Skip to main content
SpringerLink
Log in

Velocity derivative skewness in isotropic turbulence and its measurement with hot wires

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

We investigate the effect of the hot wire resolution on the measurement of the velocity derivative skewness in homogeneous isotropic turbulence. Single- and cross-wire configurations (with different lengths and separations of the wires, and temporal sampling resolution) are considered. Predictions of the attenuation on the basis of a model for the energy spectrum are compared to experimental and numerical data in grid and box turbulence, respectively. It is shown that the model-based correction is accurate for the single wire but not for the cross-wire. In the latter case, the effect of the separation between the wires is opposite to that found in the experiments and simulations. Moreover, the attenuation predicted by the numerical data is in good agreement with that observed in the experiment. For both probe configurations, the sampling resolution has a sizeable attenuation effect, but, for the X-probe, the impact of the separation between the wires is more important. In both cases, the length of the wires has only a minor effect, in the non-dimensional range of wire length investigated. Finally, the present experimental data support the conclusion that the skewness is constant with the Reynolds number, in agreement with Kolmogorov’s 41 theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Notes

  1. Note that \(\int_{0}^{\infty}k^{n}\frac{\hbox{d} G} {\hbox{d} k} =-n\int_{0}^{\infty}k^{n-1}G\hbox{d} k\;\hbox{and}\; \int_{0}^{\infty}k^{n}\frac{\hbox{d}^{2}G} {\hbox{d} k^{2}} =n(n-1)\int_{0}^{\infty}k^{n-2}G\hbox{d} k.\)

References

  • Antonia RA, Orlandi P (2004) Similarity of decaying isotropic turbulence with a passive scalar. J Fluid Mech 505:123–151

    Article  MATH  Google Scholar 

  • Batchelor GK (1953) The theory of homogeneous turbulence. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Bhatnagar P, Gross E, Krook M (1954) A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys Rev 94:511–525

    Article  MATH  Google Scholar 

  • Bremhorst K (1972) The effect of wire length and separation on X -array hot-wire anemometer measurements. IEEE Trans Instrum Meas IM-21:244–248

    Article  Google Scholar 

  • Browne LWB, Antonia RA (1987) The effect of wire length on temperature statistics in a turbulent wake. Exp Fluids 5:426–428

    Article  Google Scholar 

  • Burattini P, Antonia RA (2005) The effect of different X -wire calibration schemes on some turbulence statistics. Exp Fluids 38(1):80–89

    Article  Google Scholar 

  • Burattini P, Lavoie P, Agrawal A, Djenidi L, Antonia RA (2006) Power law of decaying homogeneous isotropic turbulence at low Reynolds number. Phys Rev E 73(066304)

  • Burattini P, Kinet M, Carati D, Knaepen B (2007) Corrections for underresolved scalar measurements in turbulent flows using a DNS database. Exp Fluids 43(1):31–37. doi:10.1007/s00348-007-0309-z

    Article  Google Scholar 

  • Champagne FH (1978) The fine-scale structure of the turbulent velocity field. J Fluid Mech 86:67–108

    Article  Google Scholar 

  • Champagne FH, Sleicher CA, Wehrmann OH (1967) Turbulence measurements with inclined hot-wires. Part 1. Heat transfer experiments with inclined hot-wire. J Fluid Mech 28:153–175

    Article  Google Scholar 

  • Derksen RW, Azad RS (1983) An examination of hot-wire length corrections. Phys Fluids 26:1751–1754

    Article  Google Scholar 

  • Elsner JW, Domaga\la P, Elsner W (1993) Effect of finite spatial resolution of hot-wire anemometry on measurements of turbulence energy dissipation. Meas Sci Technol 4:517–523

    Article  Google Scholar 

  • Ferchichi M, Tavoularis S (2000) Reynolds number effects on the fine structure of uniformly sheared turbulence. Phys Fluids 12(11):2942–2953

    Article  Google Scholar 

  • Gamard S, George WK (1999) Reynolds number dependence of energy spectra in the overlap region of isotropic turbulence. Flow Turbul Combust 63(1):443–477

    Article  Google Scholar 

  • George WK (1992) The decay of homogeneous isotropic turbulence. Phys Fluids A 4:1492–1509

    Article  MATH  MathSciNet  Google Scholar 

  • Gotoh T, Fukayama D, Nakano T (2002) Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation. Phys Fluids 14:1065–1081

    Article  MATH  MathSciNet  Google Scholar 

  • Gylfason A, Ayyalasomayajula S, Warhaft Z (2004) Intermittency, pressure and acceleration statistics from hot-wire measurements in wind-tunnel turbulence. J Fluid Mech 501:213–229

    Article  MATH  Google Scholar 

  • Ishihara T, Kaneda Y, Yokokawa M, Itakura K, Uno A (2005) Energy spectrum in the near dissipation range of high resolution direct numerical simulation of turbulence. J Phys Soc Jpn 74:1464–1471

    Article  Google Scholar 

  • Jörgensen F (1971) Directional sensitivity of wire and hot-film probes. DISA Inf 11:31–37

    Google Scholar 

  • Kerr RM (1985) High-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J Fluid Mech 153:31–58

    Article  MATH  Google Scholar 

  • Kistler AL, Vrebalovich T (1966) Grid turbulence at large Reynolds numbers. J Fluid Mech 26:37–47

    Article  Google Scholar 

  • Kolmogorov AN (1941) Dissipation of energy in the locally isotropic turbulence. Dokl Akad Nauk SSSR 32(1) (English translation in Proc R Soc Lond A 434:15–17)

    Google Scholar 

  • Kolmogorov AN (1962) A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J Fluid Mech 13:82–85

    Article  MATH  MathSciNet  Google Scholar 

  • Larssen JV, Devenport WJ (2002) The generation of high Reynolds number homogeneous turbulence. AIAA Paper 2002-2861

  • Lavoie P, Burattini P, Djenidi L, Antonia RA (2005) Effect of initial conditions on decaying grid turbulence at low R λ. Exp Fluids 39(5):865–874

    Article  Google Scholar 

  • Lavoie P, Djenidi L, Antonia R (2007) Effects of initial conditions in decaying turbulence generated by passive grids. J Fluid Mech 585:395–420

    Article  MATH  Google Scholar 

  • Maier RS, Bernard RS, Grunau DW (1996) Boundary conditions for the lattice Boltzmann method. Phys Fluids 8(7):1788–1801

    Article  MATH  Google Scholar 

  • Mansour NN, Wray AA (1994) Decay of isotropic turbulence at low Reynolds number. Phys Fluids 6(2):808–814

    Article  MATH  Google Scholar 

  • Martinez DO, Chen S, Doolen GD, Kraichnan RH, Wang LP, Zhou Y (1997) Energy spectrum in the dissipation range of fluid turbulence. J Plasma Phys 57:195–201

    Article  Google Scholar 

  • Mathieu J, Scott J (2000) An introduction to turbulent flow. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Michelet S, Antoine Y, Lemoine F, Mahouast M (1998) Direct measurement of the kinetic energy dissipation rate of turbulence using 2D LDA: application to grid-generated turbulent flow. C R Acad Sci Paris 326:621–626

    MATH  Google Scholar 

  • Monin AS, Yaglom AM (1975) Statistical fluid mechanics: mechanics of turbulence, vol 2. MIT Press, Cambridge

    Google Scholar 

  • Mydlarski L, Warhaft Z (1996) On the onset of high-Reynolds-number grid-generated wind tunnel turbulence. J Fluid Mech 320:331–368

    Article  Google Scholar 

  • Nelkin M (1994) Universality and scaling in fully developed turbulence. Adv Phys 43:143–181

    Article  Google Scholar 

  • Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Roberts JB (1973) On the correction of hot-wire turbulence measurements for spatial resolution errors. Aeronaut J 77:406–412

    Google Scholar 

  • Schedvin J, Stegen GR, Gibson CH (1974) Universal similarity at high grid Reynolds numbers. J Fluid Mech 65:561–579

    Article  Google Scholar 

  • Smith LM, Reynolds WC (1991) The dissipation-range spectrum and the velocity-derivative skewness in turbulent flows. Phys Fluids A 3(5):992–994

    Article  Google Scholar 

  • Sreenivasan KR, Antonia RA (1997) The phenomenology of small-scale turbulence. Ann Rev Fluid Mech 29:435–472

    Article  MathSciNet  Google Scholar 

  • Suzuki Y, Kasagi N (1992) Evaluation of hot-wire measurements in wall shear turbulence using a direct numerical simulation database. Exp Therm Fluid Sci 5:69–77

    Article  Google Scholar 

  • Tabeling P, Zocchi G, Belin F, Maurer J, Willaime H (1996) Probability density functions, skewness, and flatness in large Reynolds number turbulence. Phys Rev E 53:1613–1621

    Article  Google Scholar 

  • Tavoularis S, Bennett JC, Corrsin S (1978) Velocity-derivative skewness in small Reynolds number, nearly isotropic turbulence. J Fluid Mech 88:63–69

    Article  Google Scholar 

  • Taylor GI (1938) Production and dissipation of vorticity in a turbulent fluid. Proc R Soc Lond A, pp 15–23

  • Turan F, Azad RS (1993) Comparison of the zero-wire-length dissipation technique with spectral corrections and the effect of high turbulence intensity. Meas Sci Technol 6(3):292–308

    Google Scholar 

  • Uberoi MS, Kovasznay LSG (1953) On mapping and measurements of random fields. Q Appl Math 10:375–393

    MATH  MathSciNet  Google Scholar 

  • Van Atta CW, Antonia RA (1980) Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives. Phys Fluids 23:252–257

    Article  Google Scholar 

  • Vincent A, Meneguzzi M (1991) The spatial structure and statistical properties of homogeneous turbulence. J Fluid Mech 225:1–20

    Article  MATH  Google Scholar 

  • Wyngaard JC (1968) Measurement of small-scale turbulence structure with hot wires. J Phys E Sci Instrum 1:1105–1108

    Article  Google Scholar 

  • Wyngaard JC (1969) Spatial resolution of the vorticity meter and other hot-wire arrays. J Phys E Sci Instrum 2:983–987

    Article  Google Scholar 

  • Zhu Y, Antonia RA (1995) Effect of wire separation on X -probe measurements in a turbulent flow. J Fluid Mech 287:199–223

    Article  Google Scholar 

  • Zhu Y, Antonia RA (1996) The spatial resolution of hot-wire arrays for the measurement of small-scale turbulence. Meas Sci Technol 7:1349–1359

    Article  Google Scholar 

  • Zou Q, He X (1997) On pressure and velocity boundary conditions for the lattice Boltzmann BKG model. Phys Fluids 9:1591–1598

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physique Statistique et des Plasmas, Université Libre de Bruxelles, 1050, Brussels, Belgium

    Paolo Burattini

  2. Department of Aeronautics, Imperial College London, London, UK

    Philippe Lavoie

  3. Discipline of Mechanical Engineering, University of Newcastle, Newcastle, NSW, 2308, Australia

    Paolo Burattini & Robert A. Antonia

Authors
  1. Paolo Burattini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Philippe Lavoie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert A. Antonia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paolo Burattini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Burattini, P., Lavoie, P. & Antonia, R.A. Velocity derivative skewness in isotropic turbulence and its measurement with hot wires. Exp Fluids 45, 523–535 (2008). https://doi.org/10.1007/s00348-008-0495-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-008-0495-3

Keywords

Search

Navigation