Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-20T04:05:56.196Z Has data issue: false hasContentIssue false
  • English
  • Français

The decay power law in grid-generated turbulence

Published online by Cambridge University Press:  26 April 2006

Mohsen S. Mohamed  and
John C. Larue
Mohsen S. Mohamed
Affiliation:
Department of Mechanical Engineering, University of California, Irvine, CA 92717, USA Present address: The Department of Mechanical Engineering, Faculty of Engineering, Cairo University, Cairo, Egypt.
John C. Larue
Affiliation:
Department of Mechanical Engineering, University of California, Irvine, CA 92717, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of initial conditions on the decay exponent and coefficient and virtual origin in the decay power-law form for the variation of the variance of the turbulent velocity downstream of biplane grids constructed of rods of both round and square cross-section is determined. This effect is determined for data obtained as part of the present study as well as from previous studies. These studies cover a Reynolds number range from 6000 to 68000, mesh sizes of 2.54 and 5.08 cm, and solidities of 0.34 and 0.44.

It is shown that the choice of the virtual origin and the use of data in the non-homogeneous portion of the flow can have a significant influence on the value of the parameters in the decay power-law. Criteria are developed to identify the nearly homogeneous and isotropic portion of the flow. These criteria include low values of the velocity skewness, constancy of the skewness of the velocity derivative and balance of the turbulent kinetic energy equation.

Results based on data selected by means of these criteria show that the decay exponent and virtual origin are independent of initial conditions such as Reynolds number, mesh size, solidity, and rod shape and surface roughness with values of respectively 1.30 and 0. In contrast and as expected, the decay coefficient is found to be a function of these initial conditions. Thus, the downstream variation of the variance of the turbulent velocity is universally self-similar.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 219 , October 1990 , pp. 195 - 214
Copyright
© 1990 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

Baines, W. D. & Peterson, E. G., 1951 Trans. ASME 73, 467.
Batchelor, G. K. & Townsend, A. A., 1947 Proc. R. Soc. Lond. A 191, 534.
Batchelor, G. K. & Townsend, A. A., 1948 Proc. R. Soc. Lond. A 193, 539.
Batchelor, G. K.: 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Bennett, J. C. & Corrsin, S., 1978 Phys. Fluids 21, 2129.
Comte-Bellot, G. & Corrsin, S. 1966 J. Fluid Mech. 25, 657.
Comte-Bellot, G. & Corrsin, S. 1971 J. Fluid Mech. 48, 273.
Corrsin, S.: 1963 Encyclopedia of Physics, vol. 8, part 2, p. 568. Springer.
Frenkiel, F. & Klebanoff, P. S., 1971 J. Fluid Mech. 48, 183.
George, W. K.: 1988 The decay of homogeneous turbulence. In Transport Phenomena in Turbulent Flows (ed. M. Hirata & N. Kasagi), p. 1. Hemisphere.
Grant, H. L. & Nisbet, I. C., 1957 J. Fluid Mech. 2, 263.
Helland, K. N. & Stegen, G. R., 1970 Phys. Fluids 13, 2925.
Hinze, J. O.: 1959 Turbulence. McGraw-Hill.
Von Kármán, T. & Howarth, L. 1938 Proc. R. Soc. Lond. A 164, 192.
Kolmogorov, A. N.: 1941 Dokl. Akad. Nauk. SSSR 31, 538.
Mccomb, W. D., Shanmugasundaram, V. & Hutchinson, P., 1990 J. Fluid Mech. 208, 91.
Maxey, M. R.: 1987 Phys. Fluids 30, 935.
Monin, A. S. & Yaglom, A. M., 1975 Statistical Fluid Mechanics, vol. 2 (ed. J. L. Lumley), p. 113. MIT Press.
Portfors, E. A. & Keffer, J. F., 1969 Phys. Fluids 12, 1519.
Saffman, P. G.: 1967 J. Fluid Mech. 27, 581.
Sirivat, A. & Warhaft, Z., 1983 J. Fluid Mech. 128, 323.
Sreenivasan, K., Tavoularis, S. & Corrsin, S., 1980 J. Fluid Mech. 100, 597.
Stewart, R. W. & Townsend, A. A., 1951 Phil. Trans. R. Soc. Lond. A 243, 141.
Stewart, R. W. & Townsend, A. A., 1951 Phil. Trans. R. Soc. Lond. A 243, 359.
Taylor, G. I.: 1935 Proc. R. Soc. Lond. A 151, 421.
Tennekes, H. & Lumley, J. L., 1989 A First Course in Turbulence, p. 72. MIT Press.
Uberoi, M. S.: 1963 Phys. Fluids 6, 1048.
Uberoi, M. S. & Wallis, S., 1967 Phys. Fluids 10, 1216.
Uberoi, M. S. & Wallis, S., 1969 Phys. Fluids 12, 1355.
Van Atta, C. W. & Chen, W. 1969 J. Fluid Mech. 38, 743.
Wyatt, L. A.: 1955 Energy and spectra in decaying homogeneous turbulence. PhD thesis, University of Manchester.