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Direct Numerical Simulation of Low Prandtl Number Thermal Field in a Turbulent Channel Flow

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Turbulent Shear Flows 8

Abstract

A direct numerical simulation of the fully developed thermal field in a two-dimensional turbulent channel flow was carried out. The simulation was made at a molecular Prandtl number of Pr = 0.025 to investigate low Prandtl number effects on the transport mechanism in wall turbulence. The computation was executed on about 1.6 × 106 grid points by using a spectral method. Mean field parameters as well as various thermal turbulence statistics including rms temperature fluctuations, turbulent heat fluxes and turbulent Prandtl numbers were obtained. Each term in the budget equations of temperature variance, its dissipation rate and turbulent heat fluxes was also calculated in order to establish a data base of convective heat transfer for thermal turbulence modeling. The results were compared mainly with those at Pr = 0.71 obtained by Kasagi et al. (1992). In addition, the computed thermal fields were visualized to investigate the role of the near-wall quasi-coherent structures in the turbulent transport mechanism.

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Abbreviations

E+ aa :

dimensional energy spectrum of fluctuating quantity a

h:

heat transfer coefficient

k:

turbulent kinetic energy,\( \overline {{{u'}_i}{u_i}^\prime } /2 \)

k:

variance of temperature fluctuation, \( \overline {{\theta ^r}^2} /2 \)

kx, kz :

wave numbers in the x- and z-directions

Nu:

Nusselt number, 2hδ/λ

Pr:

molecular Prandtl number v /α

Pr t :

turbulent Prandtl number v t /α t

R:

timescale ratio T θ /T u

Rij :

cross-correlation coefficient, \( \overline {{u_i}{u_j}} /{u_i}_{rms}{u_j}_{rms} \)

Re m :

Reynolds number 2u m δ/v

Reτ :

Reynolds number u τ δ/v

T:

temperature

Tm :

bulk mean temperature

Tτ :

friction temperature

T+ :

dimensionless temperature, = (T − <T w >)/T τ = −θ +

um :

bulk mean velocity

uτ :

friction velocity

u,v,w:

velocity components in the x-, y- and z-directions

x,y,z:

streamwise, wall normal and spanwise coordinates

α:

thermal diffusivity

αt :

eddy-diffusivity for heat

δ:

channel half width

ε:

dissipation rate of k

εθ :

dissipation rate of k θ

θ:

temperature difference, = <T w > − T

θ + :

dimensionless temperature, = (<T w >− T) /T τ = −T +

θ m :

bulk mean temperature

λ:

thermal conductivity

V:

kinematic viscosity

vt :

eddy diffusivity

τ u :

velocity dissipation timescale k/ε

τθ :

temperature dissipation timescale k θ /ε θ

( ) ′:

fluctuating component

( ) + :

normalized by the wall variables u τ ,v and T τ

( ):

ensemble average over x-z plane and time

< >:

ensemble average over x-z direction and time

( )rms :

root mean-square value

( )w :

value at the wall

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Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan

    N. Kasagi & Y. Ohtsubo

Authors
  1. N. Kasagi
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  2. Y. Ohtsubo
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Strömungsmechanik, Friedrich-Alexander-Universität, Cauerstraße 4, W-8520, Erlangen, Germany

    Franz Durst

  2. Lehrstuhl für Fluidmechanik, Technische Universität München, Arcisstraße 21, W-8000, München 2, Germany

    Rainer Friedrich

  3. Department of Mechanical Engineering, University of Manchester, Institute of Science and Technology, P.O. Box 88, M60 1QD, Manchester, UK

    Brian E. Launder

  4. Department of Mechanical Engineering, The Pennsylvania State University, 16802, University Park, PA, USA

    Frank W. Schmidt

  5. Institut für Physik der Atmosphäre, Deutsche Forschungsanstalt für Luft- und Raumfahrt (DLR), W-8031, Oberpfaffenhofen, Germany

    Ulrich Schumann

  6. Department of Mechanical Engineering, Imperial College of Science and Technology, Exhibition Road, SW7 2BX, London, UK

    James H. Whitelaw

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© 1993 Springer-Verlag Berlin Heidelberg

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Kasagi, N., Ohtsubo, Y. (1993). Direct Numerical Simulation of Low Prandtl Number Thermal Field in a Turbulent Channel Flow. In: Durst, F., Friedrich, R., Launder, B.E., Schmidt, F.W., Schumann, U., Whitelaw, J.H. (eds) Turbulent Shear Flows 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77674-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-77674-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-77676-2

  • Online ISBN: 978-3-642-77674-8

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