A two-phase two-layer model for fluidized granular flows with dilatancy effects
A two-phase two-layer model for fluidized granular flows with dilatancy effects
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DOI：
10.1017/jfm.2016.417
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发表时间：
2016-04
影响因子：
3.7
通讯作者：
F. Bouchut;E. Fernández-Nieto;A. Mangeney;G. Narbona-Reina
中科院分区：
文献类型：
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作者：
F. Bouchut;E. Fernández-Nieto;A. Mangeney;G. Narbona-Reina
基于Roux和Radjai提出的闭合关系，我们提出了一个考虑剪胀效应的两相两薄层流态化泥石流模型。这一关系表明，颗粒材料的膨胀或收缩的发生取决于固体体积分数分别高于或低于临界值。当膨胀发生时，流体被吸入颗粒材料中，孔压降低，颗粒相上的摩擦力增加。相反，在收缩的情况下，流体从混合物中排出，孔压增加，摩擦力减小。为了考虑流体进入和流出混合物的这种情况，提出了一个两层模型，在两相混合层的顶部有一个流体层。两相满足质量守恒和动量守恒，质量和动量在两层之间传递。采用薄层近似推导平均方程，并给出精确的渐近展开式。特别注意了引起两相之间动量传递和相对于静水压力出现超孔压的阻力摩擦项。对于适当形式的剪胀定律，我们得到了与相应的三维初始系统相对应的具有耗散能量平衡的深度平均模型。
We propose a two-phase two-thin-layer model for fluidized debris flows that takes into account dilatancy effects, based on the closure relation proposed by Roux & Radjai (Physics of Dry Granular Media, 1998, Springer, pp. 229–236). This relation implies that the occurrence of dilation or contraction of the granular material depends on whether the solid volume fraction is respectively higher or lower than a critical value. When dilation occurs, the fluid is sucked into the granular material, the pore pressure decreases and the friction force on the granular phase increases. On the contrary, in the case of contraction, the fluid is expelled from the mixture, the pore pressure increases and the friction force diminishes. To account for this transfer of fluid into and out of the mixture, a two-layer model is proposed with a fluid layer on top of the two-phase mixture layer. Mass and momentum conservation are satisfied for the two phases, and mass and momentum are transferred between the two layers. A thin-layer approximation is used to derive average equations, with accurate asymptotic expansions. Special attention is paid to the drag friction terms that are responsible for the transfer of momentum between the two phases and for the appearance of an excess pore pressure with respect to the hydrostatic pressure. For an appropriate form of dilatancy law we obtain a depth-averaged model with a dissipative energy balance in accordance with the corresponding three-dimensional initial system.