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Research Papers

Laminar Natural Convection Heat Transfer From Vertical 7 × 7 Rod Bundles in Liquid Sodium

[+] Author and Article Information
Koichi Hata

Graduate School of Maritime Sciences,
Kobe University,
5-1-1, Fukae-minami,
Kobe, Hyogo 658-0022, Japan
e-mail: hatako1@people.kobe-u.ac.jp

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

Manuscript received August 24, 2017; final manuscript received December 9, 2018; published online March 15, 2019. Editor: Igor Pioro.

ASME J of Nuclear Rad Sci 5(2), 021002 (Mar 15, 2019) (15 pages) Paper No: NERS-17-1088; doi: 10.1115/1.4042356 History: Received August 24, 2017; Revised December 09, 2018

Laminar natural convection heat transfer from vertical 7 × 7 rod bundle in liquid sodium was numerically analyzed to optimize the thermal–hydraulic design for the bundle geometry with equilateral square array (ESA). 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 code of the parabolic hyperbolic or elliptic numerical integration code series (PHOENICS) was used for the calculation considering the temperature dependence of thermophysical properties concerned. The 7 × 7 heated rods for diameter (D =0.0076 m), length (L =0.2 m) and L/D (=26.32) were used in this work. The surface heat fluxes for each cylinder, which was uniformly heated along the length, were equally given for a modified Rayleigh number, (Raf,L)ij and (Raf,L)Nx×Ny,S/D, ranging from 3.08 × 104 to 4.28 × 107 (q =1 × 104∼7 × 106 W/m2) in liquid temperature (TL = 673.15 K). The values of ratio of the diagonal center-line distance between rods for bundle geometry to the rod diameter (S/D) for vertical 7 × 7 rod bundle were ranged from 1.8 to 6 on the bundle geometry with ESA. The spatial distribution of average Nusselt numbers for a vertical single cylinder of a rod bundle, (Nuav)ij, and average Nusselt numbers for a vertical rod bundle, (Nuav,B)Nx×Ny,S/D, were clarified. The average values of Nusselt number, (Nuav)ij and (Nuav,B)Nx×Ny,S/D, for the bundle geometry with various values of S/D were calculated to examine the effect of array size, bundle geometry, S/D, (Raf,L)ij and (Raf,L)Nx×Ny,S/D on heat transfer. The bundle geometry for the higher (Nuav,B)Nx×Ny,S/D value under the condition of S/D = constant was examined. The general correlations for natural convection heat transfer from a vertical Nx×Ny rod bundle with the ESA and equilateral triangle array (ETA), including the effects of array size, (Raf,L)Nx×Ny,S/D and S/D were derived. The correlations for vertical Nx×Ny rod bundles can describe the theoretical values of (Nuav,B)Nx×Ny,S/D for each bundle geometry in the wide analytical range of S/D (=1.8–6) and the modified Rayleigh number ((Raf,L)Nx×Ny,S/D = 3.08 × 104 to 4.28 × 107) within −9.49 to 10.6% differences.

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References

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Figures

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Fig. 1

Schematic diagram of a test vessel with a 0.00762-m diameter test cylinder

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Fig. 2

Schematic diagram of a 0.00762-m diameter test cylinder

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Fig. 3

Schematic diagrams: A test vessel with a 0.00762-m (0.0076-m) diameter test cylinder (a) and 1/2 Model of a test vessel for a vertical 7 × 7 rod bundle with 0.0076-m diameter heated cylinders (b)

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Fig. 4

Top view for vertical 7 × 7 rod bundle with ESA

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Fig. 5

Boundary fitted coordinates: ESA ((a) and (b))

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Fig. 6

Liquid temperatures in the conductive sublayer, δCSL, based on numerically predicted data points (solution of unsteady laminar three dimensional basic equations) for vertical single cylinder with D =0.0076 m

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Fig. 7

Experimental data of local surface temperature rises, (Ts)z − TL, for vertical single test cylinder versus the vertical distance from the leading edge of the heated section, z, at heat fluxes of 2 × 105 to 2 × 106 W/m2 compared with the numerical solutions and Eq. (13).

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Fig. 8

Heat transfer process on the vertical cylinder of D =0.00762 m and L =0.186 m without helical wire spacer compared with heat transfer curves numerically analyzed by δCSL = 2 × 10−4 m, and thickness of conductive sublayer, δCSL

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Fig. 9

Theoretical solutions of (Nuav,B)5 × 5,S/D for vertical 5 × 5 rod bundle with ESA with Eqs. (26)(28), and the correlation for vertical single cylinder

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Fig. 10

Theoretical solutions of (Nuav,B)5 × 5,S/D for vertical 5 × 5 rod bundle with ETA with Eqs. (26), (29) and (30), and the correlation for vertical single cylinder.

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Fig. 11

(Nuav)ij versus Nx for vertical 7 × 7 rod bundle with ESA with Ny as a parameter at (Raf,L)ij = 3.54 × 106 (q =1 × 106 W/m2)

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Fig. 12

(Nuav)ij versus Ny for vertical 7 × 7 rod bundle with ESA with Ny as a parameter at (Raf,L)ij = 3.54 × 106 (q =1 × 106 W/m2)

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Fig. 13

(Nuav)ij versus (Ni 1)/(Nx 1) for vertical 5 × 5 and 7 × 7 rod bundles with ESA with (Nj 1)/(Ny 1) as a parameter at (Raf,L)ij= 3.54 × 106 (q =1 × 106 W/m2)

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Fig. 14

(Nuav)ij versus (Nj 1)/(Ny 1) for vertical 5 × 5 and 7 × 7 rod bundles with ESA with (Ni 1)/(Nx 1) as a parameter at (Raf,L)ij = 3.54 × 106 (q =1 × 106 W/m2)

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Fig. 15

Contours of liquid temperature of the x–y plane on L =0.025, 0.095 and 0.195 m for a vertical 7 × 7 rod bundle of the ESA with S/D =2 at (Raf,L)7 × 7,S/D=2 = 3.54 × 106 (q= 1 × 106 W/m2)

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Fig. 16

Contours of liquid temperature at the x-z plane on iy =104 and at the y–z plane on ix =1 for a vertical 7 × 7 rod bundle of the ESA with S/D =2 at (Raf,L)7 × 7,S/D=2 = 3.54 × 106 (q =1 × 106 W/m2)

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Fig. 17

Distributions of velocity vectors of the x–y plane on iz =1, 12, 20, 30 and 37 for a vertical 7 × 7 rod bundle of the ESA with S/D =2 at (Raf,L)7 × 7,S/D=2 = 3.54 × 106 (q =1 × 106 W/m2)

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Fig. 18

Theoretical solutions of (Nuav,B)7 × 7,S/D=2 for vertical 7 × 7 rod bundle of ESA with S/D =2 and (Nuav,B)5 × 5,S/D for vertical 5 × 5 rod bundle of ESA with S/D =1.8 to 5, and Nuav for vertical single cylinder

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Fig. 19

Comparison of theoretical solutions of (Nuav,B)7 × 7,S/D=2 for vertical 7 × 7 rod bundle with ESA and (Nuav,B)5 × 5,S/D=2 for vertical 5 × 5 rod bundle with ESA with authors' correlations, Eqs. (26)(28).

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Fig. 20

Average Nusselt number, (Nuav,B)Nx×Ny,S/D, for the ESAand ETA versus the S/D at (Raf,L)Nx×Ny,S/D=3.54 × 106 (q=1 × 106 W/m2)

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Fig. 21

Comparison of theoretical solutions of (Nuav,B)7x7,S/D for vertical 7 × 7 rod bundle with ESA and (Nuav,B)5x5,S/D for vertical 5 × 5 rod bundle with ESA with authors' correlations, Eqs. (22) and (23).

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Fig. 22

Theoretical solutions of (Nuav,B)Nx×Ny,S/D for vertical 7 × 7 rod bundle with ESA with the Nuav and the correlation for vertical single cylinder

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