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Analogy between velocity and scalar fields in a turbulent channel flow

Published online by Cambridge University Press:  01 June 2009

ROBERT ANTHONY ANTONIA ,
HIROYUKI ABE  and
HIROSHI KAWAMURA
ROBERT ANTHONY ANTONIA*
Affiliation:
Discipline of Mechanical Engineering, University of Newcastle, NSW 2308, Australia
HIROYUKI ABE
Affiliation:
Japan Aerospace Exploration Agency, Tokyo 182-8522, Japan
HIROSHI KAWAMURA
Affiliation:
Department of Mechanical Engineering, Tokyo University of Science, Chiba 278-8510, Japan
*
†Email address for correspondence: robert.antonia@newcastle.edu.au
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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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 628 , 10 June 2009 , pp. 241 - 268
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Abe, H., Antonia, R. A. & Kawamura, H. 2006 Structure of the scalar dissipation field in a turbulent channel flow. In Proc. of Turbulence, Heat and Mass Transfer Conf. 5, Dubrovnik, Croatia.Google Scholar
Abe, H., Antonia, R. A. & Kawamura, H. 2008 Transport equations for the enstrophy and scalar dissipation rate in a turbulent channel flow. In Proc. of 7th Intl ERCOFTAC Symp. on Engng Turbulence Modelling and Measurements, Limassol, Cyprus.Google Scholar
Abe, H., Antonia, R. A. & Kawamura, H. 2009 Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow. J. Fluid Mech. 627, 1–32.CrossRefGoogle Scholar
Abe, H., Kawamura, H. & Choi, H. 2004 a Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to Re τ = 640. ASME J. Fluids Engng 126, 835–843.CrossRefGoogle Scholar
Abe, H., Kawamura, H. & Matsuo, Y. 2001 Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence. ASME J. Fluids Engng 123, 382–393.CrossRefGoogle Scholar
Abe, H., Kawamura, H. & Matsuo, Y. 2004 b Surface heat-flux fluctuations in a turbulent channel flow up to Re τ= 1020 with Pr = 0.025 and 0.71. Intl J. Heat and Fluid Flow 25, 404–419.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15, 41–44.CrossRefGoogle Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.CrossRefGoogle Scholar
Antonia, R. A, Chambers, A. J., Friehe, C. A & Van Atta, C. W. 1979 Temperature ramps in the atmospheric surface layer. J. Atmos. Sci. 36, 99–108.2.0.CO;2>CrossRefGoogle Scholar
Antonia, R. A. & Kim, J. 1991 Similarity between turbulent kinetic energy and temperature spectra in the near-wall region. Phys. Fluids 276, 989–991.CrossRefGoogle Scholar
Antonia, R. A., Kim, J. & Browne, L. W. B. 1991 Some characteristics of small-scale turbulence in a turbulent duct flow. J. Fluid Mech. 233, 369–388.CrossRefGoogle Scholar
Antonia, R. A. & Kim, J. 1994 A numerical study of local isotropy of turbulence. Phys. Fluids 6 (2), 834–841.CrossRefGoogle Scholar
Antonia, R. A., Krishnamoorthy, L. V. & Fulachier, L. 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), 723–730.CrossRefGoogle Scholar
Antonia, R. A., Rajagopalan, S., Subramanian, C. S. & Chambers, A. J. 1982 Reynolds-number dependence of the structure of a turbulent boundary layer. J. Fluid Mech. 121, 123–140.CrossRefGoogle Scholar
Antonia, R. A., Ould-Rouis, M., Anselmet, F. & Zhu, Y. 1997 Analogy between predictions of Kolmogorov and Yaglom. J. Fluid Mech. 332, 395–409.CrossRefGoogle Scholar
Antonia, R. A., Zhou, T. & Zhu, Y. 1998 Three-component vorticity measurements in a turbulent grid flow. J. Fluid Mech. 374, 29–57.CrossRefGoogle Scholar
Antonia, R. A., Zhu, Y., Anselmet, F. & Ould-Rouis, M. 1996 Comparison between the sum of the second-order velocity structure functions and the second-order temperature structure function. Phys. Fluids 8, 3105–3111.CrossRefGoogle Scholar
Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30, 2343–2353.CrossRefGoogle Scholar
Batchelor, G. K. 1946 The theory of axisymmetric turbulence. Proc. R. Soc. Lond. A 186, 480–502.Google Scholar
Batchelor, G. K. 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, 113–133.CrossRefGoogle Scholar
Béguier, C., Dekeyser, I. & Launder, B. E. 1978 Ratio of scalar and velocity dissipation time scales in shear flow turbulence. Phys. Fluids 21, 307–310.CrossRefGoogle Scholar
Bell, D. M. & Ferziger, J. H. 1993 Turbulent Boundary Layer DNS with passive scalars. In Near-Wall Turbulent Flows (ed. So, R. M. C., Speziale, C. G. & Launder, B. E.), pp. 327–336. Elsevier Science.Google Scholar
Blackburn, H. M., Mansour, N. N. & Cantwell, B. J. 1996 Topology of fine-scale motions in turbulent channel flow. J. Fluid Mech. 310, 269–292.CrossRefGoogle Scholar
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20 (10), S243–S252.CrossRefGoogle Scholar
Burattini, P. & Antonia, R. A. 2005 Approach to the 4/5 and 4/3 laws for nearly homogeneous and isotropic turbulence. In Eighth Australasian Heat and Mass Transfer Conf., Curtin University of Technology, Perth, Western Australia.CrossRefGoogle Scholar
Chandrasekhar, S. 1950 The theory of axisymmetric turbulence. Proc. R. Soc. Lond. A 242, 557–577.Google Scholar
Chassaing, P., Antonia, R. A., Anselmet, F., Joly, L. & Sarkar, S. 2002 Variable Density Fluid Turbulence, Kluwer Academic.CrossRefGoogle Scholar
Chen, C.-H. P. & Blackwelder, R. F. 1978 Large-scale motion in a turbulent boundary layer: a study using temperature contamination. J. Fluid Mech. 89, 1–31.CrossRefGoogle Scholar
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443.CrossRefGoogle Scholar
Corrsin, S. 1951 On the Spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22, 469–473.CrossRefGoogle Scholar
Corrsin, S. 1953 Remarks on turbulent heat transfer: an account of some features of the phenomenon in fully turbulent regions. In Proc. of the First Iowa Thermodynamics Symp., pp. 5–30. State University of Iowa, Iowa City.Google Scholar
Fulachier, L. & Antonia, R. A. 1984 Spectral analogy between temperature and velocity fluctuations in several turbulent flows. Intl J. Heat Mass Transfer 27, 987–997.CrossRefGoogle Scholar
Fulachier, L. & Dumas, R. 1976 Spectral analogy between temperature and velocity fluctuations in a turbulent boundary layer. J. Fluid Mech. 77, 257–277.CrossRefGoogle Scholar
George, W. K. & Hussein, H. J. 1991 Locally axisymmetric turbulence. J. Fluid Mech. 233, 1–23.CrossRefGoogle Scholar
Guezennec, Y., Stretch, D. & Kim, J. 1990 The structure of turbulent channel flow with passive scalar transport. In Proc. of the Summer Program 1990, Centre for Turbulence Research, pp. 127–138. Stanford University.Google Scholar
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Iritani, Y., Kasagi, N. & Hirata, M. 1985 Heat transfer mechanism and associated turbulence structure in the near-wall region of a turbulent boundary layer. In Turbulent Shear Flows 4 (ed. Bradbury, L. J. S. Durst, F. Launder, B. E. Schmidt, F. W. and Whitelaw, J. H.), pp. 223–234. Springer.CrossRefGoogle Scholar
Jiménez, J. 1998 The largest scales of turbulent wall flows. In CTR Annual Research Briefs, pp. 137–154. Stanford University.Google Scholar
Johansson, A. V. & Wikström, P. M. 1999 DNS and modelling of passive scalar transport in turbulent channel flow with a focus on scalar dissipation rate modelling. Flow Turbulence Combust. 63, 223–245.CrossRefGoogle Scholar
Kader, B. A. 1981 Temperature and concentration profiles in fully turbulent boundary layers. Intl J. Heat Mass Transfer 24, 1541–1544.CrossRefGoogle Scholar
Kasagi, N. & Ohtsubo, Y. 1993 Direct numerical simulation of low Prandtl number thermal field in a turbulent channel flow. In Turbulent Shear Flows 8 (ed. Durst, F., Friedrich, R., Launder, B. E., Schmidt, F. W., Schumann, U. and Whitelaw, J. H.), pp. 97–119. Springer.CrossRefGoogle Scholar
Kasagi, N. Tomita, Y. & Kuroda, A. 1992 Direct numerical simulation of passive scalar field in a turbulent channel flow. ASME J. Heat Transfer 144, 598–606.CrossRefGoogle Scholar
Kawamura, H., Abe, H. & Matsuo, Y. 1999 DNS of turbulent heat transfer in channel flow with respect to Reynolds and Prandtl number effects. Intl J. Heat Fluid Flow 20, 196–207.CrossRefGoogle Scholar
Kawamura, H., Abe, H. Matsuo, Y. & Choi, H. 2002 Large-scale structures of velocity and scalar fields in turbulent channel flows. In Intl Symp. on Dynamics and Statistics of Coherent Structures in Turbulence: Roles of Elementary Vortices pp. 49–64, Tokyo.Google Scholar
Kawamura, H., Abe, H. & Matsuo, Y. 2004 Very large-scale structures observed in DNS of turbulent channel flow with passive scalar transport. In Proc. of 15th Australasian Fluid Mech. Conf., The University of Sydney, Sydney, Australia.Google Scholar
Kawamura, H., Ohsaka, K., Abe, H. & Yamamoto, K. 1998 DNS of turbulent heat transfer in channel flow with low to medium–high Prandtl number fluid. Intl J. Heat Fluid Flow 19, 482–491.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1989 Transport of passive scalars in a turbulent channel flow. In Turbulent Shear Flows 6, (ed. André, J.-C., Cousteix, J., Durst, F., Launder, B. E., Schmidt, F. W. and Whitelaw, J. H.), pp. 85–96, Springer.CrossRefGoogle Scholar
Krogstad, P.-Å. & Antonia, R. A. 1994 Structure of turbulent boundary layers on smooth and rough walls. J. Fluid Mech. 277, 1–21.CrossRefGoogle Scholar
Launder, B. E. 1976 Heat and mass transport Topics Appl. Phys. 12, 231–287.CrossRefGoogle Scholar
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539-578.CrossRefGoogle Scholar
Morinishi, Y., Lund, T. S., Vasilyev, O. V. & Moin, P. 1998 Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 143, 90–124.CrossRefGoogle Scholar
Nagano, Y. & Kim, C. 1988 A two-equation model for heat transport in wall turbulent shear flows. ASME J. Heat Transfer 110, 583–589.CrossRefGoogle Scholar
Nagano, Y. & Shimada, M. 1996 Development of a two-equation heat transfer model based on direct simulations of turbulent flows with different Prandtl numbers. Phys. Fluids 8, 3379–3402.CrossRefGoogle Scholar
Pumir, A. 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), 2118–2132.CrossRefGoogle Scholar
Rajagopalan, S. & Antonia, R. A. 1979 Some properties of the large structure in a fully developed turbulent duct flow. Phys. Fluids 22 (4), 614–622.CrossRefGoogle Scholar
Robinson, S. K. 1991 The kinematics of turbulent boundary layer structure. Tech Rep. TM103859. NASA.Google Scholar
Rotta, J. C. 1964 Temperaturverteilungen in der turbulenten grenzschicht an der ebenen platte. Intl J. Heat Mass Transfer 7, 215–228.CrossRefGoogle Scholar
Ruetsch, G. R. & Maxey, M. R. 1992 The evolution of small-scale structures in homogeneous isotropic turbulence. Phys. Fluids A 4, 2747–2760.CrossRefGoogle Scholar
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297–324.CrossRefGoogle Scholar
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435–472.CrossRefGoogle Scholar
Subramanian, C. S., Rajagopalan, S., Antonia, R. A. & Chambers, A. J. 1982 Comparison of conditional sampling and averaging techniques in a turbulent boundary layer. J. Fluid Mech. 123, 335–362.CrossRefGoogle Scholar
Tanahashi, M., Kang, S.-J., Miyamoto, T., Shiokawa, S. & Miyauchi, T. 2004 Scaling law of fine scale eddies in turbulent channel flows up to Re τ = 800. Intl J. Heat Fluid Flow 25, 331–340.CrossRefGoogle Scholar
Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogeneous shear flow with a uniform mean temperature gradient. Part 1. The fine structure. J. Fluid Mech. 104, 311–347.CrossRefGoogle Scholar
Taylor, R. J. 1958 Thermal structures in the lowest layers of the atmosphere. Aust. J. Phys. 11, 168–176.CrossRefGoogle Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.CrossRefGoogle Scholar
Yoshizawa, A. 1988 Statistical modelling of passive-scalar diffusion in turbulent shear flows. J. Fluid Mech. 195, 541–555.CrossRefGoogle Scholar