Skip to main content
SpringerLink
Log in

Forced convection heat transfer to supercritical helium

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

We studied numerically the heat transfer for a turbulent flow of supercritical helium. A finite difference model is constructed with three different models of turbulence: the mixing length,k- andk-ε model. The stationary results compared to experimental data reveal that the mixing length model gives the best prediction of turbulence in this situation. A severe deterioration from the widely used Nusselt correlation by Giarratano is observed for cases near the pseudocritical temperature, while a far better correspondance is found with the more recent Yaskin correlation. The maxima and minima in the heat transfer curves can be understood by interpretation of the wall and bulk temperature together with the strong changes in density.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

A μ :

constant ink-model

A + :

constant in van Driest hypothesis

C D :

Constant ink/k-ε model

Cp :

Specific heat J/kgK

C 1 :

Constant ink-ε model

C 2 :

Constant ink-ε model

C μ :

Constant inμ t expression

D :

Pipe diameter m

G :

Mass flow kg/m2 s

Gr:

Grashoff number Δρ kg/m2s

h :

heat transfer coefficient W/m2K

H :

Enthalpy J/kg

k :

Kinetic energy of turbulence (m/s)2

l m :

Mixing length

Nu:

Nusselt numbrhD/λ

P :

Pressure N/m2 atm

Pr:

Prandtl number μ/Cpλ

q :

Heat flux W/m2

r :

radial coordinate m

R :

Pipe radius m

Re:

Reynolds number ρvD/μ

Re k :

Turbulent reynolds number ρyk 1/2/μ

T :

Temperature K

T b :

Bulk temperature K

T w :

Wall temperature K

u :

Velocity component m/s

u + :

Dimensionless velocityu(τ w/ρ)−1/2

u ++ :

Dimensionless velocity

v :

Velocity component/vector m/s

Vz:

Axial velocity component m/s

Vr:

Radial velocity component m/s

x :

Coordinate m

y :

Distance from wall m

y + :

Dimensionless distance from wally(τ w ρ)1/2/μ

y ++ :

Dimensionless distance from wall

z :

axial coordinate m

β:

compressibility −(1/ρ)(∂ρ/ϖT) 1/K

ρ:

Density kg/m3

λ:

thermal conductivity W/mK

ϕ:

Correlating factorqD 0.2/G 0.8

σ k :

Constant ink/k-ε model

σ∈ :

Constant ink-ε model

ε:

Dissipation of turbulence-energy

μ:

Laminar viscosity kg/ms

μ t :

Turbulent viscosity kg/ms

μ eff :

μ+μt

τ w :

Wall shear stress N/m2

References

  1. V. Arp, New forms of state equations for helium.Cryogenics 14 (1974) 593–598.

    Article  ADS  Google Scholar 

  2. D.J. Brassington and D.N.H. Cairns, Measurements of forced convective heat transfer to supercritical helium.Int. J. Heat Mass Transfer 20 (1977) 207–214.

    Article  Google Scholar 

  3. G. Bogner, Large scale applications of superconductivity. In: B.B. Schwarz and S. Foner (eds.)Superconductor Applications, SQUIDs and Machines. Plenum Press.

  4. L. Dresner, Stability of internally cooled superconductors a review.Cryogenics 20 (1980) 558–563.

    Article  ADS  Google Scholar 

  5. E.R. van Driest, On turbulent flow near a wall.J. of the Aeronautical Sciences (1956) 1007–1011.

  6. P.J. Giarratano, V.D. Arp and R.V. Smith, Forced convection heat transfer to supercritical helium.Cryogenics 11 (1971).

  7. P.J. Giarratano and M.C. Jones, Deterioration of heat transfer to supercritical helium at 2.5 atmosphere.Int. J. Heat Mass Transfer 18 (1975) 649–653.

    Article  ADS  Google Scholar 

  8. K. Goldmann, Heat transfer to supercritical water and other fluids with temperature-dependent properties.Nuclear Engineering. C.E.P. Symposium Series Vol. 50 (11) pp. 105–113.

  9. W.B. Hall, Heat transfer near the critical point.Adv. in Heat Transfer 7 (1971) 1–86.

    ADS  Google Scholar 

  10. S. Hassid and M. Poreh, A turbulent energy model for flows with drag reduction.J. of Fluids Engineering 97 (1975) 234–241.

    ADS  Google Scholar 

  11. E.G. Hauptmann and A. Malhotra, Axial development of unusual velocity profiles due to heat transfer in variable density fluids.J. of Heat Transfer 102 (1980) 71–74.

    Google Scholar 

  12. R.C. Hendricks, R.J. Simoneau and R.V. Smith, Survey of heat transfer to near-critical fluids.NASA TN D-5886 (1970).

  13. C. Johannes, Studies of forced convection heat transfer to helium I.Adv. in Cryogenic Engineering 17 (1972) 352–360.

    Google Scholar 

  14. W.P. Jones and B.E. Launder, The prediction of laminarization with a two-equation model of turbulence.Int. J. Heat Mass Transfer 15 (1972) 301–314.

    Article  Google Scholar 

  15. W.P. Jones and B.E. Launder, The calculation of low-Reynolds-number phenomena with a two-equation model of turbulence.Int. J. Heat Mass Transfer 16 (1973) 1119–1130.

    Article  Google Scholar 

  16. H.H. Kolm, M.J. Leupold and R.D. Hay, Heat transfer by the circulation of supercritical helium.Adv. in Cryogenic Engineering 1 (1966) 530–535.

    Google Scholar 

  17. C.K.G. Lam and K. Bremhorst, A modified form of the K-ε model for predicting wall turbulence.J. of Fluids Engineering 103 (1981) 456–460.

    Article  ADS  Google Scholar 

  18. R. D. McCarty, Thermophysical properties of helium-4 from 4 to 3000 R with pressures to 15,000 PSIA.NBS Technical Note 622 (1972).

  19. R.D. McCarty, Thermodynamic properties of helium-4 from 2–1500 K at pressures to 108 Pa.J. Phys. Chem. Ref. Data 2 (1973) 924–957.

    Article  ADS  Google Scholar 

  20. H. Ogata and S. Sato, Measurements of forced convection heat transfer to supercritical helium.Proc. ICEC4. Eindhoven: IPC Science and Techn Press. (1972).

    Google Scholar 

  21. S.V. Patankar and D.B. Spalding,Heat and Mass Transfer in Boundary Layers. London: Intertext Books (1970).

    Google Scholar 

  22. S.V. Patankar and D.B. Spalding, A calculation procedure for heat mass and momentum transfer in three-dimensional parabolic flow.Int. J. Heat Mass Transfer (1972) 1787–1806.

  23. S.V. Patankar,Numerical Heat Transfer and Fluid Flow. Washington: Hemisphere Publishing Corporation (1980).

    MATH  Google Scholar 

  24. R.H. Pletcher, On a solution for turbulent boundary layer flow with heat transfer, pressure gradients, and wall blowing or suction.Proc. 4th International Heat Transfer Conference, Paris, paper FC 2.9 (1974).

  25. H. Schlichting,Grenzschicht Theorie, Verlag H. Braun (1951).

  26. N.M. Schnurr, V.S. Sastry and A.B. Shapiro, A numerical analysis of heat transfer to fluids near the thermodynamic critical point including the thermal entrance region.J. of Heat Transfer 98 (1976) 609–615.

    Google Scholar 

  27. N.M. Schnurr, Numerical predictions of heat transfer to supercritical helium in turbulent flow through circular tubes.J. of Heat Transfer 99 (1977) 580–585.

    Google Scholar 

  28. D.B. Spalding, GENMIX—A general computer program for two dimensional parabolic phenomena, HMT,The Science and Applications of Heat and Mass Transfer, Oxford: Pergamon Press (1972).

    Google Scholar 

  29. L.A. Yaskin, M.C. Jones, V.M. Yeroshenko, P.J. Giarratano, and V.D. Arp, A correlation for heat transfer to supercritical helium in turbulent flow in small channels.Cryogenics 17 (1977) 549–552.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Applied Physics, Heat Transfer Section, Delft University of Technology, P.O. Box 5046, 2600 GA, Delft, The Netherlands

    M. C. M. Cornelissen & C. J. Hoogendoorn

Authors
  1. M. C. M. Cornelissen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. J. Hoogendoorn
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cornelissen, M.C.M., Hoogendoorn, C.J. Forced convection heat transfer to supercritical helium. Appl. Sci. Res. 42, 161–183 (1985). https://doi.org/10.1007/BF02421348

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02421348

Keywords

Search

Navigation