Experimental analysis of the pressure drop and heat transfer through metalfoams used as volumetric receivers under concentrated solar radiation

C. Albanakis a, D. Missirlis a,*, N. Michailidis b, K. Yakinthos a, A. Goulas a, H. Omar b, D. Tsipas b, B. Granier c

a Laboratory of Fluid Mechanics and Turbomachinery, Department of Mechanical Engineering, School of Engineering, Aristotle University of Thessaloniki, Egnatia Street,Thessaloniki, Greeceb Physical Metallurgy Laboratory, Department of Mechanical Engineering, School of Engineering, Aristotle University of Thessaloniki, Egnatia Street, Thessaloniki, Greecec PROMES-CNRS, 7 rue du four Solaire, 66120 Odeillo Font-Romeu, France

a r t i c l e i n f o

Article history:Received 4 April 2008Received in revised form 19 August 2008Accepted 19 August 2008

Keywords:Metal foamVolumetric receiversPressure dropHeat transfer

a b s t r a c t

The main objective of this work was to evaluate the behavior of porous materials, when treated as vol-umetric receivers under concentrated solar radiation. For this reason various porous metallic and ceramicmaterials have been tested as potential receivers for concentrated solar radiation. The experimentalinvestigation showed that their efficiency was depending on both materials parameters and flow condi-tions. In this work, a variety of foam materials such as Ni and Ni alloy, inconel, copper, aluminum and SiCwith different open cell porosity were tested as potential media to be used as volumetric receivers andheat exchangers. However, since the results were similar, for space economy, only the results of twoof them, nickel and inconel were presented in detail and compared with each other.

� 2008 Elsevier Inc. All rights reserved.

1. Literature review

The idea of using metal foams and porous materials as heatexchangers is not a new one. Initially, Tadrist et al. [1] studied me-tal foams as heat exchangers. The foams were porous materialswith random topology and high permeability values. The porositywas close to 90% and the specific area ranged from 510 m2/m3 to770 m2/m3. Additionally, Boomsma and Poulikakos [2] have devel-oped a one-dimensional heat conduction model for use with opencelled metallic foams, based on a three-dimensional description ofthe foam geometry, which showed that the changing of the fluidconductivity has a relatively small effect on increasing the effectivethermal conductivity. For their work, aluminum metal foam with95% porosity was used. However, despite the fact that the porosityof the metal foam was high, the heat conductivity of the solidphase still controlled the overall effective thermal conductivity.

Another study was made by Bhattacharya et al. [3] where ananalytical and experimental investigation for the determinationof the effective thermal conductivity, permeability and inertialcoefficient of high-porosity metal foams was presented. This workshowed that the effective thermal conductivity of the foam de-pends strongly on the porosity and the ratio of the cross sectionof the fiber and the intersection. A useful study was made by Bon-net and Topin [4] where a simple relation between the flow and the

morphological parameters of metal foams was presented. For theirinvestigation foam samples made from Cu, Ni, Ni–Cr etc for variousthicknesses were used. For the flow parameters, such as pressureand mass flux, it was shown that only the Darcy–Forchheimermodel was adapted. Additionally, the experimental data showedthat the compressibility effects have a strong impact on the mea-surements of the flow law parameters. Finally from the morpho-logical parameters, it was, also, shown that the permeabilityvalues were proportional to the square of the porous size, whilethe inertia coefficient varies with the inverse of the porous size.

Dukhan [5] presented some additional correlations of the pres-sure drop for flow through metal foams, where it was shown thatthe pressure drop was significantly higher for low porosity foams,while for high-porosity foams the effect in the pressure drop waslimited. Furthermore, Lu et al. [6] presented the effects of variousmetal foam parameters on heat transfer. The results showed thatthe overall Nusselt number of the metal foam filled pipe increasedwith the increase of relative density or pore density, especiallywhen the thermal conductivity of the solid was much higher thanthat of the fluid. Moreover, for low Reynolds numbers the effect ofthe thermal conductivity of the foam on heat transfer was quitesmall. Fend et al. [7] studied two novel high-porosity materialsas volumetric receivers for concentrated solar radiation. For hiswork two foam materials (a double layer metal foam) of differentcell density were used. The experimental results showed that theperformance of the double layer silicon carbide metal foam wasimproved, compared to a single layered material. Finally, Lacroix

0894-1777/$ - see front matter � 2008 Elsevier Inc. All rights reserved.doi:10.1016/j.expthermflusci.2008.08.007

* Corresponding author. Tel.: +30 2310996033; fax: +30 2310996002.E-mail address: misirlis@eng.auth.gr (D. Missirlis).

Experimental Thermal and Fluid Science 33 (2009) 246–252

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et al. [8] presented an interesting work describing the pressuredrop behavior of metal foam for varying values of porosity andapparent density through the use of an Ergun-type porosity model.

2. Experimental setup

Fig. 1 demonstrates the experimental setup developed toachieve the examination of the foam materials behavior under con-centrated solar radiation together with variable gas flow condi-tions. During the experiments, the pressure drop between the gasinlet and outlet was measured, together with the gas inlet and out-let temperature. The mass flow, which was one of the variableparameters of the test, was also monitored. An IR camera facili-

tated the estimation of the foam specimen temperature duringthe test.

The IR image presented in Fig. 1 is an indicative example of theimages captured during the experiment. By raising or lowering thestage, where the whole setup was mounted, it was possible to ad-just the distance of the ‘‘hot-spot” from the specimen and, thus, toset the specimen temperature at a desired level, for given gas flowparameters. The specimen was mounted within two cement hold-ers. The top holder had a conical shape to allow a better gas flowdistribution through the specimen.

In order to evaluate the performance of the specimens towardsthe flow field, pressure drop and temperature measurements wereperformed between the inlet and the outlet of the experimental

Fig. 1. Experimental test-rig.

C. Albanakis et al. / Experimental Thermal and Fluid Science 33 (2009) 246–252 247

setup. The pressure drop measurements were performed with theuse of a Bioblock Scientific MP330, digital manometer that wasconnected to the air supply slightly before the inlet of the experi-

mental setup while the outlet was always kept at ambient pres-sure. For each specimen three flow rates have been measuredcorresponding to the approximately 50%, 80% and 100% of theavailable mass flow rate of the air supply, which was correspond-ing to 30 l/min. The mass flow rate was measured with the use of aBrooks Mass Flow Controller, 5850E. At the same time the pressuredrop and temperature measurements were performed for a vary-ing distance from the focal point and, thus, for a varying surfacetemperature of the specimens, measured with a Flir Systems,SC100 thermo camera. The air outlet temperature was measuredwith the use of a thermocouple connected at the outlet of theexperimental setup (Tables 1 and 2).

The output signal of this thermocouple was connected to a PCfrom where the stabilization of the outlet temperature for eachcase could be analyzed, Fig. 2.

3. Experimental results

In order to evaluate the performance of the metal foam speci-mens towards the flow field, pressure drop and temperature mea-surements were performed between the inlet and the outlet of theexperimental setup.

During the measurements the solar energy was focused near ordirectly on the metal foam surface and, thus, its temperature wasincreasing. The point where the solar energy was focused, the focalpoint (FP), was a critical parameter to the degree of heating for themetal foam. The closer the focal point was located in relation to themetal foam surface, the higher the metal foam temperature wouldbe. Then as the air flow passes through the high temperature metalfoam the latter operates as a heat exchange device and, thus, theoutlet air temperature was increased.

Even though in this work a variety of porous materials wereexamined, such as Ni and Ni alloy, inconel, copper, aluminumand SiC, the main results of only two of them are presented herein detail for space economy. These materials are nickel and inconel.Their microstructure obtained by SEM observations and the exper-imental results are presented in Fig. 3. The geometrical propertiesof the porous materials were approximated by SEM micrographs offoam slices and appropriate image analysis, as well as in a moreaccurate way by X-ray micro-tomographs. Both procedures re-vealed a pore size of approximately 0.58–0.6 mm for the inconeland the Ni foams, respectively. The porosities were 93% and 92%for the inconel and the Ni foams, respectively. The porous materialswere produced by metal deposition on a polymer pre-form andthen sintering.

Table 1Experimental conditions for nickel

FP Tin (�C) Solar power distributionon FP (W m�2)

Mass flow(l/min)

Tsample, average (�C)

95 22 786 15.30 17721.8 788 24.12 16321.6 791 30.00 161

85 21.6 803 15.18 19721.6 806 24.15 17621.8 807 30.00 171

75 22 820 15.15 24122.4 826 24.12 21022.4 828 30.00 201

65 22.3 832 15.18 38720.7 837 24.15 33121 840 30.00 312

60 20.9 845 15.50 52521.3 849 24.18 47521.5 851 30.00 444

55 20.6 852 15.18 64020.9 855 24.24 50020.5 856 30.00 462

Table 2Experimental conditions for inconel

FP Tin (�C) Solar power distributionon FP (W m�2)

Mass flow(l/min)

Tsample, average (�C)

105 23.5 978 15.09 16523.8 980 24.03 14823.8 959 30.00 142

95 23.8 977 15.03 21423.9 980 24.00 18323.9 978 30.00 168

85 24.1 981 15.06 28024.1 981 24.00 23524.1 978 30.00 225

70 24.2 976 15.00 48524.7 978 24.09 40024.5 975 30.00 365

60 24.5 973 15.03 55024.3 971 24.18 54024.7 969 30.00 500

55 24.8 965 15.21 90025 963 24.24 61025.1 963 30.00 550

Fig. 2. Outlet temperature variation during time.

248 C. Albanakis et al. / Experimental Thermal and Fluid Science 33 (2009) 246–252

The experimental behavior of nickel and inconel is presented inFigs. 4 and 5. As it can been seen in Figs. 4a,b, and5a,b the decreaseof the focal point distance resulted in the increase of the averageand the outlet temperature of the sample. Additionally, the pres-sure drop behavior of nickel and inconel towards the inlet velocitycould be sufficiently described by a second order polynomial law,Figs. 4c and 5c, an outcome, which is in accordance with the con-clusions reported in the literature for similar set-ups.

Thus, the pressure drop of the flow through the metal foamcould be described by the general law of Darcy–Forchheimer aspresented in Eq. (1)

DPL¼ l

KV þ qCV2; ð1Þ

where DP is the static pressure drop (mbar); L is the length of theporous medium (m); l is the dynamic viscosity (Pa s); K is the per-meability (m2); V is the inlet velocity (m s�1); q is the density(kg m�3); C is the form drag coefficient (m�1).

In all cases the pressure drop of the nickel foam specimen ishigher than the one of inconel. Such a conclusion is in agreementwith the results of Lacroix et al. [8] where it is mentioned that asthe porosity of the metal foam increase the pressure drop de-creases. The derivation of the coefficients C and K can be easilymade through a trend line curve fitting procedure between theexperimental data and Eq. (1), as presented in Figs. 4d,e and 5d,efor nickel and inconel, respectively. As it can be seen, the pressureloss coefficients C and K for the nickel foam specimen are generally

higher than the ones of the inconel foam specimen. More specifi-cally, the values of the form drag coefficient C follow a linear in-crease towards the average temperature of the sample while thevalues of the permeability K seem to oscillate around a relativelyconstant mean value.

Additionally, the pressure drop measurements for a varying fo-cal point distance revealed the effect of the increase of the speci-men temperature towards the inlet velocity. In all cases, thedecrease of the distance from the focal point and, consequently,the increase of the average surface temperature of the specimenresulted in increased values of the pressure drop.

Concerning the air temperature at the outlet, a parameterreflecting the heat exchange efficiency of each specimen, themeasurements showed that the decrease of the inlet velocity,for a constant value of the focal point, resulted in a better heatexchange between the inlet air flow and the specimen, possiblydue to the increase in the available time for the heat transferand, thus, to a higher outlet air temperature as presented in Figs.4a,b and 5a,b.

In addition, the thermal performance of the metal foam can bepresented from Eq. (2) (e.g. Holman [9])

q ¼ �hDT ¼ �hSexchangeðTsample � T fluid;inÞ; ð2Þ

where q is the heat flux (W m�3); �h is the heat transfer coefficient(W m�2 K�1); DT is the temperature difference between the averagetemperature of the sample (Tsample) and the inlet temperature(Tfluid,in) of the fluid (K); Sexchange is the ratio of the heat exchangesurface per volume (m�2 m�3).

For the analysis of the experimental results the metal foammaterials are approximated and treated equivalently to anarrangement of staggered tube rows in tube bundles. Thus, theheat, which is transferred to the fluid in the pores of the sample,can be characterized by the heat transfer coefficient. Consequently,the Nusselt number (Eq. (3)) based on the mean heat transfer coef-ficient will be

NuD ¼�hDk

ð3Þ

where D is the characteristical length (m); and k is the thermal con-ductivity (W m�1 K�1). All properties of air were evaluated at theaverage temperature Tm ¼ ðTair;in þ Tair;outÞ=2. According to Lu et al.[6], and since the cross-section of fibres is not circular, a shape fac-tor for the estimation of the characteristical length has to be takeninto account. Thus, D is given from Eq. (4)

D ¼ 1� e�ðð1�eÞ=0:04Þ� �df ; ð4Þ

where df is the fibre diameter of the metal foam, given from Eq. (5)where dp is the diameter of the pore and e is the porosity of themetal foam

df

dp¼ 1:18

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1� eÞ

3p

r1

1� e�ðð1�eÞ=0:04Þ

� �: ð5Þ

Hence, the Reynolds number, based on the flow velocity in thepore, the characteristical length and the kinematic viscosity is pre-sented in Eq. (6)

ReD ¼uporeD

v; ð6Þ

where upore ¼ ufluid=e is the flow velocity in pore (m s�1); t is thekinematic viscosity (m2 s�1).

According to Zukauskas [10], for similar arrangements, the Nus-selt number can be presented (Eq. (7)) as a function of Reynoldsnumber and Prandtl number for staggered tubes, as:

NuD ¼ 0:76Re0:4Pr0:37 ðRe < 40Þ ð7Þ

Fig. 3. SEM pictures of the microstructure of the applied inconel and nickel foams.

C. Albanakis et al. / Experimental Thermal and Fluid Science 33 (2009) 246–252 249

It should be mentioned that during the experimental measure-ments it was not possible to proceed to measurements of the pre-cise value of the heat flux directly on the metal foam surface whichwould be necessary for the experimental derivation of the Nusseltnumber. Thus, the Zukauskas Nu–Re correlation, was used forshowing the behavior of the Nusselt number in order to performa comparison between the heat transfer performance of the twometal foams.

As it can be seen from Fig. 6, for the foam specimens underinvestigation, as the Reynolds number increases also the Nusseltnumber increases.

An additional comparison of the heat transfer effectiveness be-tween the nickel and inconel foam specimens is attempted in Fig. 7where the ratio of the temperature difference of air from inlet tooutlet to the temperature difference between the sample and the

inlet air is presented towards the flow velocity inside the poresof the foam specimen, upore. It should be mentioned that in orderto proceed to a representative comparison, the cases which areused are corresponding to similar values of the sample tempera-ture, Ts.

As it can be seen, the heat transfer effectiveness of nickel ishigher than the one of inconel for all cases under comparison withthe average difference between their values being, approximately,25%. Thus, in all cases the outlet air temperature through the nickelfoam specimen is always higher than the one of the inconel. As itwas mentioned the porosities for the inconel and the Ni foamsare 93% and 92%, respectively. Thus, the highest pressure dropand the highest heat transfer are related to the lowest porosityvalue. Such a conclusion is in agreement with similar results ofinternational literature, Boomsma et al. [11].

Fig. 4. Plot of (a) Taverage, sample, (b) Toutlet, air, (c) DP/L towards the inlet velocity of air and plot of (d) form drag coefficient C and (e) permeability K towards the Tm, for nickel.

250 C. Albanakis et al. / Experimental Thermal and Fluid Science 33 (2009) 246–252

Fig. 5. Plot of (a) Taverage, sample, (b) Toutlet, air, (c) DP/L towards the inlet velocity of air and plot of (d) form drag coefficient C and (e) permeability K towards the Tm, for inconel.

Fig. 6. Plot of Nusselt number versus Reynolds number for the nickel and inconel (using the Zukauskas Nu–Re correlation).

C. Albanakis et al. / Experimental Thermal and Fluid Science 33 (2009) 246–252 251

4. Conclusions

In this work an experimental analysis was presented regardingthe heat transfer and pressure drop of metal foam specimens. Forthis reason, a variety of materials was tested, however a detailedcomparison was presented, only, for the nickel and inconel metalfoams. The comparison was performed taking into account thepressure drop and the heat transfer performance of thespecimens.

Concerning the pressure drop, the experimental results showedthat the behavior of the metal foam specimens could be sufficientlydescribed by a second order-polynomial law in the form of theDarcy–Forchheimer correlation. The measurements revealed thatthe pressure drop of the nickel foam specimen was always higherthan the one of inconel for all cases under investigation.

Regarding the heat transfer performance of the metal foamspecimens, an attempt was made so as to estimate the meanNusselt number correlation for each material which was basedin the combination of a theoretical approach based on the con-clusions of Zukauskas [10] and experimental measurement. Atthe same time, the heat transfer performance of both materialswas evaluated in relation to an effectiveness coefficient, whichshowed that the heat transfer of nickel was always higher thanthe one of inconel.

The preceding analysis can be used in combination with theexperimental measurements so as to present the behavior of theflow–specimen interaction and provide a basis for the furtherdevelopment of a general purpose heat transfer and pressure dropmodel, which can be used in porous media CFD approaches of thespecimen geometry for various heat transfer and pressure dropapplications.

Acknowledgements

The authors would like to thank the PROcedes Materiaux etEnergie Solaire (PROMES)–Centre National de la Recherche Scien-tifique (CNRS) for their support in the experimental procedure, inthe frame of the European project SOLFACE.

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Fig. 7. Comparison of heat transfer effectiveness, eff, between nickel and inconel.

252 C. Albanakis et al. / Experimental Thermal and Fluid Science 33 (2009) 246–252