Coupling rheology and segregation in granular flows
Coupling rheology and segregation in granular flows
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DOI：
10.1017/jfm.2020.973
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发表时间：
2021-02-25
影响因子：
3.7
通讯作者：
Gray, J. M. N. T.
中科院分区：
文献类型：
--
作者：
Barker, T.;Rauter, M.;Gray, J. M. N. T.
在过去的15年中，颗粒材料的连续体建模出现了范式转变;最值得注意的是流变模型的发展，例如-流变学（其中摩擦力和I是惯性数），而且颗粒分离理论也有了重大进展。本文详细介绍了理论和数值框架（基于OpenFOAM），统一了这些目前脱节的努力。耦合的分离与流动，反之亦然，不仅是至关重要的一个完整的理论颗粒材料，但也有利于发展数值方法来处理不断变化的自由表面。该一般方法基于部分正则化的不可压缩流变学，其与Gray & Ancey（J. Fluid Mech.，第678卷，2011年，pp. 353-588）。这些对流-扩散-分离方程描述了组分的浓度变化，然后将其耦合回不可压缩Navier-Stokes方程中的可变粘度。该方法的新颖特征是可以包括任何数量的不同尺寸的相，其可以具有不同的摩擦特性。进一步包含过量的空气相，其从颗粒材料分离，然后允许同时捕获自由表面的复杂演变。确定了三个主要的耦合机制：（i）平流的颗粒浓度的体积速度，（ii）反馈的颗粒大小和/或摩擦性能的体积流场和（iii）的剪切速率，压力，重力，颗粒大小和颗粒大小比的影响，局部演变的偏析和扩散速率。在将完全耦合模型与Tripathi & Khakhar（Phys. Fluids，第23卷，2011年，113302）的离散元方法模拟进行比较并用于计算在方形旋转鼓中自发发展的花瓣状偏析图案之前，在单向耦合计算中对数值方法进行了广泛测试。
During the last fifteen years there has been a paradigm shift in the continuum modelling of granular materials; most notably with the development of rheological models, such as the -rheology (where is the friction and I is the inertial number), but also with significant advances in theories for particle segregation. This paper details theoretical and numerical frameworks (based on OpenFOAM) which unify these currently disconnected endeavours. Coupling the segregation with the flow, and vice versa, is not only vital for a complete theory of granular materials, but is also beneficial for developing numerical methods to handle evolving free surfaces. This general approach is based on the partially regularized incompressible -rheology, which is coupled to the gravity-driven segregation theory of Gray & Ancey (J. Fluid Mech., vol. 678, 2011, pp. 353-588). These advection-diffusion-segregation equations describe the evolving concentrations of the constituents, which then couple back to the variable viscosity in the incompressible Navier-Stokes equations. A novel feature of this approach is that any number of differently sized phases may be included, which may have disparate frictional properties. Further inclusion of an excess air phase, which segregates away from the granular material, then allows the complex evolution of the free surface to be captured simultaneously. Three primary coupling mechanisms are identified: (i) advection of the particle concentrations by the bulk velocity, (ii) feedback of the particle-size and/or frictional properties on the bulk flow field and (iii) influence of the shear rate, pressure, gravity, particle size and particle-size ratio on the locally evolving segregation and diffusion rates. The numerical method is extensively tested in one-way coupled computations, before the fully coupled model is compared with the discrete element method simulations of Tripathi & Khakhar (Phys. Fluids, vol. 23, 2011, 113302) and used to compute the petal-like segregation pattern that spontaneously develops in a square rotating drum.