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Structure of the temperature field downwind of a line source in grid turbulence

Published online by Cambridge University Press:  21 April 2006

H. Stapountzis
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ Present address: University of Thessaloniki, Box 443, Greece 54006.
B. L. Sawford
Affiliation:
CSIRO, Division of Atmospheric Research, Private Bag No. 1, Mordialloc, Victoria, 3195, Australia
J. C. R. Hunt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW
R. E. Britter
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ

Abstract

A Lagrangian stochastic model is used in conjunction with detailed wind-tunnel measurements to examine the structure and development of the temperature field behind a line source in grid turbulence. It is shown that on the scale of these experiments molecular diffusion and viscosity have an important influence on temperature fluctuations (particularly on the intensity of these fluctuations) and must be explicitly modelled. The model accounts for a wide range of the measured properties of the temperature field and provides a unified treatment of temperature fluctuations through all stages of the development of the temperature field. This development is discussed in terms of a simple physical picture in which the hot plume is initially smooth and is moved about bodily by the turbulence, but gradually develops increasing internal structure or patchiness as it grows with distance downstream until a self-similar state is reached in which this internal structure maintains the temperature fluctuations.

Type
Research Article
Copyright
© 1986 Cambridge University Press

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References

Batchblor, G. K. 1982 Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Camb. Phil. Soc. 48, 345362.Google Scholar
Bray, K. N. C. 1980 Turbulent flows with premixed reactants. In Turbulent Reacting Flows ed. P. A. Libby & P. A. Williams Springer.
Corrsin, S. 1952 Heat transfer in isotropic turbulence. J. Appl. Phys. 23, 113118.Google Scholar
Csanady, G. T. 1973 Turbulent Diffusion in the Environment. Reidel.
Durbin, P. A. 1980 A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech. 100, 279302.Google Scholar
Durbin, P. A. 1982 Analysis of the decay of temperature fluctuations in isotropic turbulence. Phys. Fluids 25, 13281332.Google Scholar
Fackrell, J. R. & Robins, A. G. 1982 Concentration fluctuations and fluxes in plumes from point sources in a turbulent boundary layer. J. Fluid Mech. 117, 126.Google Scholar
Gifford, F. 1960 Peak to average concentration ratios according to a fluctuating plume dispersion model Intl. J. Air Poll. 3, 253260.Google Scholar
Hinze, J. O. 1975 Turbulence, 2nd edn. McGraw Hill.
Hunt, J. C. R. 1976 Air Pollution Dispersion. Film PT272/07 and Programme notes made with BBC for Open University Course on Environmental Control and Public Health.
Jones, C. D. 1982 On the structure of instantaneous plumes in the atmosphere. J. Hazardous Materials 7, 87112.Google Scholar
Lamb, R. G. 1981 A scheme for simulating particle-pair motions in turbulent fluid. J. Comput. Phys. 39, 329346.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics: Mechanics of Turbulence, volume 1. MIT Press.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics–.Mechanics of Turbulence, volume 2. MIT Press.
Pope, S. B. 1979 The statistical theory of turbulent flames. Phil Trans. R. Soc. Lond A291, 529568.Google Scholar
Saffman, P. G. 1960 On the effect of molecular diffusivity in turbulent diffusion. J. Fluid Mech. 8, 273283.Google Scholar
Sawford, B. L. 1983 The effect of Gaussian particle-pair distribution functions in the statistical theory of concentration fluctuations in homogeneous turbulence. Q. J. R. Met. Soc. 109, 339354.Google Scholar
Sawford, B. L. 1984 Reply to comments by Egbert and Baker on'The effect of Gaussian particle-pair distribution functions in the statistical theory of relative dispersion. Quart. J. Roy. Met. Soc. 109, 339354. Quart. J. Roy, Met. Soc. 110, 1199–1200.Google 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, 373400.Google Scholar
Schlichtling, H. 1968 Boundary Layer Theory, 6th Edn. Pergamon.
Snyder, W. H. & Lumley, J. L. 1971 Some measurements of particle velocity auto-correlation functions in a turbulent flow. J. Fluid Mech. 48, 4171.Google Scholar
Sreenivasan, K. R., Tavoularis, S., Henry, R. & Corrsin, S. 1980 Temperature fluctuations in grid-generated turbulence. J. Fluid Mech. 100, 597623.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196212.Google Scholar
Townsend, A. A. 1954 The diffusion behind a line source in homogeneous turbulence. Proc. R. Soc. Lond. A224, 487512.Google Scholar
Uberoi, M. S. & Corrsin, S. 1953 Diffusion of heat from a line source in isotropic turbulence. NAGA Rep. 1142.Google Scholar
Warhaft, Z. 1984 The interference of thermal fields from line sources in grid turbulence J. Fluid Mech. 144, 363387.Google Scholar
Warhaft, Z. & Lumley, J. L. 1978 An experimental study of the decay of temperature fluctuations in grid-generated turbulence. J. Fluid Mech. 88, 659684.Google Scholar
Wyngaard, J. C. 1971 Spatial resolution of a resistance wire temperature sensor. Phys. Fluids 14, 20522054.Google Scholar