Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T16:53:45.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Decay of turbulence generated by a square-fractal-element grid

Published online by Cambridge University Press:  17 February 2014

R. J. Hearst  and
P. Lavoie
R. J. Hearst
Affiliation:
Institute for Aerospace Studies, University of Toronto, Toronto, ON, Canada M3H 5T6
P. Lavoie*
Affiliation:
Institute for Aerospace Studies, University of Toronto, Toronto, ON, Canada M3H 5T6
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A novel square-fractal-element grid was designed in order to increase the downstream measurement range of fractal grid experiments relative to the largest element of the grid. The grid consists of a series of square fractal elements mounted to a background mesh with spacing $L_0 = 100\, {\rm mm}$. Measurements were performed in the region $3.5 \le x/L_0 \le 48.5$, which represents a significant extension to the $x/L_0 < 20$ of previously reported square fractal grid measurements. For the region $x/L_0 \gtrsim 24$ it was found that a power-law decay region following $\langle {q}^2 \rangle \sim (x - x_0)^m$ exists with decay exponents of $m = -1.39$ and $-1.37$ at $\mathit{Re}_{L_0} = 57\, 000$ and $65\, 000$, respectively. This agrees with decay values previously measured for regular grids ($-1 \gtrsim m \gtrsim -1.4$). The turbulence in the near-grid region, $x/L_0 < 20$, is shown to be inhomogeneous and anisotropic, in apparent contrast with previous fractal grid measurements. Nonetheless, power-law fits to the decay of turbulent kinetic energy in this region result in $m = -2.79$, similar to $m \approx -2.5$ recently reported by Valente & Vassilicos (J. Fluid Mech., vol. 687, 2011, pp. 300–340) for space-filling square fractals. It was also found that $C_\epsilon $ is approximately constant for $x/L_0 \ge 25$, while it grows rapidly for $x/L_0 < 20$. These results reconcile previous fractal-generated turbulence measurements with classical grid turbulence measurements.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 741 , 25 February 2014 , pp. 567 - 584
Copyright
© 2014 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. & Orlandi, P. 2004 Similarity of decaying isotropic turbulence with a passive scalar. J. Fluid Mech. 505, 123–151.CrossRefGoogle Scholar
Antonia, R. A., Smalley, R. J., Zhou, T., Anselmet, F. & Danaila, L. 2003 Similarity of energy structure functions in decaying homogeneous isotropic turbulence. J. Fluid Mech. 487, 245–269.Google Scholar
Antonia, R. A., Zhou, T. & Zhu, Y. 1998 Three-component vorticity measurements in a turbulent grid flow. J. Fluid Mech. 374, 29–57.CrossRefGoogle Scholar
Antonia, R. A., Zhu, Y. & Kim, J. 1994 Corrections for spatial velocity derivatives in a turbulent shear flow. Exp. Fluids 16, 411–413.CrossRefGoogle Scholar
Batchelor, G. K. 1948 Energy decay and self-preserving correlation functions in isotropic turbulence. Q. Appl. Maths 6, 97–116.CrossRefGoogle Scholar
Benedict, L. H. & Gould, R. D. 1996 Towards better uncertainty estimates for turbulence statistics. Exp. Fluids 22, 129–136.Google Scholar
Burattini, P. & Antonia, R. A. 2005 The effect of different X-wire calibration schemes on some turbulence statistics. Exp. Fluids 38, 80–89.Google Scholar
Burattini, P., Lavoie, P. & Antonia, R. A. 2005 On the normalized turbulent energy dissipation rate. Phys. Fluids 17, 098103.CrossRefGoogle Scholar
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25 (4), 657–682.Google Scholar
Corrsin, S. 1963 Turbulence: experimental methods. In Handbuch der Physik (ed. Flügge, S. & Truesdell, C. A.), pp. 524–590. Springer.Google Scholar
Elsner, J. W. & Elsner, W. 1996 On the measurement of turbulence energy dissipation. Meas. Sci. Technol. 7, 1334–1348.CrossRefGoogle Scholar
Ewing, D. & George, W. K. 2000 The effect of cross-flow velocity on mean-square derivatives measured using hot wires. Exp. Fluids 25 (5), 418–428.Google Scholar
George, W. K. 1992 The decay of homogeneous isotropic turbulence. Phys. Fluids 4 (7), 1492–1509.Google Scholar
George, W. K. & Hussein, H. J. 1991 Locally axisymmetric turbulence. J. Fluid Mech. 233, 1–23.Google Scholar
Gad-el Hak, M. & Corrsin, S. 1974 Measurements of the nearly isotropic turbulence behind a uniform jet grid. J. Fluid Mech. 62, 115–143.Google Scholar
Hearst, R. J., Buxton, O. R. H., Ganapathisubramani, B. & Lavoie, P. 2012 Experimental estimation of fluctuating velocity and scalar gradients in turbulence. Exp. Fluids 53, 925–942.CrossRefGoogle Scholar
Hultmark, M. & Smits, A. J. 2010 Temperature corrections for constant temperature and constant current hot-wire anemometers. Meas. Sci. Technol. 21, 105404.Google Scholar
Hurst, D. & Vassilicos, J. C. 2007 Scalings and decay of fractal-generated turbulence. Phys. Fluids 19, 035103.Google Scholar
Krogstad, P.-A. & Davidson, P. A. 2010 Is grid turbulence Saffman turbulence?. J. Fluid Mech. 642, 373–394.CrossRefGoogle Scholar
Krogstad, P.-A. & Davidson, P. A. 2011 Freely decaying, homogeneous turbulence generated by multi-scale grids. J. Fluid Mech. 680, 417–434.Google Scholar
Krogstad, P.-A. & Davidson, P. A. 2012 Near-field investigation of turbulence produced by multi-scale grids. Phys. Fluids 24, 035103.Google Scholar
Lavoie, P., Djenidi, L. & Antonia, R. A. 2007 Effects of initial conditions in decaying turbulence generated by passive grids. J. Fluid Mech. 585, 395–420.CrossRefGoogle Scholar
Mazellier, N. & Vassilicos, J. C. 2010 Turbulence without Richardson–Kolmogorov cascade. Phys. Fluids 22, 075101.CrossRefGoogle Scholar
Meyers, J. & Meneveau, C. 2008 A functional form for the energy spectrum parametrizing bottleneck and intermittency effects. Phys. Fluids 20, 065109.Google Scholar
Mi, J., Deo, R. C. & Nathan, G. J. 2005 Fast-convergence iterative scheme for filtering velocity signals and finding Kolmogorov scales. Phys. Rev. E 71, 066304.Google Scholar
Mi, J., Xu, M. & Du, C. 2011 Digital filter for hot-wire measurements of small-scale turbulence properties. Meas. Sci. Technol. 22, 125401.Google Scholar
Miller, I. S., Shah, D. A. & Antonia, R. A. 1987 A constant temperature hot-wire anemometer. J. Phys. E: Sci. Instrum. 20, 311–314.Google Scholar
Mohamed, M. S. & LaRue, J. C. 1990 The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195–214.CrossRefGoogle Scholar
Saffman, P. J. 1967 The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27, 581–593.Google Scholar
Sreenivasan, K. R. 1984 On the scaling of the turbulence energy dissipation rate. Phys. Fluids 27 (5), 1048–1051.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT.CrossRefGoogle Scholar
Valente, P. C. & Vassilicos, J. C. 2011 The decay of turbulence generated by a class of multiscale grids. J. Fluid Mech. 687, 300–340.Google Scholar
Valente, P. C. & Vassilicos, J. C. 2012 Universal dissipation scaling for nonequilibrium turbulence. Phys. Rev. Lett. 108, 214503.Google Scholar
von Kármán, T. & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. R. Soc. Lond., Ser. A 164, 192–215.Google Scholar
Wang, H. & George, W. K. 2002 The integral scale in homogeneous isotropic turbulence. J. Fluid Mech. 459, 429–443.Google Scholar
Wyngaard, J. C. 1968 Measurements of small-scale turbulence structure with hot wires. J. Sci. Instrum 1 (2), 1105–1108.Google Scholar
Zhu, Y. & Antonia, R. A. 1995a Effect of wire separation on X-probe measurements in a turbulent flow. J. Fluid Mech. 287, 199–223.CrossRefGoogle Scholar
Zhu, Y. & Antonia, R. A. 1995b The spatial resolution of two X-probes for velocity derivative measurements. Meas. Sci. Technol. 6, 538–549.Google Scholar
Zhu, Y. & Antonia, R. A. 1996 The spatial resolution of hot-wire arrays for the measurement of small-scale turbulence. Meas. Sci. Technol. 7, 1349–1359.Google Scholar