Research Papers

Internal Transport Coefficient Measurements in Random Fiber Matrix Heat Exchangers

[+] Author and Article Information
David Geb

Department of Mechanical
and Aerospace Engineering,
School of Engineering and Applied Science,
University of California, Los Angeles,
Morrin-Gier-Martinelli Heat Transfer
Memorial Laboratory,
48-121 Engineering IV,
420 Westwood Plaza,
Los Angeles, CA 90095-1597
e-mail: dvdgb15@ucla.edu

Angelo Lerro

Politecnico di Torino,
Department of Mechanical and
Aerospace Engineering,
10129 Torino, Italy

Ivan Catton

Department of Mechanical and
Aerospace Engineering,
School of Engineering and Applied Science,
University of California, Los Angeles,
Morrin-Gier-Martinelli Heat Transfer Memorial Laboratory,
48-121 Engineering IV,
420 Westwood Plaza,
Los Angeles, CA 90095-1597

1Corresponding author.

Manuscript received January 27, 2013; final manuscript received April 27, 2013; published online October 21, 2013. Assoc. Editor: Samuel Sami.

J. Thermal Sci. Eng. Appl 6(1), 011005 (Oct 21, 2013) (9 pages) Paper No: TSEA-13-1014; doi: 10.1115/1.4024707 History: Received January 27, 2013; Revised April 27, 2013

Experimental determination of transport coefficients, in particular internal heat transfer coefficients, in heterogeneous and hierarchical heat transfer devices such as compact regenerative heat exchangers has posed a persistent challenge for designers. The goal of this study is to (1) present a new general treatment of the experimental determination of such design data, to (2) provide simple correlations for high porosity random fiber matrices for broad design applications, and to (3) illustrate how such measurements close the formidable integro-differential volume averaging theory (VAT) equations governing transport phenomena in porous media. The combined experimental and computational method employed here for determining the internal heat transfer coefficient in the porous structure is based on the VAT model and combines with simple pressure drop measurements to yield the relevant design data for eight different high porosity random fiber samples. The design data are correlated based on a porous media length scale derived from the VAT model governing equations and the transport coefficient correlations obtained are valid for gas flows over a Reynolds number range between 5 and 70. Finally, the correlations are related to explicit, rigorously derived, lower-scale expressions arising from the VAT model. With the illustration of a new experimental tool, and the production of new simple design correlations for high porosity random fiber matrices for regenerative heat transfer applications, within the context of the hierarchical VAT model, future VAT-based simulation studies of such devices may be pursued. Moreover, the nonlocal modeling provided by VAT paves the way to meaningful optimization studies due to its singular ability to provide rigorous modeling and fast numerical solutions for transport phenomena in regenerative compact heat exchangers.

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Catton, I., 2011, “Conjugate Heat Transfer Within a Heterogeneous Hierarchical Structure,” ASME J. Heat Transfer, 133(10), p. 103001. [CrossRef]
Anderson, T. B., and Jackson, R., 1967, “Fluid Mechanical Description of Fluidized Beds. Equations of Motion,” Ind. Eng. Chem. Fundam., 6(4), pp. 527–539. [CrossRef]
Slattery, J. C., 1967, “Flow of Viscoelastic Fluids Through Porous Media,” AIChE J., 13(6), pp. 1066–1071. [CrossRef]
Marle, C. M., 1967, “Ecoulements monophasiques en milieu poreux,” Rev. Inst. Francais du Petrole, 22, pp. 1471–1509.
Whitaker, S., 1967, “Diffusion and Dispersion in Porous Media,” AIChE J., 13(3), pp. 420–427. [CrossRef]
Zolotarev, P. P., and Radushkevich, L. V., 1968, “An Approximate Analytical Solution of the Internal Diffusion Problem of Dynamic Absorption in the Linear Region of an Isotherm,” Russ. Chem. Bull., 17(8), pp. 1818–1820. [CrossRef]
Slattery, J. C., 1980, Momentum, Energy and Mass Transfer in Continua, Krieger, Malabar.
Kaviany, M., 1995, Principles of Heat Transfer in Porous Media, Springer, New York.
Gray, W. G., Leijnse, A., Kolar, R. L., and Blain, C. A., 1993, Mathematical Tools for Changing Spatial Scales in the Analysis of Physical Systems, CRC Press, Boca Raton.
Whitaker, S., 1977, “Simultaneous Heat, Mass and Momentum Transfer in Porous Media: A Theory of Drying,” Adv. Heat Transfer, 13, pp. 119–203. [CrossRef]
Whitaker, S., 1997, “Volume Averaging of Transport Equations,” Int. Ser. Adv. Fluid Mech., 13, pp. 1–60.
Kheifets, L. I., and Neimark, A. V., 1982, Multiphase Processes in Porous Media, Khimia, Moscow.
Dullien, F. A. L., 1979, Porous Media Fluid Transport and Pore Structure, Academic Press, New York.
Adler, P. M., 1992, Porous Media: Geometry and Transports, Butterworth-Heinemann, New York.
Travkin, V., and Catton, I., 1992, “Models of Turbulent Thermal Diffusivity and Transfer Coefficients for a Regular Packed Bed of Spheres,” ASME Publications—HTD, Vol. 193, p. 15.
Travkin, V., and Catton, I., 1995, “A Two-Temperature Model for Turbulent Flow and Heat Transfer in a Porous Layer,” J. Fluids Eng., 117(1), pp. 181–188. [CrossRef]
Travkin, V. S., and Catton, I., 1998, “Porous Media Transport Descriptions—Non-Local, Linear and Non-Linear Against Effective Thermal/Fluid Properties,” Adv. Colloid Interface Sci., 76-77(0), pp. 389–443. [CrossRef]
Travkin, V. S., Catton, I., and Gratton, L., 1993, “Single Phase Turbulent Transport in Prescribed Non-Isotropic and Stochastic Porous Media,” ASME Publications—HTD, Vol. 240, p. 43.
Travkin, V. S., Catton, I., Hu, K., Ponomarenko, A. T., and Shevchenko, V. G., 1999, “Transport Phenomena in Heterogeneous Media: Experimental Data Reduction and Analysis,” ASME Applied Mechanics Division—Publications—AMD, Vol. 233, pp. 21–32.
Nakayama, A., Ando, K., Yang, C., Sano, Y., Kuwahara, F., and Liu, J., 2009, “A Study on Interstitial Heat Transfer in Consolidated and Unconsolidated Porous Media,” Heat Mass Transfer, 45(11), pp. 1365–1372. [CrossRef]
Nakayama, A., and Kuwahara, F., 2008, “A General Macroscopic Turbulence Model for Flows in Packed Beds, Channels, Pipes, and Rod Bundles,” J. Fluids Eng., 130(10), p. 101205. [CrossRef]
Nakayama, A., Kuwahara, F., and Hayashi, T., 2004, “Numerical Modelling for Three-Dimensional Heat and Fluid Flow Through a Bank of Cylinders in Yaw,” J. Fluid Mech., 498, pp. 139–159. [CrossRef]
Nakayama, A., Kuwahara, F., and Kodama, Y., 2006, “An Equation for Thermal Dispersion Flux Transport and Its Mathematical Modelling for Heat and Fluid Flow in a Porous Medium,” J. Fluid Mech., 563(1), pp. 81–96. [CrossRef]
Travkin, V. S., and Catton, I., 2001, “Transport Phenomena in Heterogeneous Media Based on Volume Averaging Theory,” Advances in Heat Transfer, G. G.Hari, and A. H.Charles, eds., Elsevier, New York, pp. 1–144.
Zhou, F., Hansen, N. E., Geb, D. J., and Catton, I., 2011, “Obtaining Closure for Fin-and-Tube Heat Exchanger Modeling Based on Volume Averaging Theory (VAT),” ASME J. Heat Transfer, 133(11), p. 111802. [CrossRef]
Zhou, F., and Catton, I., 2012, “Volume Averaging Theory (VAT) Based Modeling and Closure Evaluation for Fin-and-Tube Heat Exchangers,” Heat Mass Transfer, 48, pp. 1–11. [CrossRef]
Zhou, F., DeMoulin, G. W., Geb, D. J., and Catton, I., 2012, “Closure for a Plane Fin Heat Sink With Scale-Roughened Surfaces for Volume Averaging Theory (VAT) Based Modeling,” Int. J. Heat Mass Transfer, 55(25–26), pp. 7677–7685. [CrossRef]
Horvat, A., and Mavko, B., 2005, “Hierarchic Modeling of Heat Transfer Processes in Heat Exchangers,” Int. J. Heat Mass Transfer, 48(2), pp. 361–371. [CrossRef]
Vadnjal, A., 2009, “Modeling of a Heat Sink and High Heat Flux Vapor Chamber,” PhD thesis, University of California, Los Angeles, CA,” PhD thesis, University of California, Los Angeles, CA.
Rodriguez, J. I., and Mills, A. F., 1990, “Analysis of the Single-Blow Transient Testing Technique for Perforated Plate Heat Exchangers,” Int. J. Heat Mass Transfer, 33, pp. 1969–1976.
Liang, C. Y., and Yang, W.-J., 1975, “Modified Single-Blow Technique for Performance Evaluation on Heat Transfer Surfaces,” ASME J. Heat Transfer, 97(1), pp. 16–21. [CrossRef]
Stang, J. H., and Bush, J. E., 1974, “The Periodic Method for Testing Compact Heat Exchanger Surfaces,” J. Eng. Power, 96(2), pp. 87–94. [CrossRef]
Younis, L., 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]
Nie, X., Evitts, R., Besant, R., and Bolster, J., 2011, “A New Technique to Determine Convection Coefficients With Flow Through Particle Beds,” ASME J. Heat Transfer, 133(4), p. 041601. [CrossRef]
Krishnakumar, K., John, A. K., and Venkatarathnam, G., 2011, “A Review on Transient Test Techniques for Obtaining Heat Transfer Design Data of Compact Heat Exchanger Surfaces,” Exp. Therm. Fluid Sci., 35(4), pp. 738–743. [CrossRef]
Geb, D., Zhou, F., and Catton, I., 2012, “Internal Heat Transfer Coefficient Determination in a Packed Bed From the Transient Response Due to Solid Phase Induction Heating,” ASME J. Heat Transfer, 134(4), p. 042604. [CrossRef]
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]
Ibrahim, M. B., Zhiguo, Z., Rong, W., Simon, T. W., and Gedeon, D., 2002, “A 2-D CFD Model of Oscillatory Flow With Jets Impinging on a Random Wire Regenerator Matrix,” Proceedings of Energy Conversion Engineering Conference, IECEC '02. 2002 37th Intersociety, pp. 511–517.
Makoto, T., Iwao, Y., and Fumitake, C., 1990, “Flow and Heat Transfer Characteristics of the Stirling Engine Regenerator in an Oscillating Flow,” JSME Int. J. Ser. II, 33(2), pp. 283–289.
Miyabe, H., Hamaguchi, K., and Takahashi, K., 1982, “An Approach to the Design of Stirling Engine Regenerator Matrix Using Packs of Wire Gauzes,” Proc. Intersoc. Energy Convers. Eng. Conf., pp. 1839–1844.
Gedeon, D., and Wood, J., 1992, “Oscillating-Flow Regenerator Test Rig: Woven Screen and Metal Felt Results,” NASA STI/Recon Technical Report No. 92, p. 31352.
Gedeon, D., and Wood, J., 1996, “Oscillating-Flow Regenerator Test Rig: Hardware and Theory With Derived Correlations for Screens and Felts,” NASA Contractor Report No. 198442.
Simon, T. W., and Seume, J. R., 1988, “A Survey of Oscillating Flow in Stirling Engine Heat Exchangers,” NASA STI/Recon Technical Report No. 88, p. 22322.
Knowles, T., 1997, “Composite Matrix Regenerator for Stirling Engines,” Report No. 202322.
Thieme, L. G., 2001, “Friction Factor Characterization for High-Porosity Random Fiber Regenerators,” NASA Report No. NASA/TM-2001-211098.
Tew, R., Ibrahim, M., Danila, D., Simon, T., Mantell, S., Sun, L., Gedeon, D., Kelly, K., McLean, J., and Qiu, S., 2007, “A Microfabricated Involute-Foil Regenerator for Stirling Engines,” NASA Report No. NASA/TM-2007-214973.
Ibrahim, M., Danila, D., Simon, T., Mantell, S., Sun, L., Gedeon, D., Qiu, S., Wood, J., Kelly, K., and McLean, J., 2007, “A Microfabricated Segmented-Involute-Foil Regenerator for Enhancing Reliability and Performance of Stirling Engines: Phase II Final Report for the Radioisotope Power Conversion Technology NRA Contract NAS3–03124,” NASA Contractor Report No. NASA/CR—2007-215006.
Zalba, B., Marín, 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]
Knowels, T. R., 1997, “Composite Matrix Regenerator for Stirling Engines,” NASA Contractor Report No. 202322.
Koh, J. C. Y., and Fortini, A., 1973, “Prediction of Thermal Conductivity and Electrical Resistivity of Porous Metallic Materials,” Int. J. Heat Mass Transfer, 16(11), pp. 2013–2022. [CrossRef]
Kays, W. M., and London, A. L., 1984, Compact Heat Exchangers, McGraw-Hill, New York.
Whitaker, S., 1972, “Forced Convection Heat Transfer Correlations for Flow in Pipes, Past Flat Plates, Single Cylinders, Single Spheres, and for Flow in Packed Beds and Tube Bundles,” AIChE J., 18(2), pp. 361–371. [CrossRef]
Anzelius, A., 1926, “Uber Erwärmung vermittels durchströmender Medien,” Z. Angew. Math. Mech., 6(4), pp. 291–294. [CrossRef]
Schumann, T. E. W., 1929, “Heat Transfer: A Liquid Flowing Through a Porous Prism,” J. Franklin Inst., 208(3), pp. 405–416. [CrossRef]
Gedeon, D., 2011, “Sage User's Guide,” Gedeon Associates, Athens, OH.


Grahic Jump Location
Fig. 1

Test rig schematic

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Fig. 2

Iteration procedure

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Fig. 3

Heat exchanger core pressure drop. Adapted from Ref. [51]

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Fig. 4

Nusselt number data and correlation, for air

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Fig. 5

Experimental Nusselt number values plotted against the correlation values, for air

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Fig. 6

Friction factor data and correlation

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Fig. 7

Experimental friction factor values plotted against the correlation values

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Fig. 8

Nusselt number correlations

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Fig. 9

Friction factor correlations




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