Transition to turbulence in randomly packed porous media; scale estimation of vortical structures

Ziazi, Reza M.; Liburdy, James A.

doi:10.48550/arxiv.2012.15031

Cited by 1 publication

(2 citation statements)

References 127 publications

(202 reference statements)

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“…Since the eddies and vortical structure continue to grow above the critical value of Re, they effectively narrow down the flow paths within the pores, hence reducing the effective permeability. This picture is consistent with experimental observations of the Ziazi and Liburdy (2022), who analyzed vorticity locally in their porous medium, which was a packed bed of particles.…”

Section: The Effective Permeabilitysupporting

confidence: 90%

“…( 2) for the two types of boundary conditions (B.C. ), as a function of the porosity and the Reynolds number complex conjugate, = r ± i i , with the imaginary part i representing the local swirling strength (Chong et al 1990;Ziazi and Liburdy 2022), which may also be interpreted as a measure of the strength of the vorticity. Thus, we computed i , with the results shown in Fig.…”

Section: Vorticitymentioning

confidence: 99%

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The Transition from Darcy to Nonlinear Flow in Heterogeneous Porous Media: I—Single-Phase Flow

Arbabi,

Sahimi

2024

Transp Porous Med

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Using extensive numerical simulation of the Navier–Stokes equations, we study the transition from the Darcy’s law for slow flow of fluids through a disordered porous medium to the nonlinear flow regime in which the effect of inertia cannot be neglected. The porous medium is represented by two-dimensional slices of a three-dimensional image of a sandstone. We study the problem over wide ranges of porosity and the Reynolds number, as well as two types of boundary conditions, and compute essential features of fluid flow, namely, the strength of the vorticity, the effective permeability of the pore space, the frictional drag, and the relationship between the macroscopic pressure gradient $${\varvec{\nabla }}P$$ ∇ P and the fluid velocity v. The results indicate that when the Reynolds number Re is low enough that the Darcy’s law holds, the magnitude $$\omega _z$$ ω z of the vorticity is nearly zero. As Re increases, however, so also does $$\omega _z$$ ω z , and its rise from nearly zero begins at the same Re at which the Darcy’s law breaks down. We also show that a nonlinear relation between the macroscopic pressure gradient and the fluid velocity v, given by, $$-{\varvec{\nabla }}P=(\mu /K_e)\textbf{v}+\beta _n\rho |\textbf{v}|^2\textbf{v}$$ - ∇ P = ( μ / K e ) v + β n ρ | v | 2 v , provides accurate representation of the numerical data, where $$\mu$$ μ and $$\rho$$ ρ are the fluid’s viscosity and density, $$K_e$$ K e is the effective Darcy permeability in the linear regime, and $$\beta _n$$ β n is a generalized nonlinear resistance. Theoretical justification for the relation is presented, and its predictions are also compared with those of the Forchheimer’s equation.

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Section: The Effective Permeabilitysupporting

confidence: 90%

Section: Vorticitymentioning

confidence: 99%