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Heat and Mass Transfer

, Volume 42, Issue 5, pp 411–426 | Cite as

On the role of the smallest scales of a passive scalar field in a near-wall turbulent flow

  • Bergant RobertEmail author
  • Tiselj Iztok
Original

Abstract

Role of the smallest diffusive scales of a passive scalar field in the near-wall turbulent flow was examined with pseudo-spectral numerical simulations. Temperature fields were analyzed at friction Reynolds number Re τ=171 and at Prandtl numbers, Pr=1 and Pr=5.4. Results of direct numerical simulations (DNS) were compared with the under-resolved simulations where the velocity field was still resolved with the DNS accuracy, while a coarser grid was used to describe the temperature fields. Since the smallest temperature scales remained unresolved in these simulations, an appropriate spectral turbulent thermal diffusivity was applied to avoid pile-up at the higher wave numbers. In spite of coarser numerical grids, the temperature fields are still highly correlated with the DNS results, including instantaneous temperature fields. Results point to practically negligible role of the diffusive temperature scales on the macroscopic behavior of the turbulent heat transfer.

Keywords

DNS Under-resolved DNS Spectral turbulent diffusivity 

Abbreviations

a

Chebyshev coefficients

a, b

Exponents of the damping

E

Spectrum

h

Dimensionless channel half height and flume height

\(\ifmmode\expandafter\vec\else\expandafter\vecabove\fi{l}_{x}\)

Unit vector in x direction (1,0,0)

k

Wave number

kc

Cutoff wave number

kDx, kDz

Largest non-damped wave numbers

Lx, Lz

Dimensionless streamwise and spanwise lengths of box

Nx, Nz

Numbers of the Fourier terms

Pr

Prandtl number \(({\rm Pr} = \nu / \alpha) \)

p

Dimensionless pressure

Reλ

Taylor-microscale Reynolds number

Reτ

Friction Reynolds number \((Re_{\tau} = \frac{{u_{\tau} h}}{\nu})\)

Tn

Chebyshev polynomials

Tτ

Friction temperature

t

Dimensionless time

u, w, v

Dimensionless velocity components in x, y and z directions

uτ

Dissipative velocity

x, y, z

Streamwise, spanwise, wall-normal direction

α

Thermal diffusivity

ν

Kinematic viscosity

θ

Dimensionless temperature difference

()+

Normalized by u τ, T τ, ν

()′

Fluctuations

Notes

Acknowledgements

This research was financially supported by the Ministry of Higher Education, Science and Technology, Republic of Slovenia, with the contract number 3311-03-831011.

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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.“Jožef Stefan” InstituteLjubljanaSlovenia

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