Analytical and numerical investigation of fluid flow instability in porous media with the Forchheimer coefficient impact

Authors

khaje nasir university of technology

Abstract

Analysis of developed fluid flow in a porous channel is one of the classical problems of fluid mechanics. The Darcy model, Brinkman and Brinkman Forchheimer are the most well-known models for describing such flows. Among those, Darcy equation is the most simple model which widely is used to describe the relation of frictional force between fluid and porous solid network. In Brinkman equation, the viscosity term -same to Laplacian term in the Navier Stokes equation- is added to the Darcy equation. Eventually, according to the solid effect on the fluid, Forschimmer term expresses a quadrature drag term.
This paper, presents an asymptotic analysis for linear fluid instability for small wave numbers by introducing set of orthogonal eigenfunctions and resulted critical Reynolds Numbers and critical wave velocities for different values of the Darcy number. Likewise the current paper, presents the effect of the Forchheimer coefficient on these values. Compared to results of other researchers, accuracy and efficiency of the proposed method is depicted.

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References

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Journal of Solid and Fluid Mechanics
Volume 7, Issue 4
January 2018
Pages 97-104

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