Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-12-03T20:49:11.476Z Has data issue: false hasContentIssue false
  • English
  • Français

Concentration flux measurements in a polymer drag-reduced turbulent boundary layer

Published online by Cambridge University Press:  11 February 2010

V. S. R. SOMANDEPALLI ,
Y. X. HOU  and
M. G. MUNGAL
V. S. R. SOMANDEPALLI
Affiliation:
Mechanical Engineering Department, Stanford University, Stanford, CA 94305-3032, USA
Y. X. HOU
Affiliation:
Mechanical Engineering Department, Stanford University, Stanford, CA 94305-3032, USA
M. G. MUNGAL*
Affiliation:
Mechanical Engineering Department, Stanford University, Stanford, CA 94305-3032, USA School of Engineering, Santa Clara University, Santa Clara, CA 95053-0590, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The drag-reducing action of dilute solutions of long-chain polymers in a flat-plate turbulent boundary layer is studied using particle imaging velocimetry (PIV) and planar laser induced fluorescence (PLIF). The results are used to characterize and quantify the spatial distribution of the injected polymer solution and the downstream development of the DR along the flat plate. The two techniques were used simultaneously to document and study the spread of the injected polymer solution and the resulting changes in the structure and statistics of the turbulence in the boundary layer. The PLIF images provide a qualitative and quantitative measure of the dispersion of the injected polymer solution. The mean and root mean square (r.m.s.) concentration profiles obtained using PLIF showed that the polymer greatly suppressed the turbulent dispersion in the near-wall region. The quantitative concentration measurements across the boundary layer, combined with simultaneous velocity measurements, are used to obtain concentration flux measurements in the boundary layer and are used to study the effect of the turbulence on the dispersion of the injected polymer. The variation of the fluxes with concentration of the injected polymer solutions and with increasing downstream distance is also studied and documented. The action of the polymer is to reduce the streamwise fluxes in the boundary layer, the suppression increasing with concentration. Further, the fluxes are also used to estimate the turbulent Schmidt number (ScT) for the drag-reduced flow. For the polymer injection experiments, the ScT are all greater than unity with the highest magnitude measured to be around 6, with the magnitude increasing with increasing concentration of the injected solutions. However, for each experiment, the estimated ScT decreases along the length of the flat plate reflecting the loss of polymer effectiveness.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 644 , 10 February 2010 , pp. 281 - 319
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Benzi, R., De Angelis, E., L'vov, V. S. & Procaccia, I. 2005 Identification and calculation of the universal asymptote for drag reduction by polymers in wall bounded turbulence. Phys. Rev. Lett. 95, 194502.CrossRefGoogle ScholarPubMed
Brungart, T. A., Harbison, W. L., Petrie, H. L. & Merkle, C. L. 1991 A fluorescence technique for measurement of slot injected fluid concentration profiles in a turbulent boundary layer. Exp. Fluids 11, 9–16.CrossRefGoogle Scholar
Elkins, C. J. 1997 Heat transfer in the rotating disk boundary layer. PhD thesis, Stanford University, Stanford, CA.Google Scholar
Fontaine, A. A., Petrie, H. L. & Brungart, T. A. 1992 Velocity profile statistics in a turbulent boundary layer with slot-injected polymer. J. Fluid Mech. 56, 559–575.Google Scholar
Fruman, D. H. & Tulin, M. P. 1976 Diffusion of a tangential drag reducing polymer injection of a flat plate at high Reynolds numbers. J. Ship Res. 20, 171–180.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14, L73–L76.CrossRefGoogle Scholar
Gupta, V. K., Sureshkumar, R. & Khomami, B. 2005 Passive scalar transport in polymer drag-reduced turbulent channel flow. AIChE J. 51 (7), 1938–1950.CrossRefGoogle Scholar
Harder, K. J. & Tiederman, W. G. 1991 Drag reduction and turbulent structure in two-dimensional channel flows. Phil. Trans. R. Soc. Lond. A 336, 19–34.Google Scholar
Hou, Y. X., Somandepalli, V. S. R. & Mungal, M. G. 2006 A technique to determine total shear stress and polymer stress profiles in drag reduced boundary layer flows. Exp. Fluids 40, 589–600.CrossRefGoogle Scholar
Hou, Y. X., Somandepalli, V. S. R. & Mungal, M. G. 2008 Streamwise development of turbulent boundary layer drag reduction with polymer injection. J Fluid Mech. 597, 31–66.CrossRefGoogle Scholar
Kawaguchi, Y., Segawa, T., Feng, Z. P. & Li, P. W. 2002 Experimental study on drag reducing channel flow with surfactant additives – spatial structure of turbulence investigated by PIV system. Intl J. Heat Fluid Flow 23, 700–709.CrossRefGoogle Scholar
Li, P., Kawaguchi, Y., Daisaka, H., Yabe, A., Hishida, K. & Maeda, M. 2001 Heat transfer enhancement to the drag-reducing flow of surfactant solution in two-dimensional channel with mesh-screen inserts at the inlet. J. Heat Transfer 123, 779–789.CrossRefGoogle Scholar
Li, F.-Ch., Kawaguchi, Y. & Hishida, K. 2003 Investigation on heat transfer characteristics of drag-reducing flow with surfactant additive by simultaneous measurements of temperature and velocity fluctuations in thermal boundary layer. In Proceedings of the Sixth ASME/JSME Thermal Engineering Joint Conference, Hawaii.CrossRefGoogle Scholar
Luchik, T. S. & Tiederman, W. G. 1988 Turbulent structure in low-concentration drag-reducing channel flows. J. Fluid Mech. 190, 241–263.CrossRefGoogle Scholar
Lumley, J. L. 1969 Drag reduction by additives. Annu. Rev. Fluid Mech. 1, 367–384.CrossRefGoogle Scholar
L'vov, V. S., Pomyalov, A., Procaccia, I. & Tiberkevich, V. 2004 Drag reduction by polymers in wall bounded turbulence. Phys. Rev. Lett. 68, 046308.Google Scholar
Petrie, H. L., Deutsch, S., Brungart, T. A. & Fontaine, A. A. 2003 Polymer drag reduction with surface roughness in flat-plate turbulent boundary layer flow. Exp. Fluids 35, 8–23.Google Scholar
Petrie, H. L. & Fontaine, A. A. 1996 Comparison of turbulent boundary layer modification with slot-injected and homogeneous drag-reducing polymer solutions. ASME Fluids Engng Div. Conf. 237, 205–210.Google Scholar
Procaccia, I., L'vov, V. S. & Benzi, R. 2008 Theory of drag reduction by polymers in wall-bounded turbulence, Rev. of Modern Physics 80 (1), 225–247.CrossRefGoogle Scholar
Putorti, A. D. Jr, Everest, D. & Atreya, A. 2003 Simultaneous measurements of drop size and velocity in large-scale sprinkler flows using particle tracking and laser-induced fluorescence. Tech Rep. NIST GCR 03-852. National Institute of Standards and Technology.Google Scholar
Somandepalli, V. S. R. 2006 Combined PIV and PLIF measurements in a polymer drag reduced turbulent boundary layer. PhD thesis, Stanford University, Stanford CA.Google Scholar
Somandepalli, V. S. R., Hou, Y. X. & Mungal, M. G. 2005 Streamwise evolution of drag reduction in a boundary layer with polymer injection. In Proceedings of Second Intl Symp. Sea Water Drag Reduction, Busan, Korea.Google Scholar
Somandepalli, V. S. R., White, C. M. & Mungal, M. G. 2003 Boundary layer studies on polymer drag reduction using PIV and PLIF, ASME FEDSM 2003–45659. In Proceedings of the ASME FEDSM 2003, Hawaii.CrossRefGoogle Scholar
Sreenivasan, K. R. & White, C. M. 2000 The onset of drag reduction by dilute polymer additives, and the maximum drag reduction asymptote. J. Fluid Mech. 409, 149–164.CrossRefGoogle Scholar
Tabor, M. & de Gennes, P. G. 1986 A cascade theory of drag reduction. Europhys. Lett. 2 (7), 519–522.CrossRefGoogle Scholar
Toms, B. 1948 Observation on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proc. Intl Rheol. Congr. 2, 135–141.Google Scholar
Virk, P. S. 1975 Drag reduction fundamentals. AIChE J. 21, 625–656.CrossRefGoogle Scholar
Virk, P. S., Merril, E. W., Mickley, H. S., Smith, K. A. & Mollo-Christensen, E. 1967 The Toms phenomenon – turbulent pipe flow of dilute polymer solutions. J. Fluid Mech. 30, 305–328.CrossRefGoogle Scholar
Vdovin, A. V. & Smol'yakov, A. V. 1978 Diffusion of polymer solutions in a turbulent boundary layer. Zh. Prikl. Mekh. Tekh. Fiz. 2, 66–73 (translation in UDC 532.526, pp. 196–201, Plenum).Google Scholar
Walker, D. T. & Tiederman, W. G. 1990 Turbulent structure in a channel flow with polymer injection at the wall. J. Fluid Mech. 218, 377–403.CrossRefGoogle Scholar
Warholic, M. D., Heist, D. K., Katcher, M. & Hanratty, T. J. 2001 A study with particle image velocimetry of the influence of drag reducing polymers on the structure of turbulence. Exp. Fluids 31, 474–483.CrossRefGoogle Scholar
Warholic, M. D., Massah, H. & Hanratty, T. J. 1999 Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing. Exp. Fluids 27, 461–472.CrossRefGoogle Scholar
White, C. M. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235–256.CrossRefGoogle Scholar
White, C. M., Somandepalli, V. S. R., Dubief, Y. & Mungal, M. G. 2006 Dynamic contributions to the skin friction drag in polymer drag reduced wall-bounded turbulence. Phys. Fluids. Manuscript submitted for publication.Google Scholar
White, C. M., Somandepalli, V. S. R. & Mungal, M. G. 2004 The turbulence structure of drag reduced boundary layer flow. Exp. Fluids 36, 62–69.CrossRefGoogle Scholar
Winkel, E. S., Oweis, G. F., Vanapalli, S. A., Dowling, D. R., Perlin, M., Solomon, M. J. & Ceccio, S. L. 2009 High Reynolds number turbulent boundary layer friction drag reduction from wall-injected polymer solutions. J. Fluid Mech. 621, 259–288.CrossRefGoogle Scholar
Wu, J. & Tulin, M. P. 1972 Drag reduction by ejecting additive solutions into a pure water boundary layer. Trans. ASME D: J. Basic Engng 94, 749–755.CrossRefGoogle Scholar
Yoshizawa, A. 2003 Turbulence-viscosity reduction mechanism based on anisotropic turbulence effects. Phys. Fluids 15, 3875–3878.CrossRefGoogle Scholar