Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T15:40:20.116Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  01 February 2008

Y. X. HOU ,
V. S. R. SOMANDEPALLI  and
M. G. MUNGAL
Y. X. HOU
Affiliation:
Mechanical Engineering Department, Stanford University, Stanford, CA 94305, [email protected]
V. S. R. SOMANDEPALLI
Affiliation:
Mechanical Engineering Department, Stanford University, Stanford, CA 94305, [email protected]
M. G. MUNGAL
Affiliation:
Mechanical Engineering Department, Stanford University, Stanford, CA 94305, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 597 , 25 February 2008 , pp. 31 - 66
Copyright
Copyright © Cambridge University Press 2008

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

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, 9–16.CrossRefGoogle Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
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, 433–468.CrossRefGoogle Scholar
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, 1016–1027.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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, 271–280.CrossRefGoogle Scholar
Erm, L. P. 1988 Low Reynolds-number turbulent boundary layers. PhD thesis, University of Melbourne.Google Scholar
Fernholz, H. H. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerospace Sci. 32, 245–311.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
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 (11), L73–76.CrossRefGoogle Scholar
Gupta, V. K., Sureshkumar, R. & Khomami, B. 2005 Passive scalar transport in polymer drag-reduced turbulent channel flow. AIChE J., 51, 1938–1950.CrossRefGoogle 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. Exps. Fluids 40, 589–600.CrossRefGoogle Scholar
Jimenez, J. & Pinelli, A. 1999 The autonomous cycle of near wall turbulence. J. Fluid Mech. 398, 335–339.CrossRefGoogle Scholar
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.Google Scholar
Koskie, J. E. & Tiederman, W. G. 1991 b Polymer drag reduction of a zero-pressure-gradient boundary layer. Phys. Fluids A3, 2471–2473.CrossRefGoogle Scholar
Latto, B. & El Reidy, K. F. 1976 Diffusion of polymer additives in a developing turbulent boundary layer. J. Hydronaut. 10, 135–139.CrossRefGoogle Scholar
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, 547–565.CrossRefGoogle Scholar
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, 213–238.CrossRefGoogle Scholar
Oldaker, D. K. & Tiederman, W. G. 1977 Structure of the turbulent boundary layer in drag reducing pipe flow. Phys. Fluids 20, 133–144.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.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. Exps. Fluids 35, 8–23.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
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layers at low Reynolds numbers. Phys. Fluids 24, 802–811.CrossRefGoogle Scholar
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.Google Scholar
Sibilla, S. & Baron, A. 2002 Polymer stress statistics in the near-wall turbulent flow of a drag reducing solution. Phys. Fluids 14, 1123–1136.CrossRefGoogle Scholar
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.Google Scholar
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, 61–71.CrossRefGoogle Scholar
Tiederman, W. G., Luchik, T. S. & Bogard, D. G. 1985 Wall layer structure and drag reduction. J. Fluid Mech. 156, 419–437.CrossRefGoogle Scholar
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, 193–231.Google 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 (transl. in UDC 532.526, pp. 196-201, Plenum).Google Scholar
Vdovin, A. V. & Smol'yakov, A. V. 1981 Turbulent diffusion of polymers in a boundary layer. Zh. Prikl. Mekh. Tekh. Fiz. 4, 98–104 (transl. in UDC532.526 (1982) 526–531, Plenum).Google Scholar
Virk, P. S. 1975 Drag reduction fundamentals. AIChE J. 22, 625–656.CrossRefGoogle Scholar
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.Google Scholar
Walker, D. T. & Tiederman, W. G. 1989 The concentration field in a turbulent channel flow with polymer injection at the wall. Exps. Fluids 8, 86–94.CrossRefGoogle 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
Walker, D. T., Tiederman, W. G. & Luchik, T. S. 1986 Optimization of the injection process for drag reduction additives. Exps. Fluids 4, 114–120.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. Exps. Fluids 27, 461–472.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. Exps. Fluids 31, 474–483.CrossRefGoogle Scholar
White, C. M., Somandepalli, V. S. R. & Mungal, M. G. 2004 The turbulence structure of drag-reduced boundary layer flow. Exps. Fluids 36, 62–69.CrossRefGoogle Scholar
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).Google Scholar
White, F. M. 1991 Viscous Fluid Flow 2nd edn. McGraw–Hill.Google 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