Reduced-order modelling of thick inertial flows around rotating cylinders
Reduced-order modelling of thick inertial flows around rotating cylinders
复制标题
旋转圆柱体周围厚惯性流的降阶建模
DOI：
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发表时间：
2020
影响因子：
3.7
通讯作者：
R. Cimpeanu
中科院分区：
文献类型：
--
作者：
A. Wray;R. Cimpeanu
本文提出了一个新的模型，用于描述旋转圆柱体表面上的厚的二维流体层的行为，该模型考虑了惯性、旋转、粘性、重力和毛细作用的影响。对直接数值模拟（DNS）的比较显示出良好的准确性，流体层的厚度相同的顺序作为圆柱体半径，即使雷诺数高达$Resim 10$。揭示了一个丰富而复杂的参数空间，并阐明通过各种分析和数值技术。在中等的旋转速率和流体质量，系统表现出周期性的行为或收敛到一个稳定的状态，后者通常有利于更大的质量和更低的旋转速率。这些行为，以及它们之间的过渡的分叉结构，检查使用低阶模型和DNS的组合。特别关注的是参数空间的新可访问区域，包括由Lopes等人（J. Fluid Mech.，第835卷，2018年，pp. 540-574），其中相应的三重极限点分岔结构由新的低阶模型恢复。我们还检查状态，其中的接口成为多值的-从而达到的降阶模型-通过DNS。这导致高度非线性的多值周期结构出现在中等厚度和相对较大的旋转速率下。即使是更厚的薄膜也可能最终达到稳定状态（经过复杂的早期演化），只要这些稳定状态是由足够大的力来抵消重力的组合来维持的。
A new model for the behaviour of a thick, two-dimensional layer of fluid on the surface of a rotating cylinder is presented, incorporating the effects of inertia, rotation, viscosity, gravity and capillarity. Comparisons against direct numerical simulations (DNS) show good accuracy for fluid layers of thickness of the same order as the cylinder radius, even for Reynolds numbers up to $Resim 10$. A rich and complex parameter space is revealed, and is elucidated via a variety of analytical and numerical techniques. At moderate rotation rates and fluid masses, the system exhibits either periodic behaviour or converges to a steady state, with the latter generally being favoured by greater masses and lower rotation rates. These behaviours, and the bifurcation structure of the transitions between them, are examined using a combination of both the low-order model and DNS. Specific attention is dedicated to newly accessible regions of parameter space, including the multiple steady state solutions observed for the same parameter values by Lopes et al. (J. Fluid Mech., vol. 835, 2018, pp. 540–574), where the corresponding triple limit point bifurcation structure is recovered by the new low-order model. We also inspect states in which the interface becomes multivalued – and thus outside the reach of the reduced-order model – via DNS. This leads to highly nonlinear multivalued periodic structures appearing at moderate thicknesses and relatively large rotation rates. Even much thicker films may eventually reach steady states (following complex early evolution), provided these are maintained by a combination of forces sufficiently large to counteract gravity.
影响因子：
4.6
作者：
Te-Sheng Lin;S. Rogers;D. Tseluiko;U. Thiele
通讯作者：
Te-Sheng Lin;S. Rogers;D. Tseluiko;U. Thiele