Computational Study of Turbulent Heat Transfer for Heating of Water in a Short Vertical Tube Under Velocities Controlled
NURETH-14 - 2011 September 25-30


Presented at:
NURETH-14
2011 September 25-30
Location:
Toronto, Canada
Session Title:
B1-1 Computational Fluid Dynamics, Mathematical Modeling and Verification/Validation/Applications

Authors:
Koichi Hata (Institute of Advanced Energy, Kyoto University)
Naoto Kai (Kyoto University)
Yasuyuki Shirai (Kyoto University)
Suguru Masuzaki (National Institute for Fusion Science)
Akimichi Hamura (Concentration Heat and Momentum Ltd.)
  

Abstract

can not only describe the experimental data of steady-state turbulent heat transfer but also the numerical solutions within ±10 % difference for the wide ranges of temperature differences between heater inner surface temperature and liquid bulk mean temperature (ΔTL=5 to 200 K) and flow velocity (u=4.01 to 41.07 m/s).

The steady-state turbulent heat transfer coefficients in a short vertical Platinum (Pt) test tube for the flow velocities (u=4.11, 7.12, 10.07, 13.62, 21.43, 30.72 and 41.07 m/s), the inlet liquid temperatures (Tin=296.47 to 310.04 K), the inlet pressures (Pin=810.40 to 1044.21 kPa) and the increasing heat inputs (Q0exp(t/τ), exponential periods, τ, of 6.04 to 23.66 s) were systematically measured by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. Measurements were made on a 59.2 mm effective length and its three sections (upper, mid and lower positions), which were spot-welded four potential taps on the outer surface of the Pt test tube of a 6 mm inner diameter, a 69.6 mm heated length and a 0.4 mm thickness. The outer surface temperature distribution of the Pt test tube was also simultaneously observed by an infrared thermal imaging camera at intervals of 3 seconds.

Theoretical equations for turbulent heat transfer in a circular tube of a 6 mm in diameter and a 636 mm long were numerically solved for heating of water with heated section of a 6 mm in diameter and a 70 mm long by using PHOENICS code under the same condition as the experimental one considering the temperature dependence of thermo-physical properties concerned. The surface heat flux, q, and the surface temperature, Ts, on the circular tube solved theoretically under the flow velocities, u, of 4.11, 7.12, 10.07, 13.62, 21.43, 30.72 and 41.07 m/s were compared with the corresponding experimental values on heat flux, q, versus the temperature difference between heater inner surface temperature and liquid bulk mean temperature, ΔTL [=Ts-TL, TL=(Tin+Tout)/2], graph. The numerical solutions of q and ΔTL are almost in good agreement with the corresponding experimental values of q and ΔTL with the deviations less than ±10 % for the range of ΔTL tested here. The numerical solutions of local surface temperature, (Ts)z, local average liquid temperature, (Tf,av)z, and local liquid pressure drop, ΔPz, were also compared with the corresponding experimental data on (Ts)z, (Tf,av)z and ΔPz versus heated length, L, or distance from inlet of the test section, Z, graph, respectively. The numerical solutions of local surface temperature, (Ts)z and local average liquid temperature, (Tf,av)z are within ±10 % of the corresponding experimental data on (Ts)z and (Tf,av)z, although those of local liquid pressure drop, ΔPz, become 37.6 % lower than the experimental ones. The thickness of the viscous sub-layer, δVSL [=(Δr)out/2], and the non-dimensional thickness of

(1/22)The 14th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-14)Log Number: 173 Hilton Toronto Hotel, Toronto, Ontario, Canada, September 25-29, 2011.

+ ⎡⎛f0.5ρuδ ⎤ viscous sub-layer, y VSL ⎢= ⎜ F lVSL , for the turbulent heat transfer in a short vertical tube

Gnielinski: Nu d

=( f / 2 )(Red 1000 )Pr(7) 1 + 12.7 ( f / 2 )1 / 2 (Pr 2 / 3 1 )

⎢⎝2⎠μ⎥ ⎣l

under velocities controlled are clarified based on the numerical solutions.

It was confirmed in this study that authors' steady-state turbulent heat transfer correlation, Eq. (1), based on the experimental data [1]

L0.08⎛μ ⎞0.14 Nud =0.02Red0.85 Pr0.4⎜ ⎟ ⎜ l (1)

d⎠⎝μw

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