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首页> 外文期刊>International Journal of Heat and Mass Transfer >Influence of inertia and drag terms on the stability of mixed convection in a vertical porous-medium channel
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Influence of inertia and drag terms on the stability of mixed convection in a vertical porous-medium channel

机译：惯性和阻力项对垂直多孔介质通道内混合对流稳定性的影响

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摘要

In this paper, we report the influence of different terms appearing in the momentum equation on the stability of buoyancy-assisted mixed convection in a vertical channel filled with a porous medium. Four different models: (ⅰ) Darcy-Brinkman (DB), (ⅱ) Darcy-Brinkman-Forchheimer (DBF), (ⅲ) Darcy-Brinkman-Wooding (DBW), and (ⅳ) Darcy-Brinkman-Forchheimer-Wooding (DBFW) are considered and a comparative study is made based on a linear stability analysis. We consider a Prandtl number range of Pr = 0.1-10, which corresponds to water and gases. Judged from the instability boundary curves, it is found that with reduction of Darcy number there exists an equivalence of DB with DBF model from one side, and an equivalence of DBW with DBFW model from the other side. When the medium is a gas, a significant difference between DB and DBW (or DBF and DBFW) is visible, which is not the case for water. Furthermore, it is found that in case of a gas, inertia force destabilizes the flow, whereas, form drag stabilizes it. In contrast to a fluid-filled channel (where inertia term always destabilizes the buoyancy-assisted flow), here this destabilizing property might turn into a stabilizing one when fluid viscosity and permeability of the medium are changed. In the case of water, for Da = 10~(-2), the inertia term stabilizes the flow beyond Re = 25. When Da is reduced by one order of magnitude, the destabilizing effect continued up to Re = 220. The combined effect of form drag (Forchheimer term) and inertia (Wooding term) on the stability of the flow is more intensive than their individual effects provided the medium is highly permeable. In most cases studied here, the disturbance flow patterns are similar for DB and DBF from one side, and DBW and DBFW from the other side.
机译：在本文中，我们报告了动量方程中出现的不同项对充满多孔介质的垂直通道中浮力辅助混合对流稳定性的影响。四种不同的模型：（ⅰ）达西-布林克曼（DB），（ⅱ）达西-布林克曼-福希海默（DBF），（ⅲ）达西-布林克曼-伍丁（DBW）和（ⅳ）达西-布林克曼-福希海默-伍德丁（考虑DBFW），并基于线性稳定性分析进行比较研究。我们考虑普兰特数范围Pr = 0.1-10，它对应于水和气体。从不稳定性边界曲线判断，发现随着达西数的减少，从一侧来看，DBF模型与DBW等价，从另一侧来看，DBW与DBW模型具有等价性。当介质是气体时，DB和DBW（或DBF和DBFW）之间的显着差异是可见的，而水则不然。此外，发现在气体的情况下，惯性力使流动不稳定，而形式阻力使流动稳定。与充液通道（惯性项始终使浮力辅助流不稳定）相反，在此情况下，当介质的流体粘度和渗透率发生变化时，这种失稳特性可能会变成稳定的特性。在水的情况下，对于Da = 10〜（-2），惯性项使Re = 25之后的流量稳定。当Da减小一个数量级时，去稳定作用一直持续到Re =220。联合作用如果介质具有高渗透性，那么形式阻力（Forchheimer项）和惯性（Wooding项）对流动稳定性的影响要比它们各自的影响更为强烈。在这里研究的大多数情况下，从一侧来看，DB和DBF的干扰流模式是相似的，而从另一端来看，DBW和DBFW的干扰流模式是相似的。

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