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Lateral dispersion from a concentrated line source in turbulent channel flow

Published online by Cambridge University Press:  03 May 2011

J. LEPORE  and
L. MYDLARSKI
J. LEPORE
Affiliation:
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montréal, QC H3A 2K6, Canada
L. MYDLARSKI*
Affiliation:
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montréal, QC H3A 2K6, Canada
*
†Email address for correspondence: [email protected]
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Abstract

The dispersion of a passive scalar (temperature) from a concentrated line source in fully developed, high-aspect-ratio turbulent channel flow is studied herein. The line source is oriented in the direction of the inhomogeneity of the velocity field, resulting in a thermal plume that is statistically three-dimensional. This configuration is selected to investigate the lateral dispersion of a passive scalar in an inhomogeneous turbulent flow (i.e. dispersion in planes parallel to the channel walls). Measurements are recorded at six wall-normal distances (y/h = 0.10, 0.17, 0.33, 0.50, 0.67 and 1.0), six downstream positions (x/h = 4.0, 7.4, 10.8, 15.2, 18.6 and 22.0) and a Reynolds number of Re ≡ 〈U〉y = hh/v = 10200 (Reτ ≡ u∗h/v = 502). The lateral mean temperature excess profiles were found to be well represented by Gaussian distributions. The root-mean-square (r.m.s.) profiles, on the other hand, were symmetric, but non-Gaussian. Consistent with homogeneous flows (and in contrast to the work of Lavertu & Mydlarski (J. Fluid Mech., vol. 528, 2005, p. 135) studying transverse dispersion in the same flow), (i) the downstream growth rate of the centreline mean temperature excess, centreline r.m.s. temperature fluctuation and half-width of the mean and r.m.s. temperature profiles followed a power law evolution in the downstream direction, and (ii) the r.m.s. profiles evolved from single-peaked to double-peaked profiles far downstream. By comparing the measured ratios of the centreline r.m.s. temperature fluctuation to the mean temperature excess to the ratios measured in other flows, it was hypothesized that the mean-flow shear, as well as the turbulence intensity, played an important, cooperative role in increasing the mixedness of the flow. The probability density functions (PDFs) were quasi-Gaussian near the wall as well as for large-enough downstream distances. Closer to both the source and the channel centreline, the PDFs were better approximated by exponential distributions, with a sharp peak corresponding to the free-stream temperature. For intermediate downstream distances, the PDFs of the lateral dispersion were better mixed than analogous PDFs of the transverse dispersion, consistent with the mixedness measurements.

JFM classification

Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 417 - 450
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Anand, M. S. & Pope, S. B. 1985 Diffusion behind a line source in grid turbulence. In Turbulent Shear Flows (ed. Bradbury, L. J. S., Durst, F., Launder, B. E., Schmidt, F. W. & Whitelaw, J. H.), vol. 4, pp. 46–61. Springer.CrossRefGoogle Scholar
Bakosi, J., Franzese, P. & Boybeyi, Z. 2007 Probability density function modeling of scalar mixing from concentrated sources in turbulent channel flow. Phys. Fluids 19, 115106.CrossRefGoogle Scholar
Brethouwer, G., Boersma, B. J., Pourquié, M. B. J. M. & Nieuwstadt, F. T. M. 1999 Direct numerical simulation of turbulent mixing of a passive scalar in pipe flow. Eur. J. Mech. B/Fluids 18, 739–756.CrossRefGoogle Scholar
Bruun, H. H. 1995 Hot Wire Anemometry: Principles and Signal Analysis. Oxford University Press.CrossRefGoogle Scholar
Costa-Patry, E. & Mydlarski, L. 2008 Mixing of two thermal fields emitted from line sources in turbulent channel flow. J. Fluid Mech. 609, 349–375.CrossRefGoogle Scholar
Dimotakis, P. E. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329–356.CrossRefGoogle Scholar
Dupont, A., El Kabiri, M. & Paranthoën, P. 1985 Dispersion from elevated line source in a turbulent boundary layer. Intl J. Heat Mass Transfer 28, 892–894.CrossRefGoogle Scholar
Durbin, P. A. 1980 A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech. 100, 279–302.CrossRefGoogle Scholar
Fackrell, J. E. & Robins, A. G. 1982 Concentration fluctuations and fluxes in plumes from point sources in a turbulent boundary layer. J. Fluid Mech. 117, 1–26.CrossRefGoogle Scholar
Gifford, F. A. 1961 Use of routine meteorological observations for estimating atmospheric dispersion. Nucl. Safety 2, 47–51.Google Scholar
Iliopoulos, I. & Hanratty, T. J. 1999 Turbulent dispersion in a non-homogeneous field. J. Fluid Mech. 392, 45–71.CrossRefGoogle 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, 233–261.CrossRefGoogle Scholar
Kontomaris, K. & Hanratty, T. J. 1994 Effect of molecular diffusivity on point source diffusion in the center of a numerically simulated turbulent channel flow. Intl J. Heat Mass Transfer 37, 1817–1828.CrossRefGoogle Scholar
LaRue, J. C., Deaton, T. & Gibson, C. H. 1975 Measurement of high-frequency turbulent temperature. Rev. Sci. Instrum. 46, 757–764.CrossRefGoogle Scholar
Lavertu, R. A. 2002 Scalar dispersion in turbulent channel flow. Master's thesis, McGill University.Google Scholar
Lavertu, R. A. & Mydlarski, L. 2005 Scalar mixing from a concentrated source in turbulent channel flow. J. Fluid Mech. 528, 135–172.CrossRefGoogle Scholar
Lecordier, J. C., Browne, L. W. B., Masson, S. Le Dumouchel, F. & Paranthoën, P. 2000 Control of vortex shedding by thermal effect at low Reynolds numbers. Exp. Therm. Fluid Sci. 21, 227–237.CrossRefGoogle Scholar
Lemay, J. & Benaïssa, A. 2001 Improvement of cold-wire response for measurement of temperature dissipation. Exp. Fluids 31, 347–356.CrossRefGoogle Scholar
Lyons, S. L., Hanratty, T. J. & McLaughlin, J. B. 1991 Direct numerical simulation of passive heat transfer in a turbulent channel flow. Intl J. Heat Mass Transfer 34, 1149–1161.CrossRefGoogle Scholar
Na, Y. & Hanratty, T. J. 2000 Limiting behavior of turbulent scalar transport close to a wall. Intl J. Heat Mass Transfer 43, 1749–1758.CrossRefGoogle 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, characteristics of the mean concentration field). Bull. JSME 29, 1141–1148.CrossRefGoogle Scholar
Papavassiliou, D. V. & Hanratty, T. J. 1997 Transport of a passive scalar in a turbulent channel flow. Intl J. Heat Mass Transfer 40, 1303–1311.CrossRefGoogle Scholar
Paranthoën, P., Fouari, A., Dupont, A. & Lecordier, J. C. 1988 Dispersion measurements in turbulent flows (boundary layer and plane jet). Intl J. Heat Mass Transfer 31, 153–165.CrossRefGoogle Scholar
Pasquill, F. 1961 The estimation of the dispersion of windborne material. Meteorol. Mag. 90, 33–49.Google Scholar
Sakai, Y., Nakamura, I., Miyata, M. & Tsunoda, H. 1986 Diffusion of matter from a continuous point source in uniform mean shear flows (2nd report, characteristics of concentration fluctuation intensity). Bull. JSME 29, 1149–1155.CrossRefGoogle Scholar
Sawford, B. L. & Hunt, J. C. R. 1986 Effects of turbulence structure, molecular diffusion and source size on scalar fluctuations in homogeneous turbulence. J. Fluid Mech. 165, 373–400.CrossRefGoogle Scholar
Shlien, D. J. & Corrsin, S. 1976 Dispersion measurements in a turbulent boundary layer. Intl J. Heat Mass Transfer 19, 285–295.CrossRefGoogle Scholar
Shraiman, B. I. & Siggia, E. D. 2000 Scalar turbulence. Nature 405, 639–646.CrossRefGoogle ScholarPubMed
Sreenivasan, K. R. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434, 165–182.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, 401–424.CrossRefGoogle Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–212.Google Scholar
Taylor, G. I. 1935 Statistical theory of turbulence. Part 4. Diffusion in a turbulent air stream. Proc. R. Soc. Lond. A 151, 465–478.CrossRefGoogle Scholar
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186–203.Google Scholar
Taylor, G. I. 1954 The dispersion of matter in turbulent flow through a pipe. Proc. R. Soc. Lond. A 223, 446–468.Google Scholar
Townsend, A. A. 1954 The diffusion behind a line source in homogeneous turbulence. Proc. R. Soc. Lond. A 224, 487–512.Google Scholar
Uberoi, M. S. & Corrsin, S. 1953 Diffusion of heat from a line source in isotropic turbulence. NACA Rep. 1142.Google Scholar
Villermaux, E., Innocenti, C. & Duplat, J. 2001 Short circuits in the Corrsin–Obukhov cascade. Phys. Fluids 13 (1), 284–289.CrossRefGoogle Scholar
Viswanathan, S. & Pope, S. B. 2008 Turbulent dispersion from line sources in grid turbulence. Phys. Fluids 20, 101514.CrossRefGoogle Scholar
Vrieling, A. J. & Nieuwstadt, F. T. M. 2003 Turbulent dispersion from nearby point sources – interference of the concentration statistics. Atmos. Environ. 37, 4493–4506.CrossRefGoogle Scholar
Warhaft, Z. 1984 The interference of thermal fields from line sources in grid turbulence. J. Fluid Mech. 144, 363–387.CrossRefGoogle Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.CrossRefGoogle Scholar
Zukauskas, A. 1972 Heat transfer from tubes in crossflow. In Advances in Heat Transfer (ed. Hartnett, J. P. & Irvine, T. F. Jr.), vol. 8, pp. 93–160. Elsevier.Google Scholar