Research Papers

Investigation of Natural Convection Heat-Transfer Phenomena in Packed Beds: Lead-Way Toward New Nuclear Fuel Design

[+] Author and Article Information
Olugbenga O. Noah

Department of Mechanical and Aeronautical Engineering,
University of Pretoria,
Private Bag X20, Hatfield, 0028 Pretoria, South Africa
e-mail: Noah.Olugbenga@tuks.co.za

Johan F. Slabber

Department of Mechanical and Aeronautical Engineering,
University of Pretoria,
Private Bag X20, Hatfield, 0028 Pretoria, South Africa
e-mail: johan.slabber@up.ac.za

Josua P. Meyer

Department of Mechanical and Aeronautical Engineering,
University of Pretoria,
Private Bag X20, Hatfield, 0028 Pretoria, South Africa
e-mail: josua.meyer@up.ac.za

Manuscript received January 20, 2015; final manuscript received June 28, 2015; published online September 3, 2015. Assoc. Editor: Mark Anderson.

ASME J of Nuclear Rad Sci 1(4), 041014 (Sep 03, 2015) (12 pages) Paper No: NERS-15-1007; doi: 10.1115/1.4030983 History: Received January 20, 2015; Accepted July 02, 2015; Online September 16, 2015

The ability of coated particles of enriched uranium dioxide fuel encased in graphite to discontinue nuclear fission reaction without human action in the case of complete loss of cooling is a vital safety measure over traditional nuclear fuel. As a possible solution toward enhancing the safety of light water reactors (LWRs), it is envisaged that the fuel, in the form of loose, coated particles in a helium atmosphere, can be used inside the cladding tubes of the fuel elements. This study is therefore a first step toward understanding the heat-transfer characteristics under natural convective conditions within the fuel cladding tubes of such a revolutionary new fuel design. The coated particle fuels are treated as a bed, from which the heat is transferred to the cladding tube and the gas movement occurs due to natural convection. A basic unit cell model was used where a single unit of the packed bed was analyzed and taken as representative of the entire bed. The model is a combination of both analytical and numerical methods accounting for the thermophysical properties of sphere particles, the interstitial gas effect, gas temperature, contact interface between particles, particle size, and particle temperature distribution used in this study to investigate the heat-transfer effect. The experimental setup was a packed bed heated from below with gas circulation due to natural convection. This allows for the development of an appropriate, conservative thermal energy balance that can be used in determining the heat-transfer characteristics in homogeneous porous media. Success in this method, when validated with suitable correlation, such as Gunn, suggests that the heat-transfer phenomenon/characteristics in the fuel cladding tube of the new design can be evaluated using this approach for design purpose.

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Balakrishnan, A. R., and Pei, D. C., 1979, “Heat Transfer in Gas-Solid Packed Bed Systems,” Ind. Eng. Chem. Process Des. Dev., 18(1), pp. 40–46. 10.1021/i260069a004
Siu, W. W. M., and Lee, S. H.-K., 2004, “Transient Temperature Computation of Particles in Three-Dimensional Random Packings,” Int. J. Heat Mass Transfer., 47(5), pp. 887–898. 10.1016/j.ijheatmasstransfer.2003.08.022
Balakrishnan, A. R., and Pei, D. C., 1978, “Heat Transfer in Gas-Solid Packed Bed Systems—A Critical Review,” Ind. Eng. Chem. Process Des. Dev., 18(1), pp. 30–40. 10.1021/i260069a003
Bahrami, M., Yovanovich, M. M., and Culham, J. R., 2006, “Effective Thermal Conductivity of Rough Spherical Packed Beds,” Int. J. Heat Mass Transfer, 49(19–20), pp. 3691–3701. 10.1016/j.ijheatmasstransfer.2006.02.021
Van Antwerpen, W., Du Toit, C. G., and Rousseau, P. G., 2010, “A Review of Correlations to Model the Packing Structure and Effective Thermal Conductivity in Packed Beds of Mono-Sized Spherical Particles,” Nucl. Eng. Des., 240(7), pp. 1803–1818. 10.1016/j.nucengdes.2010.03.009
Chen, C. K., and Tien, C. L., 1973, “Conductance of Packed Particles in Vacuum,” J. Heat Transfer., 95(3), pp. 302–308. 10.1115/1.3450056
Yovanovich, M. M., 1973, “Apparent Conductivity of Glass Microspheres From Atmospheric Pressure to Vacuum,” Heat Transfer Conference, Atlanta, GA, ASME-AIChE, New York, ASME Paper 73-HT-43.
Kaviany, M., 1995, Principles of Heat Transfer in Porous Media, 2nd ed., Springer, New York.
Nield, D. A., and Bejan, A., 2006, Convection in Porous Media, 3rd ed., Springer, New York.
Du Toit, C. G., and Rousseau, P. G., 2012, “Modeling the Flow and Heat Transfer in a Packed Bed High Temperature Gas-Cooled Reactor in the Context of a Systems CFD Approach,” ASME J. Heat Transfer., 134(3), pp. 031015-1–031015-12. 10.1115/1.4005152
Van Antwerpen, W., Rousseau, P. G., and Du Toit, C. G., 2012, “Multi-Sphere Unit Cell Model to Calculate the Effective Thermal Conductivity in Packed Pebble Beds of Mono-Sized Spheres,” Nucl. Eng. Des., 247(1), pp. 183–201. [CrossRef]
Siu, W. W. M., and Lee, S. H.-K., 2000, “Transient Effect on the Constriction Resistance Between Particles,” Comput. Mech., 25(1), pp. 59–65. 10.1007/s004660050015
Noah, O. O., Slabber, J. F., and Meyer, J. P., 2013, “Experimental Evaluation of Natural Convection Heat Transfer in Packed Beds Contained in Slender Cylindrical Geometries,” Proceedings of the 5th International Conference on Applications of Porous Media, Romania, Presa Universitară Clujeană, Cluj-Napoca, Romania, pp. 301–316.
Rumpf, J., 1958, “Grundlagen und Methoden des Granulierens,” Chem. Ing. Tech., 30(12), pp. 144–158. 10.1002/cite.330300307
Meissner, H. P., Micheals, A. S., and Kaiser, R., 1964, “Crushing Strength of Zinc Oxide Agglomerates,” Ind. Eng. Chem. Process Des. Dev., 3(1), pp. 202–205. [CrossRef]
Ridgeway, K., and Tarbuck, K. J., 1968, “Voidage Fluctuations in Randomly-Packed Beds of Spheres Adjacent to a Containing Wall,” Chem. Eng. Sci., 23(9), pp. 1147–1155. [CrossRef]
Suzuki, M., Makino, K., Yamada, M., and Iinoya, K., 1981, “A Study on the Coordination Number in a System of Randomly Packed, Uniform-sized Spherical Particles,” Int. Chem. Eng., 21(1), pp. 482–488.
Timoshenko, S. P., and Goodie, J. N., 1970, Theory of Elasticity, McGraw-Hill Book Company, New York, Article 140.
Yovanovich, M. M., and Marotta, E. E., 2003, “Thermal Spreading and Contact Resistances,” Heat Transfer Handbook, A. Bejan, and D. Kraus, eds., John Wiley and Sons Inc., Hoboken, NY, Chap. 4.
Bahrami, M., Culham, J. R., and Yovanovich, M. M., 2004, “Thermal Joint Resistance of Non-conforming Rough Surfaces with Gas-filled Gaps,” AIAA J. Thermophys. Heat Transfer, 18(3), pp. 326–332. 10.2514/1.5482
Achenbach, E., 1995, “Heat and Fluid Flow Characteristics of Packed Beds,” Therm. Fluid Sci., 10(1), pp. 17–27. 10.1016/0894-1777(94)00077-L
Hoffmann, J. E., 2004, “Validation and Verification of CFD Simulation at PBMR,” Proceedings at the 4th South African Conference on Applied Mechanic, Johannesburg, SACAM, Muldersdrift, Johannesburg, South Africa, Vol. 2, p. 19.
Robold, K., 1982, “Wärmetransport im inneren und in der randzone von kugelschüttungen,” Kernforschungsanlage Jülich GmbH, 19, Tech. Rep. 1976.
Zehner, P., and Schlünder, E. U., 1970, “Wärmeleitfähigkeit von schüttungen bei mäBigen Temperaturen,” Chem. Ing. Tech., 2(1), pp. 933–941. 10.1002/(ISSN)1522-2640
IAEA TECDOC-1163, 2000, “Heat Transport and After Heat Removal for Gas Cooled Reactors Under Accident Conditions,” International Atomic Energy Agency.
Kaviany, M., 1991, Principles of Heat Transfer in Porous Media, Springer, New York.
Breitbach, G., and Barthels, H., 1980, “The Radiation Heat Transfer in the HTR Core After Failure of the Afterheat Removal System,” Nucl. Tech., 49(1), pp. 392–399.
Bauer, R., and Schlünder, E. U., 1978, “Effective Radial Thermal Conductivity of Packings in Gas Flow. Part 2: Thermal Conductivity of the Packing Fraction Without Gas Flow,” Int. Chem. Eng., 18(2), pp. 189–204.
Tien, C.-L., 1988, “Thermal Radiation in Packed and Fluidized Beds,” J. Heat Transfer, 110(4b), pp. 1230–1242. 10.1115/1.3250623
Kaviany, M., and Singh, B. P., 1993, “Radiative Heat Transfer in Porous Media,” Adv. Heat Transfer., 23(1), pp. 133–186. 10.1016/S0065-2717(08)70006-6
Gunn, D. J., 1978, “Transfer of Heat or Mass To Particles in Fixed and Fluidised Beds,” Int. J. Heat Mass Transfer., 21(4), pp. 467–476. 10.1016/0017-9310(78)90080-7
Kugeler, K., 2009, “HTR Technology,” NUCI 878 EB Study Guide, North-West University, Potchefstroom.
Koster, A, Matzner, H. D., and Nicholsi, D. R., 2003, “PBMR Design for the Future,” Nucl. Eng. Des., 222(2–3), pp. 231–245. [CrossRef]
Noah, O. O., Slabber, J. F., and Meyer, J. P., 2015, “Experimental and Theoretical Investigation of the Natural Convection Heat Transfer from Heated Micro-Spheres in a Slender Cylindrical Geometry,” Ph.D. Thesis, University of Pretoria, Pretoria, South Africa.


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Fig. 5

Thermal resistance network for spherical Hertzian contact

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Fig. 4

Heat conduction between two smooth-elastic particles in perfect contact

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Fig. 3

(a) Schematic representation of contacting adjacent particles, (b) control volumes with grid points, (c) finite contact spot of smooth contacting spherical surfaces, and (d) temperature distribution with increasing length along particle diameter

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Fig. 2

(a) Schematic diagram of experimental setup (for illustration purpose), (b) sectional view of instrumented test particle/particle test sample, and (c) experimental setup

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Fig. 1

Section through part of the test facility with a particle test sample highlighted. (i) Heat transfer by particle-to-fluid mode, (ii) heat transfer by fluid-to-particle mode, (iii) heat transfer from the bed wall to the particles, (iv) heat transfer by particle-to-particle mode, (v) radiant heat transfer between particles, and (vi) radiant heat transfer between side wall and particles.

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Fig. 9

Nusselt number in the packed bed as a function of convective fluid-to-particle heat-transfer coefficient

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Fig. 10

Variation of Nusselt number on the Rayleigh number for fluid-to-particle heat transfer

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Fig. 6

Schematics of the regular LWR cladding tube with fuel pellets

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Fig. 7

Schematics of proposed coated particle fuel design in a cladding SiC tube

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Fig. 8

Effect of gas thermal conductivity on convective fluid-to-particle heat-transfer coefficient in the packed bed




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