Skip to main content
×
Home
    • Aa
    • Aa

Analogy between velocity and scalar fields in a turbulent channel flow

  • ROBERT ANTHONY ANTONIA (a1), HIROYUKI ABE (a2) and HIROSHI KAWAMURA (a3)
Abstract

The relationship between the fluctuating velocity vector and the temperature fluctuation has been examined using direct numerical simulation databases of a turbulent channel flow with passive scalar transport using a constant time-averaged heat flux at each wall for h+ = 180, 395, 640 and 1020 (where h is the channel half-width with the superscript denoting normalization by wall variables) at Prandtl number Pr=0.71. The analogy between spectra corresponding to the kinetic energy and scalar variance is reasonable in both inner and outer regions irrespective of whether the spectra are plotted in terms of kx or kz, the wavenumbers in the streamwise and spanwise directions respectively. Whereas all three velocity fluctuations contribute to the energy spectrum when kx is used, the longitudinal velocity fluctuation is the major contributor when kz is used. The quality of the analogy in the spectral domain is confirmed by visualizations in physical space and reflects differences between spatial organizations in the velocity and scalar fields. The similarity between the spectra corresponding to the enstrophy and scalar dissipation rate is not as good as that between the kinetic energy and scalar variance, emphasizing the prominence of the scalar sheets as the centre of the channel is approached. The ratio R between the characteristic time scales of the velocity and scalar fluctuations is approximately constant over a major part of the channel and independent of h+, when the latter is sufficiently large. This constancy, which is not observed in quantities such as the turbulent Prandtl number, follows from the spectral similarities discussed in this paper and has implications for turbulent heat transport models.

Copyright
Corresponding author
Email address for correspondence: robert.antonia@newcastle.edu.au
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

H. Abe , H. Kawamura & H. Choi 2004 aVery large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to Reτ = 640. ASME J. Fluids Engng 126, 835843.

H. Abe , H. Kawamura & Y. Matsuo 2001 Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence. ASME J. Fluids Engng 123, 382393.

H. Abe , H. Kawamura & Y. Matsuo 2004 bSurface heat-flux fluctuations in a turbulent channel flow up to Reτ= 1020 with Pr = 0.025 and 0.71. Intl J. Heat and Fluid Flow 25, 404419.

J. C. del Álamo & J. Jiménez 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15, 4144.

R. Antonia A, A. J. Chambers , C. A Friehe & C. W. Van Atta 1979 Temperature ramps in the atmospheric surface layer. J. Atmos. Sci. 36, 99108.

R. A. Antonia & J. Kim 1994 A numerical study of local isotropy of turbulence. Phys. Fluids 6 (2), 834841.

R. A. Antonia , L. V. Krishnamoorthy & L. Fulachier 1988 Correlation between the longitudinal velocity fluctuation and temperature fluctuation in the near-wall region of a turbulent boundary layer. Intl J. Heat Mass Transfer 31 (4), 723730.

R. A. Antonia , Y. Zhu , F. Anselmet & M. Ould-Rouis 1996 Comparison between the sum of the second-order velocity structure functions and the second-order temperature structure function. Phys. Fluids 8, 31053111.

W. T. Ashurst , A. R. Kerstein , R. M. Kerr & C. H. Gibson 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30, 23432353.

G. K. Batchelor 1946 The theory of axisymmetric turbulence. Proc. R. Soc. Lond. A 186, 480502.

G. K. Batchelor 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113133.

C. Béguier , I. Dekeyser & B. E. Launder 1978 Ratio of scalar and velocity dissipation time scales in shear flow turbulence. Phys. Fluids 21, 307310.

G. L. Brown & A. S. W. Thomas 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20 (10), S243S252.

P. Chassaing , R. A. Antonia , F. Anselmet , L. Joly & S. Sarkar 2002 Variable Density Fluid Turbulence, Kluwer Academic.

S. Corrsin 1951 On the Spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22, 469473.

L. Fulachier & R. A. Antonia 1984 Spectral analogy between temperature and velocity fluctuations in several turbulent flows. Intl J. Heat Mass Transfer 27, 987997.

S. Hoyas & J. Jiménez 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511.

Y. Iritani , N. Kasagi & M. Hirata 1985 Heat transfer mechanism and associated turbulence structure in the near-wall region of a turbulent boundary layer. In Turbulent Shear Flows 4 (ed. L. J. S. Bradbury F. Durst B. E. Launder F. W. Schmidt and J. H. Whitelaw ), pp. 223234. Springer.

A. V. Johansson & P. M. Wikström 1999 DNS and modelling of passive scalar transport in turbulent channel flow with a focus on scalar dissipation rate modelling. Flow Turbulence Combust. 63, 223245.

B. A. Kader 1981 Temperature and concentration profiles in fully turbulent boundary layers. Intl J. Heat Mass Transfer 24, 15411544.

H. Kawamura , H. Abe & Y. Matsuo 1999 DNS of turbulent heat transfer in channel flow with respect to Reynolds and Prandtl number effects. Intl J. Heat Fluid Flow 20, 196207.

H. Kawamura , K. Ohsaka , H. Abe & K. Yamamoto 1998 DNS of turbulent heat transfer in channel flow with low to medium–high Prandtl number fluid. Intl J. Heat Fluid Flow 19, 482491.

J. Kim & P. Moin 1989 Transport of passive scalars in a turbulent channel flow. In Turbulent Shear Flows 6, (ed. J.-C. André , J. Cousteix , F. Durst , B. E. Launder , F. W. Schmidt and J. H. Whitelaw ), pp. 8596, Springer.

B. E. Launder 1976 Heat and mass transport Topics Appl. Phys. 12, 231287.

P. Moin & K. Mahesh 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539-578.

Y. Morinishi , T. S. Lund , O. V. Vasilyev & P. Moin 1998 Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 143, 90124.

Y. Nagano & C. Kim 1988 A two-equation model for heat transport in wall turbulent shear flows. ASME J. Heat Transfer 110, 583589.

Y. Nagano & M. Shimada 1996 Development of a two-equation heat transfer model based on direct simulations of turbulent flows with different Prandtl numbers. Phys. Fluids 8, 33793402.

A. Pumir 1994 A numerical study of the mixing of a passive scalar in three dimensions in the presence of a mean gradient. Phys. Fluids 6 (6), 21182132.

S. Rajagopalan & R. A. Antonia 1979 Some properties of the large structure in a fully developed turbulent duct flow. Phys. Fluids 22 (4), 614622.

J. C. Rotta 1964 Temperaturverteilungen in der turbulenten grenzschicht an der ebenen platte. Intl J. Heat Mass Transfer 7, 215228.

G. R. Ruetsch & M. R. Maxey 1992 The evolution of small-scale structures in homogeneous isotropic turbulence. Phys. Fluids A 4, 27472760.

P. R. Spalart , R. D. Moser & M. M. Rogers 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297324.

K. R. Sreenivasan & R. A. Antonia 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435472.

M. Tanahashi , S.-J. Kang , T. Miyamoto , S. Shiokawa & T. Miyauchi 2004 Scaling law of fine scale eddies in turbulent channel flows up to Reτ = 800. Intl J. Heat Fluid Flow 25, 331340.

S. Tavoularis & S. Corrsin 1981 Experiments in nearly homogeneous shear flow with a uniform mean temperature gradient. Part 1. The fine structure. J. Fluid Mech. 104, 311347.

R. J. Taylor 1958 Thermal structures in the lowest layers of the atmosphere. Aust. J. Phys. 11, 168176.

Z. Warhaft 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203240.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax