Stability of plane Couette flow of a granular material
Stability of plane Couette flow of a granular material
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粒状材料平面库埃特流的稳定性
DOI：
10.1017/s002211209800295x
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发表时间：
1998
影响因子：
3.7
通讯作者：
P. Nott
中科院分区：
文献类型：
--
作者：
Meheboob Alam;P. Nott
本文提出了一个线性稳定性分析的平面库埃特流的颗粒材料使用的动力学理论为基础的模型的流变介质。的稳定性分析，仅限于二维扰动，进行了三组说明性的粮食和壁的属性，对应的墙壁是完全绝热的，源和汇的波动能量。当壁不绝热且库埃特间隙H足够大时，稳定充分发展流的基本状态由缓慢变形的“塞”层和快速剪切层组成，其中塞层的堆积密度接近最大堆积密度，而快速剪切层的堆积密度相当低。当壁充当能量汇时，塞子邻近壁，并且当塞子充当能量源时，塞子以对称轴为中心。对于每一组性能，确定了H和平均固体分数[barvee ]范围内的稳定性。对于给定的[barvee ]值，如果H足够小，则流动是稳定的;当H增加时，它易受不稳定性的影响，其形式为在流动方向上没有变化的横流分层波，以及在流动和梯度方向上有变化的驻波和行波。分层不稳定性占上风的H和[barvee ]的所有设置的壁属性的实质性范围。然而，它的增长远远慢于强驻波和行波不稳定性，在较大的H变得活跃。当壁面作为能量汇时，强烈的行波不稳定性完全消失，取而代之的是增长相对缓慢的长波不稳定性。对于绝热壁的情况下，有另一个定常不稳定性的稀流时，颗粒碰撞是准弹性的，这些模式变得稳定时，颗粒碰撞是完全弹性或非常非弹性。所有模式的不稳定性是由颗粒碰撞的非弹性驱动的。
This paper presents a linear stability analysis of plane Couette flow of a granular material using a kinetic-theory-based model for the rheology of the medium. The stability analysis, restricted to two-dimensional disturbances, is carried out for three illustrative sets of grain and wall properties which correspond to the walls being perfectly adiabatic, and sources and sinks of fluctuational energy. When the walls are not adiabatic and the Couette gap H is sufficiently large, the base state of steady fully developed flow consists of a slowly deforming ‘plug’ layer where the bulk density is close to that of maximum packing and a rapidly shearing layer where the bulk density is considerably lower. The plug is adjacent to the wall when the latter acts as a sink of energy and is centred at the symmetry axis when it acts as a source of energy. For each set of properties, stability is determined for a range of H and the mean solids fraction [barvee ]. For a given value of [barvee ], the flow is stable if H is sufficiently small; as H increases it is susceptible to instabilities in the form of cross-stream layering waves with no variation in the flow direction, and stationary and travelling waves with variation in the flow and gradient directions. The layering instability prevails over a substantial range of H and [barvee ] for all sets of wall properties. However, it grows far slower than the strong stationary and travelling wave instabilities which become active at larger H. When the walls act as energy sinks, the strong travelling wave instability is absent altogether, and instead there are relatively slow growing long-wave instabilities. For the case of adiabatic walls there is another stationary instability for dilute flows when the grain collisions are quasi-elastic; these modes become stable when grain collisions are perfectly elastic or very inelastic. Instability of all modes is driven by the inelasticity of grain collisions.