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Prediction of forced convective heat transfer and critical heat flux for subcooled water flowing in miniature tubes

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Abstract

The heat transfer characteristics of forced convection for subcooled water in small tubes were clarified using the commercial computational fluid dynamic (CFD) code, PHENICS ver. 2013. The analytical model consists of a platinum tube (the heated section) and a stainless tube (the non-heated section). Since the platinum tube was heated by direct current in the authors’ previous experiments, a uniform heat flux with the exponential function was given as a boundary condition in the numerical simulation. Two inner diameters of the tubes were considered: 1.0 and 2.0 mm. The upward flow velocities ranged from 2 to 16 m/s and the inlet temperature ranged from 298 to 343 K. The numerical results showed that the difference between the surface temperature and the bulk temperature was in good agreement with the experimental data at each heat flux. The numerical model was extended to the liquid sublayer analysis for the CHF prediction and was evaluated by comparing its results with the experimental data. It was postulated that the CHF occurs when the fluid temperature near the heated wall exceeds the saturated temperature, based on Celata et al.’s superheated layer vapor replenishment (SLVR) model. The suggested prediction method was in good agreement with the experimental data and with other CHF data in literature within ±25%.

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Abbreviations

C :

Courant number

C 1ε C 2ε C 3ε C μ :

Model constants

C f /2 :

Skin friction coefficient

c p :

Specific heat, J/kg K

d :

Inner diameter of tube, m

G :

Volumetric production rate of turbulent energy

g :

Gravity, m/s2

h :

= c p T, enthalpy, J/kg, and heat transfer coefficient, W/m2 K

k :

Turbulent kinetic energy, m2/s

L :

Heated length of tube, m

P :

Pressure, kPa

Q :

Heat input per unit volume, W/m3

q :

Heat flux, W/m2

q 0 :

Initial heat flux, W/m2

Re :

=ud/ν, Reynolds number

R T :

Electric resistance of the platinum tube, Ω

R 0 :

Electric resistance at 0 °C, Ω

r :

Radial distance in cylindrical coordinate, m, and radius of tube, m

St :

= q/ρc p u(T s -T b ), Stanton number

t :

Time, s

T :

Temperature, K

u :

Velocity, m/s

z :

Rectangular coordinate, m

α :

Coefficient in Eq.(8)

β :

Coefficient in Eq.(8)

δ TBL :

Thickness of thermal boundary layer, m

ε :

Dissipation rate of turbulent energy

θ :

Angle in cylindrical coordinate, radian

λ :

Thermal conductivity, W/m K

μ :

Viscosity, Ns/m2

ν :

= μ/ρ, kinematic viscosity, m2/s

μ t :

= C μ k 2/ε, turbulent kinematic viscosity, m2/s

ρ :

Density, kg/m3

τ :

e-folding time, s

σ k :

Prandtl number for k

σ t :

turbulent Prandtl number

σ e :

Prandtl number for ε

a :

Average

b :

Bulk

cal :

Calculation

cell :

Center of control volume

cr :

Critical

exp :

Experiment

in :

Inlet

L :

Liquid

out :

Outlet

s :

Surface

t :

Turbulent

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Acknowledgements

This work was partially supported by the JSPS KAKENHI Grant Numbers JP16K18322 and JP15K05828. This work was partially performed with the support and under the auspices of NIFS Collaboration Research program (NIFS17KEMF100).

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Authors and Affiliations

  1. Graduate School of Maritime Sciences, Kobe University, 5-1-1 Fukaeminamimachi, Higashinada, Kobe, Hyogo, 658-0022, Japan

    Makoto Shibahara, Katsuya Fukuda, Qiusheng Liu & Koichi Hata

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  1. Makoto Shibahara
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  2. Katsuya Fukuda
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Correspondence to Makoto Shibahara.

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Shibahara, M., Fukuda, K., Liu, Q. et al. Prediction of forced convective heat transfer and critical heat flux for subcooled water flowing in miniature tubes. Heat Mass Transfer 54, 501–508 (2018). https://doi.org/10.1007/s00231-017-2155-8

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