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Proceedings ArticleDOI

Permeability and Thermal Transport in Compressed Open-Celled Foams

01 Jan 2008-pp 475-484
TL;DR: In this paper, a computational methodology is proposed to describe the fluid transport in compressed open-celled metallic foams and a corrected model is proposed for the permeability of compressed foams as a function of strain for flows transverse to the direction of compression.
Abstract: A computational methodology is proposed to describe the fluid transport in compressed open-celled metallic foams. Various unit-cell foam geometries are numerically deformed under uniaxial loads using a finite element method. An algorithm is developed and implemented to deform the fluid domain mesh inside the unit-cell foam based on the deformed solid unit-cell geometry. Direct simulations of the fluid transport in these deformed meshes are then performed over a range of Reynolds numbers used in practical applications. The model is validated against available experimental results and correlations. A corrected model is proposed for the permeability of compressed foams as a function of strain for flows transverse to the direction of compression. The thermal conductivity of fluid-saturated foams is also computed. Compression of foams increases the conductivity transverse to the direction of compression and decreases the conductivity parallel to it.Copyright © 2008 by ASME

Summary (2 min read)

1 INTRODUCTION

  • Open-celled foams possess a number of interesting physical properties which has led to a wide range of research studies during the last two decades.
  • The mechanical, thermal and fluid-dynamical properties of such compressed foams are of great industrial and research interest.
  • Three-dimensional MRI images of the velocity f elds of water flow inside the foam were obtained.
  • The modeling technique is specific to the pore geometry obtained from the MRI images and cannot be generalized.
  • No effective parameters such as permeability were reported.

2 GEOMETRIC MODEL

  • The authors use the same methodology for geometry creation as discussed in [15].
  • Figure 1b shows sample open-cell structures formed for three different lattice arrangements.
  • To mimic the plastic behavior of the material, a very low Young’s modulus is applied once the material crosses th yield strength of the bulk material.

Convective Flow and Heat Transfer

  • It should be noted that there may be other periodic boundaries in the module, but there is no net inflow through any of these boundaries.
  • A constant heat flux is imposed on the metal foam surfaces.
  • Details of the mathematical model are available in [15, 25], while the numerical methods for periodic flow on unstructured meshes along with the implementation are outlined in [26].
  • The geometry was discretized into three-dimensional finite volumes using hybrid (tetrahedral and hexagonal) elements in GAMBIT by specifying the minimum edge length.
  • Grid-independence tests were performed using the procedures detailed in [15].

Coupling Methodology

  • One-way coupling is established between ANSYS and FLUENT to solve for flow through compressed foams.
  • The solid and fluid parts of the unit cell are meshed at the same time in GAMBIT so that the nodes at the solid/liquid interface match.
  • The nodal displacements of the solid/liquid surface are extracted and fed into FLUENT.
  • Custom user-defined functions (UDFs) are written utilizing the dynamic remeshing capabilities in FLUENT to remesh the FLUENT mesh to match the interface node displacement obtained from the ANSYS compression model.
  • The new compressed mesh is used to predict the convective flow characte istics of the compressed foams.

4 RESULTS

  • The BCC, FCC and A15 lattice foam geometries are structurally compressed and the effective Young’s modulus is predicted for different porosities.
  • The geometry which best matches the experimentally measured values of Young’s modulus of open-celled foams is chosen as the structure for further study of the effect of compression on convecti flow and heat transfer characteristics.

Aluminum Foams

  • With the numerical methodology validated above, the model is applied to the prediction of permeability in compressed aluminum foams.
  • The solid and liquid domains of the foam are deformed for the effective thermal conductivity calculations using the coupled model described previously.
  • Details of the mathematical model and numerical method are outlined in [15, 35].
  • Also plotted in the figure are the predictions from the available numerical and semi-empirical models and experimental measurements from the literature for uncompressed open-celled foams [36,37,38,39,40].
  • Hence the conductivity parallel to the direction of compression decreases.

5 CORRECTED GENT AND RUSCH MODEL

  • Gent and Rusch did not consider the effect of lateral expansion while calculating the effective diameter of compressed foams.
  • The corrected model improves on the original Gent and Rusch model in predicting the permeability in transverse flow.

6 CONCLUSIONS

  • A model which couples structural deformation with fluid flow and heat transfer computations has been developed to predict the permeability of compressed m tal foams.
  • Three different foam unit cell models, BCC, FCC and A15 are considered.
  • A correction to the Gent and Rusch model [4] is proposed to better predict the permeability of flow in the direction transverse to the compression direction.
  • Compression of foams increases the transverse heat transfer and reduces parallel heat transfer.
  • The effect of compression is to increase the transverse conductivity and reduce parallel conductivity.

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Purdue University
Purdue e-Pubs
CTRC Research Publications Cooling Technologies Research Center
3-1-2008
Permeability and #ermal Transport in
Compressed Open-Celled Foams
Ravi Annapragada
asravi@purdue.edu
S V. Garimella
Purdue University, sureshg@purdue.edu
Jayathi Y. Murthy
School of Mechanical Engineering, Purdue University, jmurthy@purdue.edu
Follow this and additional works at: h=p://docs.lib.purdue.edu/coolingpubs
<is document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for
additional information.
Annapragada, Ravi; Garimella, S V.; and Murthy, Jayathi Y., "Permeability and <ermal Transport in Compressed Open-Celled Foams"
(2008). CTRC Research Publications. Paper 95.
h=p://dx.doi.org/10.1080/10407790802154173

1
Permeability and Thermal Transport in Compressed Open-Celled Foams
*
S. Ravi Annapragada, Jayathi Y. Murthy, Suresh V. Garimella
,
School of Mechanical Engineering, 585 Purdue Mall, Purdue University,
West Lafayette, IN-47907 USA
Abstract
A computational methodology is proposed to describe the fluid transport in compressed open-
celled metallic foams. Various unit-cell foam geometries are numerically deformed under uniaxial
loads using a finite element method. An algorithm is developed and implemented to deform the fluid
domain mesh inside the unit-cell foam based on the deformed solid unit-cell geometry. Direct
simulations of the fluid transport in these deformed meshes are then performed over a range of
Reynolds numbers used in practical applications. The model is validated against available
experimental results and correlations. A corrected model is proposed for the permeability of
compressed foams as a function of strain for flows transverse to the direction of compression. The
thermal conductivity of fluid-saturated foams is also computed. Compression of foams increases the
conductivity transverse to the direction of compression and decreases the conductivity parallel to it.
*
Submitted for possible publication in Numerical Heat Transfer, March 2008
Corresponding author, Email: sureshg@purdue.edu, Tel: 765-494-5646, Fax: 765-494-0539

2
NOMENCLATURE
a edge length of the unit cell, m
A area, m
2
C
P
specific heat, J g
−1
K
−1
D diameter of the pore, m
Da Darcy number
E Young’s modulus, Nm
-2
f friction factor
J diffusion flux vector, m
2
s
-1
K permeability, m
2
k thermal conductivity, Wm
-1
K
-1
L length of the periodic module, m
Nu Nusselt number
q” heat flux, Wm
-2
P pressure, Nm
-2
Pr Prandtl number
Pe Peclet number
R radius of the pore, m
Re Reynolds number
s center-to-center distance, m
T temperature, K
t time, s
u,v,w velocities along x,y,z directions, ms
-1
V volume, m
3
x,y,z Cartesian coordinates
Greek
α
thermal diffusivity, m
2
s
-1
δ displacement, m
ε
strain
λ Lame’s constant
µ
dynamic viscosity, kg m
-1
s
-1
ρ density, kg m
-3
Φ porosity
Superscripts
- average or mean
Subscripts
0 uncompressed
B bulk
bc body center
comp compression
D Darcian
Eff effective value for the foam
f fluid, foam
in inlet
int intersection
K permeability
s solid
sa surface area
sc spherical cap
solid bulk value of solid
top top surface
unrestrained lateral sides free to move

3
1 INTRODUCTION
Open-celled foams possess a number of interesting physical properties which has led to a wide range
of research studies during the last two decades. These foams have been used as sound absorbents, as
scaffolds in tissue engineering, in hydrogen storage, catalysis and other applications [1,2]. More recently,
metal foams have been considered for electronics cooling applications [3]. In many of these applications,
low-porosity foams are created by compressing high-porosity open-celled foams. The mechanical,
thermal and fluid-dynamical properties of such compressed foams are of great industrial and research
interest.
Gent and Rusch made the first attempt to study the effect of compression of an open-cell
polyurethane foam on the resulting fluid transport [4]. The foam was represented by an array of circular
tubes. Based on this assumption, the effective cell diameter associated with the compressed foam was
related to the strain (
ε
) by the relationship,
1/2
0
(1 )
d d
ε
= + . A simple model based on scaling was defined
to arrive at the permeability of compressed polyurethane foams as a function of
ε
. They also
experimentally observed that Darcy flow (with viscosity dominating) was valid until Re
D
1, beyond
which inertial forces were found to dominate. An extension to the model was proposed by Hilyard and
Collier [5], who used packed-bed theory to relate permeability to compression and porosity in
polyurethane foams. Mills and Lyn [6] used the Hilyard and Collier model to account for the effect of air
pressure during the deformation under impact of a polyurethane foam.
Recently, Dawson et al. [7] performed controlled experiments in which foams were compressed to
80% of their original linear dimension. The flow direction was always the same as the direction of
compression. For polyurethane foams, the foam was observed to exhibit elastic behavior for small
amounts of compression. Beyond a certain strain (
ε
= 7.5%), the foams buckled along bands and the
densification was observed to occur along these regions. The experiments also showed that the
permeability is independent of the cell size. A model was proposed to predict the effect of applied strain
on permeability, with the experiments providing an empirical model constant in the densified region.
Schulenburg et al. [8] computed pore-scale velocities in an impacted foam using the lattice-
Boltzmann method and compared the results to measurements made via Magnetic Resonance Imaging
(MRI). Three-dimensional MRI images of the velocity fields of water flow inside the foam were
obtained. The regions with velocities below a particular threshold level were assumed to constitute the
foam walls. These images provided the geometry used in the lattice-Boltzmann fluid simulations. The
modeling technique is specific to the pore geometry obtained from the MRI images and cannot be
generalized. Also, no effective parameters such as permeability were computed from the simulations.

4
The compressive behavior of metal foams is different from that of polyurethane foams. Kwon et al.
[9] showed that the mode of failure in metals is through plastic collapse at the joints, finally leading to
complete collapse of the cell. The flow through these metal foams has received little attention until
recently. Experimental results [10, 11, 12] for permeability of compressed metal foams available through
about the year 2005 were summarized in Dukhan et al. [10]. Boomsma et al. [13] measured the thermal
performance of metal foams compressed to strains of -0.5, -0.75, -0.83 and -0.88. Metal foams were
recommended for use in compact heat exchangers since the thermal resistance was shown to be lower,
and the efficiency greater, than that of existing heat exchangers. Klein et al. [14] constructed a heat
exchanger using compressed foams and studied the thermal performance relative to the extent and
direction of compression for Reynolds number of 100-1000. The thermal performance was observed to
be independent of the direction of compression. No effective parameters such as permeability were
reported.
The research to date has concentrated on the performance of foams compressed well beyond the
plastic limit and into the crushed regime. In the present work, we investigate the performance of
compressed foams at compressions within the plastic-collapse limit ( 10% compression). The unit cell
modeling approach of Krishnan et al. [15] forms the starting point for this work. We develop a new
coupled unit-cell model to understand the effect of compression on the flow and thermal characteristics of
these foams. The model is validated against experiments and correlations for polyurethane foams and is
extended to model the fluid and thermal transport in metal foams.
2 GEOMETRIC MODEL
In this work, we use the same methodology for geometry creation as discussed in [15]. The shape of
the pore is assumed to be spherical and spheres of equal volume are arranged according to the following
three lattice structures: (i) BCC, body-centered cubic, (ii) FCC, face-centered cubic, and (iii) A15 lattice,
which is similar to the Weaire- Phelan (WP) structure [16, 17]. The periodic foam unit-cell geometry is
obtained by subtracting the spheres at the various lattice points from the unit cell cube as shown in Figure
1a. The cross-section of the foam ligaments is a set of convex triangles (Plateau borders), all of which
meet at symmetric tetrahedral vertices [16]. It is noted that there is a non-uniform distribution of metal
mass along the length of the ligament, with more mass accumulating at the vertices (nodes) and resulting
in a thinning at the center of the ligament as experimentally observed in foam samples by many authors
(e.g., [18]). Figure 1b shows sample open-cell structures formed for three different lattice arrangements.
The distinguishing features of this approach are that: (i) the geometry creation is simple; (ii) it captures
many of the important features of real foams; and (iii) meshing of the geometry is easier compared to the

Citations
More filters
Journal ArticleDOI
TL;DR: In this paper, the porosity of aluminum foams of varying pore sizes was investigated through CT-scanning at 20 micron resolution, and the convective heat transfer results exhibited a dependence on the linear porosity, even though the corresponding volumetric porosity is the same for all the samples considered.
Abstract: Important heat transfer parameters of aluminum foams of varying pore sizes are investigated through CT-scanning at 20 micron resolution. Small sub-samples from the resulting images are processed to generate feature-preserving, finite-volume meshes of high quality. All three foam samples exhibit similar volumetric porosity (in the range ∼91–93%), and thereby a similar thermal conductivity. Effective tortuosity for conduction along the coordinate directions is also calculated. Permeability simulations in the Darcy flow regime with air and water show that the foam permeability is isotropic and is of the order of 10−7 m2. The convective heat transfer results computed for this range of Reynolds numbers exhibit a dependence on the linear porosity, even though the corresponding volumetric porosity is the same for all the samples considered.

97 citations


Cites background from "Permeability and Thermal Transport ..."

  • ...They have been shown [10, 11] to provide an effective solution to many thermal problems....

    [...]

Journal ArticleDOI
TL;DR: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted by as mentioned in this paper, where the authors conducted a comprehensive survey.
Abstract: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted Due to the immenseness of the literature volume, the survey

58 citations

Journal ArticleDOI
TL;DR: In this article, a nodal network representation of three aluminum foam samples from DUOCEL is constructed out of X-ray microtomography data obtained by computed tomography (CT) scanning of the samples using a commercial CT scanner.

41 citations

Journal ArticleDOI
TL;DR: In this article, a preconditioned density-based finite-volume method is proposed to simulate the coupled fluid flow and heat transfer problems in hybrid porous/fluid/solid domains.
Abstract: A preconditioned density-based finite-volume method is proposed to simulate the coupled fluid flow and heat transfer problems in hybrid porous/fluid/solid domains. In the porous zone, the momentum equation is formulated by the Darcy-Brinkman-Forchheimer model; and the thermal nonequilibrium model is adopted for the energy equation. At the porous/fluid interface, both the stress-jump and stress-continuity models are applied for interfacial hydrodynamic conditions. The preconditioning method for solving the flow equation of porous domain is developed, aiming to eliminate the stiffness of the equation for porous seepage flows. Three test cases in hybrid porous/fluid and porous/solid domains are presented to demonstrate the applicability and accuracy of the numerical algorithm.

17 citations

Dissertation
01 Nov 2012
TL;DR: In this article, the performance of open cell metal foams was investigated under forced convection conditions and it was found that all the foams tested can have favorable heat transfer behaviour under certain conditions asymmetric behaviour can be obtained when non-uniform pore sizes are present; a factor that could be exploited in heat exchanger design.
Abstract: Open cell metal foams show great potential as a heat exchangers, due to their permeability to fluids and the high conductivity of the metallic network. In this study, aluminium foams were produced using the replication technique with NaCl, flour and water used to create the preform. The samples produced included both uniform pore sizes and examples where different pore sizes were created in different parts of the sample as well as these, samples made commercially by a similar technique (Corevo foams) and by an investment casting process (Duocel foams) were examined. A bespoke rig was designed, built and used to measure the thermal and fluid flow performance of all foams being investigated under forced convection conditions. Results for heat transfer coefficient and pressure drop across the sample with the comparison between each type of sample are presented. It was found that all the foams tested can have favourable heat transfer behaviour under certain conditions asymmetric behaviour can be obtained when non-uniform pore sizes are present; a factor that could be exploited in heat exchanger design.

6 citations

References
More filters
Journal ArticleDOI
TL;DR: In this paper, the porosity of aluminum foams of varying pore sizes was investigated through CT-scanning at 20 micron resolution, and the convective heat transfer results exhibited a dependence on the linear porosity, even though the corresponding volumetric porosity is the same for all the samples considered.
Abstract: Important heat transfer parameters of aluminum foams of varying pore sizes are investigated through CT-scanning at 20 micron resolution. Small sub-samples from the resulting images are processed to generate feature-preserving, finite-volume meshes of high quality. All three foam samples exhibit similar volumetric porosity (in the range ∼91–93%), and thereby a similar thermal conductivity. Effective tortuosity for conduction along the coordinate directions is also calculated. Permeability simulations in the Darcy flow regime with air and water show that the foam permeability is isotropic and is of the order of 10−7 m2. The convective heat transfer results computed for this range of Reynolds numbers exhibit a dependence on the linear porosity, even though the corresponding volumetric porosity is the same for all the samples considered.

97 citations

Journal ArticleDOI
TL;DR: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted by as mentioned in this paper, where the authors conducted a comprehensive survey.
Abstract: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted Due to the immenseness of the literature volume, the survey

58 citations

Journal ArticleDOI
TL;DR: In this article, a nodal network representation of three aluminum foam samples from DUOCEL is constructed out of X-ray microtomography data obtained by computed tomography (CT) scanning of the samples using a commercial CT scanner.

41 citations

Journal ArticleDOI
TL;DR: In this article, a preconditioned density-based finite-volume method is proposed to simulate the coupled fluid flow and heat transfer problems in hybrid porous/fluid/solid domains.
Abstract: A preconditioned density-based finite-volume method is proposed to simulate the coupled fluid flow and heat transfer problems in hybrid porous/fluid/solid domains. In the porous zone, the momentum equation is formulated by the Darcy-Brinkman-Forchheimer model; and the thermal nonequilibrium model is adopted for the energy equation. At the porous/fluid interface, both the stress-jump and stress-continuity models are applied for interfacial hydrodynamic conditions. The preconditioning method for solving the flow equation of porous domain is developed, aiming to eliminate the stiffness of the equation for porous seepage flows. Three test cases in hybrid porous/fluid and porous/solid domains are presented to demonstrate the applicability and accuracy of the numerical algorithm.

17 citations

Dissertation
01 Nov 2012
TL;DR: In this article, the performance of open cell metal foams was investigated under forced convection conditions and it was found that all the foams tested can have favorable heat transfer behaviour under certain conditions asymmetric behaviour can be obtained when non-uniform pore sizes are present; a factor that could be exploited in heat exchanger design.
Abstract: Open cell metal foams show great potential as a heat exchangers, due to their permeability to fluids and the high conductivity of the metallic network. In this study, aluminium foams were produced using the replication technique with NaCl, flour and water used to create the preform. The samples produced included both uniform pore sizes and examples where different pore sizes were created in different parts of the sample as well as these, samples made commercially by a similar technique (Corevo foams) and by an investment casting process (Duocel foams) were examined. A bespoke rig was designed, built and used to measure the thermal and fluid flow performance of all foams being investigated under forced convection conditions. Results for heat transfer coefficient and pressure drop across the sample with the comparison between each type of sample are presented. It was found that all the foams tested can have favourable heat transfer behaviour under certain conditions asymmetric behaviour can be obtained when non-uniform pore sizes are present; a factor that could be exploited in heat exchanger design.

6 citations

Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "Permeability and thermal transport in compressed open-celled foams" ?

In this paper, a computational methodology is proposed to describe the fluid transport in compressed opencelled metallic foams.