Instability of Vertical Throughflows in Bidisperse Porous Media

The linear instability and the nonlinear stability analyses have been performed to examine the combined impact of a uniform vertical throughflow and a depth-dependent viscosity on bidispersive porous convection using the Darcy theory with a single temperature field. The validity of the principle of exchange of stability is proved. The eigenvalue problems resulting from both linear instability and nonlinear stability analyses with variable coefficients are numerically solved using the Chebyshev pseudo-spectral method. The equivalence of linear instability and nonlinear stability boundaries is established in the absence of throughflow, while in its presence, the subcritical instability is shown to be evident. The stability of the system is independent of the direction of throughflow in the case of constant viscosity, whereas upflow is found to be more stabilizing than downflow when the viscosity is varying with depth. While the viscosity parameter offers a destabilizing influence on the onset of convection in the absence of throughflow, it imparts both stabilizing and destabilizing effects on the same in its presence. The influence of the ratio of permeabilities and the interphase momentum transfer parameter is to make the system more stable. The findings of a mono-disperse porous medium are presented as a specific case within the broader context of this investigation.

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Effect of viscous dissipation on thermal convection in bidispersive porous media with vertical throughflow: Global stability analysis

S. M.,

Ragoju,

Reddy

2024

Physics of Fluids

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This article investigates the onset of convection in a bidispersive porous medium, considering the impact of viscous dissipation and throughflow using both linear and nonlinear theories. The flow is modeled using the Oberbeck–Boussinesq approximation and Darcy's law, with local thermal equilibrium between the fluid and solid phases. The temperature field depends solely on the vertical coordinate in the basic solution. The study employs a two-pronged approach to analyze the system's stability, utilizing the normal mode technique for linear analysis and the energy method for nonlinear analysis. The article confirms the validity of the principle of exchange of stabilities. The numerical solution of the eigenvalue problem for both linear and nonlinear theories is obtained using the bvp4c routine. The research explores the influence of various physical parameters on the system's stability. Viscous dissipation's effect on convection onset is noticeable only with significant throughflow. In the absence of viscous dissipation, the throughflow direction does not affect the system's stability. The effective permeability ratio stabilizes the system with upward throughflow and exhibits opposite behavior with downward throughflow. The sub-critical region remains unchanged for the Gebhart number range but increases with higher moment transfer coefficient and effective permeability ratio. Additionally, an analytical expression is derived for the small Peclet number regime of the Rayleigh number using asymptotic analysis.

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Instability of Vertical Throughflows in Bidisperse Porous Media

Cited by 4 publications

References 28 publications

Analytical study of Brinkman–Bénard convection in a bidisperse porous medium: Linear and weakly nonlinear study

Analytical study of Brinkman–Bénard convection in a bidisperse porous medium: Linear and weakly nonlinear study

Global nonlinear stability of bidispersive porous convection with throughflow and depth-dependent viscosity

Effect of viscous dissipation on thermal convection in bidispersive porous media with vertical throughflow: Global stability analysis

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