Research Papers: Porous Media

Solidification of Phase Change Materials Infiltrated in Porous Media in Presence of Voids

[+] Author and Article Information
Mahmoud Moeini Sedeh

Department of Mechanical Engineering,
Auburn University,
1418 Wiggins Hall,
Auburn, AL 36849-5341
e-mail: moeini@auburn.edu

J. M. Khodadadi

Alumni Professor
Department of Mechanical Engineering,
Auburn University,
1418 Wiggins Hall,
Auburn, AL 36849-5341
e-mail: khodajm@auburn.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 24, 2013; final manuscript received August 18, 2014; published online September 16, 2014. Assoc. Editor: Sujoy Kumar Saha.

J. Heat Transfer 136(11), 112603 (Sep 16, 2014) (9 pages) Paper No: HT-13-1664; doi: 10.1115/1.4028354 History: Received December 24, 2013; Revised August 18, 2014

Infiltration of phase change materials (PCM) into highly conductive porous structures effectively enhances the thermal conductivity and phase change (solidification and melting) characteristics of the resulting thermal energy storage (TES) composites. However, the infiltration process contributes to formation of voids as micron-size air bubbles within the pores of the porous structure. The presence of voids negatively affects the thermal and phase change performance of TES composites due to the thermophysical properties of air in comparison with PCM and porous structure. This paper investigates the effect of voids on solidification of PCM, infiltrated into the pores of graphite foam as a highly conductive porous medium with interconnected pores. A combination of the volume-of-fluid (VOF) and enthalpy-porosity methods was employed for numerical investigation of solidification. The proposed method takes into account the variation of density with temperature during phase change and is able to predict the volume shrinkage (volume contraction) during the solidification of liquids. Furthermore, the presence of void and the temperature gradient along the liquid–gas interface (the interface between void and PCM) can trigger thermocapillary effects. Thus, Marangoni convection was included during the solidification process and its importance was elucidated by comparing the results among cases with and without thermocapillary effects. The results indicated that the presence of voids within the pores causes a noticeable increase in solidification time, with a sharper increase for cases without thermocapillary convection. For verification purposes, the amount of volume shrinkage during the solidification obtained from numerical simulations was compared against the theoretical volume change due to the variation of density for several liquids with contraction and expansion during the freezing process. The two sets of results exhibited good agreement.

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Greiner, M., Chen, R. F., and Wirtz, R. A., 1990, “Heat Transfer Augmentation Through Wall-Shape-Induced Flow Destabilization,” ASME J. Heat Transfer, 112(2), pp. 336–341. [CrossRef]
Rachedi, R., and Chikh, S., 2001, “Enhancement of Electronic Cooling by Insertion of Foam Materials,” Heat Mass Transfer, 37(4–5), pp. 371–378. [CrossRef]
Moeini Sedeh, M., and Khodadadi, J. M., 2013, “Energy Efficiency Improvement and Fuel Savings in Water Heaters Using Baffles,” Appl. Energy, 102, pp. 520–533. [CrossRef]
Riaz, M., 1977, “Analytical Solutions for Single-and Two-Phase Models of Packed-Bed Thermal Storage Systems,” ASME J. Heat Transfer, 99(3), pp. 489–492. [CrossRef]
Farid, M. M., Khudhair, A. M., Razack, S. A. K., and Al-Hallaj, S., 2004, “A Review on Phase Change Energy Storage: Materials and Applications,” J. Energy Conv. Manag., 45(9–10), pp. 1597–1615. [CrossRef]
Zalba, B., Marin, J. M., Cabeza, L. F., and Mehling, H., 2003, “Review on Thermal Energy Storage With Phase Change: Materials, Heat Transfer Analysis and Applications,” Appl. Therm. Eng., 23(3), pp. 251–283. [CrossRef]
Jegadheeswaran, S., and Pohekar, S. D., 2009, “Performance Enhancement in Latent Heat Thermal Storage System: A Review,” Int. J. Renewable Sustainable Energy Rev., 13(9), pp. 2225–2244. [CrossRef]
Zhang, Y., and Faghri, A., 1996, “Heat Transfer Enhancement in Latent Heat Thermal Energy Storage System by Using the Internally Finned Tube,” Int. J. Heat Mass Transfer, 39(15), pp. 3165–3173. [CrossRef]
Shatikian, V., Ziskind, G., and Letan, R., 2005, “Numerical Investigation of a PCM-Based Heat Sink With Internal Fins,” Int. J. Heat Mass Transfer, 48(17), pp. 3689–3706. [CrossRef]
Tong, X., Khan, J. A., and Amin, M. R., 1996, “Enhancement of Heat Transfer by Inserting a Metal Matrix Into a Phase Change Material,” J. Numer. Heat Transfer, Part A, 30(2), pp. 125–141. [CrossRef]
Nayak, K. C., Saha, S. K., Srinivasan, K., and Dutta, P., 2006, “A Numerical Model for Heat Sinks With Phase Change Materials and Thermal Conductivity Enhancers,” Int. J. Heat Mass Transfer, 49(11–12), pp. 1833–1844. [CrossRef]
Fan, L., and Khodadadi, J. M., 2011, “Thermal Conductivity Enhancement of Phase Change Materials for Thermal Energy Storage: A Review,” Int. J. Renewable Sustainable Energy Rev., 15(1), pp. 24–46. [CrossRef]
Khodadadi, J. M., and Hosseinizadeh, S. F., 2007, “Nanoparticle-Enhanced Phase Change Materials (NEPCM) With Great Potential for Improved Thermal Energy Storage,” Int. Commun. Heat Mass Transfer, 34(5), pp. 534–543. [CrossRef]
Wang, X. Q., and Mujumdar, A. S., 2007, “Heat Transfer Characteristics of Nanofluids: A Review,” Int. J. Therm. Sci., 46(1), pp. 1–19. [CrossRef]
Kiwan, S., and Al-Nimr, M. A., 2001, “Using Porous Fins for Heat Transfer Enhancement,” ASME J. Heat Transfer, 123(4), pp. 790–795. [CrossRef]
Alkam, M. K., Al-Nimr, M. A., and Hamdan, M. O., 2001, “Enhancing Heat Transfer in Parallel-Plate Channels by Using Porous Inserts,” Int. J. Heat Mass Transfer, 44(5), pp. 931–938. [CrossRef]
Abu-Hijleh, B. A. K., 2003, “Enhanced Forced Convection Heat Transfer From a Cylinder Using Permeable Fins,” ASME J. Heat Transfer, 125(5), pp. 804–811. [CrossRef]
Vafai, K., and Kim, S. J., 1990, “Analysis of Surface Enhancement by a Porous Substrate,” ASME J. Heat Transfer, 112(3), pp. 700–706. [CrossRef]
Boomsma, K., and Poulikakos, D., 2001, “On the Effective Thermal Conductivity of a Three-Dimensionally Structured Fluid-Saturated Metal Foam,” Int. J. Heat Mass Transfer, 44(4), pp. 827–836. [CrossRef]
Krishnan, S., Murthy, J. Y., and Garimella, S. V., 2006, “Direct Simulation of Transport in Open-Cell Metal Foam,” ASME J. Heat Transfer, 128(8), pp. 793–799. [CrossRef]
Krishnan, S., Garimella, S. V., and Murthy, J. Y., 2008, “Simulation of Thermal Transport in Open-Cell Metal Foams: Effect of Periodic Unit-Cell Structure,” ASME J. Heat Transfer, 130(2), p. 024503. [CrossRef]
Siahpush, A., O'Brien, J., and Crepeau, J., 2008, “Phase Change Heat Transfer Enhancement Using Copper Porous Foam,” ASME J. Heat Transfer, 130(8), p. 082301. [CrossRef]
Zhao, C. Y., Lu, W., and Tian, Y., 2010, “Heat Transfer Enhancement for Thermal Energy Storage Using Metal Foams Embedded Within Phase Change Materials (PCMs),” Sol. Energy, 84(8), pp. 1402–1412. [CrossRef]
Kamath, P. M., Balaji, C., and Venkateshan, S. P., 2013, “A Simple Thermal Resistance Model for Open Cell Metal Foams,” ASME J. Heat Transfer, 135(3), p. 032601. [CrossRef]
Yu, Q., Thompson, B. E., and Straatman, A. G., 2006, “A Unit Cube-Based Model for Heat Transfer and Fluid Flow in Porous Carbon Foam,” ASME J. Heat Transfer, 128(4), pp. 352–360. [CrossRef]
Yorwearth, L., Jamin, Y. L., and Mohamad, A. A., 2008, “Natural Convection Heat Transfer Enhancements From a Cylinder Using Porous Carbon Foam: Experimental Study,” ASME J. Heat Transfer, 130(12), p. 122502. [CrossRef]
Garrity, P. T., and Klausner, J. F., 2010, “Performance of Aluminum and Carbon Foams for Air Side Heat Transfer Augmentation,” ASME J. Heat Transfer, 132(12), p. 121901. [CrossRef]
DeGroot, C. T., and Straatman, A. G., 2012, “Numerical Results for the Effective Flow and Thermal Properties of Idealized Graphite Foam,” ASME J. Heat Transfer, 134(4), p. 042603. [CrossRef]
Klett, J., Hardy, R., Romine, E., Walls, C., and Burchella, T., 2000, “High-Thermal-Conductivity, Mesophase-Pitch-Derived Carbon Foams: Effect of Precursor on Structure and Properties,” Carbon, 38(7), pp. 953–973. [CrossRef]
Klett, J. W., McMillan, A. D., Gallego, N. C., and Walls, C., 2004, “The Role of Structure on the Thermal Properties of Graphitic Foams,” J. Mater. Sci., 39(11), pp. 3659–3676. [CrossRef]
Leong, K. C., and Li, H. Y., 2011, “Theoretical Study of the Effective Thermal Conductivity of Graphite Foam Based on a Unit Cell Model,” Int. J. Heat Mass Transfer, 54(25–26), pp. 5491–5496. [CrossRef]
Moeini Sedeh, M., and Khodadadi, J. M., 2013, “Thermal Conductivity Improvement of Phase Change Materials/Graphite Foam Composites,” Carbon, 60, pp. 117–128. [CrossRef]
Lafdi, K., Mesalhy, O., and Elgafy, A., 2008, “Graphite Foams Infiltrated With Phase Change Materials as Alternative Materials for Space and Terrestrial Thermal Energy Storage Applications,” Carbon, 46(1), pp. 159–168. [CrossRef]
Moeini Sedeh, M., and Khodadadi, J. M., 2013, “Interface Behavior and Void Formation During Infiltration of Liquids Into Porous Structures,” Int. J. Multiphase Flow, 57, pp. 49–65. [CrossRef]
Moeini Sedeh, M., and Khodadadi, J. M., 2012, “Effect of Voids on Solidification of Phase Change Materials Infiltrated in Graphite Foams,” Proceedings of the ASME Summer Heat Transfer Conference, Rio Grande, PR, July 8–12, pp. 495–502.
Mehling, H., Hiebler, S., and Ziegler, F., 2000, “Latent Heat Storage Using a PCM–Graphite Composite Material,” Proceedings of Terrastock 2000, Stuttgart, Germany, Aug. 28–Sept. 1, pp. 375–380.
Moeini Sedeh, M., and Khodadadi, J. M., 2013, “Effect of Marangoni Convection on Solidification of Phase Change Materials Infiltrated in Porous Media in Presence of Voids,” ASME Paper No. HT2013-17316. [CrossRef]
Voth, T. E., and Liu, A., 1992, “Thermocapillary Convection During Solid–Liquid Phase Change,” ASME J. Heat Transfer, 114(4), pp. 1068–1070. [CrossRef]
Khodadadi, J. M., and Zhang, Y., 2000, “Effects of Thermocapillary Convection on Melting Within Droplets,” Numer. Heat Transfer, Part A, 37(2), pp. 133–153. [CrossRef]
Arlabosse, P., Tadrist, L., Tadrist, H., and Pantaloni, J., 2000, “Experimental Analysis of the Heat Transfer Induced by Thermocapillary Convection Around a Bubble,” ASME J. Heat Transfer, 122(1), pp. 66–73. [CrossRef]
Savino, R., and Fico, S., 2006, “Buoyancy and Surface Tension Driven Convection Around a Bubble,” Phys. Fluids, 18(5), p. 057104. [CrossRef]
Kostarev, K., Viviani, A., and Zuev, A., 2006, “Thermal and Concentrational Maragoni Convection at Liquid/Air Bubble Interface,” ASME J. Appl. Mech., 73(1), pp. 66–71. [CrossRef]
Nota, F., Savino, R., and Fico, S., 2006, “The Interaction Between Droplets and Solidification Front in Presence of Marangoni Effect,” Acta Astronaut., 59(1–5), pp. 20–31. [CrossRef]
Kassemi, M., Barsi, S., Kaforey, M., and Matthiesen, D., 2001, “Effect of Void Location on Segregation Patterns in Microgravity Solidification,” J. Cryst. Growth, 225(2–4), pp. 516–521. [CrossRef]
Matsunaga, K., and Kawamura, H., 2006, “Influence of Thermocapillary Convection on Solid–Liquid Interface,” Fluid Dyn. Mater. Process., 2(1), pp. 59–64. [CrossRef]
Typical Material Properties, PocoFoam®, Poco Graphite Inc., Decatur, TX, 2013, http://www.poco.com/Portals/0/Literature/Semiconductor/78962v2PocoFoamFlyer.pdf
Hirt, C. W., and Nichols, B. D., 1981, “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Comput. Phys, 39(1), pp. 201–225. [CrossRef]
Beckermann, C., and Viskanta, R., 1988, “Double-Diffusive Convection During Dendritic Solidification of a Binary Mixture,” J. Physicochem. Hydrodyn., 10(2), pp. 195–213.
Brent, A. D., Voller, V. R., and Reid, K. J., 1988, “Enthalpy-Porosity Technique for Modeling Convection–Diffusion Phase Change: Application to the Melting of a Pure Metal,” Numer. Heat Transfer Part A, 13(3), pp. 297–318. [CrossRef]
Brackbill, J. U., Kothe, D. B., and Zemach, C., 1992, “A Continuum Method for Modeling Surface Tension,” J. Comput. Phys., 100(2), pp. 335–354. [CrossRef]
Moeini Sedeh, M., and Khodadadi, J. M., 2013, “Experimental Investigation of Wicking Flow Through a Porous Medium as a Verification Approach for Numerical Simulations,” ASME Paper No. FEDSM2013-16466. [CrossRef]
Schulze, T. P., and Grae Worster, M., 1999, “Weak Convection, Liquid Inclusions and the Formation of Chimneys in Mushy Layers,” J. Fluid Mech., 388, pp. 197–215. [CrossRef]
Crowley, A. B., and Ockendon, J. R., 1987, “Modeling Mushy Regions,” Appl. Sci. Res., 44(1–2), pp. 1–7. [CrossRef]
Dantzig, J. A., and Rappaz, M., 2009, Solidification, EPFL Press, Lausanne, Switzerland. [PubMed] [PubMed]
Yaws, C. L., 2008, Thermophysical Properties of Chemicals and Hydrocarbons, 1st ed., William Andrew, Norwich, NY.
Sulfredge, C. D., Chow, L. C., and Tagavi, K. A., 1999, “Initiation and Growth of Solidification Shrinkage Voids,” Annual Reviews of Heat Transfer, Vol. 10, Begell House, Inc., New York, pp. 221–278.
ansysfluent 13.0 Theory Guide, 2010, ansys Inc., Cecil, PA.
Ubbink, O., and Issa, R. I., 1999, “A Method for Capturing Sharp Fluid Interfaces on Arbitrary Meshes,” J. Comput. Phys., 153(1), pp. 26–50. [CrossRef]


Grahic Jump Location
Fig. 1

Scanning electron microscope (SEM) image of the graphite foam (PocoFoam) showing its microstructure at (a) 100×, (b) 200× magnifications, and (c) the developed 2D model of the pore and its features

Grahic Jump Location
Fig. 2

(a) Grid-independence study (spatial) and (b) detailed view of the grid system

Grahic Jump Location
Fig. 3

Evolving VOF volume fraction distribution (λ) during the infiltration of cyclohexane into the pore at time instants of (a) 0.5, (b) 1.2, (c) 1.56, (d) 1.75, (e) 2.1, (f) 2.5, (g) 3 ms, and (h) the final state of infiltration with 9.8% void content (evaluated based on area), selected as the initial condition for solidification [35]

Grahic Jump Location
Fig. 4

Variations of density with temperature for cyclohexane as a typical hydrocarbon-based PCM

Grahic Jump Location
Fig. 5

Time-evolving contours of liquid fraction during the solidification of cyclohexane in the absence of thermocapillary effects (i.e., constant surface tension of 0.025 N/m) at time instants of (a) 5, (b) 25, (c) 50, (d) 100, (e) 150, (f) 250, (g) 350, and (h) 450 ms

Grahic Jump Location
Fig. 6

Time rate of solidification of cyclohexane (typical PCM) within the pore

Grahic Jump Location
Fig. 7

Time-evolving contours of liquid fraction during the solidification of cyclohexane in the presence of thermocapillary effects (i.e., surface tension is a function of temperature) at time instants of (a) 5, (b) 25, (c) 50, (d) 100, (e) 150, (f) 250, (g) 350, and (h) 450 ms

Grahic Jump Location
Fig. 8

The convection pattern within the pore at time instant of 25 ms for cases of (a) excluding and (b) including thermocapillary effects in solidification (arrows indicate velocity vectors in PCM)



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