Multiple solutions for granular flow over a smooth two-dimensional bump
Multiple solutions for granular flow over a smooth two-dimensional bump
复制标题
平滑二维凹凸上颗粒流的多种解决方案
DOI：
10.1017/jfm.2017.41
复制
发表时间：
2017
影响因子：
3.7
通讯作者：
J. Gray
中科院分区：
文献类型：
--
作者：
S. Viroulet;J. Baker;A. Edwards;C. Johnson;C. Gjaltema;P. Clavel;J. Gray
地球物理颗粒流，如雪崩、泥石流、火山泥流和火山碎屑流，总是强烈地受到它们流过的基底地形的影响。特别是，局部颠簸或障碍物可能会产生流动厚度和速度的快速变化，或冲击波，这会消耗大量的能量。因此，了解颗粒状物质如何受到底层地形的影响对于减灾目的至关重要，例如，改进用于雪崩的偏转或捕获坝的设计。此外，与固体边界的相互作用在工业过程中也有重要的应用。本文通过小尺度实验研究了二维光滑对称凸块上颗粒雪崩的流动。实验表明，根据初始条件，可以观察到两种不同的稳态制度：要么形成一个脱离射流下游的凸块，或冲击上游it.the之间的过渡两种情况下，可以通过添加不同量的可侵蚀颗粒在前面的障碍物控制。一个深度平均地形跟随雪崩理论，在曲线坐标系中制定的是用来模拟系统。结果表明，这两个政权的实验吻合良好。对于冲击波的情况下，随时间变化的数值模拟的整个系统的平衡状态的演变，以及沉积的颗粒上游的凸块时，流入停止。地形跟随理论相比，一个标准的深度平均雪崩模型在一个对齐的笛卡尔坐标系。对于这个非常敏感的问题，它表明，稳定的冲击政权被捕获显着更好的地形跟随雪崩模型，标准理论是无法预测的起飞点的喷气。为了保持使用笛卡尔坐标的实际简单性，但具有改进的地形跟随模型的预测能力，使用坐标映射将地形跟随方程从曲线坐标变换到笛卡尔坐标。地形跟随模型，在笛卡尔坐标系中，作出相同的预测，原来的曲线公式，但更容易实现。
Geophysical granular flows, such as avalanches, debris flows, lahars and pyroclastic flows, are always strongly influenced by the basal topography that they flow over. In particular, localised bumps or obstacles can generate rapid changes in the flow thickness and velocity, or shock waves, which dissipate significant amounts of energy. Understanding how a granular material is affected by the underlying topography is therefore crucial for hazard mitigation purposes, for example to improve the design of deflecting or catching dams for snow avalanches. Moreover, the interactions with solid boundaries can also have important applications in industrial processes. In this paper, small-scale experiments are performed to investigate the flow of a granular avalanche over a two-dimensional smooth symmetrical bump. The experiments show that, depending on the initial conditions, two different steady-state regimes can be observed: either the formation of a detached jet downstream of the bump, or a shock upstream of it. The transition between the two cases can be controlled by adding varying amounts of erodible particles in front of the obstacle. A depth-averaged terrain-following avalanche theory that is formulated in curvilinear coordinates is used to model the system. The results show good agreement with the experiments for both regimes. For the case of a shock, time-dependent numerical simulations of the full system show the evolution to the equilibrium state, as well as the deposition of particles upstream of the bump when the inflow ceases. The terrain-following theory is compared to a standard depth-averaged avalanche model in an aligned Cartesian coordinate system. For this very sensitive problem, it is shown that the steady-shock regime is captured significantly better by the terrain-following avalanche model, and that the standard theory is unable to predict the take-off point of the jet. To retain the practical simplicity of using Cartesian coordinates, but have the improved predictive power of the terrain-following model, a coordinate mapping is used to transform the terrain-following equations from curvilinear to Cartesian coordinates. The terrain-following model, in Cartesian coordinates, makes identical predictions to the original curvilinear formulation, but is much simpler to implement.