0
Research Papers: Porous Media

Numerical Analysis of Heat Transfer and Pressure Drop in Metal Foams for Different Morphological Models

[+] Author and Article Information
Marcello Iasiello

Dipartimento di Ingegneria Industriale,
Università degli Studi di Napoli Federico II,
P.le Tecchio 80,
Napoli 80125, Italy
e-mail: marcello.iasiello@unina.it

Salvatore Cunsolo

Dipartimento di Ingegneria Industriale,
Università degli Studi di Napoli Federico II,
P.le Tecchio 80,
Napoli 80125, Italy
e-mail: sal.cuns@gmail.com

Maria Oliviero

Istituto per i Polimeri, Compositi e Biomedici,
Consiglio Nazionale delle Ricerche,
P.le Fermi 1,
Portici (Napoli) 80055, Italy
e-mail: maria.oliviero@unina.it

William M. Harris

Mem. ASME
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: wmasonharris@gmail.com

Nicola Bianco

Dipartimento di Ingegneria Industriale,
Università degli Studi di Napoli Federico II,
P.le Tecchio 80,
Napoli 80125, Italy
e-mail: nicola.bianco@unina.it

Wilson K. S. Chiu

Mem. ASME
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: wchiu@engr.uconn.edu

Vincenzo Naso

Dipartimento di Ingegneria Industriale,
Università degli Studi di Napoli Federico II,
P.le Tecchio 80,
Napoli 80125, Italy
e-mail: vincenzo.naso@unina.it

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 18, 2013; final manuscript received July 25, 2014; published online August 18, 2014. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 136(11), 112601 (Aug 18, 2014) (10 pages) Paper No: HT-13-1655; doi: 10.1115/1.4028113 History: Received December 18, 2013; Revised July 25, 2014

Because of their light weight, open porosity, high surface area per unit volume, and thermal characteristics, metal foams are a promising material for many industrial applications involving fluid flow and heat transfer. The pressure drop and heat transfer in porous media have inspired a number of experimental and numerical studies, and many models have been proposed in the literature that correlate the pressure gradient and the heat transfer coefficient with the mean cell size and porosity. However, large differences exist among results predicted by different models, and most studies are based on idealized periodic cell structures. In this study, the true three-dimensional microstructure of the metal foam is obtained by employing x-ray computed microtomography (XCT). This is the “real” structure. For comparison, ideal Kelvin foam structures are developed in the free-to-use software “surface evolver” surface energy minimization program. These are “ideal” structures. Pressure drop and heat transfer are then investigated in each structure using the CFD module of COMSOL® Multiphysics code. A comparison between the numerical predictions from the real and ideal geometries is carried out. The predictions showed that heat transfer characteristics are very close for low values of Reynolds number, but larger Reynolds numbers create larger differences between the results of the ideal and real structures. Conversely, the differences in pressure drop at any Reynolds number are nearly 100%. Results from the models are then validated by comparing them with experimental results taken from the literature. The validation suggests that the ideal structure poorly predicts the heat transfer and pressure drops.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Boomsma, K., Poulikakos, D., and Zwick, F., 2003, “Metal Foams as Compact High Performance Heat Exchangers,” Mech. Mater., 35(12), pp. 1161–1176. [CrossRef]
Gauthier, S., Nicolle, A., and Baillis, D., 2008, “Investigation of the Flame Structure and Nitrogen Oxides Formation in Lean Porous Premixed Combustion of Natural Gas/Hydrogen Blends,” Int. J. Hydrogen Energy, 33(18), pp. 4893–4905. [CrossRef]
Fuller, A. J., Kim, T., Hodson, H. P., and Lu, T. J., 2005, “Measurement and Interpretation of the Heat Transfer Coefficients of Metal Foams,” J. Mech. Eng. Sci., 219(2), pp. 183–191. [CrossRef]
Kurtbasa, I., and Celikb, N., 2009, “Experimental Investigation of Forced and Mixed Convection Heat Transfer in a Foam-Filled Horizontal Rectangular Channel,” Int. J. Heat Mass Transfer, 52(5–6), pp. 1313–1325. [CrossRef]
Hsieh, W. H., Wu, J. Y., Shih, W. H., and Chiu, W. C., 2004, “Experimental Investigation of Heat-Transfer Characteristics of Aluminum-Foam Heat Sinks,” Int. J. Heat Mass Transfer, 47(23), pp. 5149–5157. [CrossRef]
Poulikakos, D., and Kazmierczak, M., 1987, “Forced Convection in a Duct Partially Filled With a Porous Material,” ASME J. Heat Transfer, 109(3), pp. 653–662. [CrossRef]
Kuznetsov, A. V., 1998, “Analytical Study of Fluid Flow and Heat Transfer During Forced Convection in a Composite Channel Partly Filled With a Brinkman–Forchheimer Porous Medium,” Flow, Turbul. Combust., 60(2), pp. 173–192. [CrossRef]
Kim, S. Y., Kang, B. H., and Kim, J. H., 2001, “Forced Convection From Aluminum Foam Materials in an Asymmetrically Heated Channel,” Int. J. Heat Mass Transfer, 44(6), pp. 1451–1454. [CrossRef]
Kim, S. Y., Koo, J., and Kuznetsov, A. V., 2001, “Effect of Anisotropy in Permeability and Effective Thermal Conductivity on Thermal Performance of an Aluminum Foam Heat Sink,” Numer. Heat Transfer, Part A, 40(1), pp. 21–36. [CrossRef]
Kuwahara, F., Shirota, M., and Nakayama, A., 2001, “A Numerical Study of Interfacial Convective Heat Transfer Coefficient in Two-Energy Equation Model for Convection in Porous Media,” Int. J. Heat Mass Transfer, 44(6), pp. 1153–1159. [CrossRef]
Ghosh, I., 2008, “Heat-Transfer Analysis of High Porosity Open-Cell Metal Foam,” ASME J. Heat Transfer, 130(3), p. 034501. [CrossRef]
Boomsma, K., and Poulikakos, D., 2001, “On the Effective Thermal Conductivity of a Three-Dimensionally Structured Fluid-Saturated Metal Foam,” Int. J. Heat Fluid Flow, 44(4), pp. 827–836. [CrossRef]
Lord Kelvin (Sir William Thomson), 1887, “On the Division of Space With Minimum Partitional Area,” Acta Math.-Djursholm, 11(1–4), pp. 121–134. [CrossRef]
Phelan, R., Weaire, D., Verbist, G., and Petres, E. A. J. F., 1996, “The Conductivity of a Foam,” J. Phys.: Condens. Matter, 8(34), pp. 475–482. [CrossRef]
Haussener, S., Coray, P., Lipinski, W., Wyss, P., and Steinfeld, A., 2010, “Tomography-Based Heat and Mass Transfer Characterization of Reticulate Porous Ceramics for High-Temperature Processing,” ASME J. Heat Transfer, 132(2), p. 023305. [CrossRef]
Petrasch, J., Meier, F., Friess, H., and Steinfeld, A., 2008, “Tomography Based Determination of Permeability, Dupuit–Forchheimer Coefficient, and Interfacial Heat Transfer Coefficient in Reticulate Porous Ceramics,” Int. J. Heat Fluid Flow, 29(1), pp. 315–326. [CrossRef]
Petrasch, J., Wyss, P., and Steinfeld, A., 2008, “Tomography-based Determination of the Effective Thermal Conductivity of Fluid-Saturated Reticulate Porous Ceramics,” ASME J. Heat Transfer, 130(3), p. 032602. [CrossRef]
Coquard, R., Rousseau, B., Echegut, P., Baillis, D., Gomart, H., and Iacona, E., 2012, “Investigations of the Radiative Properties of Al–Nip Foams Using Tomographic Images and Stereoscopic Micrographs,” Int. J. Heat Mass Transfer, 55(5–6), pp. 1606–1619. [CrossRef]
Loretz, M., Coquard, R., Baillis, D., and Maire, E., 2008, “Metallic Foams: Radiative Properties/Comparison Between Different Models,” J. Quant. Spectrosc. Radiat. Transfer, 109(1), pp. 16–27. [CrossRef]
Bear, J., 1972, Dynamics of Fluids in Porous Media, Elsevier, New York.
Du Plessis, P., Montillet, A., Comiti, J., and Legrand, J., 1994, “Pressure-Drop Prediction for Flow Through High Porosity Metallic Foams,” Chem. Eng. Sci., 49(21), pp. 3545–3553. [CrossRef]
Fourie, J. G., and Plessis, J. P. D., 2002, “Pressure Drop Modeling in Cellular Metallic Foams,” Chem. Eng. Sci., 57(14), pp. 2781–2789. [CrossRef]
Izzo, J. R., Jr., Joshi, A. S., Peracchio, A. A., Grew, K. N., Chiu, W. K. S., Tkachuk, A. T., Wang, S. H., and Yun, W., 2008, “Nondestructive Reconstruction and Analysis of Solid Ooxide Fuel Cell Anodes Using X-Ray Computed Tomography at Sub-50 Nm Resolution,” J. Electrochem. Soc., 155(5), pp. B504–B508. [CrossRef]
Otsu, N., 1979, “A Threshold Selection Method From Gray-Level Histograms,” IEEE Trans. Syst., Man., Cybern., 9(1), pp. 62–66. [CrossRef]
Grew, K. N., Peracchio, A. A., Joshi, A. S., Izzo, J. R., Jr., and Chiu, W. K. S., 2010, “Characterization and Analysis Methods for the Examination of the Heterogeneous Solid Oxide Fuel Cell Electrode Microstructure. Part 1: Volumetric Measurements of the Heterogeneous Structure,” J. Power Sources, 195(24), pp. 7930–7942. [CrossRef]
Grew, K. N., Peracchio, A. A., and Chiu, W. K. S., 2010, “Characterization and Analysis Methods for the Examination of the Heterogeneous Solid Oxide Fuel Cell Electrode Microstructure: Part 2. Quantitative Measurement of the Microstructure and Contributions to Transport Losses,” J. Power Sources, 195(24), pp. 7943–7958. [CrossRef]
Laurencin, J., Quey, R., Delette, G., Suhonen, H., Cloetens, P., and Bleuet, P., 2012, “Characterization of Solid Oxide Fuel Cell Ni–8YSZ Substrate by Synchrotron X-Ray Nano-Tomography: From 3D Reconstruction to Microstructure Quantification,” J. Power Sources, 198, pp. 182–189. [CrossRef]
Rajon, D., Patton, P., Shah, A., Watchman, C., and Bolch, W., 2002, “Surface Area Overestimation Within Three-Dimensional Digital Images and Its Consequence for Skeletal Dosimetry,” Med. Phys., 29(5), pp. 682–693. [CrossRef] [PubMed]
Howell, J., Hall, M., and Ellzey, J., 1999, “Combustion of Hydrocarbon Fuels Within Porous Inert Media,” Prog. Energy Combust., 22(2), pp. 121–145. [CrossRef]
Vicente, J., Topin, F., and Daurelle, J. V., 2006, “Open Celled Material Structural Properties Measurement: From Morphology to Transport Properties,” Mater. Trans., 47(9), pp. 2195–2202. [CrossRef]
Zhang, D., Zhang, R., Chen, S., and Soll, W. E., 2000, “Pore Scale Study of Flow in Porous Media: Scale Dependency, REV, and Statistical REV,” Geophys. Res. Lett., 27(8), pp. 1195–1198. [CrossRef]
Brakke, K. A., 1992, “The Surface Evolver,” Exp Math, 1(2), pp. 141–165. [CrossRef]
Dukhan, N., and Patel, P., 2008, “Equivalent Particle Diameter and Length Scale for Pressure Drop in Porous Metals,” Exp. Therm. Fluid Sci., 32(5), pp. 1059–1067. [CrossRef]
Dybbs, A., and Edwards, R. V., 1984, A New Look at Porous Media Fluid Mechanics—Darcy Turbulent, J.Bear, and Y.Corapcioglu, eds., Martinus Nijhoff, Dordrecht, The Netherlands, Vol. 82, pp. 199–256.
Nakayama, A., Kuwahara, F., and Sano, Y., 2007, “Concept of Equivalent Diameter for Heat and Fluid Flow in Porous Media,” AIChE J., 53(3), pp. 732–736. [CrossRef]
Wu, Z., Caliot, C., Bai, F., Flamant, G., Wang, Z., Zhang, J., and Tian, C., 2010, “Experimental and Numerical Study on Pressure Drop in Ceramic Foams for Volumetric Solar Receiver Applications,” Appl. Energy, 87(2), pp. 504–513. [CrossRef]
Hall, M. J., and Hiatt, P. J., 1996, “Measurements of Pore Scale Flows Within and Exiting Ceramic Foams,” Exp. Fluids, 20(6), pp. 433–440. [CrossRef]
Kaviany, M., 1995, Principles of Heat Transfer in Porous Media, Springer-Verlag, New York.
Tien, C. L., and Vafai, K., 1981, “Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media,” Int. J. Heat Mass Transfer, 24(2), pp. 195–203. [CrossRef]
Nield, D. A., Kuznetsov, A. V., and Xiong, M., 2002, “Effect of Local Thermal Non-equilibrium on Thermally Developing Forced Convection in a Porous Medium,” Int. J. Heat Mass Transfer, 45(25), pp. 4949–4955. [CrossRef]
Wu, Z., Caliot, C., Flamant, G., and Wang, Z., 2011, “Numerical Study of Convective Heat Transfer Between Air Flow and Ceramic Foams to Optimize Volumetric Solar Air Receiver Performances,” Int. J. Heat Mass Transfer, 54(7–8), pp. 1527–1537. [CrossRef]
Younis, L. B., and Viskanta, R., 1993, “Experimental Determination of the Volumetric Heat Transfer Coefficient Between Stream of Air and Ceramic Foam,” Int. J. Heat Mass Transfer, 36(6), pp. 1425–1434. [CrossRef]
Hwang, J. J., Hwang, G. J., Yeh, R. H., and Chao, C. H., 2002, “Measurement of Interstitial Convective Heat Transfer and Frictional Drag for Flow Across Metal Foams,” ASME J. Heat Transfer, 124(1), pp. 120–129. [CrossRef]
. Calmidi, V. V., 1998, “Transport Phenomena in High Porosity Fibrous Metal Foams,” Ph.D. thesis, University of Colorado, Boulder, CO.
Bhattacharya, A., Calmidi, V. V., and Mahajan, R. L., 2002, “Thermophysical Properties of High Porosity Metal Foams,” Int. J. Heat Mass Transfer, 45(5), pp. 1017–1031. [CrossRef]
Dukhan., N., 2006, “Correlations for the Pressure Drop for Flow through Metal Foam,” Exp. Fluids, 41(4), pp. 665–672. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Photograph of the cylindrical foam sample

Grahic Jump Location
Fig. 2

Tomography reconstruction of the foam sample

Grahic Jump Location
Fig. 3

Normalized distribution of the solid sizes versus diameter

Grahic Jump Location
Fig. 4

SEM image of the sample: pore diameter, dp; cell diameter, dc

Grahic Jump Location
Fig. 5

Mean porosity and mean specific surface area versus normalized cross-sectional dimension of the RVE (solid lines). Dashed lines represent the error curves, adding or subtracting the standard deviation from the mean value.

Grahic Jump Location
Fig. 6

The domain: a) real and b) ideal

Grahic Jump Location
Fig. 7

Details of generated meshes: a) real and b) ideal

Grahic Jump Location
Fig. 8

Grid independence check for the real model

Grahic Jump Location
Fig. 9

Grid independence check for the ideal model

Grahic Jump Location
Fig. 10

Mean convective heat transfer coefficient versus superficial velocity

Grahic Jump Location
Fig. 11

Mean volumetric heat transfer coefficient versus superficial velocity

Grahic Jump Location
Fig. 12

Mean Nusselt number versus Reynolds number

Grahic Jump Location
Fig. 13

Mean volumetric Nusselt number versus Reynolds number

Grahic Jump Location
Fig. 14

Pressure drop versus superficial velocity

Grahic Jump Location
Fig. 15

Pressure drop per length versus the superficial velocity

Grahic Jump Location
Fig. 16

Pressure drop versus superficial velocity, for the isothermal flow (q = 0 W/m2) and the nonisothermal flow (q = 5000 W/m2 imposed heat flux): (a) real model and (b) ideal model

Grahic Jump Location
Fig. 17

Volumetric Nusselt number versus Reynolds number

Grahic Jump Location
Fig. 18

Ratio of the pressure drop to the length of the domain versus superficial velocity

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In