Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-15T03:45:04.606Z Has data issue: false hasContentIssue false
  • English
  • Français

Temperature fluctuations and scales in grid-generated turbulence

Published online by Cambridge University Press:  19 April 2006

K. R. Sreenivasan ,
S. Tavoularis ,
R. Henry  and
S. Corrsin
K. R. Sreenivasan
Affiliation:
Department of Mechanics and Materials Science, Johns Hopkins University, Baltimore, Maryland 21218
S. Tavoularis
Affiliation:
Department of Mechanics and Materials Science, Johns Hopkins University, Baltimore, Maryland 21218
R. Henry
Affiliation:
Department of Mechanics and Materials Science, Johns Hopkins University, Baltimore, Maryland 21218
S. Corrsin
Affiliation:
Department of Mechanics and Materials Science, Johns Hopkins University, Baltimore, Maryland 21218
Get access Rights & Permissions [Opens in a new window]

Abstract

To study the mixing of a passive scalar in nearly isotropic turbulence, experiments have been made in isotropically mixed thermal fields with thermal mesh size Mθ (a) equal to the momentum mesh size M, (b) larger than M (obtained by heating only alternate rods of the turbulence generating grid), and (c) smaller than M. This last condition was achieved by inserting a fine heating screen with Mθ < M, at locations downstream of the turbulence grid. The heating screen was designed to produce negligible statistical change in the velocity field a short distance downstream. In all the heated grid experiments, for a given initial configuration of the thermal field, the intensity of temperature fluctuations θ normalized by the mean temperature rise ΔT, and the decay rate of $\overline{\theta^2} $ were both independent of the temperature of the grid. The principal effect of having Mθ > M was an increase in the relative intensity of temperature fluctuations compared with the Mθ = M case, and a marginal increase in their decay rate; contrary to expectation, the ratio R of temperature to velocity integral scales in the region of approximate homogeneity did not differ from that corresponding to Mθ = M. In heated screen experiments, the relative decay rate was independent of Mθ/M and ΔT. For the three locations of the heating screen used in these experiments, the decay rate was also independent of the relative distance xs of the heating screen from the turbulence generating grid; however, larger xs was associated with larger relative intensity of fluctuations. To a first approximation, the ratio R approached unity according to the empirical relation R = 1 − A exp [− αxθ/(UT0)], where xθ is downstream distance measured from the heating screen, and T0 is a characteristic turbulence decay time scale at x0 = 0. It was also verified that the skewness of the streamwise temperature derivative is approximately zero sufficiently downstream of the heating screen. Where the present study overlaps with previous measurements, an extensive comparison reveals several points of agreement as well as departure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 100 , Issue 3 , 16 October 1980 , pp. 597 - 621
Copyright
© 1980 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., Chambers, A. J., Van Atta, C. W., Friehe, C. A. & Helland, K. N. 1978 Skewness of temperature derivative in a heated grid flow. Phys. Fluids 21, 509.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Comte-Bellot, G. & Corrsin, S. 1971 Simple Eulerian time correlation of full- and narrow-band velocity signals in grid-generated ‘isotropic’ turbulence. J. Fluid Mech. 48, 273.Google Scholar
Corrsin, S. 1951a The decay of isotropic temperature fluctuations in an isotropic turbulence. J. Aero. Sci. 18, 417.Google Scholar
Corrsin, S. 1951b On the spectrum of isotropic temperature fluctuations in isotropic turbulence. J. Appl. Phys. 22, 469.Google Scholar
Corrsin, S. 1963 Turbulent flow, experimental methods. Handbuch der Physik, vol. 8, part 2. (ed. S. Flugge & C. Truesdell), p. 524. Springer.
Corrsin, S. 1964 The isotropic turbulent mixer. II. Arbitrary Schmidt number. A.I.Ch.E. J. 10, 870.Google Scholar
Corrsin, S. & Karweit, M. J. 1972 A note on the angular dispersion of a fluid line element in isotropic turbulence. J. Fluid Mech. 55, 289.Google Scholar
Dryden, H. L. & Schubauer, G. B. 1947 The use of damping screens for the reduction of wind tunnel turbulence. J. Aero. Sci. 14, 221.Google Scholar
Gibson, C. H. & Schwarz, W. H. 1963 The universal equilibrium spectra of turbulent velocity and scalar fields. J. Fluid Mech. 16, 365.Google Scholar
Kármán, T. von & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. Roy. Soc. A 164, 192.Google Scholar
Kellogg, R. M. 1965 Evolution of a spectrally local disturbance in a grid-generated turbulent flow. Ph.D. thesis, The Johns Hopkins University.
Kellogg, R. M. & Corrsin, S. 1979 Evolution of a spectrally local disturbance in grid-generated, nearly-isotropic turbulence. J. Fluid Mech. 96, 641.Google Scholar
Kistler, A. L., O'Brien, V. & Corrsin, S. 1954 Preliminary measurements of turbulence and temperature fluctuations behind a heated grid. N.A.C.A. RM 54D19.Google Scholar
Kistler, A. L., O'Brien, V. & Corrsin, S. 1956 Double and triple correlations behind a heated grid. J. Aero. Sci. 23, 96.Google Scholar
Kovasznay, L. S. G. 1949 Hot-wire investigation of the wake behind cylinders at low Reynolds numbers. Proc. Roy. Soc. A 198, 174.Google Scholar
Lin, S. C. & Lin, S. C. 1973 Study of strong temperature mixing in subsonic grid turbulence. Phys. Fluids 16, 1587.Google Scholar
Mills, R. R., Kistler, A. L., O'brien, V. & Corrsin, S. 1958 Turbulence and temperature fluctuations behind a heated grid. N.A.C.A. Tech. Note 4288.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. Massachusetts Institute of Technology Press.
Newman, G. R., Warhaft, Z. & Lumley, J. L. 1977 The decay of temperature fluctuations in isotropic turbulence. Proc. 6th Australasian Hydraulics & Fluid Mech. Conf., Adelaide.
Oboukhov, A. M. 1949 Structure of the temperature field in turbulent flow. Izv. Akad. Nauk. S.S.S.R., Ser. Geogr. i Geofiz. 13, 58.Google Scholar
Saffman, P. G. 1967 Note on decay of homogeneous turbulence. Phys. Fluids 10, 1349.Google Scholar
Sepri, P. 1976 Two-point turbulence measurements downstream of a heated grid. Phys. Fluids 19, 1876.Google Scholar
Sreenivasan, K. R. & Antonia, R. A. 1977 Skewness of temperature derivatives in turbulent shear flows. Phys. Fluids 20, 1986.Google Scholar
Sreenivasan, K. R. & Tavoularis, S. 1980 On the skewness of the temperature derivative in turbulent flows. J. Fluid Mech. (to appear).Google Scholar
Tavoularis, S. 1978a A circuit for the measurement of instantaneous temperature in heated turbulent flows. J. Phys. E, Sci. Instrum. 11, 21.Google Scholar
Tavoularis, S. 1978b Experiments in turbulent transport and mixing. Ph.D. thesis, The Johns Hopkins University.
Townsend, A. A. 1951 The passage of turbulence through wire gauzes. Quart. J. Mech. Appl. Math. 4, 308.Google Scholar
Warhaft, Z. & Lumley, J. L. 1978a The decay of temperature fluctuations and heat flux in grid generated turbulence. In Structure and Mechanisms of Turbulence, vol. 2. Lectures notes in physics, vol. 76. Springer.
Warhaft, Z. & Lumley, J. L. 1978b An experimental study of the decay of temperature fluctuations in grid generated turbulence. J. Fluid Mech. 88, 659.Google Scholar
Yeh, T. T. & Van Atta, C. W. 1973 Spectral transfer of scalar and velocity fields in heated-grid turbulence. J. Fluid Mech. 58, 233.Google Scholar