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Diffusion mixing in grid turbulence without mean shear

Published online by Cambridge University Press:  19 April 2006

Barry Gilbert
Barry Gilbert
Affiliation:
Research Department, Grumman Aerospace Corporation, Bethpage, New York 11714
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Abstract

An experimental examination of the fundamental properties of free turbulent interactions in a mixing flow has been conducted. A turbulent, two-dimensional, incompressible, uniform-density mixing layer was produced by using a parallel bar grid of different bar spacings but the same space to bar diameter ratio M/D = 2. In this unique mixing-flow geometry, two initially parallel flowing streams of air were formed in such a way as to possess the same mean structure but different turbulent kinetic energy. The mixing phenomenon was driven solely by the turbulent kinetic-energy self-diffusion process.

The data showed the development of the turbulent properties without the interference caused by turbulence generated by a mean shear flow. A simple diffusion model was constructed by assuming an analogy between the unsteady gradient diffusion process and the transport of turbulent kinetic energy by the fluctuations. An empirical error function least squares curve fit, a diffusional power law and diffusion coefficients were derived. The empirical coefficients of self-diffusion were found to be 10.4 and 68.6 cm2 s−1 for the longitudinal and transverse turbulent energy components, or about a hundred and five hundred times faster than molecular viscous shear diffusion, respectively. This self-diffusion mechanism by microscale size eddies may account for some of the error found by other investigators in balancing the measured terms of the turbulent kinetic-energy equation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 100 , Issue 2 , 25 September 1980 , pp. 349 - 365
Copyright
© 1980 Cambridge University Press

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References

Baker, R. L., Tao, L. N. & Weinstein, H. 1970 The mixing of two parallel streams of dissimilar fluids. Part I. Analytical development. A.S.M.E. Paper, no. 70-WA/APM-37.Google Scholar
Bendat, J. S. & Piersol, A. G. 1971 Random Data: Analysis and Measurement Procedures. Wiley.
Blackman, R. B. & Tukey, J. W. 1959 The Measurement of Power Spectra from the Point of View of Communications Engineering. Dover.
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 51, 81.Google Scholar
Corrsin, S. 1963 Turbulence: experimental methods. In Handbook der Physiks, vol. 8, part 2. Springer.
Gentleman, W. M. & Sande, G. 1966 Fast Fourier Transforms for Fun and Profit. AFIPS Proc. 1966 Fall Joint Computer Conf. Washington, D.C. 29, p. 563.
Gilbert, B. L. 1975 An experimental investigation of turbulent mixing of fluids with different dynamically significant scales. Ph.D. thesis, Dept. of Energy Engng, University of Illinois, Chicago.
Gilbert, B. L. & Komar, J. J. 1977 Turbulent mixing of fluids with different dynamic scales. Proc. 5th Biennial Symp. on Turbulence, Rolla, Mo.
Hong, Z. C. 1975 Turbulent chemically reacting flows according to a kinetic theory, Ph.D. thesis, Dept. of Energy Engng, University of Illinois, Chicago.
Liepmann, H. W. & Laufer, J. 1949 Investigation of free turbulent mixing. N.A.C.A. Tech. Note 1257.Google Scholar
Patankar, S. V. & Spalding, D. B. 1970 Heat and Mass Transfer in Boundary Layers, 2nd edn. London: Intertet.
Rose, W. G. 1966 Results of an attempt to generate a homogeneous turbulent shear flow. J. Fluid Mech. 25, 97.Google Scholar
Sande, G. 1965 On an alternative method for calculating covariance functions. Princeton Computer Memo. Princeton, New Jersey.
Skelland, A. H. P. 1974 Diffusional Mass Transfer. Wiley.
Spalding, D. B. 1969 The calculation of the length scale of turbulence in some shear flows remote from walls. Prog. Heat Mass Transfer 2, 255.Google Scholar
Spencer, B. & Jones, B. G. 1971 Statistical investigation of pressure and velocity fields in the turbulent two-stream mixing layer. A.I.A.A. Paper 71–613.Google Scholar
Van Atta, C. W. & Chen, W. Y. 1968 Correlation measurements in grid turbulence using digital harmonic analysis. J. Fluid Mech. 34, 497.Google Scholar
Van Atta, C. W. & Chen, W. Y. 1969 Measurement of spectral energy transfer in grid turbulence. J. Fluid Mech. 38, 743.Google Scholar
Wygnanski, I. & Fiedler, H. 1970 The two-dimensional mixing region. J. Fluid Mech. 41, 327.Google Scholar