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The use of a contraction to improve the isotropy of grid-generated turbulence

Published online by Cambridge University Press:  28 March 2006

Geneviéve Comte-Bellot
Affiliation:
Mechanics Department, The Johns Hopkins University
Stanley Corrsin
Affiliation:
Mechanics Department, The Johns Hopkins University

Abstract

It is found that when the average kinetic energies of normal velocity components in decaying, grid-generated turbulence are equilibrated by a symmetric contraction of the wind tunnel, this equality can persist downstream. A second result is further confirmation of the fact that the best power-law fit to the inverse turbulent energy during the early part of decay is near (x–x1)1·25, for both rod grids and disk grids. The Kolmogorov decay law $\sim (t - t_1)^{\frac{10}{7}}$ is re-derived by a spectral method which is essentially equivalent to the original. Finally, a crude theoretical estimate of component energies in the straight duct after a weak contraction seems to support the experiments.

Type
Research Article
Copyright
© 1966 Cambridge University Press

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References

Baines, W. D. & Peterson, E. G. 1951 An investigation of flow through screens. Trans. Amer. Soc. Mech. Engr. 73, 467.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. & Proudman, I. 1954 The effect of rapid distortion of a fluid in turbulence motion. Quart. J. Mech. Appl. Math. 7, 83.Google Scholar
Batchelor, G. K. & Proudman, I. 1956 The large-scale structure of homogeneous turbulence. Phil. Trans., A 248, 396.Google Scholar
Batchelor, G. K. & Stewart, R. W. 1950 Anisotropy of the spectrum of turbulence at small wave-numbers. Quart. J. Mech. Appl. Math. 3, 1.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1947 Decay of vorticity in isotropic turbulence. Proc. Roy. Soc., A 190, 534.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1948 Decay of isotropic turbulence in the initial period. Proc. Roy. Soc., A 193, 539.Google Scholar
Comte-Bellot, G. & Mathieu, J. 1958 Sur la détermination expérimentale des coefficients de sensibilité aux fluctuations de vitesse et de température des anémomètres à fil chaud. C.R. Acad. Sci., Paris, 246, 3219.Google Scholar
Comte-Bellot, G. 1960 Valeurs efficaces, coefficients de dissymetrie et d'aplatissement des fluctuations transversales de vitesse dans un tunnel bidimensionnel à parois parallèles. C.R. Acad. Sci., Paris, 251, 2656.Google Scholar
Corrsin, S. 1942 Decay of turbulence behind three similar grids. Aero Eng. Thesis, California Institute of Technology.
Corrsin, S. 1957 Some current problems in turbulent shear flows. Symposium on Naval Hydrodynamics, chap. 15. Publ. 515 of Nat. Acad. Sci.-Nat. Res. Council, Washington.Google Scholar
Corrsin, S. 1958 Local isotropy in turbulent shear flow. NACA R & M 58B11.Google Scholar
Corrsin, S. 1959 Outline of some topics in homogeneous turbulent flow. J. Geophys. Res. 64, 2134.Google Scholar
Corrsin, S. 1963a Turbulence: experimental methods. Handbuch der Physik, vol. VIII/2, (eds. S. Flugge and C. A. Truesdell). Berlin: Springer.
Corrsin, S. 1963b Estimates of the relations between Eulerian and Lagrangian scales in large Reynolds number turbulence, J. Atmos. Sci. 20, 11.Google Scholar
Corrsin, S. 1964 The isotropic turbulence mixer: Part II. Amer. Inst. Chem. Engr. J. 10, 870.Google Scholar
Deissler, R. G. 1960 A theory of decaying homogeneous turbulence. Phys. Fluids, 3, 176.Google Scholar
Dryden, H. L. 1943 A review of the statistical theory of turbulence. Quart. Appl. Math. 1, 7.Google Scholar
Dryden, H. L., Schubauer, G. B., Mock, W. C. & Skramstad, H. K. 1937 Measurements of the intensity and scale of wind tunnel turbulence and their relation to the critical Reynolds number of spheres. NACA Rep. no. 581.Google Scholar
Dumas, R. 1964 Contribution a l’étude des spectres de turbulence. Pub. Sci. Tech. Min. de l'Air, Paris, no. 404.Google Scholar
Gibson, M. M. 1963 Spectra of turbulence in a round jet. J. Fluid Mech. 15, 161.Google Scholar
Goldstein, S. 1951 On the law of decay of homogeneous isotropic turbulence and the theories of the equilibrium and similarity spectra. Proc. Camb. Phil. Soc. 47, 554.Google Scholar
Grant, H. L. & Nisbet, I. C. T. 1957 The inhomogeneity of grid turbulence. J. Fluid Mech. 2, 263.Google Scholar
Grant, H. L., Stewart, R. W. & Moilliet, A. 1962 Turbulence spectra from a tidal channel. J. Fluid. Mech. 12, 241.Google Scholar
Von Kármán, T. & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. Roy. Soc., A 164, 192.Google Scholar
Kistler, A. L. & Vrebalovich, T. 1961 Turbulence measurements at the 8 by 10-foot Cooperative Wind Tunnel. Jet Prop. Lab. Res. Summary, no. 36–4, 12 (also private communication).Google Scholar
Kolmogorov, A. N. 1941a The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C.R. Akad. Sci. SSSR (Dok.), 30, 301.Google Scholar
Kolmogorov, A. N. 1941b On degeneration of isotropic turbulence in an incompressible viscous liquid. C.R. Akad. Sci. SSSR (Dokl.), 31, 538.Google Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497.Google Scholar
Kraichnan, R. H. 1963 Direct-interaction approximation for a system of several interacting simple shear waves. Phys. Fluids, 6, 1603.Google Scholar
Lin, C. C. 1947 Remarks on the spectrum of turbulence. Proc. 1st Symp. Appl. Math. New York: McGraw-Hill.
Lin, C. C. 1948 Note on the law of decay of isotropic turbulence. Proc. Nat. Acad. Sci. 34, 540.Google Scholar
Loitsianskii, L. G. 1939 Some basic laws of isotropic turbulent flow. Cent. Aero. Hydro. Inst., Moscow, Rep. no. 440. (Translation in NACA TM no. 1079.)Google Scholar
Macphail, D. C. 1940 An experimental verification of the isotropy of turbulence produced by a grid. J. Aero Sci. 8, 73.Google Scholar
Mills, R. R. & Corrsin, S. 1959 Effect of contraction on turbulence and temperature fluctuations generated by a warm grid. NASA Memo 5–5–59W.Google Scholar
Mills, R. R., Kistler, A. L., O'Brien, V. & Corrsin, S. 1958 Turbulence and temperature fluctuations behind a heated grid. NACA TN no. 4288.Google Scholar
Onsager, L. 1949 Statistical hydrodynamics. Nuovo Cim. 6, 279.Google Scholar
Prandtl, L. 1932 Herstellung einwandfreier Luftströme (Windkanale). Handbuch der Exp. Physik, Leipzig. (Translated inNACA TM no. 726.)Google Scholar
Proudman, I. & Reid, W. H. 1954 On the decay of a normally distributed and homogeneous turbulent velocity field. Phil. Trans., A 247, 163.Google Scholar
Ribner, H. S. & Tucker, M. 1953 Spectrum of turbulence in a contracting stream. NACA Rep. no. 1113. (Originally NACA TN no. 2606.)Google Scholar
Simmons, L. F. G. & Salter, C. 1934 Experimental investigation and analysis of the velocity variations in turbulent flow. Proc. Roy. Soc., A 145, 212.Google Scholar
Taylor, G. I. 1935a Turbulence in a contracting stream. Z. Angew. Math. Mech. 15, 91.Google Scholar
Taylor, G. I. 1935b Statistical theory of turbulence, parts I and II. Proc. Roy. Soc., A 151, 421.Google Scholar
Townsend, A. A. 1954 The uniform distortion of homogeneous turbulence. Quart. J. Mech. Appl. 7, 104.Google Scholar
Tsuji, H. & Hama, F. R. 1953 Experiment on the decay of turbulence behind two grids. J. Aero. Sci. 20, 848.Google Scholar
Uberoi, M. S. 1956 The effect of wind tunnel contraction on free stream turbulence. J. Aero. Sci. 23, 754.Google Scholar
Uberoi, M. S. 1957 Equipartition of energy and local isotropy in turbulent flows. J. Appl. Phys. 28, 1165.Google Scholar
Uberoi, M. S. 1963 Energy transfer in isotropic turbulence. Phys. Fluids, 6, 1048.Google Scholar
Uberoi, M. S. 1965 Effect of grid geometry on turbulence decay (abstract). Bull. Am. Phys. Soc. 10, 265.Google Scholar
Uberoi, M. S. & Corrsin, S. 1953 Diffusion of heat from a line source in isotropic turbulence. NACA Rep. no. 1142. (See also NACA TN no. 2710.)Google Scholar
Uberoi, M. S. & Wallis, S. 1964 Realization of isotropic turbulence (abstract), Bull. Amer. Phys. Soc. 9, 58.Google Scholar
Uberoi, M. S. & Wallis, S. 1966 Small axisymmetric contraction of grid turbulence. J. Fluid Mech. 24, 539.Google Scholar
Wyatt, L. A. 1955 Energy and spectra in decaying homogeneous turbulence. Ph.D. Thesis, University of Manchester.