Skip to main content Accessibility help

Streamwise development of turbulent boundary-layer drag reduction with polymer injection

  • Y. X. HOU (a1), V. S. R. SOMANDEPALLI (a1) and M. G. MUNGAL (a1)


Zero-pressure-gradient turbulent boundary-layer drag reduction by polymer injection has been studied with particle image velocimetry. Flow fields ranging from low to maximum drag reduction have been investigated. A previously developed technique – the (1 − y/δ) fit to the total shear stress profile – has been used to evaluate the skin friction, drag reduction and polymer stress. Current results agree well with the semi-log plot of drag reduction vs. normalized polymer flux which has been used by previous workers and can be used as a guide to optimize the use of polymer from a single injector. Detailed flow-field statistics show many special features that pertain to polymer flow. It is shown that the mean velocity responds quickly to the suddenly reduced wall shear stress associated with polymer injection. However, it takes a much longer time for the entire Reynolds shear stress profile to adjust to the same change. The Reynolds shear stress profiles in wall units can be higher than unity and this unique feature can be used to further judge whether the flow is in equilibrium. The streamwise evolution of drag reduction magnitude is used to divide the flow into three regions: development region; steady-state region; and depletion region. The polymer stress is estimated and found to be proportional to drag reduction in the depletion region, but not necessarily so in the other regions. The interaction between injected polymer and turbulent activity in a developing boundary-layer flow is dependent upon the flow history and it produces an equally complex relationship between polymer stress and drag reduction. The stress balance in the boundary layer and the dynamical contribution of the various stresses to the total stress are evaluated and it is seen that the polymer stresses can account for up to 25% of the total stress. This finding is in contrast to channel flows with homogeneous polymer injection where the polymer stress is found to account for up to 60% of the total stress.



Hide All
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. Exps. Fluids 11, 916.
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319346.
Dimitropoulos, C., Sureshkumar, R. & Beris, A. 1998 Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: effect of variation of rheological parameters. J. Non-Newtonian Fluid Mech. 79, 433468.
Dimitropoulos, C., Sureshkumar, R., Beris, A. & Handler, R. 2001 Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow. Phys. Fluids 13, 10161027.
Dimitropoulos, C. D., Dubief, Y., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2005 Direct numerical simulation of polymer-induced drag reduction in turbulent boundary layer flow. Phys. Fluids 17, 011705.
Dubief, Y., White, C., Terrapon, V. E., Shaqfeh, E., Moin, P. & Lele, S. 2004 On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows. J. Fluid Mech. 514, 271280.
Erm, L. P. 1988 Low Reynolds-number turbulent boundary layers. PhD thesis, University of Melbourne.
Fernholz, H. H. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerospace Sci. 32, 245311.
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, 435466.
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, 171180.
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids, 14 (11), L7376.
Gupta, V. K., Sureshkumar, R. & Khomami, B. 2005 Passive scalar transport in polymer drag-reduced turbulent channel flow. AIChE J., 51, 19381950.
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. Exps. Fluids 40, 589600.
Jimenez, J. & Pinelli, A. 1999 The autonomous cycle of near wall turbulence. J. Fluid Mech. 398, 335339.
Koskie, J. E. & Tiederman, W. G. 1991 a Turbulent structure and polymer drag reduction in adverse pressure gradient boundary layers. PME-FM-91-3, Office of Naval Research.
Koskie, J. E. & Tiederman, W. G. 1991 b Polymer drag reduction of a zero-pressure-gradient boundary layer. Phys. Fluids A3, 24712473.
Latto, B. & El Reidy, K. F. 1976 Diffusion of polymer additives in a developing turbulent boundary layer. J. Hydronaut. 10, 135139.
McComb, W. D. & Rabie, L. H. 1982 Local drag reduction due to injection of polymer solution into turbulent flow in a pipe. Part 1: dependence on local polymer concentration; and Part II: laser Doppler measurements of turbulence structure. AIChE J. 28, 547565.
Min, T., Yoo, J. Y., Choi, H. & Joseph, D. D. 2003 Drag reduction by polymer additives in a turbulent channel flow. J. Fluid Mech. 486, 213238.
Oldaker, D. K. & Tiederman, W. G. 1977 Structure of the turbulent boundary layer in drag reducing pipe flow. Phys. Fluids 20, 133144.
Paschkewitz, J. S., Dimitropoulos, C. D., Hou, Y. X., Somandepalli, V. S. R., Mungal, M. G., Shaqfeh, E. S. G. & Moin, P. 2005 An experimental and numerical investigation of drag reduction in a turbulent boundary layer using a rigid rodlike polymer. Phys. Fluids 17, 085101.
Petrie, H. L. & Fontaine, A. A. 1996 Comparison of turbulent boundary layer modifications with slot-injected and homogeneous drag-reducing polymer solutions, Proc. Fluids Eng. Div. Conf. ASME vol. 2, pp. 205–210.
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. Exps. Fluids 35, 823.
Poreh, M. & Cermak, J. E. 1964 Study of diffusion from a line source in a turbulent boundary layer. Intl J. Heat Mass Transfer 7, 10831095.
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layers at low Reynolds numbers. Phys. Fluids 24, 802811.
Roach, P. E. & Brieley, D. H. 1989 The influence of a turbulent freestream on zero pressure gradient transitional boundary layer development including the condition test cases T3A and T3B. In Numerical Simulation of Unsteady Flows and Transition to Turbulence (ed. Pironneau, O. et al. ), Cambridge University Press.
Sibilla, S. & Baron, A. 2002 Polymer stress statistics in the near-wall turbulent flow of a drag reducing solution. Phys. Fluids 14, 11231136.
Somandepalli, V. S. R. 2006 Combined PIV and PLIF measurements in a polymer drag reduced turbulent boundary layer. PhD thesis, Mechanical Engineering Department, Stanford University.
Terrapon, V., Dubief, Y., Moin, P., Shaqfeh, E. & Lele, S. 2004 Simulated polymer stretch in a turbulent flow using Brownian dynamics. J. Fluid Mech. 504, 6171.
Tiederman, W. G., Luchik, T. S. & Bogard, D. G. 1985 Wall layer structure and drag reduction. J. Fluid Mech. 156, 419437.
denToonder, J. Toonder, J., Hulsen, M., Kuiken, G. & Nieuwstadt, F. 1997 Drag reduction by polymer additives in a turbulent pipe flow: numerical and laboratory experiments. J. Fluid Mech. 337, 193231.
Vdovin, A. V. & Smol'yakov, A. V. 1978 Diffusion of polymer solutions in a turbulent boundary layer. Zh. Prikl. Mekh. Tekh. Fiz. 2, 6673 (transl. in UDC 532.526, pp. 196-201, Plenum).
Vdovin, A. V. & Smol'yakov, A. V. 1981 Turbulent diffusion of polymers in a boundary layer. Zh. Prikl. Mekh. Tekh. Fiz. 4, 98104 (transl. in UDC532.526 (1982) 526–531, Plenum).
Virk, P. S. 1975 Drag reduction fundamentals. AIChE J. 22, 625656.
Walker, D. T. & Tiederman, W. G. 1988 Turbulent structure and mass transport in a channel flow with polymer injection. Rep. PME-FM-22-2. Purdue University.
Walker, D. T. & Tiederman, W. G. 1989 The concentration field in a turbulent channel flow with polymer injection at the wall. Exps. Fluids 8, 8694.
Walker, D. T. & Tiederman, W. G. 1990 Turbulent structure in a channel flow with polymer injection at the wall. J. Fluid Mech. 218, 377403.
Walker, D. T., Tiederman, W. G. & Luchik, T. S. 1986 Optimization of the injection process for drag reduction additives. Exps. Fluids 4, 114120.
Warholic, M. D., Massah, H. & Hanratty, T. J. 1999 Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing. Exps. Fluids 27, 461472.
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. Exps. Fluids 31, 474483.
White, C. M., Somandepalli, V. S. R. & Mungal, M. G. 2004 The turbulence structure of drag-reduced boundary layer flow. Exps. Fluids 36, 6269.
White, C. M., Somandepalli, V. S. R., Dubief, Y. & Mungal, M. G. 2006 Dynamical contributions to the skin friction in polymer drag reduced wall-bounded turbulence. Phys. Fluids (submitted).
White, F. M. 1991 Viscous Fluid Flow 2nd edn. McGraw–Hill.
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, 749755.
MathJax is a JavaScript display engine for mathematics. For more information see

Related content

Powered by UNSILO

Streamwise development of turbulent boundary-layer drag reduction with polymer injection

  • Y. X. HOU (a1), V. S. R. SOMANDEPALLI (a1) and M. G. MUNGAL (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.