，我们检查了单分量系统的稳定性，该系统以逆向和正常模式运行，并计算了一维行波解。比较了具有互为固相密度比δ的床，以研究δ和无量纲Froude（ Fr ）数如何影响稳定性和分叉结构。 Fr 值似乎是原发不稳定性的强度的良好指标，而δ似乎可以控制这种不稳定性的发作。高振幅的一维行波解表现出波结构的反向不对称性，垂直行波总是沿流体流动方向传播。检查了二元混合物的水动力稳定性，以确定混合物是否固有地比其分离的同类物更稳定。在线性稳定性分析中，玻璃和碳的混合床总是比（单组分）玻璃床更稳定，并且总是比（单组分）碳床更不稳定。此外，流体速度的增加对应于混合物中碳含量的增加，从而导致更稳定的混合物。这些结果表明较大和较轻的物质的存在有助于稳定混合床。

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