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Stability of Poiseuille flow of a Bingham fluid overlying an anisotropic and inhomogeneous porous layer

Published online by Cambridge University Press:  11 July 2019

Sourav Sengupta  and
Sirshendu De Open the ORCID record for Sirshendu De [Opens in a new window]
Sourav Sengupta
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
Sirshendu De*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
*
†Email address for correspondence: sde@che.iitkgp.ac.in
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Abstract

Modal and non-modal stability analyses are performed for Poiseuille flow of a Bingham fluid overlying an anisotropic and inhomogeneous porous layer saturated with the same fluid. In the case of modal analysis, the resultant Orr–Sommerfeld type eigenvalue problem is formulated and solved via the Chebyshev collocation method, using QZ decomposition. It is found that no unstable eigenvalues are present for the problem, indicating that the flow is linearly stable. Therefore, non-modal analysis is attempted in order to observe the short-time response. For non-modal analysis, the initial value problem is solved, and the response of the system to initial conditions is assessed. The aim is to evaluate the effects on the flow stability of porous layer parameters in terms of depth ratio (ratio of the fluid layer thickness $d$ to the porous layer thickness $d_{m}$), Bingham number, Darcy number and slip coefficient. The effects of anisotropy and inhomogeneity of the porous layer on flow transition are also investigated. In addition, the shapes of the optimal perturbations are constructed. The mechanism of transient growth is explored to comprehend the complex interplay of various factors that lead to intermediate amplifications. The present analysis is perhaps the first attempt at analysing flow stability of viscoplastic fluids over a porous medium, and would possibly lead to better and efficient designing of flow environments involving such flow.

JFM classification

Flow Control: Instability control Low-Reynolds-number flows: Porous media Instability: Transition to turbulence

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JFM Papers
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Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 573 - 605
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© 2019 Cambridge University Press 

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