Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T19:24:57.011Z Has data issue: false hasContentIssue false
  • English
  • Français

Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow

Published online by Cambridge University Press:  25 May 2009

HIROYUKI ABE ,
ROBERT ANTHONY ANTONIA  and
HIROSHI KAWAMURA
HIROYUKI ABE*
Affiliation:
Japan Aerospace Exploration Agency, 182-8522 Tokyo, Japan
ROBERT ANTHONY ANTONIA
Affiliation:
Discipline of Mechanical Engineering, University of Newcastle, 2308 NSW, Australia
HIROSHI KAWAMURA
Affiliation:
Department of Mechanical Engineering, Tokyo University of Science, 278-8510 Chiba, Japan
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations of a turbulent channel flow with passive scalar transport are used to examine the relationship between small-scale velocity and scalar fields. The Reynolds number based on the friction velocity and the channel half-width is equal to 180, 395 and 640, and the molecular Prandtl number is 0.71. The focus is on the interrelationship between the components of the vorticity vector and those of the scalar derivative vector. Near the wall, there is close similarity between different components of the two vectors due to the almost perfect correspondence between the momentum and thermal streaks. With increasing distance from the wall, the magnitudes of the correlations become smaller but remain non-negligible everywhere in the channel owing to the presence of internal shear and scalar layers in the inner region and the backs of the large-scale motions in the outer region. The topology of the scalar dissipation rate, which is important for small-scale scalar mixing, is shown to be associated with the organized structures. The most preferential orientation of the scalar dissipation rate is the direction of the mean strain rate near the wall and that of the fluctuating compressive strain rate in the outer region. The latter region has many characteristics in common with several turbulent flows; viz. the dominant structures are sheetlike in form and better correlated with the energy dissipation rate than the enstrophy.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 627 , 25 May 2009 , pp. 1 - 32
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

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. & 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. 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 Fluid Flow 25, 404–419.CrossRefGoogle Scholar
Antonia, R. A., Abe, H. & Kawamura, H. 2008 Analogy between velocity and scalar fields in a turbulent channel flow. J. Fluid Mech. Submitted.CrossRefGoogle Scholar
Antonia, R. A. & Browne, L. W. B. 1983 The destruction of temperature fluctuations in a turbulent plane jet. J. Fluid Mech. 134, 67–83.CrossRefGoogle Scholar
Antonia, R. A. & Chambers, A. J. 1980 On the correlation between turbulent velocity and temperature derivatives in the atmospheric surface layer. Boundary-Layer Meteorol. 18, 399–410.CrossRefGoogle Scholar
Antonia, R. A., Chambers, A. J., Britz, D. & Browne, L. W. B. 1986 Organized structures in a turbulent plane jet: topology and contribution to momentum and heat transport. J. Fluid Mech. 172, 211–229.CrossRefGoogle Scholar
Antonia, R. A. & Kim, J. 1991 Turbulent Prandtl number in the near-wall region of a turbulent channel flow. Intl J. Heat Mass Transfer 34 (7), 1905–1908.CrossRefGoogle Scholar
Antonia, R. A. & Kim, J. 1994 a Low-Reynolds-number effects on near-wall turbulence. J. Fluid Mech. 276, 61–80.CrossRefGoogle Scholar
Antonia, R. A. & Kim, J. 1994 b A numerical study of local isotropy of turbulence. Phys. Fluids 6 (2), 834–841.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., 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. & Mi, J. 1993 Temperature dissipation in a turbulent round jet. J. Fluid Mech. 250, 531–551.CrossRefGoogle Scholar
Antonia, R. A. & Orlandi, P. 2003 Effect of Schmidt number on small-scale passive scalar turbulence. Appl. Mech. Rev. 56 (6), 615–632.CrossRefGoogle Scholar
Antonia, R. A. & Orlandi, P. 2004 Similarity of decaying isotropic turbulence with a passive scalar. J. Fluid Mech. 505, 123–151.CrossRefGoogle Scholar
Antonia, R. A. & Van Atta, C. W. 1975 On the correlation between temperature and velocity dissipation fields in a heated turbulent jet. J. Fluid Mech. 67, 273–288.CrossRefGoogle Scholar
Antonia, R. A. & Van Atta, C. W. 1979 Skewness of spatial derivatives of temperature in a turbulent boundary layer. Phys. Fluids 22 (12), 2430–2431.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
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
Brethouwer, G., Hunt, J. C. R. & Nieuwstadt, F. T. M. 2003 Micro-structure and Lagrangian statistics of the scalar field with a mean gradient in isotropic turbulence. J. Fluid Mech. 474, 193–225.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
Browne, L. W. B., Antonia, R. A. & Shah, D. A. 1987 Turbulent energy dissipation in a wake. J. Fluid Mech. 179, 307–326.CrossRefGoogle Scholar
Buch, K. A. & Dahm, W. J. A. 1998 Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 2. Sc ≈ 1. J. Fluid Mech. 364, 1–29.CrossRefGoogle Scholar
Chandrasekhar, S. 1950 The theory of axisymmetric turbulence. Proc. R. Soc. Lond. A 242, 557–577.Google Scholar
Chen, C. 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
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 Symposium, pp. 5–30, State University of Iowa, Iowa City.Google Scholar
George, W. K. & Hussein, H. J. 1991 Locally axisymmetric turbulence. J. Fluid Mech. 233, 1–23.CrossRefGoogle Scholar
Gonzalez, M. 2002 Effect of vorticity on second- and third-order statistics of passive scalar gradients. Phys. Rev. E 60, 056307.Google Scholar
Holzer, M. & Siggia, E. D. 1994 Turbulent mixing of a passive scalar. Phys. Fluids 6, 1820–1837.CrossRefGoogle Scholar
Horiuti, K. 2001 A classification method for vortex sheet and tube structures in turbulent flows. Phys. Fluids 13, 3756–3774.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
Iwamoto, K., Kasagi, N. & Suzuki, Y. 2005 Direct numerical simulation of turbulent channel flow at Re τ = 2320. In Proc. of the 6th Symp. on Smart Control of Turbulence, pp. 327–333, Tokyo.Google Scholar
Jiménez, J. 1992 Kinematic alignment effects in turbulent flows. Phys. Fluids A 4, 652–654.CrossRefGoogle Scholar
Jiménez, J., del Álamo, J. C. & Flores, O. 2004 The large scale dynamics near-wall turbulence. J. Fluid Mech. 505, 179–199.CrossRefGoogle Scholar
Jiménez, J., Moin, P., Moser, R. & Keefe, L. 1988 Ejection mechanism in the sublayer of a turbulent channel flow. Phys. Fluids 31, 1311–1313.CrossRefGoogle Scholar
Jiménez, J., Wray, A. A., Saffmann, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.CrossRefGoogle Scholar
Johansson, A. V., Alfredsson, P. H. & Kim, J. 1991 Evolution and dynamics of shear-layer structure in near-wall turbulence. J. Fluid. Mech. 224, 579–599.CrossRefGoogle 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 Turb. Combust. 63, 223–245.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
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
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. & Shingai, K. 2000 DNS of turbulence and heat transport in a channel flow with different Reynolds and Prandtl numbers and boundary conditions. In Proc. of the 3rd Intl Symp. on Turbulence, Heat and Mass Transfer (ed. Nagano, Y., Hanjalic, K. and Tsuji, T.), pp. 15–32, Aichi Shuppan.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
Kerr, R. M. 1985 Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58.CrossRefGoogle Scholar
Kim, J. 1988 Investigation of heat and mass transport in turbulent flows via numerical simulation. In Transport Phenomena in Turbulent Flows: Theory, Experiment and Numerical Simulation (ed. Hirata, M. & Kasagi, N.), pp. 157–170. Hemisphere Publishing.Google 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
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kravchenko, A. G. & Moin, P. 1997 On the effect of numerical errors in large eddy simulations of turbulent flows. J. Comput. Phys. 131, 310–322.CrossRefGoogle Scholar
Krishnamoorthy, L. V. & Antonia, R. A. 1987 Temperature-dissipation measurements in a turbulent boundary layer. J. Fluid Mech. 176, 265–281.CrossRefGoogle Scholar
Moin, P. & Kim, J. 1985 The structure of the vorticity field in turbulent channel flow. Part 1. Analysis of instantaneous fields and statistical correlatins. J. Fluid. Mech. 155, 441–464.CrossRefGoogle Scholar
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539–578.CrossRefGoogle Scholar
Moin, P., Adrian, R. & Kim, J. 1987 Stochastic estimation of organized structures in turbulent channel flow. In Proc. of the 6th Symp. on Turbulent Shear Flows, pp. 16-9-1–16-9-8, Toulouse, France.Google Scholar
Moisy, F., Willaime, H., Andersen, J. S. & Tabeling, P. 2001 Passive scalar intermittency in low temperature helium flows. Phys. Rev. Lett. 86, 4827–4830.CrossRefGoogle ScholarPubMed
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
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Re τ = 590. Phys. Fluids 11, 943–945.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
Namazian, M., Schefer, R. W. & Kelly, J. 1988 Scalar dissipation measurements in the developing region of a jet. Comb. Flame 74, 147–160.CrossRefGoogle Scholar
Nomura, K. K. & Elghobashi, S. E. 1992 Mixing characteristics of an inhomogeneous scalar in isotropic and homogeneous sheared turbulence. Phys. Fluids A 4 (3), 606–625.CrossRefGoogle Scholar
Orlandi, P., Leonardi, S. & Antonia, R. A. 2006 Vortex structures in a rough-wall channel flow and their influence on passive scalar. In Proc. of IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamics (ed. Kida, S.), pp. 39–49, Springer.CrossRefGoogle Scholar
Österlund, J. M. 1999 Experimental studies of zero pressure-gradient turbulent boundary layer Flow. PhD thesis, Royal Institute of Technology, Stockholm.Google Scholar
Peters, N. 2000 Turbulent Combustion. Cambridge University Press.CrossRefGoogle Scholar
Prasad, R. R. & Sreenivasan, K. R. 1990 Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows. J. Fluid Mech. 216, 1–34.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
Robinson, S. K. 1991 The kinematics of turbulent boundary layer structure. Tech Rep. TM103859. NASA.Google Scholar
Rodi, W. & Mansour, N. N. 1993 Low Reynolds number k-ϵ modelling with the aid of direct simulation data. J. Fluid Mech. 250, 509–529.CrossRefGoogle Scholar
Ruetsch, G. R. & Maxey, M. R. 1991 Small-scale features of vorticity and passive scalar fields in homogeneous isotropic turbulence. Phys. Fluids A 3, 1587–1597.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
She, Z.-S., Jackson, E. & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226–228.CrossRefGoogle Scholar
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27–54.CrossRefGoogle Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to R θ = 1410. J. Fluid Mech. 187, 61–98.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. Comp. Phys. 96, 297–324.CrossRefGoogle Scholar
Sreenivasan, K. R., Antonia, R. A. & Britz, D. 1979 Local isotropy and large structures in a heated turbulent jet. J. Fluid Mech. 94, 745–775.CrossRefGoogle Scholar
Sreenivasan, K. R., Antonia, R. A. & Danh, H. Q. 1977 Temperature dissipation fluctuations in a turbulent boundary layer. Phys. Fluids 20 (8), 1238–1249.CrossRefGoogle Scholar
Sreenivasan, K. R. 1990 Turbulence and the tube. Nature 344, 192–193.CrossRefGoogle Scholar
Sreenivasan, K. R. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434, 165–182.Google Scholar
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435–472.CrossRefGoogle Scholar
Su, L. K. & Clemens, N. T. 2003 The structure of fine-scale scalar mixing in gas-phase planar turbulent jets. J. Fluid Mech. 488, 1–29.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 2. The fine structure. J. Fluid Mech. 104, 349–367.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. The MIT pressCrossRefGoogle Scholar
Vedula, P., Yeung, P. K. & Fox, R. O. 2001 Dynamics of scalar dissipation in isotropic turbulence: a numerical and modelling study. J. Fluid Mech. 433, 29–60.CrossRefGoogle Scholar
Vincent, A. & Meneguzzi, M. 1994 The dynamics of vorticity tubes in homogeneous turbulence. J. Fluid Mech. 258, 245–254.CrossRefGoogle Scholar
Wang, L.-P., Chen, S. & Brasseur, J. G. 1999 Examination of hypothesis in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 2. Passive scalar field. J. Fluid Mech. 400, 163–197.CrossRefGoogle Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.CrossRefGoogle Scholar
Watanabe, T. & Gotoh, T. 2004 Statistics of a passive scalar in homogeneous turbulence. New J. Phys. 6, 40. http://www.njp.org/.CrossRefGoogle Scholar
Watanabe, T. & Gotoh, T. 2007 Inertial-range intermittency and accuracy of direct numerical simulation for turbulence and passive scalar turbulence. J. Fluid Mech. 590, 117–146.CrossRefGoogle Scholar
Yeung, P. K. 2001 Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations. J. Fluid Mech. 427, 241–274.CrossRefGoogle Scholar
Yeung, P. K., Donzis, D. A. & Sreenivasan, K. R. 2005 High-Reynolds-number simulation of turbulent mixing. Phys. Fluids 17, 081703.CrossRefGoogle Scholar
Yeung, P. K., Xu, S. & Sreenivasan, K. R. 2002 Schmidt number effects on turbulent transport with uniform mean scalar gradient. Phys. Fluids 14 (12), 4178–4191.CrossRefGoogle Scholar
Yoshizawa, A. 1988 Statistical modelling of passive-scalar diffusion in turbulent shear flows. J. Fluid Mech. 195, 541–555.CrossRefGoogle Scholar
Zhou, T. & Antonia, R. A. 2000 Approximations for turbulent kinetic energy and temperature variance dissipation rates in grid turbulence. Phys. Fluids 12, 335–344.CrossRefGoogle Scholar