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On the onset of high-Reynolds-number grid-generated wind tunnel turbulence

Published online by Cambridge University Press:  26 April 2006

L. Mydlarski  and
Z. Warhaft
L. Mydlarski
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
Z. Warhaft
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

Using an active grid devised by Makita (1991), shearless decaying turbulence is studied for the Taylor-microscale Reynolds number, Rλ, varying from 50 to 473 in a small (40 × 40 cm2 cross-section) wind tunnel. The turbulence generator consists of grid bars with triangular wings that rotate and flap in a random way. The value of Rλ is determined by the mean speed of the air (varied from 3 to 14 m s–1) as it passes the rotating grid, and to a lesser extent by the randomness and rotation rate of the grid bars. Our main findings are as follows. A weak, not particularly well-defined scaling range (i.e. a power-law dependence of both the longitudinal (u) and transverse (v) spectra, F11(k1) and F22(k1) respectively, on wavenumber k1) first appears at Rλ ∼ 50, with a slope, n1, (for the u spectrum) of approximately 1.3. As Rλ was increased, n1 increased rapidly until Rλ ∼ 200 where n ∼ 1.5. From there on the increase in n1 was slow, and even by Rλ = 473 it was still significantly below the Kolmogorov value of 1.67. Over the entire range, 50 [les ] Rλ [les ] 473, the data were well described by the empirical fit: $n_1 = \frac{5}{3}(1-3.15R_\lambda^{-2/3})$. Using a modified form of the Kolmogorov similarity law: F11(k1) = C1*ε2/3k1–5/3(k 1η)5/3–n1 where ε is the turbulence energy dissipation rate and η is the Kolmogorov microscale, we determined a linear dependence between n1 and C1*: C1* = 4.5 – 2.4n1. Thus for n1 = 5/3 (which extrapolation of our results suggests will occur in this flow for Rλ ∼ 104), C1* = 0.5, the accepted high-Reynolds-number value of the Kolmogorov constant. Analysis of the p.d.f. of velocity differences Δu(r) and Δv(r) where r is an inertial subrange interval, conditional dissipation, and other statistics showed that there was a qualitative difference between the turbulence for Rλ < 100 (which we call weak turbulence) and that for Rλ > 200 (strong turbulence). For the latter, the p.d.f.s of Δu(r) and Δv(r) had super Gaussian tails and the dissipation (both of the u and v components) conditioned on Δu(r) and Δv(r) was a strong function of the velocity difference. For Rλ < 100, p.d.f.s of Δu(r) and Δv(r) were Gaussian and conditional dissipation statistics were weak. Our results for Rλ > 200 are consistent with the predictions of the Kolmogorov refined similarity hypothesis (and make a distinction between the dynamical and kinematical contributions to the conditional statistics). They have much in common with similar statistics done in shear flows at much higher Rλ, with which they are compared.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 320 , 10 August 1996 , pp. 331 - 368
Copyright
© 1996 Cambridge University Press

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References

Anselmet, F., Gagne, Y., Hopfinger, E. J. & Antonia, R. A. 1984 High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Browne, L. W. B., Antonia, R. A. & Chua, L. P. 1989 Calibration of X-probes for turbulent flow measurements. Exps. Fluids 7, 201–208.Google Scholar
Chambers, A. J. & Antonia, R. A. 1984 Atmospheric estimates of power law exponents μ and μθ. Boundary Layer Met. 28, 343–352.Google Scholar
Champagne, F. H. 1978 The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 86, 67–108.Google Scholar
Chen, S., Doolen, S. D., Kraichnan, R. H. & She, Z.-S. 1993 On statistical correlations between velocity increments and locally averaged dissipation in homogeneous turbulence. Phys. Fluids A 5, 458–463.Google Scholar
Chen, S., Doolen, S. D., Kraichanan, R. H. & Wang, L.-P. 1995 Is the Komogorov refined similarity relation dynamic or kinematic. Phys. Rev. Lett. 74 1755–1758.Google Scholar
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25, 657–682.Google Scholar
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, 273–337.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
Hunt, J. C. R. & Vassilicos, J. C. 1991 Kolmogorov's contributions to the physical and geometrical understanding of small-scale turbulence and recent developments. Proc. R. Soc. Lond. A 434, 183–210.Google Scholar
Jayesh & Warhaft, Z. 1992 Probability distribution, conditional dissipation, and transport of passive temperature fluctuations in grid-generated turbulence. Phys. Fluids A 4, 2292–2307.Google Scholar
Jayesh Tong, C. & Warhaft, Z. 1994 On temperature spectra in grid turbulence. Phys. Fluids 6, 306–312.Google Scholar
Kistler, A. L. & Vrebalovich, T. 1966 Grid turbulence at large Reynolds numbers. J. Fluid Mech. 26, 37–47.Google Scholar
Kolmogorov, A. N. 1941a The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30 301–305 (referred to herein as K41).Google Scholar
Kolmogorov, A. N. 1941b Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk. SSSR 32 16–18 (referred to herein as K41).Google Scholar
Kolmogorov, A. N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at very high Reynolds numbers. J. Fluid Mech. 13 82–85 (referred to herein as K62).Google Scholar
Kraichnan, R. 1991 Turbulent cascade and intermittency growth. J. Fluid Mech. 434, 65–78.Google Scholar
Lesieur, M. 1990 Turbulence in Fluids, 2nd Edn. Kluwer.
Ling, S. C. & Wan, C. A. 1972 Decay of isotropic turbulence generated by a mechanically agitated grid. Phys. Fluids 15, 1363–1369.Google Scholar
Makita, H. 1991 Realization of a large-scale turbulence field in a small wind tunnel. Fluid Dyn. Res. 8, 53–64.Google Scholar
Makita, H. & Sassa, K. 1991 Active turbulence generation in a laboratory wind tunnel. Advances in Turbulence 3 (ed. A. V. Johansson & P. H. Alfredsson). Springer.
Makita, H., Sassa, K., Iwasaki, T. & Iidu, A. 1987 Trans. Japan Soc. Mech. Engng B 53, 3180. (In Japanese).
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, Volume 2. MIT Press.
Nelkin, M. 1994 Universality and scaling in fully developed turbulence. Adv. Phys. 43, 143–181.Google Scholar
Praskovsky, A. A. 1992 Experimental verification of the Kolmogorov refined similarity hypothesis. Phys. Fluids A 4, 2589–2591.Google Scholar
Praskovsky, A. A. & Oncley, S. 1994 Measurements of the Kolmogorov constant and intermittency exponent at very high Reynolds numbers. Phys. Fluids 6, 2886–2888.Google Scholar
Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268 333–372 (referred to herein as S & V).Google Scholar
Sirivat, A. & Warhaft, Z. 1983 The effect of a passive cross-stream temperature gradient on the evolution of temperature variance and heat flux in grid turbulence. J. Fluid Mech. 128, 323–346.Google Scholar
Sreenivasan, K. R. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434, 165–182.Google Scholar
Sreenivasan, K. R. 1995 On the universality of the Kolmogorov constant. Phys. Fluids 7, 2778–2784.Google Scholar
Stolovitzky, G. Kailasnath, P. & Sreenivasan, K. R. 1992 Kolmogorov's refined similarity hypotheses. Phys. Rev. Lett. 69, 1178–1181.Google Scholar
Thoroddsen, S. T. 1995 Reevaluation of the experimental support for the Kolmogorov refined similarity hypothesis. Phys. Fluids 7, 691–693.Google Scholar
Tong, C. & Warhaft, Z. 1994 On passive scalar derivative statistics in grid turbulence. Phys. Fluids 6, 2165–2176.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd Edn. Cambridge University Press.
Wang, L., Chen, S., Brasseur, J. G. & Wyngaard, J. C. 1996 Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 1. Velocity field. J. Fluid Mech. 309, 113–156.Google Scholar
Wyngaard, J. C. 1968 Measurements of small-scale turbulence structure with hot wires. J. Sci. Instrum. 1, 1105–1108.Google Scholar
Wyngaard, J. C. & Tennekes, H. 1970 Measurement of the small scale structure of turbulence at moderate Reynolds numbers. Phys. Fluids 13 1962–1969.Google Scholar
Yoon, K. & Warhaft, Z. 1990 The evolution of grid-generated turbulence under conditions of stable thermal stratification. J. Fluid Mech. 215, 601–638.Google Scholar
Zhu, Y., Antonia, R. A. & Hosokawa, I. 1995 Refined similarity hypotheses for turbulent velocity and temperature fields. Phys. Fluids 7, 1637–1648.Google Scholar