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Flow-induced degradation of drag-reducing polymer solutions within a high-Reynolds-number turbulent boundary layer

Published online by Cambridge University Press:  22 February 2011

BRIAN R. ELBING ,
MICHAEL J. SOLOMON ,
MARC PERLIN ,
DAVID R. DOWLING  and
STEVEN L. CECCIO
BRIAN R. ELBING*
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
MICHAEL J. SOLOMON
Affiliation:
Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
MARC PERLIN
Affiliation:
Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA
DAVID R. DOWLING
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
STEVEN L. CECCIO
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
*
†Present address: Pennsylvania State University, Applied Research Laboratory, State College, PA 16804, USA. Email address for correspondence: [email protected]
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Abstract

Polymer drag reduction, diffusion and degradation in a high-Reynolds-number turbulent boundary layer (TBL) flow were investigated. The TBL developed on a flat plate at free-stream speeds up to 20ms−1. Measurements were acquired up to 10.7m downstream of the leading edge, yielding downstream-distance-based Reynolds numbers up to 220 million. The test model surface was hydraulically smooth or fully rough. Flow diagnostics included local skin friction, near-wall polymer concentration, boundary layer sampling and rheological analysis of polymer solution samples. Skin-friction data revealed that the presence of surface roughness can produce a local increase in drag reduction near the injection location (compared with the flow over a smooth surface) because of enhanced mixing. However, the roughness ultimately led to a significant decrease in drag reduction with increasing speed and downstream distance. At the highest speed tested (20ms−1) no drag reduction was discernible at the first measurement location (0.56m downstream of injection), even at the highest polymer injection flux (10 times the flux of fluid in the near-wall region). Increased polymer degradation rates and polymer mixing were shown to be the contributing factors to the loss of drag reduction. Rheological analysis of liquid drawn from the TBL revealed that flow-induced polymer degradation by chain scission was often substantial. The inferred polymer molecular weight was successfully scaled with the local wall shear rate and residence time in the TBL. This scaling revealed an exponential decay that asymptotes to a finite (steady-state) molecular weight. The importance of the residence time to the scaling indicates that while individual polymer chains are stretched and ruptured on a relatively short time scale (~10−3s), because of the low percentage of individual chains stretched at any instant in time, a relatively long time period (~0.1s) is required to observe changes in the mean molecular weight. This scaling also indicates that most previous TBL studies would have observed minimal influence from degradation due to insufficient residence times.

JFM classification

Flow Control: Drag reduction Non-Newtonian Flows: Polymers Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 670 , 10 March 2011 , pp. 337 - 364
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Bailey, F. E. & Callard, R. W. 1959 Some properties of poly(ethylene oxide) in aqueous solutions. J. Appl. Polym. Sci. 1 (1), 56–62.CrossRefGoogle Scholar
Benzi, R., Ching, E. S. C., Horesh, N. & Procaccia, I. 2004 Theory of concentration dependence in drag reduction by polymers and of the maximum drag reduction asymptote. Phys. Rev. Lett. 92 (7), 078302.Google Scholar
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
Choi, H. J. & Jhon, M. S. 1996 Polymer-induced turbulent drag reduction. Indust. Engng Chem. Res. 35 (9), 2993–2998.CrossRefGoogle Scholar
Culter, J. D., Zakin, J. L. & Patterson, G. K. 1975 Mechanical degradation of dilute solutions of high polymers in capillary tube flow. J. Appl. Polym. Sci. 19, 3235–3240.CrossRefGoogle Scholar
Dubief, Y., White, C. M., Terrapon, V. E., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2004 On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows. J. Fluid Mech. 514, 271–280.CrossRefGoogle Scholar
Elbing, B. R., Dowling, D. R., Perlin, M. & Ceccio, S. L. 2010 Diffusion of drag-reducing polymer solutions within a rough-walled turbulent boundary layer. Phys. Fluids 22, 045102.CrossRefGoogle Scholar
Elbing, B. R., Winkel, E. S., Lay, K. A., Ceccio, S. L., Dowling, D. R. & Perlin, M. 2008 Bubble-induced skin-friction drag reduction and the abrupt transition to air-layer drag reduction. J. Fluid Mech. 612, 201–236.CrossRefGoogle Scholar
Elbing, B. R., Winkel, E. S., Solomon, M. J. & Ceccio, S. L. 2009 Degradation of homogeneous polymer solutions in high shear turbulent pipe flow. Exp. Fluids 47, 1033–1044.CrossRefGoogle Scholar
Etter, R. J., Cutbirth, J. M., Ceccio, S. L., Dowling, D. R. & Perlin, M. 2005 High Reynolds number experimentation in the U.S. Navy's William B. Morgan large cavitation channel. Meas. Sci. Technol. 16 (9), 1701–1709.CrossRefGoogle 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. 238, 435–466.CrossRefGoogle Scholar
Frenkel, J. 1944 Orientation and rupture of linear macromolecules in dilute solutions under the influence of viscous flow. Acta Physicochim. URSS 19 (1), 51–76.Google Scholar
Fruman, D. H. & Tulin, M. P. 1976 Diffusion of a tangential drag-reducing polymer injection on a flat plate at high Reynolds number. J. Ship Res. 20 (3), 171–180.CrossRefGoogle Scholar
Gupta, V. K., Sureshkumar, R. & Khomami, B. 2004 Polymer chain dynamics in Newtonian and viscoelastic turbulent channel flows. Phys. Fluids 16 (5), 1546–1566.CrossRefGoogle Scholar
Hansen, R. J. & Little, R. C. 1971 Pipe diameter, molecular weight, and concentration effects on the onset of drag reduction. Chem. Engng Prog. Symp. Ser. 67, 93–97.Google Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Kalashnikov, V. N. 1994 Shear-rate dependent viscosity of dilute polymer solutions. J. Rheol. 38 (5), 1385–1403.CrossRefGoogle Scholar
Kalashnikov, V. N. 1998 Dynamical similarity and dimensionless relations for turbulent drag reduction by polymer additives. J. Non-Newtonian Fluid Mech. 75, 209–230.CrossRefGoogle Scholar
Kalashnikov, V. N. 2002 Degradation accompanying turbulent drag reduction by polymer additives. J. Non-Newtonian Fluid Mech. 103, 105–121.CrossRefGoogle Scholar
Kim, C. A., Kim, J. T., Lee, K., Choi, H. J. & Jhon, M. S. 2000 Mechanical degradation of dilute polymer solutions under turbulent flow. Polymer 41 (21), 7611–7615.CrossRefGoogle Scholar
Kim, K., Adrian, R. J., Balachandar, S. & Sureshkumar, R. 2008 Dynamics of hairpin vortices and polymer-induced turbulent drag reduction. Phys. Rev. Lett. 100, 134504.Google Scholar
Kim, K., Li, C. F., Sureshkumar, R., Balachandar, S. & Adrian, R. J. 2007 Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. J. Fluid Mech. 584, 281–299.CrossRefGoogle Scholar
Koskie, J. E. & Tiederman, W. G. 1991 Polymer drag reduction of a zero-pressure-gradient boundary layer. Phys. Fluids 3 (10), 2471–2473.CrossRefGoogle Scholar
Larson, R. G. 1992 Instabilities in viscoelastic flows. Rheol. Acta 31 (3), 2123–263.CrossRefGoogle Scholar
Larson, R. G. 1999 The Structure and Rheology of Complex Fluids. Oxford University Press.Google Scholar
Li, W., Xi, L. & Graham, M. D. 2006 Nonlinear travelling waves as a framework for understanding turbulent drag reduction. J. Fluid Mech. 565, 353–362.CrossRefGoogle Scholar
Little, R. C. & Patterson, R. L. 1974 Turbulent friction reduction by aqueous poly(ethylene oxide) polymer solutions as a function of salt concentration. J. Appl. Polym. Sci. 18, 1529–1539.CrossRefGoogle Scholar
Merrill, E. W. & Horn, A. F. 1984 Scission of macromolecules in dilute solution: extensional and turbulent flows. Polym. Commun. 25 (5), 144–146.Google Scholar
Moussa, T. & Tiu, C. 1994 Factors affecting polymer degradation in turbulent pipe flow. Chem. Engng Sci. 49 (10), 1681–1692.CrossRefGoogle Scholar
Nakken, T., Tande, M. & Elgsaeter, A. 2001 Measurements of polymer induced drag reduction and polymer scission in Taylor flow using standard double-gap sample holders with axial symmetry. J. Non-Newtonian Fluid Mech. 97 (1), 1–12.Google Scholar
Oweis, G. F., Winkel, E. S., Cutbirth, J. M., Perlin, M., Ceccio, S. L. & Dowling, D. R. 2010 The mean velocity profile of a smooth flat-plate turbulent boundary layer at high Reynolds number. J. Fluid Mech. 665, 357–381.CrossRefGoogle Scholar
Paterson, R. W. & Abernathy, F. H. 1970 Turbulent flow drag reduction and degradation with dilute polymer solutions. J. Fluid Mech. 43 (4), 689–710.CrossRefGoogle Scholar
Petrie, H. L., Brungart, T. A. & Fontaine, A. A. 1996 Drag reduction on a flat plate at high Reynolds number with slot-injected polymer solutions. Proc. ASME Fluids Engng Div. 237, 3–9.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 modifications with slot-injected and homogeneous drag-reducing polymer solutions. Proc. ASME Fluids Engng Div. 237, 205–210.Google Scholar
Petrie, H., Fontaine, A., Moeny, M. & Deutsch, S. 2005 Experimental study of slot-injected polymer drag reduction. In Proc. 2nd Intl. Symp. on Seawater Drag Reduction, Busan, Korea, pp. 605–620.Google Scholar
Poreh, M. & Cermak, J. E. 1964 Study of diffusion from a line source in a turbulent boundary layer. Intl J. Heat Mass Transfer 7, 1083–1095.CrossRefGoogle Scholar
Sanders, W. C., Winkel, E. S., Dowling, D. R., Perlin, M. & Ceccio, S. L. 2006 Bubble friction drag reduction in a high-Reynolds-number flat-plate turbulent boundary layer. J. Fluid Mech. 552, 353–380.CrossRefGoogle Scholar
Sellin, R. H. J., Hoyt, J. W., Pollert, J. & Scrivener, O. 1982 The effect of drag-reducing additives on fluid flows and their industrial applications. Part 2. Basic applications and future proposals. J. Hydraul. Res. 20 (3), 235–292.CrossRefGoogle Scholar
Sim, H. G., Khomami, B. & Sureshkumar, R. 2007 Flow-induced chain scission in dilute polymer solutions: algorithm development and results for scission dynamics in elongational flow. J. Rheol. 51 (6), 1223–1251.CrossRefGoogle Scholar
Stone, P. A., Roy, A., Larson, R. G., Waleffe, F. & Graham, M. D. 2004 Polymer drag reduction in exact coherent structures of plan shear flow. Phys. Fluids 16 (9), 3470–3482.CrossRefGoogle Scholar
Stone, P. A., Waleffe, F. & Graham, M. D. 2002 Toward a structural understanding of turbulent drag reduction: non-linear coherent states in viscoelastic shear flows. Phys. Rev. Lett. 89, 208301.Google Scholar
Vanapalli, S. A., Ceccio, S. L. & Solomon, M. J. 2006 Universal scaling for polymer chain scission in turbulence. Proc. Natl Acad. Sci. USA 103 (45), 16660–16665.Google Scholar
Vanapalli, S. A., Islam, M. T. & Solomon, M. J. 2005 Scission-induced bounds on maximum polymer drag reduction in turbulent flow. Phys. Fluids 17 (9), 095108.Google Scholar
Vdovin, A. V. & Smol'yakov, A. V. 1978 Diffusion of polymer solutions in a turbulent boundary layer. J. Appl. Mech. Tech. Phys. 19 (2), 66–73.CrossRefGoogle Scholar
Vdovin, A. V. & Smol'yakov, A. V. 1981 Turbulent diffusion of polymers in a boundary layer. J. Appl. Mech. Tech. Phys. 22 (4), 98–104.Google Scholar
Virk, P. S. 1975 Drag reduction fundamentals. J. Am. Inst. Chem. Engng 21 (4), 625–656.Google Scholar
Virk, P. S., Merrill, E. W., Mickley, H. S., Smith, K. A. & Mollo-Christensen, E. L. 1967 The toms phenomenon: turbulent pipe flow of dilute polymer solutions. J. Fluid Mech. 20, 22–30.Google 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.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
White, F. M. 2006 Viscous Fluid Flow, 3rd edn, pp. 430–438. McGraw-Hill.Google Scholar
Winkel, E. S., Oweis, G., Vanapalli, S. A., Dowling, D. R., Perlin, M., Solomon, M. J. & Ceccio, S. L. 2006 Friction drag reduction at high Reynolds numbers with wall injected polymer solutions. In 26th Symp. on Naval Hydrodynamics, Rome, Italy.Google Scholar
Winkel, E. S., Oweis, G., 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.Google Scholar
Wu, J. & Tulin, M. P. 1972 Drag reduction by ejecting additive solutions into pure-water boundary layer. Trans. ASME: J. Basic Engng 94, 749–756.Google Scholar