From Kinetic Theory to Hydrodynamics: re-imagining two fluid models of particle-laden flows

许多重要的技术都涉及到对颗粒流的操纵。这些行业包括制药、发电厂技术、食品加工等。各种环境保护和安全问题都植根于对颗粒流动力学的理解，例如雪崩、沙尘暴和城市空气污染。这些模型传统上是从统计水平上的稀气体类比得来的，从连续体水平上的传统流体力学推导出来的。然而，在实验中，已知快速颗粒流动显示出在常规流体流动中看不到的各种流变学和流动物理。在模拟快速颗粒流动的先前研究中，采用了在强非平衡状态下为稀薄气体开发的输运模型。这种方法产生了包含高阶梯度项的本构方程（其中最著名的是Burnett和超级Burnett方程组）。然而，已知这种高阶流体力学违反了几个基本的热力学和力学性质。不同的现象学方法已经单独发展起来，它们借鉴了连续介质力学的方法。然而，这些目前还不能总是声称对快速颗粒流所表现出的各种现象提供良好的预测。中等固体体积分数状态下的流动行为，以及不同流动状态之间的转换，仍然是复杂的、有争议的和有问题的。在这个项目中，我们将尝试通过开发和测试复杂的新模型来解决其中的一些问题，该模型采用两种流体方法来稀释颗粒流。这些模型将建立在对微观尺度流体动力学和非平衡粒子统计的良好理解之上。更好地解决粒子/粒子和流体/粒子相互作用的基本物理问题，将使新的本构方程能够超越现象学模型的预测能力。我们的新模型将以一种适合未来研究和工业模拟的形式，在开源计算流体动力学软件OpenFOAM中实现。

A number of important technologies involve the manipulation of particle-laden flows. These include pharmaceuticals manufacturing, power plant technologies, food processing, and many others. Various environmental protection and safety issues are rooted in the understanding of the dynamics of granular flows, for example, avalanches, sandstorms, and city air pollution. Models for these are traditionally derived from analogies with dilute gases at the statistical level, and from conventional fluid mechanics at the continuum level. Rapid granular flows are, however, known experimentally to display a variety of rheological and flow physics not seen in conventional fluid flows. Previous research in modelling rapid granular flows has co-opted transport models developed for rarefied gases under strong non-equilibrium. This approach produces constitutive equations that incorporate high order gradient terms (the best known of which are the Burnett and super-Burnett set of equations). However, this higher order hydrodynamics is known to violate several fundamental thermodynamic and mechanical properties. Alternative phenomenological approaches have been developed separately, which draw on continuum mechanics approaches. These, however, cannot at present always claim to provide good predictions of the various phenomena exhibited by rapid granular flows. Flow behaviour in the moderate solid volume fraction regime, and the transitions between different flow regimes, are still complex, controversial and problematic.In this project we will attempt to resolve some of these problems by developing and testing sophisticated new models within a two-fluid approach to dilute granular flows. These models will be founded on a sound understanding of both the micro-scale fluid dynamics and the non-equilibrium particle statistics. Better resolution of the fundamental physics of both particle/particle and fluid/particle interactions will enable new constitutive equations that leapfrog the predictive capabilities of phenomenological models. Our new models will be implemented in the open source computational fluid dynamics software OpenFOAM, in a form suitable for both future research and industrial simulation.