Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer and Convective Boiling

Abstract

The first part of this work deals with flow laws of gas, liquid and mixtures in metallic foam. This experimental work is based on the stationary pressure profile measurement in a channel filled with metallic foam of several grades or materials for several controlled flow rates. Several foam samples with different characteristics (10, 40, 60, 100 ppi) of copper and of nickel are studied. In single-phase conditions, we evaluate the permeability and inertial the coefficient according to the Forchheimer model. In the gas flow case, compressibility effects are taken into account. Emphasis is given on the relative contributions of inertial and viscous effects. The specific behavior linked to compressibility effect is thoroughly studied. The adiabatic (air-water) conditions are analyzed; the results are reported in term of biphasic multipliers according to a simple homogeneous model, to study the impact of foam texture and gas quality on flow laws. Several aspects of the two-phase flow case (i.e. liquid-vapor) are discussed: phase repartition, pressure drops, characteristic boiling curve …. In single phase conditions, the heat transfer coefficient was improved by two orders of magnitude with the presence of metallic foam with only a limited increase in pressure drop. In biphasic conditions, the study of convective boiling regime also showed significant heat transfer enhancement with very low-pressure drops. A simple one dimensional homogeneous model was used and allows a good description of global flow behavior across the test section.

Full text

DOI: 10.1002/adem.200600102
Experimental Analysis of Multiphase Flow in
Metallic foam: Flow Laws, Heat Transfer and
Convective Boiling**
By FrØdØric Topin,* Jean-Phillipe Bonnet,Brahim Madani,Louns Tadrist
1. Introduction
Metal foams are a relatively new class of materials with
low densities and attractive thermal, mechanical, electrical
and acoustic properties.
[1]
They are widely quoted to present
a random topology, high open porosity, low relative density
and high thermal conductivity of the cell edges, large accessi-
ble surface area per unit volume. All these characteristics
make metal foam heat exchangers efficient, compact and light
weight. Moreover, they also promote mixing and have excel-
lent mechanical properties. Metallic foams uses and applica-
tions have been widening quickly during the last few years
and they are proposed for use in numerous applications such
as compact heat exchangers, reformers, biphasic cooling sys-
tems and spreaders for increasing heat transfer; improve mix-
ture and chemical reaction.
[2±4]
Different types of metal foams
are used as a buffer between a stiff structure and a fluctuating
temperature field. They are also used in geothermal opera-
tions and in petroleum reservoirs.
[5]
Ceramic foams are used
in advanced burners and heat pipes. Foams have been used
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±
[*] jPlease check title and addresses of authors!j
Prof. F. Topin, Prof. J.-P. Bonnet, Prof. B. Madani,
Prof. L. Tadrist
Ecole Polytechnique Universitaire de Marseille, Laboratoire
I.U.S.T.I
CNRS- UMR 6595 UniversitØ de Provence
Technopôle de Château-Gombert ± 5
Rue Enrico Fermi, 13453 Marseille Cedex 13, France
[**] The authors wish to thank Recemat Company and SCPS Com-
pany for providing the samples, and the French government
financial support in the frameworks of a PACo programme and
CNRS Energy program: PR Specimousse.
The first part of this work deals with flows laws of gas, liquid and mixture in metallic foam. This
experimental work is based on the stationary pressure profile measurement in a channel filled with
metallic foam of several grade or material for several controlled flow rates. Several foam samples with
different characteristics (10, 40, 60, 100 ppi) of copper or nickel are studied. In single-phase condi-
tions, we evaluate permeability and inertial coefficient according to the Forchheimer model. In the gas
flow case, compressibility effects are taken in account. Emphasis is given on the relative contributions
of inertial and viscous effect. The specific behavior linked to compressibility effect is thoroughly
studied. The adiabatic (air-water) conditions are analyzed; the results are reported in term of biphasic
multipliers according to a simple homogeneous model to study the impact of foam texture and gas
quality on flow laws. Several aspects of the two-phase flow case (i.e. liquid-vapor) are discussed: phase
repartition, pressure drops, characteristic boiling curve _. In single phase conditions, the heat transfer
coefficient was improved by two orders of magnitude by the presence of metallic foam with only a
limited increase of pressure drop. In biphasic condition, the study of convective boiling regime also
showed significant heat transfer enhancement with very low-pressure drop. A simple one dimensional
homogeneous model was used and allows a good description of global flow behavior across the test
section.

Topin et al./Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer
in high-power batteries for lightweight cordless electronics,
and catalytic field application such as fuel cells systems.
[6]
Due to their novelty, peculiar structure and varied manufac-
turing processes, metal foams are still incompletely character-
ized. Accurate evaluation of these properties becomes critical
for various uses.
The control of the texture of porous materials used for the
optimization of given application represents a significant
technological stake Accurate determination of transport prop-
erties, in respect with convenient geometrical parameters, is
needed for both single phase and boiling conditions flows in
order to understand transport phenomena in these materials
and eventually optimize their texture for given application.
Models widely used for low porosity media are more difficult
to apply to high porosity materials.
Most of the works dealing with foam transport properties
are based on arbitrary periodic structures which represent
with variable degree the real texture of the foam. The mor-
phology of such open-celled structure is often characterized
using cell ligament diameter or pore size and the relative den-
sity.
[7,8]
assumed a rectangular distribution of solid material
in a representative unit cell. Several authors
[9±11]
used a sim-
ple cubic cell consisting of slender cylinder as edges. Dimen-
sions of the representative unit cell are obtained in function
of relative foam density. Analogy between flow through the
foam and through a bank of cylinders is used to derive ana-
lytical expressions for pressure drop.
[12]
More complex peri-
odic structure were tested using 3D numerical simulation of
flow through idealized open-celled metal foam.
[13]
Thus,
model remains, yet only qualitative.
[14±19]
During the last decade, numerous experimental and theo-
retical works on single-phase flow in cellular material have
been lead. It exists, on the other hand far less data about
hydrodynamics of gas/liquid flow in such media. Moreover
it appears a strong dispersion of literature results which limit
the development and validation of model of flow properties
in function of geometrical parameters of such foam. Data of
the literature reported that metal foams of grade and porosity
exhibit extremely different transport properties. Friction coef-
ficient variations versus Reynolds number, both based on
pore size:
k2DPdp
LqU2Formula 1
and
Re Udp
mformula 2
as reported by
[20]
are plotted on Figure 1. The divergence of
these coefficients measured for metallic foam samples of com-
parable porosities and grade (PPI) is obvious on this figure.
The values of friction factor differ from more than 1 decade
depending on Reynolds number. These discrepancies in
experimental results and theoretical models, can be attributed
to the lack of in one hand, to the experimental procedures
used to determine the hydrodynamic properties of these ma-
terials and in the other hand, to the lack in methods allowing
accurate determination of metallic foam microstructure char-
acteristics related to flow/transport properties.
We present here, experimental studies aiming at estimate
characteristic transport properties of metallic foam in order to
correlate them to their morphology.
[24,25]
The flow properties
are analyzed for these foams: permeability, inertial coeffi-
cient, friction factors. Several aspects of adiabatic two-phase
flow are discussed. The second part is devoted to single-
phase heat transfer and characterization of convective boiling
phenomena (i.e. liquid-vapor).
Single-phase Flow
2.1. Experimental Set-Up
This experimental work is based on the stationary pressure
profile measurement in a channel filled with metallic foam of
various grade or material and crossed by controlled flow
rates. Several foam samples with different characteristics
(grade from 10 up to 100 ppi) of copper, nickel, or allied nick-
el are studied (see Tab. 1 for details).This experimental set-up
is designed, to study the impact of the solid matrix on flow
phenomena in the foam in both single-phase and adiabatic
two-phase flow conditions. This apparatus consists of three
main parts: test section, fluid loop and data acquisition sys-
tem as shown on Figure 2.
The test section (250 mm length, 50 mm wide and adjust-
able height) is instrumented with 12 pressure sensor (Sen-
sym

, sensitivity 2.6 lV per Pa) placed every centimeter
along the main flow axis. Additional pressure sensor are
placed along 3 lines perpendicular to the flow direction to
asses the one-dimensional nature of the flow. Foam samples
(whose lengths vary from 130 up to 200 mm) are placed in
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Fig. 1. Friction factor versus Reynolds Number (both based on Pore diameter). Lines:
literature data [13,20±23], Symbol: present work all samples, air and water results.

Topin et al./Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer
the central part of the channel in order to keep a tranquiliza-
tion zone upstream and downstream of the sample. Test sec-
tion is placed horizontally in order to avoid uncertainties due
to hydrostatic effects.
[20]
The liquid fluid loop is constituted by a storage tank (50 l
capacity) and a variable velocity gear pump which can give a
constant flow rate in the range of 0±10
±4
m
3
s
-1
independently
of pump downstream conditions. Constant air flow (range
0±4 10
±3
Nm
3
s
±1
) is obtained using a compressor and a pres-
sure regulation valve. The test section is connected, down-
stream, to a separator which is installed for the two-phase
flow experiments. The liquid flows by gravity down the stor-
age tank while the air is simply released to atmosphere. A
weighted tank could be inserted in the liquid loop to assess
the mass flow rate. Liquid flow rate is monitored (upstream
of the test section) using two turbine flow meters (Mac-Mill-
an

) for optimal accuracy over the full range of experiments.
The first one works in the range of 3.33 10
±5
± 8.10
±5
m
3
s
±1
and
the other one in the range 1.6 10
±6
± 3.33 10
±5
m
3
s
±1
. The
weighting device arranged in downstream of the test section
has a sensitivity of about 1 g and a capacity of 3 l. Air flow is
monitored upstream of the test section using three mass- flow
meters (Aalborg

) respective operating range: 0±50,
0±100 and 0±250 Nl/min. An accuracy of about
0.1 % overall flow rate range is thus obtained. Hy-
drodynamic (null flow) profile is checked before
and after each experiment in order to eliminate all
offset between pressure sensors. Pressures, temper-
ature and inlet flow rate of both fluid (air and
water) are continuously monitored.
The same experimental procedure is used for all
tests. Before each series of measurement, the foam
sample was flooded a long times ensuring initial
wetting (water) or drying (air), and established
flow. The fluid is then, maintained on circulation
for about half an hour after system has reached a
stationary regime. Hydrodynamic (null flow) pro-
file is checked before experiment in order to elimi-
nate all offset between pressure sensors. For each
measurement, an averaging procedure (averaging
time 1 min. data acquisition 500 Hz) is used to re-
duce measurement noise, after checking stationary
behavior of pressure and flow rate signal. Accuracy
of pressure measurement is better than 5 Pa.
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Table 1. Flow laws parameters & sample properties. Cu 45 (a) standard; Cu 45 (b) increased surface roughness, Cu 45 (c) washcoated with alumina.
Sample
Pore
diameter
d
p
[lm]
Porosity
e
Specific
surface
Sp [m
2
/m
3
]
Water
permeability
K
water
[m
2
]
Air
permeability
K
air
[m
2
]
Permeability
K
WA
[m
2
]
Water inertia
coefficient
b
Water
[m
±1
]
Air inertia
coefficient
b
air
[m
±1
]
Inertia
coefficient
b
WA
[m
±1
]
Ni 100 500 1.63E-09 1.42E-09 1.38E-09 1670 2010 1686
Ni10 4429 680 2.00E-07 5.76E-08 7.63E-08 272 261 248
NC 4753 400 0.9 5600 2.28E-09 1.85E-09 2.01E-09 2194 2138 2175
NC 3743 569 0.87 5303 2.68E-09 2.13E-09 2.11E-09 1622 1330 1329
NC 2733 831 0.91 3614 6.19E-09 4.44E-09 4.79E-09 1130 1075 1088
NC 1723 1840 0.88 1658 2.32E-08 2.81E-08 1.14E-08 631 490 446
NC 1116 2452 0.89 1295 2.98E-08 6.02E-08 3.62E-08 400 381 364
Cu 40 1500 0.95 1.62E-08 1.22E-08 7.20E-08 783 1000 1107
Cu 45
(a)
1000 4.49E-09 6.09E-09 5.30E-09 1056 1281 1167
Cu 45
(b)
1000 6.20E-09 7.58E-09 3.62E-09 1139 1615 1133
Cu 45
(c)
900 5.35E-09 1768
Cu 10 4055 0.92 758 8.17E-08 201
Fig. 2. Experimental set-up for single-phase and adiabatic two-phase flow laws characterization.

Topin et al./Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer
After each measurement series, the flow is stopped and
the hydrostatic pressure profile is measured anew and com-
pared to the previous hydrostatic one. In this way we could
ensure that pressure sensors bias has not changed with the
time.
Gravity and capillarity driven flow through cell edges dur-
ing the manufacture of metallic foams induce material prop-
erty gradients (tortuosity, cell size _) and cells themselves
are not spherical.
[26]
Slight anisotropy of geometrical parame-
ters is observed for ours sample. Nevertheless at this stage of
the study we neglect these effects. Measurement of full per-
meability and inertial coefficient tensor is, yet, difficult and
the precision of our set-up in the studied configuration
doesn't allow measurement of transverse pressure gradient
with an accuracy compatible with the objectives of this
work.
[27]
2.2. Flow Law
It is well established that flows at very low flow rates
through a porous medium are governed by Darcy's law.
[28]
For homogeneous porous media, ªhigh-velocityº flows are
characterized by a nonlinear relationship between the pres-
sure drop and the flow rate. At high Reynolds number the
empirical Forchheimer equation is used to account for the
deviation from Darcy's law:
[29]
dP
dz l
Kubq u21
Where qis the fluid density, K(permeability; m
2
) and b(iner-
tial coefficient; m
±1
) are intrinsic parameter of the solid matrix
and depend only on its structural properties. In this formula-
tion the Brinkman correction is neglected. That means that
the pressure drop is considered as the sum of two terms: vis-
cous (u, Darcy law) and inertia (u
2
) terms. The pressure gradi-
ent across the foam is a function of system geometry (porosi-
ty, pore and ligament size...), and physical properties of the
fluid phase (viscosity, density). We measured the pressure
drop using two different fluids: a liquid (water) and a gas
(air) in order to confirm that, K,bare independent of the fluid
nature (Table 1).
2.3. Pressure Profiles-Compressibility Effects
As we measured pressure profiles along the main flow
axis, we could check sample heterogeneities, entrance effects
and non-linearity due to compressibility effects.
[20,30]
In the
water flow case, for all tested samples, a linear regression fit
with a very good accuracy the experimental pressure profiles.
Residual of these interpolations are always negligible and
comparable to measurement noise. On the other hand, in gas
flow case, experimental data shown that pressure drop ver-
sus position is clearly not linear. As air flow compressibility
effects are not negligible because DP/P»1
[31]
pressure pro-
files gradient vary along main flow axis (Fig. 3). The curva-
ture of pressure profile increases with pressure difference;
this effect is thus maximal for the smallest pore size samples.
We identify parameters of Forchheimer Equation 1 which
takes the following forms using mass flux m:
dqP
dz yl
Kgbg
22
y=2Perfect gas,y=1Liquid
The ªdensity x pressureº (called ªqPº in the following text)
profiles along main flow axis are linear at all tested velocities
and for both fluids. Thus, for a given sample, the gradient of
this quantity depend only on mass velocity. Except near inlet
(entrance effect, flow not established) the gas case, linear
regression of qPversus the position fit with a very good accu-
racy the different profiles. Thus, the gradient of this quantity
depend only on mass velocity and is evaluated by linear
regression on these profiles (Fig. 4).
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Fig. 3. Pressure profiles for several air mass fluxes- compressibility effect. Sample NC
4753. Grey lines: linear approximation.
Fig. 4. ªqPº profiles for several air mass flux densities. Sample 4753.

Topin et al./Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer
Permeability and inertial coefficient are identified from
order 2 polynomial regression of qPgradient variations in
function of mass flux. Experimental results follow, indeed, a
quadratic law and deviation between experimental values
and model are very low (1 up to 3 %).
Figure 5 illustrate these results, on the tested range of
Reynolds number (10 ± 10000), experimental data are best
fitted with by a quadratic law. A detailed view of region near
the origin highlights the importance of inertial effects even
for relatively low Reynolds number: (Re
Dp
: 5 ± 100). This
holds true for each sample and indicates that in the most
commonly encountered use of metallic foam Forchheimer
model has to be used to model flow behavior properly.
Nevertheless, using more viscous fluid, we could have
acceded to very low Re
Dp
number (< 1) flow regime, and a
Darcian behavior may probably have been observed. We
compare the relative intensity of inertial and viscous contri-
bution to pressure drop deduced from water flow results on
Figure 6. Indeed, inertial effects exist for all tested velocities.
These latter even constitute the main contribution to pressure
drop for the greater part of tested velocity range. This trend
being accentuated for bigger pore sizes. On the other hand,
even if viscous contributions are lower than inertial one, they
are not negligible in these experiments and the preponder-
ance of viscous over inertial effects at low velocity is clearly
visible, relative importance of viscous effect is inversely pro-
portional to the pore size of these foams. Nevertheless, this
ratio remains in the range (0.05 ± 10) for all tested cases.
Comparing values of permeability and inertial coefficient
determined using liquid (resp. gas) data alone versus values
obtained using data for both fluids simultaneously show up a
good agreement (Tab. 1). As compressibility effects have been
taken into account, the nature of the fluid doesn't change the
measured values even if slight differences could be observed.
Although Reynolds number (based on pore size) range is
identical for the two fluids the mass fluxes are quite different
(0±30 kg.m
±2
.s
±1
for the gas and 0 ± 500 kg.m±
2
.s
±1
for the liq-
uid) and thus may explain the difference in inertial coefficient
and permeability values. Indeed the reduced pressure gradi-
ent, plotted in function of Reynolds number for all samples
on Figure 7, highlight that there is no influence of fluid
nature on the flow laws. Similar trend are observed for all
curves, that are, indeed, representative of weak inertia
flow.
[29]
For each sample, pressure gradient asymptotically con-
verge toward a fully inertial behavior (Slope 2 on this log-log
plot) at high Reynolds number. At low Reynolds, results
slope decrease slightly and are expected to converge to Dar-
cian flow (Slope 1) for Reynolds inferior to one. Clearly, data
obtained for the sample of greater pore size are more repre-
sentative of inertial regime, thus sensibility to inertial coeffi-
cient is better in this case. On the other hand, for the smaller
pore size this flow is more representative of a viscous one
(even if inertial effects exist). This indicates that Kand besti-
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Fig. 5. ªqPº gradient versus mass flux density (white: air; black: water). Symbol shape
correspond to sample (see Fig. 7)
Fig. 6. Relative viscous and inertia effects contribution on pressure gradient versus
water flow velocity for several sample.
Fig. 7. Reduced pressure drop versus Reynolds number (pore size) ± air (white) and
water (black) flow data. Shape of symbol indicates sample.

Topin et al./Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer
mation is not always done in an optimal way. Uncertainties
on Kand bare consequently different depending on pore
size. Nevertheless, most of the data are, indeed representative
of transition zone.
2.4. Flow Law Parameters
Kand bcoefficients depend on porosity, pore diameter
strut size, specific surface... Analysis of our experimental data
allows us to determine the main parameter governing the
variations of permeability and inertial coefficient. Viscous
effects are governed by pore size while it is the specific sur-
face that produces the best fit of our results with an Ergun
like law.
[3]
Kfe3d2
1e2and bnSp
with f1:391 104and n1:32 3
Inertial pressure drop are linked to acceleration (direction
and magnitude). Indeed microscopic flow in foam could be
modeled by flow around obstacle. Thus the natural parame-
ters to describe such flow are strut diameter and pores size
thus specific surface. Figure 8 show the experimental results
and the model. A good agreement is observed.
2.5. Comparison with Literature Data
We compare our results to literature data
[3,10,13,15,22,23,32±36]
gathered by.
[20]
As shown in Figure 1, the major part of works
gives similar trend of pressure drop coefficient but results ob-
tained for similar foam are scattered on a rather wide range.
Some data are obtained using liquid flow
[32]
and several
authors gives results obtained with gas flow.
[3,10,14,15,23]
The
commonly used technique to determine flow law in porous
media is to evaluate pressure gradient using only inlet and
outlet pressure Moreover several results obtained with gas
flow neglect compressibility effect even when DP/P is not nil,
at high velocity regimes. This leads to an important disper-
sion of results and even to aberrant (non-physical) values of
the permeability.
Analysis of permeability data in function of porosity for
several pore densities highlights the wide dispersions of per-
meability as expected from error analysis.
[20]
Nevertheless,
some trends could be inferred: permeability decreases
slightly as the pore density increases and increases slightly as
the porosity increases. Anyway, these variations should be
considered with caution as uncertainties are greater than the
observed variations.
Figure 9 shows inertial coefficient versus pore size for
several ligaments diameters. On this figure, we can notice
that *decreases as pores and ligament diameters increase.
Upon data gathered from the literature, the inertial coefficient
is given proportional to the pore density and inversely pro-
portional to the ligaments and pore diameters. In opposite,
using the gathered data base, we can not detect any clear rela-
tion linking inertial coefficient to the porosity. These observa-
tions derived from the literature results need to be analyzed
systematically. They must be carried out using well known
geometrical characteristics of metallic foams.
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Fig. 8. Variation of inertia coefficient versus specific surface (up). Variation of perme-
ability versus pore diameter (down).
Fig. 9. Variation of inertia coefficient versus pore diameter. Comparison with litera-
ture.

Topin et al./Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer
3. Adiabatic Two-phase Flow
3.1. Pressure Drop
We present on Figure 10 the results concerning pressure
losses obtained for air-water mixture flow in foams. The gas
quality of the flow is our experiments vary from 0.5 up to
25 % and the void fraction (evaluated from a no-slip model) is
in the range 80 % up to 99 %. The compressibility effects
should thus appear clearly on two-phase pressure profile as
the mixture is mainly composed of gas. Due to density varia-
tion with local pressure the mixture velocity should increase
from inlet to outlet producing an increasing pressure gradi-
ent. But, as experimental results are correctly modeled by lin-
ear approximation, it should exist an antagonist effect (void
fraction variation probably) that mask this behavior.
Figure 11 illustrates the influence of air flow rate on bipha-
sic pressure gradient. For a given total mass flux the pressure
loss is proportional to air flow rate. In other words, pressure
gradient is proportional to flow quality. The curvature of
these curves is inversely proportional to the quality of the
flow. This indicates that viscous effects depend more strongly
on quality than inertial one.
3.2. Biphasic Multiplier
We do not find any other data in literature for biphasic
flow in metallic foam and it do not exist, yet, agreement on a
model of biphasic flow in porous media.
[12,37±39]
Thus in order
to compare our results to reference cases we choose, consider-
ing the very high porosity of the foam to compare to two-
phase flow in tube. The flow is established in the studied
zone and is globally one-dimensional. Taking into account
the precise structure of the two-phase flow is not yet possible
as both slip velocity and void fraction could not be measured.
Consequently we suppose that the mixture behave as an
incompressible homogeneous fluid with null slip velocity.
The pressure losses of the mixture are thus described using
the biphasic multiplier approach,
[31]
with vflow quality (gas
mass flux/total mass flux):
f2
LS dP=dzLG
dP=dzL
1xql
qg
11xll
lg
1c4
Using the experimental values of biphasic multiplier
are simply calculated by forming the ratio of biphasic pres-
sure drop over single-phase one. An adjustment of exponent
(c~±0.7) of the viscosity term appearing in the biphasic multi-
plier expression allows to model all experimental data with
reasonable agreement. Figure 12 present the comparison of
experimental results with the correlation proposed by Mac
Adams (c= ±0.25) for laminar flow in tubes.
[31]
All experimen-
tal data are roughly located on a unique curve similar to the
literature correlation. Nevertheless a slight influence of pore
size is visible on this figure. When pore size increase the
biphasic multiplier seems to be closer to the value obtained
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Fig. 10. Two-phases flow pressure profile. Sample Ni100.
Fig. 11. Biphasic pressure gradient versus total mass flux variations for several air
mass fluxes. Sample Ni100.
Fig. 12. Biphasic multiplier versus quality. Comparison of results from several samples
with tube correlation.

Topin et al./Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer
for tube. But more experimental data are needed to interpret
this effect. This approach has been applied with reasonable
agreement in convective boiling case, using biphasic multi-
plier given by Mac Adam correlation.
[40]
Figure 13 presents a comparison of calculated and mea-
sured pressure profile obtained for one flow rate and two
different heating power in case of convective boiling of
n-pentane.
The model predicts with a good accuracy the pressure pro-
file at moderate heating power. On the other hand a clear dis-
crepancy between experiment and model is observed at high-
er heat flux. This is probably due to flow regime transition at
high vapor quality. Globally, the model presents a reasonable
accuracy (20 % error max) on the global pressure drop of the
channel but is not usable to determine local pressure profiles.
4. Convective Boiling
4.1. Experimental Set-Up
The boiling mechanisms in copper foam and the evalua-
tion of the impact of the solid matrix on flow and heat trans-
fer phenomena were experimentally studied. It consisted of
2 rectangular channels (10  50  100 (resp.200) mm) that
contained a 40 ppi grade copper foam. The smallest one is
welded to the wall, as the other is just inserted in the channel
A liquid (i.e., n-pentane, low toxicity, low boiling point: 36 C
at atmospheric pressure, low phase-change enthalpy) flowed
through the porous media vertically from the bottom to the
top (Fig. 14). The channel was instrumented with 40 thermo-
couples and 15 pressure sensors.
[40,41]
Before each experiment,
we apply repeated Boiling-cooling sequence in order to elimi-
nate non-condensable substances, then flow is imposed at the
desired flow rate (0± 80 kg m
±2
s
±1
). After stationary regime is
reached heating power (range 0 ± 25 W cm
±2
) is applied. All
data are continuously monitored. When stationary regime is
reached temperature and pressure profiles are recorded as
well as flow rate, heating power_
4.2. Single-phase Heat Transfer
Figure 15 shows experimental local Nusselt number pro-
file along main flow direction in the case of copper foam sim-
ply inserted in the channel (no welding with channel wall).
The Nusselt number is based on channel hydraulic diameter
and fluid thermal conductivity. One could remark the sharp
decrease of Nusselt along the main flow axis that indicates
macroscopic establishment of heat transfer and fluid flow.
The entrance zone length is proportional to Reynolds number
as expected as A boundary layer model lead to a Nusselt
number varying like z
±1/2
. Outside the entrance zone variation
RESEARCH NEWS
8http://www.aem-journal.com  2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ADVANCED ENGINEERING MATERIALS 2006,8, No. 9
Model
12000
10000
8000 Q= 3060W
G = 24 kg/m2s
Vapor quality = 54%
6000
4000
2000
0
0 0.05 0.150.1 0.2
Experiment
Q = 1637W
G = 24 kg/m2s
Vapor quality = 24%
Fig. 13. Measured an calculated pressure profile in convective boiling experiments
[40].
Fig. 14. Experimental set-up for boiling experiments [40]. 1. Storage tank, 2. Gears
pump, 3. Tube, 4. Cryostat, 5. Flowmeters, 6. Test section, 7. Cyclone, 8. Venturi, 9.
Condenser, 10. Weighted tank, 11. Valve, 12. Data acquisition, 13. Pressure sensors.
Not shown: thermocouples.
Fig. 15. Experimental local Nusselt number profiles. Inserted foam and litterature
data.

Topin et al./Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer
of Nusselt number are mainly linked to experimental uncer-
tainties on temperatures (about 0.1 C and these transfer coef-
ficients are deduced from local temperature difference) and
used interpolation technique
[41]
.
High heat transfer coefficient is obtained compared to tube
(increase of 2 orders of magnitude). These 3D foam present
clearly better thermal performance than honeycomb struc-
ture, comparable to those obtained with sintered bronze
fibers in similar conditions,
[3]
but these performance are
obtained for a pressure drop far smaller than the one of the
fibers bed. Moreover, the fibers bed porosity is about 60 %
thus at same metal mass thermo-hydraulic performance of
the foam are far netter than those of the other structures.
Influence of wall±foam contact is determinant on heat trans-
fer phenomena as wall-foam heat transfer resistance is a lim-
iting factor in thermal performance of such porous media.
[41]
The boiling curve (Fig. 16) shows the heat flux as a func-
tion of the wall superheat (DT: temperature difference
between the wall and the fluid) in log-log scale. This curve
was measured for two cases (i) the foam welded to the wall
and (ii) the foam just inserted in the channel. The onset of
boiling starts at very low superheat (DT~0.1 and 1 C,
respectively) compared to the ªemptyº channel whose DTis
about 10 C. The heat flux strongly increases when the super-
heat increases. The fluid velocity has no influence on the heat
flux, even at low superheat and very low fluid velocity (10±
40 kg m
±2
s
±1
). The critical heat flux, for which the walls dry
out (formation of an insulating vapor film on the walls lead-
ing to a overheating), was not reachable with our set-up, and
so, largely exceeds 30 kW.m
2
even at lowest tested velocity.
Performances of copper foam were compared to other
fibrous materials. The boiling curve obtained in the same con-
ditions for bronze sintered fibers, which are known for their
high thermal performances
[3]
is similar to the foam inserted at
low superheat. However, when the superheat exceeds 10 C,
the heat flux is far smaller than the one obtained in the foam.
The high performance of the foam is linked to its open
structure that permits an easy evacuation of the vapor formed
near the wall. This improves the heat transfer and avoids the
phenomenon of dry out. Moreover, the pressure drop gener-
ated in the foam is 10 times smaller than those in the sintered
fibers for the same heat transfer and velocity conditions.
We present, on Figure 17, channel global heat exchange
coefficient in boiling condition. We plotted the single-phase
value and the variation of this coefficient in function of inlet
liquid velocity for several heating power. This figure illus-
trates the very strong increase of heat transfer induced by liq-
uid-vapor phase change phenomena.
For a given velocity the heat transfer coefficient is propor-
tional to the heat flux in the studied boiling regime. This indi-
cates a stable behavior (no risk of burn-out) of any biphasic
heat exchanger working in these conditions of heat and mass
flux.
5. Concluding Remarks
This work presents an original experimental method to
determine the hydrodynamic characteristics of metallic
foams. For this, the determination of the pressure profile
along the channel is obtained using multiple pressure sen-
sors. We determine single-phase flow laws for foam covering
a wide range of pore size. Compressibility effects are studied
and an adapted treatment of experimental data is proposed.
An expression modeling the dependence of inertial coeffi-
cient and permeability in function of morphology of the foam
is proposed.
The adiabatic (air-water) conditions were analyzed. Re-
sults, reported in term of biphasic multipliers according to a
simple homogeneous model, show up the impact of foam tex-
ture and gas quality on flow laws.
We developed an experimental methodology to analyze
biphasic flow and heat transfer phenomena in metallic foam.
This study illustrates the improvement of both single-phase
and biphasic heat transfer given by the use of foam in a chan-
nel. The superheat at the onset of boiling is reduced and the
RESEARCH NEWS
ADVANCED ENGINEERING MATERIALS 2006,8, No. 9  2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.aem-journal.com 9
Fig. 16. Boiling Curve: copper foam compared to sintered bronze fibers.*: inserted;
x: welded; stars: bronze fibers. [42]
Fig. 17. Boiling heat transfer coefficient in a rectangular channel equipped with welded
copper foam versus liquid n-pentane velocity.

Topin et al./Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer
heat transfer is increased. The flow laws in these materials
are dominated by inertial effects, but the pressure drop gen-
erated in these materials remains very low. These results
show a very strong impact of the foam structure on heat
transfer and fluid flow.
Received: j
Final version: j
±
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RESEARCH NEWS
10 http://www.aem-journal.com  2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ADVANCED ENGINEERING MATERIALS 2006,8, No. 9
______________________

Topin et al./Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat Transfer
RESEARCH NEWS
ADVANCED ENGINEERING MATERIALS 2006,8, No. 9  2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.aem-journal.com 11
Experimental Analysis of Multiphase Flow in Metallic foam: Flow Laws, Heat
Transfer and Convective Boiling
F. Topin, J.-P. Bonnet, B. Madani, L. Tadrist
Permeability and inertial coefficient are obtained using stationary pressure profile measurement in a channel
filled with various metallic foams. Compressibility effects are studied. In single phase, heat transfer is X 100
with only a limited increase of pressure drop. Convective boiling regime showed significant heat transfer
enhancement with very low-pressure drop. Global flow behavior across the test section is described by 1D
homogeneous model.
ADV. ENG. MATER. 2006, 8 ................................................ j... j