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Research Papers: Multiphase Flows

# Influence of Morphology on Flow Law Characteristics in Open-Cell Foams: An Overview of Usual Approaches and Correlations

[+] Author and Article Information
Prashant Kumar

Technopole de Château Gombert,
IUSTI, CNRS UMR 7343,
Aix-Marseille Université,
IUSTI-CNRS UMR 7343,
Technopôle de Château Gombert,
5, Rue Enrico Fermi,
Marseille Cedex 13 13453, France
e-mail: prashant.kumar@etu.univ-amu.fr

Frédéric Topin

Technopole de Château Gombert,
IUSTI, CNRS UMR 7343,
Aix-Marseille Université,
IUSTI-CNRS UMR 7343,
Technopôle de Château Gombert,
5, Rue Enrico Fermi,
Marseille Cedex 13 13453, France
e-mail: frederic.topin@univ-amu.fr

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 3, 2015; final manuscript received February 10, 2017; published online April 24, 2017. Assoc. Editor: Kausik Sarkar.

J. Fluids Eng 139(7), 071301 (Apr 24, 2017) (12 pages) Paper No: FE-15-1530; doi: 10.1115/1.4036160 History: Received August 03, 2015; Revised February 10, 2017

## Abstract

Foam structures have been a subject of intensive research since the last decade. The pore space in open-cell foam is interconnected, forming perforated channels of varying cross-sectional areas where fluid can flow. Knowledge of pressure drop induced by these foam matrices is essential for successful design and operation of high-performance industrial systems. In this context, analytical correlations were derived for the determination of Darcian permeability ($KD$) and Forchheimer inertia coefficient ($CFor$) in open-cell foams of different strut shapes. It has been shown that the flow law characteristics are strongly dependent on strut shape, strut characteristic dimension, and length. The applicability of new correlations was examined by comparing and validating the numerical and experimental flow law characteristics data against the predicted ones. An excellent agreement has been observed for the foam structures of different materials and variable texture in a wide range of porosity and Reynolds number.

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## Figures

Fig. 1

Performance of the pressure drop correlations reported in the literature (black line corresponds to the computational fluid dynamics (CFD) numerical data of Kumar and Topin [3,4]). The comparison presented above is performed for equilateral triangular strut shape (top) and circular strut shape (bottom).

Fig. 2

Representation of different 3D strut and ligament shapes: (a) circular, (b) equilateral triangle, (c) square, (d) diamond (double equilateral triangle), (e) hexagon, (f) star, and (g) rotated square. The characteristic dimensions of struts are also presented (see Kumar and Topin [3,4]).

Fig. 3

Plot of flow law characteristics: KD (left) and CFor (right) as combination of porosity and dimensionless strut radius and ligament length. The plots are shown for circular strut shape in the porosity range 0.60 <εo< 0.95.

Fig. 4

Relationship between KD and CFor with dimensionless strut radius and ligament length. The plot is shown for circular strut shape in the porosity range 0.60 <εo< 0.95.

Fig. 5

Comparison and validation of numerical () and analytical () friction factors versus Reynolds number based on square root of Darcian permeability. Analytical correlations of KD  and CFor integrated with dimensionless geometrical properties predict an excellent agreement. Zoom view: friction factor in transition and inertia regimes are clearly shown and are not constant with increasing velocity. Results are shown for circular strut shape.

Fig. 6

Comparison and validation of numerical () and analytical () friction factors versus Reynolds number based on square root of Darcian permeability for different strut shapes at 80% porosity. Zoom view: friction factor in transition and inertia regimes are clearly shown and are not constant even for foams of same porosity and same pore size.

Fig. 7

Validation of predicted data against experimental flow law characteristics data [15,3133] for various metal foams of different pore sizes and porosities: (a) permeability and (b) inertia coefficient. Predicted data were calculated using the correlation of triangular strut shape (Table 3, Eq. (22)).

Fig. 8

Validation of predicted data against experimental flow law characteristics data [1,2,5,18,21,22] for ceramic foams of different pore sizes and porosities: (a) permeability and (b) inertia coefficient. Predicted data were calculated using the correlation of circular strut shape (Eq. (20)).

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