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Examining the inertial subrange with nanoscale cross-wire measurements of turbulent pipe flow at high Reynolds number near the centreline

Published online by Cambridge University Press:  26 May 2021

Clayton P. Byers Open the ORCID record for Clayton P. Byers [Opens in a new window] ,
Marcus Hultmark ,
Ivan Marusic Open the ORCID record for Ivan Marusic [Opens in a new window]  and
Matt K. Fu Open the ORCID record for Matt K. Fu [Opens in a new window]
Clayton P. Byers
Affiliation:
Department of Engineering, Trinity College, Hartford, CT06106, USA
Marcus Hultmark
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Ivan Marusic
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria3010, Australia
Matt K. Fu*
Affiliation:
GALCIT, Caltech, Pasadena, CA91125, USA
*
†Email address for correspondence: [email protected]
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Abstract

Highly resolved, two-component velocity measurements were made near the centreline of turbulent pipe flow for Reynolds numbers in the range $102 \le Re_\lambda \leq 411$ ($1800 \le Re_\tau \leq 24\,700$). These unique data were obtained with a nanoscale cross-wire probe and used to examine the inertial subrange scaling of the longitudinal and transverse velocity components. Classical dissipation rate estimates were made using both the integration of one-dimensional dissipation spectra for each velocity component and the third-order moment of the longitudinal structure function. Although the second-order moments and one-dimensional spectra for each component showed behaviour consistent with local isotropy, clear inertial range similarity and behaviour were not exhibited in the third-order structure functions at these Reynolds numbers. When corrected for the effects of radial inhomogeneities at the centreline following the generalized expression of Danaila et al. (J. Fluid Mech., vol. 430, 2001, pp. 87–109), re-derived for the pipe flow domain, the third-order moments of the longitudinal structure function exhibited a clearer plateau per the classical Kolmogorov ‘four-fifths law’. Similar corrections described by Danaila et al. (J. Fluid Mech., vol. 430, 2001, pp. 87–109) applied to the analogous equation for the mixed structure functions (i.e. the ‘four-thirds law’) also yielded improvement over all ranges of scale, improving with increasing Reynolds number. The rate at which the ‘four-fifths’ law and ‘four-thirds’ law were approached by the third-order structure functions was found to be more gradual than decaying isotropic turbulence for the same Reynolds numbers.

JFM classification

Turbulent Flows: Pipe flow Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A21
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Anselmet, F., Antonia, R.A. & Ould-Rouis, M. 2000 Relations between third-order and second-order structure functions for axisymmetric turbulence. J. Turbul. 1, N3.CrossRefGoogle Scholar
Antonia, R.A. & Burattini, P. 2006 Approach to the 4/5 law in homogeneous isotropic turbulence. J. Fluid Mech. 550 (1), 175–184.CrossRefGoogle Scholar
Antonia, R.A., Tang, S.L., Djenidi, L. & Zhou, Y. 2019 Finite Reynolds number effect and the 4/5 law. Phys. Rev. Fluids 4 (8), 084602.CrossRefGoogle Scholar
Antonia, R.A., Zhou, T. & Romano, G.P. 1997 Second- and third-order longitudinal velocity structure functions in a fully developed turbulent channel flow. Phys. Fluids 9 (11), 3465–3471.CrossRefGoogle Scholar
Bailey, S.C.C., Kunkel, G.J., Hultmark, M., Vallikivi, M., Hill, J.P., Meyer, K.A., Tsay, C., Arnold, C.B. & Smits, A.J. 2010 Turbulence measurements using a nanoscale thermal anemometry probe. J. Fluid Mech. 663, 160–179.CrossRefGoogle Scholar
Batchelor, G.K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Burattini, P., Antonia, R.A. & Danaila, L. 2005 Scale-by-scale energy budget on the axis of a turbulent round jet. J. Turbul. 6, N19.CrossRefGoogle Scholar
Chamecki, M. & Dias, N.L. 2004 The local isotropy hypothesis and the turbulent kinetic energy dissipation rate in the atmospheric surface layer. Meteorol. Soc. 130, 2733–2752.CrossRefGoogle Scholar
Chen, S., Sreenivasan, K.R., Nelkin, M. & Cao, N. 1997 Refined similarity hypothesis for transverse structure functions in fluid turbulence. Phys. Rev. Lett. 79 (12), 2253.CrossRefGoogle Scholar
Danaila, L., Anselmet, F., Zhou, T. & Antonia, R.A. 2001 Turbulent energy scale budget equations in a fully developed channel flow. J. Fluid Mech. 430, 87–109.CrossRefGoogle Scholar
Danaila, L., Antonia, R.A. & Burattini, P. 2004 Progress in studying small-scale turbulence using ‘exact’ two-point equations. New J. Phys. 6 (1), 128.CrossRefGoogle Scholar
Fan, Y., Arwatz, G., Van Buren, T.W., Hoffman, D.E. & Hultmark, M. 2015 Nanoscale sensing devices for turbulence measurements. Exp. Fluids 56 (7), 138.CrossRefGoogle Scholar
Fu, M.K., Fan, Y. & Hultmark, M. 2019 Design and validation of a nanoscale cross-wire probe (X-NSTAP). Exp. Fluids 60, 99.CrossRefGoogle Scholar
Hill, R.J. 1997 Applicability of Kolmogorov's and Monin's equations of turbulence. J. Fluid Mech. 353, 67–81.CrossRefGoogle Scholar
von Kármán, T. & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. R. Soc. Lond. A 164 (917), 192–215.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 a Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16–18.Google Scholar
Kolmogorov, A.N. 1941 b The local structure of turbulence in incompressible viscous fluid with very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305.Google Scholar
Kolmogorov, A.N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13 (1), 82–85.CrossRefGoogle Scholar
Lindborg, E. 1999 Correction to the four-fifths law due to variations of the dissipation. Phys. Fluids 11 (3), 510–512.CrossRefGoogle Scholar
Lundgren, T.S. 2002 Kolmogorov two-thirds law by matched asymptotic expansion. Phys. Fluids 14 (2), 638–642.CrossRefGoogle Scholar
McKeon, B.J. & Morrison, J.F. 2007 Asymptotic scaling in turbulent pipe flow. Phil. Trans. R. Soc. A 365 (1852), 771–787.CrossRefGoogle ScholarPubMed
McKeon, B.J., Li, J., Jiang, W., Morrison, J.F. & Smits, A.J. 2003 Pitot probe corrections in fully developed turbulent pipe flow. Meas. Sci. Technol. 14 (8), 1449–1458.CrossRefGoogle Scholar
McKeon, B.J., Swanson, C.J., Zagarola, M.V., Donnelly, R.J. & Smits, A.J. 2004 Friction factors for smooth pipe flow. J. Fluid Mech. 511, 41–44.CrossRefGoogle Scholar
Monin, A.S. & Yaglom, A.M. 2013 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. Courier Corporation.Google Scholar
Morrison, J.F., Vallikivi, M. & Smits, A.J. 2016 The inertial subrange in turbulent pipe flow: centreline. J. Fluid Mech. 788, 602–613.CrossRefGoogle Scholar
Mydlarski, L. & Warhaft, Z. 1996 On the onset of high-Reynolds-number grid-generated wind tunnel turbulence. J. Fluid Mech. 320, 331–368.CrossRefGoogle Scholar
Rosenberg, B.J., Hultmark, M., Vallikivi, M., Bailey, S.C.C. & Smits, A.J. 2013 Turbulence spectra in smooth- and rough-wall pipe flow at extreme Reynolds numbers. J. Fluid Mech. 731, 46–63.CrossRefGoogle Scholar
Saddoughi, S.G. 1997 Local isotropy in complex turbulent boundary layers at high Reynolds number. J. Fluid Mech. 348, 201–245.CrossRefGoogle Scholar
Saddoughi, S.G. & Veeravalli, S.V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372.CrossRefGoogle Scholar
Sadeghi, H., Lavoie, P. & Pollard, A. 2016 Scale-by-scale budget equation and its self-preservation in the shear-layer of a free round jet. Intl J. Heat Fluid Flow 61, 85–95.CrossRefGoogle Scholar
Sadeghi, H., Lavoie, P. & Pollard, A. 2018 Effects of finite hot-wire spatial resolution on turbulence statistics and velocity spectra in a round turbulent free jet. Exp. Fluids 59 (3), 40.CrossRefGoogle Scholar
Shen, X. & Warhaft, Z. 2000 The anisotropy of the small scale structure in high Reynolds number ($R_\lambda \sim 1000$) turbulent shear flow. Phys. Fluids 12 (11), 2976–2989.CrossRefGoogle Scholar
Sinhuber, M., Bodenschatz, E. & Bewley, G.P. 2015 Decay of turbulence at high Reynolds numbers. Phys. Rev. Lett. 114 (3), 034501.CrossRefGoogle ScholarPubMed
Sreenivasan, K.R. 1995 On the universality of the Kolmogorov constant. Phys. Fluids 7 (11), 2778–2784.CrossRefGoogle Scholar
Sreenivasan, K.R. 1998 An update on the energy dissipation rate in isotropic turbulence. Phys. Fluids 10 (2), 528–529.CrossRefGoogle Scholar
Taylor, G.I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151 (873), 421–444.Google Scholar
Vallikivi, M. 2014 Wall-bounded turbulence at high Reynolds numbers. PhD thesis, Princeton University.Google Scholar
Vallikivi, M. & Smits, A.J. 2014 Fabrication and characterization of a novel nanoscale thermal anemometry probe. J. Microelectromech. Syst. 23 (4), 899–907.CrossRefGoogle Scholar
Van Atta, C. 1991 Local isotropy of the smallest scales of turbulent scalar and velocity fields. Proc. R. Soc. A 434 (1890), 139–147.Google Scholar
Vassilicos, J.C. 2015 Dissipation in turbulent flows. Annu. Rev. Fluid Mech. 47 (1), 95–114.CrossRefGoogle Scholar
Wyngaard, J.C. 1968 Measurement of small-scale turbulence structure with hot wires. J. Phys. E 1 (11), 1105–1108.CrossRefGoogle Scholar
Wyngaard, J.C. 1969 Spatial resolution of the vorticity meter and other hot-wire arrays. J. Phys. E 2 (11), 983–987.CrossRefGoogle Scholar
Zagarola, M.V. & Smits, A.J. 1998 Mean-flow scaling of turbulent pipe flow. J. Fluid Mech. 373, 33–79.CrossRefGoogle Scholar
Zhao, R., Li, J. & Smits, A. 2004 A new calibration method for crossed hot wires. Meas. Sci. Technol. 15 (9), 1926–1931.CrossRefGoogle Scholar