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On similitude of near wall turbulence in viscous sublayer

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Abstract

Power spectral density (PSD) of wall velocity gradient fluctuations has been measured using electrochemical (electrodiffusion) method in two rectangular channels with different hydraulic diameters and aspect ratio. The problem of the probes inertia at high frequency range has been smoothed by means of the transfer function; the reliability of the obtained results is justified by using of two circular probes with different diameter. For studied range of Reynolds numbers (6 × 103 < Re h < 4 × 104) all spectra functions tend to a unique curve when a suitable dimensionless coordinates are used. These coordinates depend on the mean value of the velocity gradient S, the intensity of the velocity gradient fluctuations \(\overline {s'^2 }\) and the liquid viscosity ν, only. Thus, the obtained results reveal the similitude of the turbulence in the viscous sublayer with respect to Re number and flow geometry. Sure, this hypothesis should be tested with more representative base of experimental data. The revealed similitude can be important for chemical engineering applications. Indeed, for these applications the Reynolds numbers are rather small and correspond to the studied range and the intensity of the velocity gradient fluctuations are well related with the mean value of the velocity gradient value. So, the knowing of the mean velocity gradient S allows the prediction of the PSD of the velocity gradient fluctuations, if the viscosity of the fluid ν is known.

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References

  1. Kolmogorov, A., Dokl. Akad. Nauk SSSR, 1941, vol. 30, p. 299.

    Google Scholar 

  2. Monin, A.S. and Yaglom, A.M., Statistical Fluid Mechanics: Mechanics of Turbulence, USA: MIT Press, 1975.

    Google Scholar 

  3. Adolphe, X., Danaila, L., and Martemianov, S., Journal of Electroanalytical Chemistry, 2007, vol. 600, p. 119.

    Article  CAS  Google Scholar 

  4. Lesage, F., Midoux, N., and Latifi, M.A., Experiments in Fluids, 2004, vol. 3, p. 257.

    Google Scholar 

  5. Alekseenko, S.V., Markovich, D.M., Evseev, A.R., Bobylev, A.V., Tarasov, B.V., and Karsten, V.M., Theoretical Foundations of Chemical Engineering, 2007, vol. 41, p. 417.

    Article  CAS  Google Scholar 

  6. Wragg, A.A., Simpson, N.P., Patrick, M.A., Kalcikova, J., and Krysa, J., Russian Journal of Electrochemistry, 2008, vol. 44, p. 413.

    Article  CAS  Google Scholar 

  7. Dumas, T., Lesage, F., Sobolik, V., and Latifi, M.A., Chemical Engineering Research and Design, 2009, vol. 8, p. 962.

    Article  Google Scholar 

  8. Blel, W., Le Gentil-Lelièvre, C, Bénézech, T., Legrand, J., and Legentilhomme, P., Journal o Food Engineering, 2009, vol. 90, p. 422.

    Article  Google Scholar 

  9. Barbier, J.F., Alemany, A., and Martemianov, S., Fusion Engineering and Design, 1998, vol. 43, p. 199.

    Article  CAS  Google Scholar 

  10. Boutoudj, M.S., Ouibrahim, A., Barbeu, F., Deslouis, C, and Martemianov, S., Chemical Engineering and Processing: Process Intensification, 2008, vol. 47, p. 793.

    Article  CAS  Google Scholar 

  11. Huchet, F., Comiti, J., Legentilhomme, P., Solliec, C., Legrand, J., and Montillet, A., International Journal of Heat and Fluid Flow, 2008, vol. 29, p. 1411.

    Article  CAS  Google Scholar 

  12. Huchet, F., Comiti, J., Tihon, J., Montillet, A., and Legentilhomme, P., Journal of Applied Electrochemistry, 2007, vol. 37, p. 49.

    Article  CAS  Google Scholar 

  13. Ngo Bourn, G.B., Martemianov, S., and Alemany, A., International Journal of Heat and Mass Transfer, 1999, vol. 42, p. 2849.

    Article  Google Scholar 

  14. Pallares, J. and Grau, F.X., International Journal of Heat and Mass Transfer, 2008, vol. 51, p. 4753.

    Article  CAS  Google Scholar 

  15. Parys, H.V., Tourwe, E., Breugelmans, T., Depauw, M., Deconinck, J., and Hubin, A., Journal of Electroanalytical Chemistry, 2008, vol. 622, p. 44.

    Article  Google Scholar 

  16. Legrand, J. and Martemyanov, S.A., J. Appl. Electrochem., 1994, vol. 24, p. 737.

    Article  CAS  Google Scholar 

  17. Martemianov, S. and Okulov, V.L., J. Appl. Electrochem., 2002, vol. 32, p. 25.

    Article  CAS  Google Scholar 

  18. Leveque, M.A., Annales des Mines, 1928, vol. 13, p. 201.

    Google Scholar 

  19. Adolphe, X., Martemianov, S., Palchetti, I., and Mascini, M., J. Appl. Electrochem., 2005, vol. 35, p. 599.

    Article  CAS  Google Scholar 

  20. Sobolik, V., Tihon, J., Wein, O., and Witcherle, K., J. Appl. Electrochem., 1998, vol. 28, p. 329.

    Article  CAS  Google Scholar 

  21. Dib, A., Martemianov, S., Makhloufi, L., and Saidani, B., International Journal of Heat and Fluid Flow, 2008, vol. 29, p. 219.

    Article  CAS  Google Scholar 

  22. Hanratty, T.J. and Campbell J.A., Measurement of Wall Shear Stress, in Fluid Mechanics Measurements, Goldstein, J.R., Ed., Hemisphere, Washington, 1983, p. 559.

  23. Skurygin, E., Martemianov, S., Vorontyntsev, M., and Grafov, B., Soviet Electrochemistry, 1989, vol. 25, p. 685.

    Google Scholar 

  24. Deslouis, C., Gil, O., and Tribollet, B., J. Fluid Mech., 1990, vol. 215, p. 85.

    Article  CAS  Google Scholar 

  25. Schlichting, H., Bounadary Layer Theory, Mac Grawhill, USA, 1987.

  26. Idel’cik, I.E., Memento des pertes de charges, Coefficients de pertes de charge singulieres etde pertes de charges par frottement. Eyrolles, Paris, 1999.

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Authors and Affiliations

  1. Laboratoire de Technologie des Matériaux et de Génie des Procédés (L.T.M.G.P) Département de Génie des Procédés, Faculté de la technologie, Université de Bejaia, 06000, Bejaia, Algérie

    A. Dib

  2. Institut P’—UPR 3346 CNRS, Universite de Poitiers, ENSMA Bailment Mécanique, 3ème étage, Campus Sud, 40, avenue du Recteur Pineau, 86022, Poitiers, France

    S. Martemianov

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  1. A. Dib
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  2. S. Martemianov
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Correspondence to S. Martemianov.

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Published in Russian in Elektrokhimiya, 2011, Vol. 47, No. 9, pp. 1050–1057.

The article is published in the original.

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Dib, A., Martemianov, S. On similitude of near wall turbulence in viscous sublayer. Russ J Electrochem 47, 980–987 (2011). https://doi.org/10.1134/S1023193511090035

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