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Diffusion of matter by a non-buoyant plume in grid-generated turbulence

Published online by Cambridge University Press:  21 April 2006

Ikuo Nakamura ,
Yasuhiko Sakai  and
Masafumi Miyata
Ikuo Nakamura
Affiliation:
Department of Mechanical Engineering, 1, Nagoya 464, Japan
Yasuhiko Sakai
Affiliation:
The College of General Education, Nagoya University, Nagoya 464, Japan
Masafumi Miyata
Affiliation:
Department of Mechanical Engineering, Yamanashi University, Kofu 400, Japan
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Abstract

The turbulent diffusion process is investigated for a continuous point source of a non-buoyant plume in grid-generated water turbulence. Two kinds of biplanar grids with a mesh length of 10 mm and 20 mm were used. The mesh Reynolds numbers were 1480 and 2970, respectively. The mean and fluctuating concentration fields of aqueous dye solution were measured by the light absorption method. Experimental results for both grids were compared.

For both grids, the mean concentration radial profiles proved to have a similar Gaussian shape, and the mean concentration on the plume axis obeys the hyperbolic decay law well. These mean concentration profiles and their decay show an excellent agreement with the results deduced from the similarity analysis for the mean concentration field.

Radial profiles of the fluctuation r.m.s. value and relative intensity (i.e. the ratio of the r.m.s. value to the mean concentration) were found also to be nearly similar, and the centreline r.m.s. value decays downstream as a hyperbola. The relative intensity on the centreline tends to increase slightly downstream. All experimental results obtained were much less scattered and more reliable than those reported earlier.

The similarity for the concentration fluctuation intensity has been analysed using a thin-layer approximation. Also, an approximate analysis of the fluctuating concentration field is given by replacing the fluctuating concentration signal by a randomly spaced sequence of rectangular waves with various heights and widths.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 379 - 403
Copyright
© 1987 Cambridge University Press

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References

Anand, M. S. & Pope, S. B. 1983 Diffusion behind a line source in grid turbulence. In Proc. 4th Symp. on Turbulent Shear Flows, Karlsrule Germany, pp. 46–61. Springer.
Baldwin, L. V. & Mickelsen, W. R. 1962 Turbulent diffusion and anemometer measurements. Proc. Am. Soc. Civ. Engrs 88, 37–69.Google Scholar
Batchelor, G. K. 1949 Diffusion in a field of homogeneous turbulence. Austral. J. Sci. Res. 2, 437–450.Google Scholar
Batchelor, G. K. 1952 Diffusion in a field of homogeneous turbulence, the relative motion of particles. Proc. Camb. Phil. Soc. 48, 345–362.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1948 Decay of isotropic turbulence in the initial period. Proc. R. Soc. Lond. A 193, 539–558.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1956 Turbulent diffusion. In Surveys in Mechanics, pp. 352–399. Cambridge University Press.
Becker, H. A., Rosensweig, R. E. & Gwozdz, J. R. 1966 Turbulent dispersion in a pipe flow. AIChE J. 12, 964–972.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
Belorgey, M., Nguyen, A. D. & Trinite, M. 1979 Diffusion from a line source in a turbulent boundary layer with transfer to the wall. In Proc. 2nd Symp. on Turbulent Shear Flows, Imperial College, London, pp. 129–142. Springer.
Britter, R. E., Hunt, J. C. R., Marsh, G. L. & Snyder, W. H. 1983 The effects of stable stratification on turbulent diffusion and the decay of grid turbulence. J. Fluid Mech. 127, 27–44.Google Scholar
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids, p. 266. Oxford University Press.
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25, 657–682.Google Scholar
Crum, G. F. & Hanratty, T. J. 1965 Dissipation of a sheet of heated air in a turbulent flow. Appl. Sci. Res. A 15, 177–195.Google Scholar
Csanady, G. T. 1966 Dispersal of foreign matter by the currents and eddies of the Great Lakes. Pub. No. 15 Great Lakes Res. Div. Univ. Michigan (Proc. 9th Conf. on Great Lakes Res.), pp. 283–294.
Csanady, G. T. 1967 Concentration fluctuation in turbulent diffusion. J. Atmos. Sci. 24, 21–28.Google Scholar
Csanady, G. T. 1980 Turbulent Diffusion in the Environment, pp. 222–248. D. Reidel.
Csanady, G. T., Hilst, G. R. & Bowne, N. E. 1968 Turbulent diffusion from a cross-wind line source in shear flow at Fort Wayne, Indiana. Atmos. Environ. 2, 273–292.Google Scholar
Durbin, P. A. 1980 A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech. 100, 279–302.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
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Kalinske, A. A. & Pien, C. L. 1944 Eddy diffusion. Ind. Engng Chem. (Intl Edn), 36, 220–223.Google Scholar
Kampe De Feriet, J. 1938 Some recent researches on turbulence. In Proc. 5th Intern. Cngr. Appl. Mech. Cambridge, Mass., pp. 352–355.
Lamb, R. G. 1981 A scheme for similating particle pair motions in turbulent fluid. J. Comp. Phys. 39, 329–346.Google Scholar
Lee, J. & Brodkey, R. S. 1963 Light probe for the measurement of turbulent concentration fluctuations. Rev. Sci. Instrum. 34, 1086–1090.Google Scholar
Lee, J. L. & Brodkey, R. S. 1964 Turbulent motion and mixing in a pipe. AIChE. J. 10, 187–193.Google Scholar
Lundgren, R. S. 1981 Turbulent pair dispersion and scalar diffusion. J. Fluid Mech. 111, 27–57.Google Scholar
Maccarter, R. J., Stutzman, L. F. & Koch, H. A. 1949 Temperature gradients and eddy diffusivities in turbulent fluid flow. Ind. Engng Chem. 41, 1290–1295.Google Scholar
Mickelsen, W. R. 1960 Measurements of the effect of molecular diffusivity in turbulent diffusion. J. Fluid Mech. 1, 397–400.Google Scholar
Murthy, C. R. & Csanady, G. T. 1971 Experimental studies of relative diffusion in Lake Huron. J. Phys. Oceanogr. 1, 17–24.Google Scholar
Nakamura, I., Miyata, M. & Sakai, Y. 1983 On a method of the concentration measurement by the use of light absorption law. Bull. JSME 26, 1357–1365.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, Characteristics of the mean concentration field). Bull. JSME 29, 1141–1148.Google Scholar
Nye, J. O. & Brodkey, R. S. 1967a The scalar spectrum in the viscous-convective subrange. J. Fluid Mech. 29, 151–163.Google Scholar
Nye, J. O. & Brodkey, R. S. 1967b Light probe for measurements of turbulent concentration fluctuations. Rev. Sci. Instrum. 38, 26–28.Google Scholar
Ramsdell, J. W. & Hinds, W. T. 1971 Concentration fluctuations and peak to mean concentration ratios in plumes from a ground-level continuous point source. Atmos. Environ. 5, 483–495.Google Scholar
Sakai, Y. 1984 Experimental study on the turbulent diffusion of matter by light-absorption method. Ph.D. thesis, Nagoya University (in Japanese).
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.Google Scholar
Sawford, B. L. 1983 The effect of Gaussian particle-pair distribution fluctuations in the statistical theory of concentration fluctuations in homogeneous turbulence. Q. J. R. Met. Soc. 109, 339–354.Google Scholar
Sreenivasan, K. R., Tavoularis, S., Herry, R. & Corrsin, S. 1980 Temperature fluctuations and scales in grid-generated turbulence. J. Fluid Mech. 100, 597–621.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.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–212.Google Scholar
Tennekes, H. & Lumley, J. L. 1979 A First Course in Turbulence. MIT Press.
Towle, W. L. & Sherwood, T. K. 1939 Eddy diffusion, mass transfer in the central portion of a turbulent air stream. Ind. Engng Chem. 31, 457–462.Google Scholar
Towle, W. L., Sherwood, T. K. & Seder, L. A. 1939 Effect of a screen grid on the turbulence of an air stream. Ind. Engng Chem. 31, 462–463.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. No. 1142.Google Scholar
Warhaft, Z. 1984 The interference of thermal fields from line sources in grid turbulence. J. Fluid Mech. 144, 363–387.Google Scholar
Yamamoto, K. & Sato, Y. 1979 Measurements of Lagrangian behaviors of turbulent fluid. Study of Fundamental Engineering for Materials in Yokohama National University, no. 14, pp. 25–36 (in Japanese).
Yeh, T. T. & Van Atta, C. W. 1973 Special transfer of scalar and velocity fields in heated-grid turbulence. J. Fluid Mech. 58, 233–261.Google Scholar