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Heat and Mass Transfer

, Volume 55, Issue 1, pp 175–195 | Cite as

Conductive and viscous sub-layers on forced convection and mechanism of critical heat flux during flow boiling of subcooled water in a circular tube at high liquid Reynolds number

  • K. HataEmail author
  • Q. S. Liu
  • S. Masuzaki
Article
  • 53 Downloads

Abstract

The turbulent heat transfer, the subcooled boiling heat transfer and the steady state CHF for a Pt-circular test tube of a 3 mm inner diameter and a 100 mm heated length are measured with a wide range of inlet subcooling and flow velocity at high liquid Reynolds number, i.e. Red = 3.01×104 to 1.43×105. The inner surface temperature of the Pt-circular test tube calculated by the steady one-dimensional heat conduction equation is compared with the values derived from authors’ turbulent heat transfer correlation and with the numerical solutions of the RANS equations (Reynolds Averaged Navier-Stokes Simulation) of k-ε turbulence model for the flow velocities ranging from 4 to 21 m/s. The thicknesses of conductive sub-layer from non-boiling regime to CHF are measured by numerically analyzing the heat transfers with conductive sub-layer on forced convection and with thinner one dissipated by the evaporation on nucleate boiling. The thicknesses of viscous sub-layer on forced convection are estimated from the thicknesses of the conductive sub-layer and Prandtl numbers of the surface temperature on the heated surface. Furthermore, the thicknesses of conductive sub-layer at the CHF point are extrapolated from the measured values at various flow velocities. The experimental values of the CHF are also compared with authors’ widely and precisely predictable correlations of critical heat flux during flow boiling of subcooled water and the corresponding theoretical values of the liquid sub-layer dry-out models suggested by other researchers, respectively. The authors’ correlations and other researchers’ theoretical values can represent the subcooled boiling CHFs obtained in this study within the ranges of −13.27 to 6.76% difference and − 32.51 to 13.16% one, respectively. A suggestion based on the experimental data as to what the dominant mechanism is for critical heat flux during flow boiling of subcooled water on a vertical circular tube is confirmed again at high liquid Reynolds number. The transitions to film boiling at the subcooled water flow boiling on the Pt test tube of d = 3 mm and L = 100 mm would occur due to the liquid sub-layer dry-out model at the steady-state CHF as well as those on the Pt test tube of d = 3 mm and L = 66.5 mm, but not due to the heterogeneous spontaneous nucleation and the hydro-dynamic instability.

Nomenclature

Bo

q/Ghfg, boiling number

Bocr

qcr,sub,st/Ghfg, boiling number at CHF point

C1, C2, C3, C4, C5, C6

Constants in Eqs. (3) and (4)

cpl

Specific heat at constant pressure, J/kgK

d

Test tube inner diameter, m

fF

Fanning friction factor

G

ρlu, mass velocity, kg/m2s

hfg

Latent heat of vaporization, J/kg

L

Heated length, m

Leff

Effective length, m

Nud

hd/λl, nusselt number

Pcr

22064 kPa, critical pressure, kPa

Pin

Pressure at inlet of heated section, kPa

Pipt

Pressure measured by inlet pressure transducer, kPa

Pout

Pressure at outlet of heated section, kPa

Popt

Pressure measured by outlet pressure ransducer, kPa

Pr

cpμ/λ, Prandtl number

(Pr)Ts

Prandtl number of the surface temperature on the heated surface under forced convection

Q

Heat input per unit volume, W/m3

Q0

Initial exponential heat input, W/m3

q

Heat flux, W/m2

qcr,sub,st

Steady-state CHF for subcooled condition, W/m2

Ra

Average roughness, μm

Red

Gd/μl, Reynolds number

Rmax

Maximum roughness depth, μm

Rz

Mean roughness depth, μm

ri

Test tube inner radius, m

ro

Test tube outer radius, m

(Δr)out

Outer control volume width for r-component, m

TEM

Calculated temperature of the outer control volume, K

T

Water temperature, C

\( \overline{T} \)

Average temperature of test tube, K

Tf,av

Average liquid temperature, K

Tin

Inlet liquid temperature, K

TL

(Tin+Tout)/2, liquid bulk mean temperature, K

Tout

Outlet liquid temperature, K

Ts

Heater inner surface temperature, K

Tsat

Saturation temperature, K

Tso

Heater outer surface temperatures, K

Ts,av

Average inner surface temperature, K

ΔTL

(Ts,av-TL), temperature difference between average inner surface temperature and liquid bulk mean temperature, K

ΔTsat

Ts-Tsat, inner surface superheat, K

u

Flow velocity, m/s

y+

y(τwρl)0.5l, dimensionless normal-distance coordinate

y+CSL

(fF/2)0.5ρlCSL/μl, non-dimensional thickness of conductive sub-layer

δ

Conductive sub-layer on nucleate boiling heat transfer

δCSL

(Δr)out/2, thickness of conductive sub-layer and conductive sub-layer on forced convection

δVSL

Thickness of viscous sub-layer on forced convection

ε

Rate of dissipation of turbulent energy, m2/s3

μl

Viscosity, Ns/m2

μw

Viscosity at tube wall temperature, Ns/m2

νl

μll, kinematic viscosity of fluid, Ns m/kg

ρl

Density of fluid, kg/m3

τw

shear stress at the wall, N/m2

χ

Vaper quality

Notes

Acknowledgements

This research was performed as a LHD joint research project of NIFS (National Institute for Fusion Science), Japan, NIFS15KEMF066, 2015, 2016 and 2017.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of Maritime SciencesKobe UniversityKobeJapan
  2. 2.National Institute for Fusion ScienceGifuJapan

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