Assessment of Models for Nonlinear Oscillatory Flow Through a Hexagonal Sphere Pack

IF 2.7 3区 工程技术 Q3 ENGINEERING, CHEMICAL
Lukas Unglehrt, Michael Manhart
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Abstract

We review models for unsteady porous media flow in the volume-averaging framework and we discuss the theoretical relations between the models and the definition of the model coefficients (and the uncertainty therein). The different models are compared against direct numerical simulations of oscillatory flow through a hexagonal sphere pack. The model constants are determined based on their definition in terms of the Stokes flow, the potential flow and steady nonlinear flow. Thus, the discrepancies between the model predictions and the simulation data can be attributed to shortcomings of the models’ parametrisation. We found that an extension of the dynamic permeability model of Pride et al. (PRB 47(9):4964–4978, 1993) with a Forchheimer-type nonlinearity performs very well for linear flow and for nonlinear flow at low and medium frequencies, but the Forchheimer term with a coefficient obtained from the steady-state overpredicts the nonlinear drag at high frequencies. The model reduces to the unsteady Forchheimer equation with an acceleration coefficient based on the static viscous tortuosity for low frequencies. The unsteady Forchheimer equation with an acceleration coefficient based on the high-frequency limit of the dynamic tortuosity has large errors for linear flow at medium and high frequencies, but low errors for nonlinear flow at all frequencies. This is explained by an error cancellation between the inertial and the nonlinear drag.

Abstract Image

评估流经六边形球包的非线性振荡流模型
我们回顾了体积平均框架下的非稳态多孔介质流模型,并讨论了模型之间的理论关系以及模型系数(及其不确定性)的定义。我们将不同的模型与通过六边形球包的振荡流动的直接数值模拟进行了比较。模型常数是根据斯托克斯流、势流和稳定非线性流的定义确定的。因此,模型预测与模拟数据之间的差异可归因于模型参数化的缺陷。我们发现,Pride 等(PRB 47(9):4964-4978,1993 年)的动态渗透模型扩展了 Forchheimer 型非线性,在低频和中频的线性流和非线性流中表现很好,但带有稳态系数的 Forchheimer 项在高频时对非线性阻力的预测过高。在低频情况下,该模型简化为带有基于静态粘性湍流的加速度系数的非稳态福赫海默方程。对于中高频率的线性流动,加速度系数基于动态曲率的高频极限的非稳态福克海默方程误差较大,但对于所有频率的非线性流动,误差较小。这是因为惯性阻力和非线性阻力之间存在误差抵消。
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来源期刊
Transport in Porous Media
Transport in Porous Media 工程技术-工程:化工
CiteScore
5.30
自引率
7.40%
发文量
155
审稿时长
4.2 months
期刊介绍: -Publishes original research on physical, chemical, and biological aspects of transport in porous media- Papers on porous media research may originate in various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering)- Emphasizes theory, (numerical) modelling, laboratory work, and non-routine applications- Publishes work of a fundamental nature, of interest to a wide readership, that provides novel insight into porous media processes- Expanded in 2007 from 12 to 15 issues per year. Transport in Porous Media publishes original research on physical and chemical aspects of transport phenomena in rigid and deformable porous media. These phenomena, occurring in single and multiphase flow in porous domains, can be governed by extensive quantities such as mass of a fluid phase, mass of component of a phase, momentum, or energy. Moreover, porous medium deformations can be induced by the transport phenomena, by chemical and electro-chemical activities such as swelling, or by external loading through forces and displacements. These porous media phenomena may be studied by researchers from various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering).
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