Transitional behaviour of convective patterns in free convection in porous media

2017 ◽  
Vol 818 ◽  
Author(s):  
Hamid Karani ◽  
Christian Huber
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Stability Analysis ◽  
Transition Point ◽  
Stability Diagram ◽  
Saturated Porous Media ◽  
Two Dimensional ◽  
Cell Pattern ◽  
Convection In Porous Media ◽  
Basin Stability

The present study focuses on the transition between steady convective patterns in fluid-saturated porous media. We conduct experiments to identify the transition point from the single- to double-cell pattern in a two-dimensional porous medium. We then perform a basin stability analysis to assess the relative stability of different convective modes. The resulting basin stability diagram not only provides the domains of coexistence of different modes, but it also shows that the likelihood of finding convective patterns depends strongly on the Rayleigh number. The experimentally observed transition point from single- to double-cell mode agrees well with the stochastically preferred mode inferred from the basin stability diagram.

An Historical and Topical Note on Convection in Porous Media

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
D. A. Nield ◽  
A. V. Kuznetsov
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Porous Materials ◽  
Analytical Modeling ◽  
Single Phase ◽  
Saturated Porous Media ◽  
Early Literature ◽  
The Third ◽  
Convection In Porous Media

This note deals with three main themes. The first is a discussion of the early literature on convection in porous media. The second is a brief overview of current analytical modeling of single-phase convection in saturated porous media and in composite fluid/porous-medium domains. The third is a brief discussion of some pertinent recent studies involving nanofluids, cellular porous materials, bidisperse and tridisperse porous media.

scholarly journals Nonstationary filtration in partially saturated porous media

1994 ◽  
Vol 5 (3) ◽  
pp. 405-429 ◽  
Author(s):  
Xinfu Chen ◽  
Avner Friedman ◽  
Tsuyoshi Kimura
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Unique Solution ◽  
Boundary Data ◽  
Saturated Porous Media ◽  
Two Dimensional ◽  
Free Boundaries ◽  
Partially Saturated ◽  
Nonstationary Filtration ◽  
Partially Saturated Porous Media

Nonstationary two-dimensional filtration in a porous medium is considered, whereby part of the medium is saturated, another part is unsaturated but wet, and the remaining part is dry. The saturated/unsaturated and unsaturated/dry interfaces are free boundaries. It is shown that there exists a unique solution, and that the saturation function is continuous in the wet portion of the medium; this implies that the two interfaces are separated. Under some monotonicity-type conditions on the initial and boundary data it is shown that the free boundaries are continuous.

scholarly journals Predicting porosity, permeability, and tortuosity of porous media from images by deep learning

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Krzysztof M. Graczyk ◽  
Maciej Matyka
Keyword(s):  
Neural Networks ◽  
Porous Medium ◽  
Porous Media ◽  
Deep Learning ◽  
Lattice Boltzmann ◽  
Good Accuracy ◽  
Two Dimensional ◽  
Empirical Estimate ◽  
Flow Through ◽  
Boltzmann Method

AbstractConvolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ($$\varphi$$ φ ), permeability (k), and tortuosity (T). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method. The analysis has been performed for the systems with $$\varphi \in (0.37,0.99)$$ φ ∈ ( 0.37 , 0.99 ) which covers five orders of magnitude a span for permeability $$k \in (0.78, 2.1\times 10^5)$$ k ∈ ( 0.78 , 2.1 × 10 5 ) and tortuosity $$T \in (1.03,2.74)$$ T ∈ ( 1.03 , 2.74 ) . It is shown that the CNNs can be used to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between T and $$\varphi$$ φ has been obtained and compared with the empirical estimate.

Analytical Prediction of the Transition to Chaos in Porous Media Natural Convection

2008 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Porous Media ◽  
Natural Convection ◽  
Stability Analysis ◽  
Analytical Solution ◽  
Linear Stability Analysis ◽  
Transition Point ◽  
Analytical Prediction ◽  
Linear Solution ◽  
Transition To Chaos ◽  
Validity Condition

The failure of the linear stability analysis to predict accurately the transition point from steady to chaotic solutions in porous media natural convection motivates this study. A weak non-linear solution to the problem is shown to produce an accurate analytical expression for the transition point as long as the validity condition and consequent accuracy of the latter solution is fulfilled. The analytical results are compared to accurate computational solutions showing an excellent fit within the validity domain of the analytical solution.

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