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Research Papers: Natural and Mixed Convection

Natural Convection Heat Transfer From Vertical 5 × 5 Rod Bundles in Liquid Sodium

[+] Author and Article Information
Koichi Hata, Katsuya Fukuda

Graduate School of Maritime Sciences,
Kobe University,
5-1-1, Fukae-minami,
Kobe, Hyogo 658-0022, Japan

Tohru Mizuuchi

Institute of Advanced Energy,
Kyoto University,
Gokasho,
Uji, Kyoto 611-0011, Japan

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 8, 2016; final manuscript received October 20, 2016; published online January 4, 2017. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 139(3), 032502 (Jan 04, 2017) (11 pages) Paper No: HT-16-1447; doi: 10.1115/1.4035069 History: Received July 08, 2016; Revised October 20, 2016

Natural convection heat transfer from vertical 5 × 5 rod bundles in liquid sodium was numerically analyzed for two types of the bundle geometry (equilateral square array (ESA) and equilateral triangle array (ETA)). The unsteady laminar three-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady-state. The phoenics code was used for the calculation considering the temperature dependence of thermophysical properties concerned. The 5 × 5 test rods for diameter (D = 7.6 mm), heated length (L = 200 mm), and L/d (=26.32) were used in this work. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, (Rf,L)ij and (Rf,L)5×5,S/D, ranging from 3.08 × 104 to 4.19 × 107 (q = 1 × 104–7 × 106 W/m2) in liquid temperature (TL = 673.15 K). The values of S/D, which are ratios of the diameter of flow channel for bundle geometry to the rod diameter, for vertical 5 × 5 rod bundles were ranged from 1.8 to 6 on each bundle geometry. The spatial distribution of local and average Nusselt numbers, (Nuav)ij and (Nuav,B)5×5,S/D, on vertical rods of a bundle was clarified. The average value of Nusselt numbers, (Nuav)ij and (Nuav,B)5×5,S/D, for the two types of the bundle geometry with various values of S/D were calculated to examine the effect of the bundle geometry, S/D, (Rf,L)ij, and (Rf,L)5×5,S/D on heat transfer. The bundle geometry for the higher (Nuav,B)5×5,S/D value under the condition of S/D = constant was examined. The correlations for (Nuav,B)5×5,S/D for two types of bundle geometry above mentioned including the effects of (Rf,L)5×5,S/D and S/D were developed. The correlations can describe the theoretical values of (Nuav,B)5×5,S/D for the two types of the bundle geometry at S/D ranging from 1.8 to 6 within −12.64% to 7.73% difference.

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References

Hata, K. , Takeuchi, Y. , Hama, K. , Shiotsu, M. , Shirai, Y. , and Fukuda, K. , 2014, “ Natural Convection Heat Transfer From a Vertical Cylinder in Liquid Sodium,” Mech. Eng. J., 1(1), pp. 1–12. [CrossRef]
Hata, K. , Fukuda, K. , and Mizuuchi, T. , 2016, “ Natural Convection Heat Transfer From Vertical Rod Bundles in Liquid Sodium,” Mech. Eng. J., 3(3), pp. 1–16. [CrossRef]
Hata, K. , Shiotsu, M. , Takeuchi, Y. , and Sakurai, A. , 1995, “ Natural Convection Heat Transfer on Two Horizontal Cylinders in Liquid Sodium,” 7th International Meeting on Nuclear Reactor Thermal-Hydraulics, Saratoga Springs, NY, Sept. 10–15, Vol. 2, pp. 1333–1350.
Hata, K. , Shiotsu, M. , Takeuchi, Y. , and Sakurai, A. , 1995, “ Natural Convection Heat Transfer From Two Parallel Horizontal Cylinders in Liquid Sodium,” International Mechanical Engineering Congress and Exposition, Proceedings of the ASME Heat Transfer Division, ASME Publications, New York, HTD-Vol. 317-1, Book No. H1032A-1995, pp. 245–257.
Hata, K. , Shiotsu, M. , Takeuchi, Y. , Hama, K. , Sakurai, A. , and Sagayama, Y. , 1997, “ Natural Convection Heat Transfer From Horizontal Rod Bundles in Liquid Sodium,” Eighth International Topical Meeting on Nuclear Reactor Thermal Hydraulics, Vol. 2, pp. 817–827.
Hata, K. , Takeuchi, Y. , Shiotsu, M. , and Sakurai, A. , 1999, “ Natural Convection Heat Transfer From a Horizontal Cylinder in Liquid Sodium—Part 1: Experimental Results,” Nucl. Eng. Des., 193(1–2), pp. 105–118. [CrossRef]
Hata, K. , Takeuchi, Y. , Shiotsu, M. , and Sakurai, A. , 1999, “ Natural Convection Heat Transfer From a Horizontal Cylinder in Liquid Sodium—Part 2: Generalized Correlation for Laminar Natural Convection Heat Transfer,” Nucl. Eng. Des., 194(2–3), pp. 185–196. [CrossRef]
Hata, K. , Takeuchi, Y. , Hama, K. , and Shiotsu, M. , 2015, “ Natural Convection Heat Transfer From Horizontal Rod Bundles in Liquid Sodium—Part 1: Correlations for Two Parallel Horizontal Cylinders Based on Experimental and Theoretical Results,” J. Nucl. Sci. Technol., 52(2), pp. 214–227. [CrossRef]
Hata, K. , Takeuchi, Y. , Hama, K. , and Shiotsu, M. , 2014, “ Natural Convection Heat Transfer From Horizontal Rod Bundles in Liquid Sodium—Part 2: Correlations for Horizontal Rod Bundles Based on Theoretical Results,” J. Nucl. Sci. Technol., 52(3), pp. 342–354. [CrossRef]
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing, New York.
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LeFevre, E. J. , and Ede, A. J. , 1957, “ Laminar Free Convection From the Outer Surface of a Vertical Circular Cylinder,” 9th International Congress on Applied Mechanics Brussels, Vol. 4, pp. 175–183.
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Figures

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Fig. 1

Schematic diagram 1/2 model of a test vessel for a vertical 5 × 5 rod bundle with 7.6-mm diameter test cylinders

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Fig. 2

Top view for vertical 5 × 5 rod bundles with equilateral square array (ESA) (a) and equilateral triangle array (ETA) (b)

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Fig. 3

Boundary fitted coordinates: equilateral square array (ESA) ((a-1) and (a-2)) and equilateral triangle array (ETA) ((b-1) and (b-2))

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Fig. 4

Theoretical solutions of (Nuav,B)N for vertical rod bundles of a two parallel, equilateral triangle and equilateral square arrays with the Nuav, and the correlation for vertical single cylinder [2]

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Fig. 5

(Nuav)ij versus Nx for vertical 5 × 5 rod bundle with equilateral square array (ESA) with Ny as a parameter at (Rf,L)ij = 3.52 × 106 (q = 1 × 106 W/m2)

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Fig. 6

(Nuav)ij versus Nx for vertical 5 × 5 rod bundle with equilateral triangle array (ETA) with Ny as a parameter at (Rf,L)ij = 3.52 × 106 (q = 1 × 106 W/m2)

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Fig. 7

Contours of liquid temperature of the x–y plane on L = 25, 95, and 195 mm for a vertical rod bundle of the equilateral square array (ESA) at (Rf,L)5×5,S/D=2 = 3.52 × 106 (q = 1 × 106 W/m2)

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Fig. 8

Contours of liquid temperature and velocity of the x–z plane on iy = 80 for a vertical rod bundle of the equilateralsquare array (ESA) at (Rf,L)5×5,S/D=2 = 3.52 × 106 (q = 1 × 106 W/m2)

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Fig. 9

Contours of liquid temperature and velocity of the y–z plane on ix = 1 for a vertical rod bundle of the equilateral square array (ESA) at (Rf,L)5×5,S/D=2 = 3.52 × 106 (q = 1 × 106 W/m2)

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Fig. 10

Theoretical solutions of (Nuav,B)5x5,S/D=2 for vertical 5 × 5 rod bundles with equilateral square and triangle arrays (ESA and ETA) and (Nuav,B)N for vertical rod bundles of a two parallel, equilateral triangle and equilateral square arrays with the Nuav, and the correlation for vertical single cylinder

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Fig. 11

Average Nusselt number, (Nuav,B)5×5,S/D=2, for the equilateral square and triangle arrays (ESA and ETA) versus the S/D at (Rf,L)5×5,S/D=2 = 3.52 × 106 (q = 1 × 106 W/m2)

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Fig. 12

Theoretical solutions of (Nuav,B)5×5,S/D for vertical 5 × 5 rod bundle with equilateral square array (ESA) with the Nuav, and the correlation for vertical single cylinder

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Fig. 13

Theoretical solutions of (Nuav,B)5×5,S/D for vertical 5 × 5 rod bundle with equilateral triangle array (ETA) with the Nuav, and the correlation for vertical single cylinder

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Fig. 14

Value of C1 versus S/D for (Nuav,B)5×5,S/D = C1 × (Rf,L)5×5,S/Dn (ESA and ETA)

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Fig. 15

Value of n versus S/D for (Nuav,B)5×5,S/D = C1 × (Rf,L)5×5,S/Dn (ESA and ETA)

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