Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-08T15:59:34.507Z Has data issue: false hasContentIssue false
  • English
  • Français

A simple and unifying physical interpretation of scalar fluctuation measurements from many turbulent shear flows

Published online by Cambridge University Press:  26 April 2006

P. C. Chatwin  and
Paul J. Sullivan
P. C. Chatwin
Affiliation:
Department of Mathematics and Statistics, Brunei University, Uxbridge, UBS 3PH, UK
Paul J. Sullivan
Affiliation:
Department of Applied Mathematics, University of Western Ontario. London, Canada N6A 5B9
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that measurements of the statistical properties of the concentration distributions of dispersing scalars taken from many different turbulent shear flows have a great number of common features. In particular the same simple relationship between the mean concentration and the mean-square fluctuation is shown to hold in all the flows, and this relationship is derived theoretically from well-known results for the unreal case when there is no molecular diffusion by a natural hypothesis about the effects of molecular diffusion. Application of the hypothesis to the higher moments and shape parameters gives results that agree reasonably well with the data (given the unavoidable experimental errors). The hypothesis should be subjected to further experimental analysis, and could simplify the application of turbulence closures and similar models. Extensions of the ideas to the probability density function of the scalar concentration suggest that it becomes self-similar. A final conclusion is that more attention to experimental errors due to instrument smoothing is highly desirable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 212 , March 1990 , pp. 533 - 556
Copyright
© 1990 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

Antonia, R. A., Browne, L. W. B., Chambers, A. J. & Rajagopalan, S., 1983a Budget of the temperature variance in a turbulent plane jet. Intl J. Heat Mass Transfer 26, 41–48.Google Scholar
Antonia, R. A., Chambers, A. J. & Elena, M., 1983b Points of symmetry in turbulent shear flows. Intl Commun. Heat Mass Transfer 10, 395–402.Google Scholar
Antonia, R. A., Prabhu, A. & Stephenson, S. E., 1975 Conditionally sampled measurements in a heated turbulent jet. J. Fluid Mech. 72, 455–480.Google Scholar
Antonia, R. A. & Sreenivasan, K. R., 1976 Statistical properties of velocity and temperature fluctuations in a turbulent heated jet. T. N. F. M. 3. Dept of Mech. Eng., Univ. of Newcastle, NSW, Australia.Google Scholar
Batchelor, G. K.: 1952 The effect of homogeneous turbulence on material lines and surfaces. Proc. R. Soc. Lond. A 213, 349–366.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.Google Scholar
Batchelor, G. K., Howells, I. D. & Townsend, A. A., 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 2. The case of large conductivity. J. Fluid Mech. 5, 134–139.Google Scholar
Becker, H. A., Hottel, H. C. & Williams, G. C., 1967 The nozzle-fluid concentration field of the round turbulent free jet. J. Fluid Mech. 30, 285–303.Google Scholar
Birch, A. D., Brown, D. R., Dodson, M. G. & Thomas, J. R., 1978 The turbulent concentration field of a methane jet. J. Fluid Mech. 88, 431–449.Google Scholar
Browne, L. W. B., Antonia, R. A. & Chambers, A. J., 1984 The interaction region of a turbulent plane jet. J. Fluid Mech. 149, 355–373.Google Scholar
Carn, K. K. & Chatwin, P. C., 1985 Variability and heavy gas dispersion. J. Haz. Mat. 11, 281–300.Google Scholar
Chatwin, P. C. & Sullivan, P. J., 1979 The relative diffusion of a cloud of passive contaminant in incompressible turbulent flow. J. Fluid Mech. 91, 337–355.Google Scholar
Chatwin, P. C. & Sullivan, P. J., 1985 Effects of instrumentation and averaging on turbulent diffusion data. In Proc. 5th Symp. on Turbulent Shear Flows, Cornell Univ., Ithaca, NY, pp. 11.1–11.5.Google Scholar
Chatwin, P. C. & Sullivan, P. J., 1987a Perceived statistical properties of scalars in turbulent shear flows. In Proc. 6th Symp. on Turbulent Shear Flows, Toulouse, France, pp. 9.1.1–9.1.6.Google Scholar
Chatwin, P. C. & Sullivan, P. J., 1987b The probability density function for contaminant concentrations in some self-similar turbulent flows. In Proc. 2nd Intl Symp. on Transport Phenomena in Turbulent Flows, Tokyo, pp. 215–226.Google Scholar
Chatwin, P. C. & Sullivan, P. J., 1989a The intermittency factor of scalars in turbulence. Phys. Fluids A 1, 761–763.Google Scholar
Chatwin, P. C. & Sullivan, P. J., 1989b The intermittency factor of dispersing scalars in turbulent shear flows. Some applications of a new definition. In Proc. 7th Symp. on Turbulent Shear Flows, Stanford University, pp. 29.4.1–29.4.6.Google Scholar
Chevray, R. & Tutu, N. A., 1977 Conditional measurements in a heated turbulent jet. In Structure and Mechanisms in Turbulence II (ed. H. Fiedler), pp. 73–84. Springer.
Derksen, R. W. & Sullivan, P. J., 1987 Deriving contaminant concentration fluctuations from time averaged records. Atmos. Environ. 21, 789–798.Google Scholar
Derksen, R. W. & Sullivan, P. J., 1989 Moment approximations for probability density functions. Combust. Flame (submitted).Google Scholar
Dowling, D. R. & Dimotakis, P. E., 1988 On mixing and structure of the concentration field of turbulent jets. In Proc. AIAA/ASME/SIAM/APS 1st Natl Fluid Dyn. Cong., Cincinnati, Ohio. Part 2, pp. 982–988.Google Scholar
Drake, M. C., Shyy, W. & Pitz, R. W., 1985 Superlayer contributions to conserved scalar pdfs in a H2 turbulent jet diffusion flame. In Proc. 5th Symp. on Turbulent Shear Flows, Cornell Univ., Ithaca, NY, pp. 10.13–10.18.Google Scholar
Effelsberg, E. & Peters, N., 1983 A composite model for the conserved scalar PDF. Combust. Flame 50, 351–360.Google 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.Google Scholar
Gad-el-Hak, M. & Morton, J. B. 1979 Experiments on the diffusion of smoke in isotropic turbulent flow. AIAA J. 17, 558–562.Google Scholar
Kendall, M. G. & Stuart, A., 1977 The Advanced Theory of Statistics, Vol. 1. Distribution Theory (4th edn). London: Charles Griffin.
LaRue, J. C. & Libby, P. A., 1974 Temperature fluctuations in the plane turbulent wake. Phys. Fluids 17, 1956–1967.Google Scholar
LaRue, J. C. & Libby, P. A., 1981 Thermal mixing layer downstream of half-heated turbulence grid. Phys. Fluids 24, 597–603.Google Scholar
Mole, N.: 1989 Estimating statistics of concentration fluctuations from measurements. In Proc. 7th Symp. on Turbulent Shear Flows, Stanford University, pp. 29.5.1–29.5.6.Google Scholar
Mole, N.: 1990 A model of instrument smoothing and thresholding in measurements of turbulent dispersion. Atmos. Environ. (to appear).Google Scholar
Mole, N. & Chatwin, P. C., 1987 Assessing and modelling variability in dispersing vapour clouds. In Proc. Intl Conf. on Vapor Cloud Modeling, Cambridge, Mass (ed. J. L. Woodward), pp. 779–800. AIChE.
Nakamura, I., Sakai, Y. & Miyata, M., 1987 Diffusion of matter by a non-buoyant plume in grid-generated turbulence. J. Fluid Mech. 178, 379–403.Google Scholar
Pitts, W. M. & Kashiwagi, T., 1984 The application of laser-induced Rayleigh light scattering to the study of turbulent mixing. J. Fluid Mech. 141, 391–429.Google Scholar
Sakai, Y., Nakamura, I., Tsunoda, H. & Shengian, L., 1989 On the influence of disturbances generated by obstacles on point source plume diffusion in grid turbulence. Characteristics of concentration fluctuations and conditional statistics. Manuscript in preparation. (Material presented at Euromech 253, Brunel University, 30 August-1 September 1989).Google Scholar
Shaughnessy, E. J. & Morton, J. B., 1977 Laser light-scattering measurements of particle concentration in a turbulent jet. J. Fluid Mech. 80, 129–148.Google Scholar
Sreenivasan, K. R.: 1981 Evolution of the centerline probability density function of temperature in a plane turbulent wake. Phys. Fluids 24, 1232–1234.Google Scholar
Sreenivasan, K. R., Danh, H. Q. & Antonia, R. A., 1976 Diffusion from a heated wall-cylinder immersed in a turbulent boundary layer. In Proc. Thermofluids Conf., Hobart, Inst. of Engineers, Australia, pp. 103–106.Google Scholar
Sullivan, P. J.: 1984 Whence the fluctuations in measured values of mean-square fluctuations? In Proc. 4th Joint Conf. on Applications of Air Pollution Meteorology, Portland. Oregon (ed. G. A. Beals and N. E. Browne), pp. 115–121. American Meteorological Society, Boston.
Wilson, D. J., Robins, A. G. & Fackrell, J. E., 1982 Predicting the spatial distribution of concentration fluctuations from a ground level source. Atmos. Environ. 16, 497–504.Google Scholar