Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-20T15:27:54.389Z Has data issue: false hasContentIssue false

Measurements of turbulent diffusion in uniformly sheared flow

Published online by Cambridge University Press:  07 August 2014

Christina Vanderwel
Affiliation:
Department of Mechanical Engineering, University of Ottawa, Ottawa, ON K0A 3H0, Canada
Stavros Tavoularis*
Affiliation:
Department of Mechanical Engineering, University of Ottawa, Ottawa, ON K0A 3H0, Canada
*
Email address for correspondence: [email protected]

Abstract

The diffusion of a plume of dye in uniformly sheared turbulent flow in a water tunnel was investigated using simultaneous stereoscopic particle image velocimetry (SPIV) and planar laser-induced fluorescence (PLIF). Maps of the mean concentration and the turbulent concentration fluxes in planes normal to the plume axis were constructed, from which all components of the second-order turbulent diffusivity tensor were determined for the first time. Good agreement between the corresponding apparent and true diffusivities was observed. The turbulent diffusivity tensor was found to have strong off-diagonal components, whereas the streamwise component appeared to be counter-gradient. The different terms in the advection–diffusion equation were estimated from the measurements and their relative significance was discussed. All observed phenomena were explained by physical arguments and the results were compared to previous ones.

Type
Papers
Copyright
© 2014 Cambridge University Press 

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

Adrian, R. J. & Westerweel, J. 2011 Particle Image Velocimetry. Cambridge University Press.Google Scholar
Anand, M. S. & Pope, S. B. 1985 Diffusion behind a line source in grid turbulence. In Turbulent Shear Flows 4 (ed. Bradbury, L. J., Durst, F., Launder, B. E., Schmidt, F. W. & Whitelaw, J. H.), pp. 4661. Springer.CrossRefGoogle Scholar
Arya, S. P. 1999 Air Pollution Meteorology and Dispersion. Oxford University Press.Google Scholar
Batchelor, G. K. 1949 Diffusion in a field of homogeneous turbulence. I. Eulerian analysis. Austral. J. Chem. 2 (4), 437450.Google Scholar
Borg, A., Bolinder, J. & Fuchs, L. 2001 Simultaneous velocity and concentration measurements in the near field of a turbulent low-pressure jet by digital particle image velocimetry–planar laser-induced fluorescence. Exp. Fluids 31 (2), 140152.Google Scholar
Chang, K.-A. & Cowen, E. A. 2002 Turbulent Prandtl number in neutrally buoyant turbulent round jet. J. Engng Mech. ASCE 128 (10), 10821087.CrossRefGoogle Scholar
Corrsin, S. 1975 Limitations of gradient transport models in random walks and in turbulence. Adv. Geophys. 18 (Part A), 2560.CrossRefGoogle Scholar
Csanady, G. T. 1963 Turbulent diffusion in Lake Huron. J. Fluid Mech. 17 (3), 360384.Google Scholar
Deardorff, J. W. 1966 The counter-gradient heat flux in the lower atmosphere and in the laboratory. J. Atmos. Sci. 23, 503506.2.0.CO;2>CrossRefGoogle Scholar
van Dop, H. & Verver, G. 2001 Countergradient transport revisited. J. Atmos. Sci. 58 (15), 22402247.Google Scholar
Fukushima, C., Aanen, L. & Westerweel, J. 2000 Investigation of the mixing process in an axisymmetric turbulent jet using PIV and LIF. In Laser Techniques for Fluid Mechanics (ed. Adrian, R. J., Durao, D. F. G., Heitor, M. V., Maeda, M., Tropea, C. & Whitelaw, J. H.), pp. 339356. Springer.Google Scholar
Gendron, P. O., Avaltroni, F. & Wilkinson, K. J. 2008 Diffusion coefficients of several rhodamine derivatives as determined by pulsed field gradient–nuclear magnetic resonance and fluorescence correlation spectroscopy. J. Fluorescence 18 (6), 10931101.Google Scholar
Hay, J. S. & Pasquill, F. 1959 Diffusion from a continuous source in relation to the spectrum and scale of turbulence. Adv. Geophys. 6, 345365.Google Scholar
Karnik, U. & Tavoularis, S. 1987 Generation and manipulation of uniform shear with the use of screens. Exp. Fluids 5, 247254.Google Scholar
Karnik, U. & Tavoularis, S. 1989 Measurements of heat diffusion from a continuous line source in a uniformly sheared turbulent flow. J. Fluid Mech. 202, 233261.Google Scholar
Karnik, U. & Tavoularis, S. 1990 Lagrangian correlations and scales in uniformly sheared turbulence. Phys. Fluids A 2 (4), 587591.Google Scholar
Lemoine, F., Wolff, M. & Lebouche, M. 1996 Simultaneous concentration and velocity measurements using combined laser-induced fluorescence and laser Doppler velocimetry: application to turbulent transport. Exp. Fluids 20 (5), 319327.Google Scholar
Lepore, J. & Mydlarski, L. 2011 Lateral dispersion from a concentrated line source in turbulent channel flow. J. Fluid Mech. 678, 417450.Google Scholar
Nakamura, I., Sakai, Y., Miyata, M. & Tsunoda, H. 1986 Diffusion of matter from a continuous point source in uniform mean shear flows (1st report). Bull. JSME 29 (250), 11411148.CrossRefGoogle Scholar
O’Neill, P. L., Nicolaides, D., Honnery, D. & Soria, J.2004 Autocorrelation functions and the determination of integral length with reference to experimental and numerical data. In Proceedings of the Fifteenth Australasian Fluid Mechanics Conference. The University of Sydney, Australia, 13–17 December 2004.Google Scholar
Paranthoën, P., Godard, G., Weiss, F. & Gonzalez, M. 2004 Counter gradient diffusion vs ‘counter diffusion’ temperature profile? Intl J. Heat Mass Transfer 47 (4), 819825.Google Scholar
Pope, S. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Prasad, A. K. & Jensen, K. 1995 Scheimpflug stereocamera for particle image velocimetry in liquid flows. Appl. Opt. 34 (30), 70927099.CrossRefGoogle ScholarPubMed
Rahman, S. & Webster, D. R. 2005 The effect of bed roughness on scalar fluctuations in turbulent boundary layers. Exp. Fluids 38 (3), 372384.Google Scholar
Riley, J. J. & Corrsin, S. 1974 The relation of turbulent diffusivities to Lagrangian velocity statistics for the simplest shear flow. J. Geophys. Res. 79 (12), 17681771.Google Scholar
Roberts, O. F. T. 1923 The theoretical scattering of smoke in a turbulent atmosphere. Proc. R. Soc. Lond. A 104 (728), 640654.Google Scholar
Roberts, P. J. W. & Webster, D. R. 2002 Turbulent diffusion. In Environmental Fluid Mechanics: Theories and Applications (ed. Shen, H.), pp. 745. American Society of Civil Engineers.Google Scholar
Rogers, M. M., Mansour, N. N. & Reynolds, W. C. 1989 An algebraic model for the turbulent flux of a passive scalar. J. Fluid Mech. 203 (1), 77101.Google Scholar
de Roode, S. R., Jonker, H. J. J., Duynkerke, P. G. & Stevens, B. 2004 Countergradient fluxes of conserved variables in the clear convective and stratocumulus-topped boundary layer: the role of the entrainment flux. Boundary-Layer Meteorol. 112 (1), 179196.Google Scholar
De Souza, F. A., Nguyen, V. D. & Tavoularis, S. 1995 The structure of highly sheared turbulence. J. Fluid Mech. 303, 155167.Google Scholar
Sreenivasan, K. R., Tavoularis, S. & Corrsin, S. 1982 A test of gradient transport and its generalizations. In Turbulent Shear Flows 3 (ed. Bradbury, L. J. S., Durst, F., Launder, B. E., Schmidt, F. W. & Whitelaw, J. H.), pp. 96112. Springer.Google Scholar
Stapountzis, H., Sawford, B. L., Hunt, J. C. R. & Britter, R. E. 1986 Structure of the temperature field downwind of a line source in grid turbulence. J. Fluid Mech. 165, 401424.CrossRefGoogle Scholar
Sutton, O. G. 1932 A theory of eddy diffusion in the atmosphere. Proc. R. Soc. Lond. A 135 (826), 143165.Google Scholar
Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 1. J. Fluid Mech. 104, 311347.Google Scholar
Tavoularis, S. & Corrsin, S. 1985 Effects of shear on the turbulent diffusivity tensor. Intl J. Heat Mass Transfer 28 (1), 265276.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20 (2), 196211.Google Scholar
Vanderwel, C. & Tavoularis, S. 2011 Coherent structures in uniformly sheared turbulent flow. J. Fluid Mech. 689, 434464.Google Scholar
Vanderwel, C. & Tavoularis, S. 2014a On the accuracy of PLIF measurements in slender plumes. Exp. Fluids (in press).Google Scholar
Vanderwel, C. & Tavoularis, S. 2014b Relative dispersion of a passive scalar plume in turbulent shear flow. Phys. Rev. E 89 (4), 041005(R).CrossRefGoogle ScholarPubMed
Veeravalli, S. & Warhaft, Z. 1990 Thermal dispersion from a line source in the shearless turbulence mixing layer. J. Fluid Mech. 216, 3570.Google Scholar
Warhaft, Z. 1984 The interference of thermal fields from line sources in grid turbulence. J. Fluid Mech. 144, 363387.Google Scholar
Webster, D. R., Rahman, S. & Dasi, L. P. 2003 Laser-induced fluorescence measurements of a turbulent plume. J. Engng Mech. ASCE 129, 11301137.Google Scholar
Webster, D. R., Roberts, P. J. W. & Ra’ad, L. 2001 Simultaneous DPTV/PLIF measurements of a turbulent jet. Exp. Fluids 30, 6572.CrossRefGoogle Scholar
Wilson, D. J., Robins, A. G. & Fackrell, J. E. 1985 Intermittency and conditionally-averaged concentration fluctuation statistics in plumes. Atmos. Environ. 19 (7), 10531064.Google Scholar
Würth, C., González, M. G., Niessner, R., Panne, U., Haisch, C. & Genger, U. R. 2012 Determination of the absolute fluorescence quantum yield of Rhodamine 6G with optical and photoacoustic methods – providing the basis for fluorescence quantum yield standards. Talanta 90, 3037.Google Scholar
Younis, B. A., Speziale, C. G. & Clark, T. T. 2005 A rational model for the turbulent scalar fluxes. Proc. R. Soc. Lond. A 461, 575594.Google Scholar