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On the generation of large-scale homogeneous turbulence

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Abstract

An active turbulence generating grid, based on the rotating-vane design of Makita (1991), was developed for a large wind tunnel. At 2.14 m square, the grid is the largest of this type ever developed. To improve the isotropy of the turbulence generated, the grid was placed in the wind tunnel contraction. Measurements show that the grid produces a closely uniform mean flow and homogeneous isotropic turbulence to within two integral scales from the wall. By systematically varying the flow speed and parameters controlling the random motion of the vanes, grid turbulence with a wide variety of characteristics was produced and the dependence of those characteristics on the operating parameters of the grid revealed. Taylor Reynolds numbers of the grid turbulence varied from 100 to 1,360 and integral scales from 5 to almost 70 cm. The extreme cases represent some of the highest Reynolds number and largest scale homogeneous turbulent flows ever generated in a wind tunnel.

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Notes

  1. The same results (in a slightly different form) were also independently derived by Ribner and Tucker (1953).

  2. Note that a tilde indicates a given instance of the random parameter in question.

  3. Kang et al. (2003) kept the cruise time constant at 1 s with a randomized rotation rate.

  4. The Rossby number is the ratio of inertial forces to rotational forces, usually applied to the Coriolis force in the atmosphere. It has been extended here to obtain a non-dimensional grid rotation rate.

  5. Active grid turbulence generally requires a much shorter development length than conventional grid turbulence (see e.g. Makita 1991; Larssen 2005) and all measurement points in Table 1 are believed to be contained within the initial period of decay.

  6. This estimate is obtained by treating the wind tunnel walls as part of an infinite cascade and a blade spacing of 4.8L 11.

  7. For the test case shown in Fig. 7 \( \tilde{\Upomega } \) ranges between 2 and 6 rev/s.

  8. In Fig. 10, Ω has been held constant at 4 Hz to keep the Rossby number from differing between the datapoints.

  9. The turbulence kinetic energy is defined as k = (u 2 + v 2 + w 2)/2. In true isotropic turbulence where u 2 = v 2 = w 2, this simply reduces to k = 3u 2/2.

  10. Even though the modified single random forcing protocol was used by Kang et al. (2003) it has been shown here that the cruise time parameter has very little effect on the resulting turbulence intensity. This indicates that the modified single random scheme is almost equivalent to a double random forcing protocol in terms of the turbulence it produces as long as T is not set to zero.

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Acknowledgments

The authors would like to thank the Office of Naval Research, in particular Dr. Ronald Joslin, for their support under grants N00014-01-1-0406 and N00014-03-1-0199.

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Author notes

  1. Jon V. Larssen

    Present address: Acoustics and Fluid Mechanics Technology, The Boeing Company, P.O. Box 3707, MC 0R-JF, Seattle, WA, 98124-2207, USA

Authors and Affiliations

  1. Department of Aerospace and Ocean Engineering, Virginia Tech, 215 Randolph Hall, Blacksburg, VA, 24061, USA

    Jon V. Larssen & William J. Devenport

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  1. Jon V. Larssen
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  2. William J. Devenport
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Correspondence to Jon V. Larssen.

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Larssen, J.V., Devenport, W.J. On the generation of large-scale homogeneous turbulence. Exp Fluids 50, 1207–1223 (2011). https://doi.org/10.1007/s00348-010-0974-1

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