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Heat and Mass Transfer

, Volume 53, Issue 9, pp 2999–3012 | Cite as

Effects of outlet subcoolings and heat generation rates on transient critical heat flux for subcooled flow boling of water in a vertical tube

  • M. ShibaharaEmail author
  • K. Fukuda
  • Q. S. Liu
  • K. Hata
Original

Abstract

Critical heat fluxes (CHFs) for subcooled flow boiling of water in a vertical tube due to steady and exponentially heat inputs were measured. The platinum tube with an inner diameter of 2.0 mm and a length of 94.8 mm was placed vertically in the experimental water loop. The upward flow velocity was approximately 2.5 m/s and the outlet subcooling ranged from 18 to 48 K. The heat generation rate was varied exponentially to investigate the effect of e-folding time on the CHFs. As an experimental result, the CHFs increased with a decrease in the e-folding time. When the e-folding times were longer, the CHFs were almost constant, whereas the CHFs increased for shorter e-folding times. The CHFs were independent on outlet subcoolings at low flow conditions. Moreover, it was considered that the explosive-like CHF occurred when the inner surface temperature of the tube exceeded the lower limit of heterogeneous spontaneous nucleation (HSN) temperature.

Keywords

Critical Heat Flux Boiling Heat Transfer Outlet Pressure Experimental Tube Heat Generation Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

A

Surface area (m2)

a

Thermal diffusivity (m2/s)

b

Basis limit

C

Coefficient in Eq. (26)

c

Coefficient in Eq. (28)

CD

Drag coefficient

ch

Specific heat (J/kg K)

cp

Specific heat at constant pressure (J/kg K)

d

Inner diameter of tube (m)

Db

Vapor equivalent diameter

F

Ratio of activation energy

f

Friction factor

f(β)

Function of contact angle (=0.02–0.03)

Fo = a/d2

Fourier number

G

Mass velocity (kg/m2 s)

g

Acceleration of gravity (m/s2)

hfg

Latent heat of vaporization (J/kg)

I = VI/Rs

Current (A)

J

Probability density (l/m2 s)

K3

Coefficient in Eq. (29)

k

Boltzmann constant

L

Heated length (m)

m

Mass (kg)

N

Number of molecules per unit volume (l/m3)

n

Dissolved gas concentration (ml)

P

Pressure (kPa)

Pr = cp/λ

Prandtl number

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 inlet pressure transducer (kPa)

Pvb

Vapor pressure inside a bubble (Pa)

ΔP = Pvb − P

Pa

\(\dot{Q}\)

Heat input per unit volume (W/m3)

Q

Heat transfer rate (W)

Q0

Initial heat input (W/m3)

q

Heat flux (W/m3)

r

Radius of tube (m)

R

Resistance (Ω)

Ra

Average roughness (μm)

Rs

Standard resistance (Ω)

Ry

Maximum roughness depth (μm)

Rz

Mean roughness depth (μm)

Re = ud/

Reynolds number

R0

Normal resistance (Ω)

SLB

Sound level of boiling

s

Precision index

T

Temperature (K)

Ta

Mean temperature of tube (K)

Tcr

Critical temperature (K)

THET,L

Lower limit of HSN temperature (K)

Tin

Inlet liquid temperature (K)

Tout

Outlet liquid temperature (K)

Ts

Inner surface temperature (K)

Tsat

Saturation temperature (K)

t

Time (s)

t95

Confidence level

TL = (Tin + Tout)/2

Average bulk liquid temperature (K)

ΔTsat = (Ts − Tsat)

Inner surface superheat (K)

ΔTsub,out = (Tsat − Tout)

Outlet liquid subcooling (K)

U

Uncertainty

u

Flow velocity (m/s)

V

Volume of the experimental tube (m3)

VI

Voltage of the standard resistance (V)

VR

Voltage of the experimental tube (V)

VT

Voltage difference (V)

w

Weight coefficient

We = G2d/ρlσ

Weber number

y*

Superheated layer

α

Coefficient in Eq. (2)

β

Aperture angle of conical cavity (rad)

θ

Liquid–solid contact angle (rad)

εr

Emissivity

ε

Surface roughness

δ

Initial thickness of liquid sublayer

λ

Thermal conductivity (W/mK)

τ

E-folding time (s)

ν

Kinematic viscosity (m2/s)

ρ

Density (kg/m3)

μl

Viscosity (N s/m2)

μw

Viscosity at tube wall temperature (N s/m2)

σ

Surface tension (N/m)

σsf

Stefan–Boltzmann constant (=5.67 × 10−8 W/m2 K4)

δ

Liquid sublayer initial thickness (m), Maximum relative deviation

χ

Quality

Subscripts

a

Average

AMP

Amplifier

B

Bulk

b

Vapor blanket

cal

Calculation

cr

CHF

g

Vapor

h

Heater

I

Current

in

Inlet

l

Liquid

LS

Least square

o

Outer

ONB

Onset of nucleate boiling

out

Outlet

R

Electric resistance

r

Radiation

RSS

Root sum square

st

Steady state

sub

Subcooled condition

sat

Saturated conditions

TC

Thermocouple

V

Voltage

w

Wall

wnh

Without heating

Notes

Acknowledgements

This work was supported by the Kansai Research Foundation for technology promotion (KRF) and the Japan Society for the promotion of Science (JSPS) (Grant-in Aid for Scientific Research (C), KAKENHI, Grant Number JP15K05828). The authors would like to thank to S. Watanabe for assistances in the experiments.

References

  1. 1.
    Mudawar I (2011) Two-phase microchannel heat sinks: theory, applications, and limitations. J Electron Packag 133:41002–1–41002–31. doi: 10.1115/1.4005300 CrossRefGoogle Scholar
  2. 2.
    Bergles AE, Lienhard VJH, Kendall GE, Griffith P (2003) Boiling and evaporation in small diameter channels. Heat Transf Eng 24:18–40. doi: 10.1080/01457630304041 CrossRefGoogle Scholar
  3. 3.
    Alavi Fazel SA, Arabi Shamsabadi A, Sarafraz MM, Peyghambarzadeh SM (2011) Artificial boiling heat transfer in the free convection to carbonic acid solution. Exp Therm Fluid Sci 35:645–652. doi: 10.1016/j.expthermflusci.2010.12.014 CrossRefGoogle Scholar
  4. 4.
    Murshed SMS, Nieto de Castro CA, Lourenço MJV et al (2011) A review of boiling and convective heat transfer with nanofluids. Renew Sustain Energy Rev 15:2342–2354. doi: 10.1016/j.rser.2011.02.016 CrossRefGoogle Scholar
  5. 5.
    Sarafraz MM, Hormozi F, Peyghambarzadeh SM, Vaeli N (2015) Upward flow boiling to DI-water and Cuo nanofluids inside the concentric annuli. J Appl Fluid Mech 8:651–659CrossRefGoogle Scholar
  6. 6.
    Sarafraz MM, Peyghambarzadeh SM (2013) Experimental study on subcooled flow boiling heat transfer to water–diethylene glycol mixtures as a coolant inside a vertical annulus. Exp Therm Fluid Sci 50:154–162. doi: 10.1016/j.expthermflusci.2013.06.003 CrossRefGoogle Scholar
  7. 7.
    Peyghambarzadeh SM, Sarafraz MM, Vaeli N et al (2013) Forced convective and subcooled flow boiling heat transfer to pure water and n-heptane in an annular heat exchanger. Ann Nucl Energy 53:401–410. doi: 10.1016/j.anucene.2012.07.037 CrossRefGoogle Scholar
  8. 8.
    Sarafraz MM, Hormozi F (2014) Application of thermodynamic models to estimating the convective flow boiling heat transfer coefficient of mixtures. Exp Therm Fluid Sci 53:70–85. doi: 10.1016/j.expthermflusci.2013.11.004 CrossRefGoogle Scholar
  9. 9.
    Mori S, Utaka Y (2017) Critical heat flux enhancement by surface modification in a saturated pool boiling: a review. Int J Heat Mass Transf 108:2534–2557. doi: 10.1016/j.ijheatmasstransfer.2017.01.090 CrossRefGoogle Scholar
  10. 10.
    Kim BJ, Lee JH, Kim KD (2016) Improvements of critical heat flux models for pool boiling on horizontal surfaces using interfacial instabilities of viscous potential flows. Int J Heat Mass Transf 93:200–206. doi: 10.1016/j.ijheatmasstransfer.2015.10.012 CrossRefGoogle Scholar
  11. 11.
    Roday AP, Jensen MK (2009) A review of the critical heat flux condition in mini-and microchannels. J Mech Sci Technol 23:2529–2547. doi: 10.1007/s12206-009-0711-y CrossRefGoogle Scholar
  12. 12.
    Uchikawa S, Okubo T, Kugo T et al (2007) Conceptual design of innovative water reactor for flexible fuel cycle (FLWR) and its recycle characteristics. J Nucl Sci Technol 44:277–284. doi: 10.3327/jnst.44.277 CrossRefGoogle Scholar
  13. 13.
    Chiang J-H, Aritomi M, Inoue R, Mori M (1994) Thermo-hydraulics during start-up in natural circulation boiling water reactors. Nucl Eng Des 146:241–252. doi: 10.1016/0029-5493(94)90332-8 CrossRefGoogle Scholar
  14. 14.
    Schoesse T, Aritomi M, Kataoka Y et al (1997) Critical heat flux in a vertical annulus under low upward flow and near atmospheric pressure. J Nucl Sci Technol 34:559–570. doi: 10.1080/18811248.1997.9733709 CrossRefGoogle Scholar
  15. 15.
    Kim HC, Baek W-P, Chang SH (2000) Critical heat flux of water in vertical round tubes at low pressure and low flow conditions. Nucl Eng Des 199:49–73. doi: 10.1016/S0029-5493(99)00074-6 CrossRefGoogle Scholar
  16. 16.
    Moon S-K, Chun S-Y, Cho S, Baek W-P (2005) An experimental study on the critical heat flux for low flow of water in a non-uniformly heated vertical rod bundle over a wide range of pressure conditions. Nucl Eng Des 235:2295–2309. doi: 10.1016/j.nucengdes.2005.04.004 CrossRefGoogle Scholar
  17. 17.
    Raffray AR, Nygren R, Whyte DG et al (2010) High heat flux components—readiness to proceed from near term fusion systems to power plants. Fusion Eng Des 85:93–108. doi: 10.1016/j.fusengdes.2009.08.002 CrossRefGoogle Scholar
  18. 18.
    Vandervort CL, Bergles AE, Jensen MK (1994) An experimental study of critical heat flux in very high heat flux subcooled boiling. Int J Heat Mass Transf 37:161–173. doi: 10.1016/0017-9310(94)90019-1 CrossRefGoogle Scholar
  19. 19.
    Nariai H, Inasaka F, Shimura T (1987) Critical heat flux of subcooled fow boiling in narrow tube. Proc 1987 ASME-JSME Therm Eng Joint Conf 5:455–462Google Scholar
  20. 20.
    Inasaka F, Nariai H (1992) Critical heat flux of subcooled flow boiling for water in uniformly heated straight tubes. Fusion Eng Des 19:329–337. doi: 10.1016/0920-3796(92)90007-Q CrossRefGoogle Scholar
  21. 21.
    Celata GP, Cumo M, Mariani A (1993) Burnout in highly subcooled water flow boiling in small diameter tubes. Int J Heat Mass Transf 36:1269–1285. doi: 10.1016/S0017-9310(05)80096-1 CrossRefGoogle Scholar
  22. 22.
    Mudawar I, Bowers MB (1999) Ultra-high critical heat flux (CHF) for subcooled water flow boiling—I: CHF data and parametric effects for small diameter tubes. Int J Heat Mass Transf 42:1405–1428. doi: 10.1016/S0017-9310(98)00241-5 CrossRefGoogle Scholar
  23. 23.
    Hall DD, Mudawar I (1999) Ultra-high critical heat flux (CHF) for subcooled water flow boiling—II: high-CHF database and design equations. Int J Heat Mass Transf 42:1429–1456. doi: 10.1016/S0017-9310(98)00242-7 CrossRefGoogle Scholar
  24. 24.
    Kaya A, Özdemir MR, Koşar A (2013) High mass flux flow boiling and critical heat flux in microscale. Int J Therm Sci 65:70–78. doi: 10.1016/j.ijthermalsci.2012.10.021 CrossRefGoogle Scholar
  25. 25.
    Katto Y, Ohno H (1984) An improved version of the generalized correlation of critical heat flux for the forced convective boiling in uniformly heated vertical tubes. Int J Heat Mass Transf 27:1641–1648. doi: 10.1016/0017-9310(84)90276-X CrossRefGoogle Scholar
  26. 26.
    Sarma PK, Srinivas V, Sharma KV et al (2006) A correlation to evaluate critical heat flux in small diameter tubes under subcooled conditions of the coolant. Int J Heat Mass Transf 49:42–51. doi: 10.1016/j.ijheatmasstransfer.2004.07.052 CrossRefGoogle Scholar
  27. 27.
    Kosar A, Peles Y, Bergles AE, Cole GS (2009) Experimental investigation of critical heat flux in microchannels for flow-field probes. In: Proceedings of the ASME 7th international conference on nanochannels, microchannels, minichannels, p ICNMM2009-82214Google Scholar
  28. 28.
    Roday AP, Jensen MK (2009) Study of the critical heat flux condition with water and R-123 during flow boiling in microtubes. Part I: experimental results and discussion of parametric effects. Int J Heat Mass Transf 52:3235–3249. doi: 10.1016/j.ijheatmasstransfer.2009.02.003 CrossRefGoogle Scholar
  29. 29.
    Celata GP, Cumo M, Mariani A et al (1994) Rationalization the prediction of existing mechanistic models for of water subcooled flow boiling critical heat flux. Int J Heat Mass Transf 37:347–360. doi: 10.1016/0017-9310(94)90035-3 CrossRefGoogle Scholar
  30. 30.
    Sakurai A, Shiotsu M, Hata K, Fukuda K (1998) Mechanisms of subcooled flow boiling critical heat fluxes on vertical cylinder surface and on short tube inner surface in water flowing upward at various pressures. In: Proceedings of the 11th international heat transfer conference, 2, pp 351–356Google Scholar
  31. 31.
    Sakurai A, Fukuda K (2001) Mechanisms of subcooled water flow boiling CHFs for outlet subcooling at a flow velocity with pressures for test sections with various shapes. In: Proceedings of the ASME international mechanical engineering congress and exposition. 2001. New York, p HTD-Vol.369-2, IMECE2001/HTD-24163Google Scholar
  32. 32.
    Sakurai A, Fukuda K (2003) Mechanisms of subcooled water flow boiling ultra-high CHFs in short small diameter tubes for high flow velocities at high pressures. In: Proceedings of the 10th international topical meeting on nuclear reactor thermal hydraulics, p C00217Google Scholar
  33. 33.
    Sakurai, A, Fukuda K (2006) Prediction for nonlinear trend of subcooled water flow boiling CHFs with different mechanisms for outlet subcoolings in heated tubes at outlet pressures for flow velocities. In: Proceedings of the 13th international heat transfer conference, pp 1–8Google Scholar
  34. 34.
    Sakurai A (2000) Mechanisms of transitions to film boiling at CHFs in subcooled and pressurized liquids due to steady and increasing heat inputs. Nucl Eng Des 197:301–356. doi: 10.1016/S0029-5493(99)00314-3 CrossRefGoogle Scholar
  35. 35.
    Kataoka I, Serizawa A, Sakurai A (1983) Transient boiling heat transfer under forced convection. Int J Heat Mass Transf 26:583–595. doi: 10.1016/0017-9310(83)90009-1 CrossRefGoogle Scholar
  36. 36.
    Su G-Y, Bucci M, McKrell T, Buongiorno J (2016) Transient boiling of water under exponentially escalating heat inputs. Part I: pool boiling. Int J Heat Mass Transf 96:667–684. doi: 10.1016/j.ijheatmasstransfer.2016.01.032 CrossRefGoogle Scholar
  37. 37.
    Su G-Y, Bucci M, McKrell T, Buongiorno J (2016) Transient boiling of water under exponentially escalating heat inputs. Part II: flow boiling. Int J Heat Mass Transf 96:685–698. doi: 10.1016/j.ijheatmasstransfer.2016.01.031 CrossRefGoogle Scholar
  38. 38.
    Celata GP, Cumo M, D’Annibale F (1992) A data set of critical heat flux of boiling R-12 in uniformly heated vertical tubes under transient conditions. Exp Therm Fluid Sci 5:78–107. doi: 10.1016/0894-1777(92)90058-D CrossRefGoogle Scholar
  39. 39.
    Hata K, Noda N (2008) Transient critical heat fluxes of subcooled water flow boiling in a short vertical tube caused by exponentially increasing heat inputs. J Heat Transf 130:54503–1–54503–9. doi: 10.1115/1.2887850 CrossRefGoogle Scholar
  40. 40.
    Hata K, Shiotsu M, Noda N (2006) Critical heat flux of subcooled water flow boiling for high L/d region. Nucl Sci Eng 154:94–109CrossRefGoogle Scholar
  41. 41.
    Shibahara M, Fukuda K, Liu QS, Hata K (2017) Correlation of high critical heat flux during flow boiling for water in a small tube at various subcooled conditions. Int Commun Heat Mass Transf 82:74–80. doi: 10.1016/j.icheatmasstransfer.2017.02.012 CrossRefGoogle Scholar
  42. 42.
    Shibahara M, Fukuda K, Liu QS, Hata K (2017) Steady and transient critical heat flux for subcooled water in a mini channel. Int J Heat Mass Transf 104:267–275. doi: 10.1016/j.ijheatmasstransfer.2016.08.054 CrossRefGoogle Scholar
  43. 43.
    Vines RF (2012) The platinum metals and their alloys. Literary Licensing, LLC, WhitefishGoogle Scholar
  44. 44.
    Golobic I, Bergles AE (1997) Effects of heater-side factors on the saturated pool boiling critical heat flux. Exp Therm Fluid Sci 15:43–51. doi: 10.1016/S0894-1777(96)00170-7 CrossRefGoogle Scholar
  45. 45.
    Davis EJ, Anderson GH (1966) The incipience of nucleate boiling in forced convection flow. AIChE J 12:774–780. doi: 10.1002/aic.690120426 CrossRefGoogle Scholar
  46. 46.
    ASME (1987) Measurement uncertainty, supplement on instruments and apparatus, Part 1., ASME Performance Test Codes, ANSI/ASME PTC19.1-1985, translated by JSMEGoogle Scholar
  47. 47.
    Touloukian YS, DeWitt DP (1970) Thermophysical properties of matter, thermal radiative properties, metallic elements and alloys, vol 7. IFI/Plenum, New YorkGoogle Scholar
  48. 48.
    Shibahara M, Fukuda K, Liu QS, Hata K (2016) Steady and transient forced convection heat transfer for water flowing in small tubes with exponentially increasing heat inputs. Heat Mass Transf Stoffuebertrag. doi: 10.1007/s00231-016-1860-z Google Scholar
  49. 49.
    Bergles AE, Rohsenow WM (1964) The determination of forced-convection surfaceboiling heat transfer. J Heat Transf Trans ASME Ser C 86:365–372CrossRefGoogle Scholar
  50. 50.
    Sato T, Matsumura H (1963) On the conditions of incipient subcooled-boiling with forced convection. Bull JSME 7:392–398CrossRefGoogle Scholar
  51. 51.
    Gahiaasiaan SM (2008) Two-phase flow, boiling, and condensation in conventional and miniature systems. Cambridge university press, New York, pp 328–346Google Scholar
  52. 52.
    Rohsenow WM (1952) A method of correlating heat-transfer data for surface boiling of liquids. Trans ASME 74:969–976Google Scholar
  53. 53.
    McAdams WH, Kennel WE, Minden CSL, Carl R, Picornell PM, Dew JE (1949) Heat transfer at high rates to water with surface boiling. Ind Eng Chem 41:1945–1953CrossRefGoogle Scholar
  54. 54.
    Jens WH, Lottes PA (1951) Analysis of heat transfer burnout, pressure drop and density data for high pressure water. ANL-4627, Argonne National Laboratory, Chicago, p 71Google Scholar
  55. 55.
    Thom JRS, Walker WM, Fallon TA, Reising GFS (1966) Boiling in subcooled water during flow up heated tubes or annuli. Inst Mech Eng 180:226–246Google Scholar
  56. 56.
    Kottowsky H (1973) The Mechanism of nucleation, superheating and reducing effects on the activation energy of nucleation. Pergamon Press, OxfordGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Graduate School of Maritime SciencesKobe UniversityKobeJapan

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