Выходит 12 номеров в год
ISSN Печать: 1091-028X
ISSN Онлайн: 1934-0508
Indexed in
MODIFICATION TO DARCY-FORCHHEIMER MODEL DUE TO PRESSURE-DEPENDENT VISCOSITY: CONSEQUENCES AND NUMERICAL SOLUTIONS
Краткое описание
The standard Darcy model is based on a plethora of assumptions. One of the key assumptions is that the drag coefficient is constant. However, there is irrefutable experimental evidence that viscosities of organic liquids and carbon dioxide, for example, depend on the pressure. Experiments have also shown that the drag varies nonlinearly with respect to the velocity and its gradient at high flow rates. The flow characteristics and pressure variation under varying drag are both quantitatively and qualitatively different from that of a constant drag. Motivated by experimental evidence, we consider an application of the Darcy model where the drag coefficient depends on both the pressure and velocity. We focus on major modifications to the Darcy model based on the Barus formula and Forchheimer approximation in this paper. The proposed modifications to the Darcy model result in nonlinear partial differential equations that are not amenable to analytical solutions. To this end, we present a mixed finite element formulation based on the variational multiscale (VMS) formulation for the resulting governing equations. We also illustrate how to recover local mass conservation through a postprocessing technique based on convex optimization.With the proposed modifications to the Darcy model and the associated finite element framework, we study the competition between the nonlinear dependence of drag on the velocity and the dependence of viscosity on the pressure. To the best of the authors' knowledge such a systematic study has not been reported in the literature.
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Joodat S.H.S., Nakshatrala K.B., Ballarini R., Modeling flow in porous media with double porosity/permeability: A stabilized mixed formulation, error analysis, and numerical solutions, Computer Methods in Applied Mechanics and Engineering, 337, 2018. Crossref
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Mapakshi N.K., Chang J., Nakshatrala K.B., A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity, Journal of Computational Physics, 359, 2018. Crossref
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Spiridonov Denis, Huang Jian, Vasilyeva Maria, Huang Yunqing, Chung Eric T., Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model, Mathematics, 7, 12, 2019. Crossref
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Rezaei A., Nakshatrala K. B., Siddiqui F., Dindoruk B., Soliman M., A global sensitivity analysis and reduced-order models for hydraulically fractured horizontal wells, Computational Geosciences, 24, 3, 2020. Crossref
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Zaytoon M.S. Abu, Hamdan M.H., Fluid Mechanics at the Interface between a Variable Viscosity Fluid Layer and a Variable Permeability Porous Medium, WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER, 16, 2021. Crossref
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Phatak T., Nakshatrala K. B., On Optimal Designs Using Topology Optimization for Flow Through Porous Media Applications, Transport in Porous Media, 138, 2, 2021. Crossref
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Zaytoon M.S. Abu, Dajani S. Jayyousi, Hamdan M.H., Effects of the Porous Microstructure on the Drag Coefficient in Flow of a Fluid with Pressure-Dependent Viscosity, International Journal of Mechanics, 15, 2021. Crossref
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Dajani S. Jayyousi, Zaytoon M. S. Abu, Hamdan M. H., Two-Pressure Model of Particle-Fluid Mixture Flow with Pressure-Dependent Viscosity in a Porous Medium, WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS, 16, 2021. Crossref
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Abu Zaytoon M. S., Xiao Yiyun (Lisa), Hamdan M. H., Flow of a Fluid with Pressure-Dependent Viscosity through Variable Permeability Porous Layer, WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS, 16, 2021. Crossref
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Roach D. C., Hamdan M. H., On the Sigmoid Function as a Variable Permeability Model for Brinkman Equation, WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS, 17, 2022. Crossref
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Nakshatrala Kalyana B., How to pose material design problems for flow through porous media applications? Sensitivity of dissipation rate to medium's permeability holds the key, Physics of Fluids, 34, 2, 2022. Crossref
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Mandal Mani Shankar, Mukhopadhyay Swati, Some aspects of flow over a non-isothermal unsteady stretched exterior fixed in porous medium among heat production/amalgamation, Forces in Mechanics, 9, 2022. Crossref