TURBULENT DRAG REDUCTION

A very remarkable effect was observed by Toms during World War II when pumping Napalm (a jellied solution of a polymer in gasoline). He found that the polymer solution could be pumped through pipes in turbulent flow with considerably lower friction loss than exhibited by the gasoline at the same flow rate in the same pipe without the polymer. This phenomenon, 

Although the exact mechanism is debatable, Darby and Chang (1984) and Darby and Pivsa-Art (1991) have presented a model for turbulent drag reduction based on the fact that solutions of very high polymers are visco- 

The model for turbulent drag reduction developed by Darby and Chang (1984) and later modified by Darby and Pivsa-Art (1991) shows that for smooth tubes the friction factor versus Reynolds number relationship for Newtonian fluids (e.g., the Colebrook or Churchill equation) may also be used for drag-reducing flows, provided (1) the Reynolds number is defined with respect to the properties (e.g., viscosity) of the Newtonian solvent and (3) the Fanning friction factor is modified as follows  

The complete expression for tVDe is given by Darby and Pivsa-Art (1991) as a function of the viscoelastic fluid properties of the fluid (i.e., the Carreau parameters /y0, X, and p). This expression is 

ARe s is the Reynolds number based on the solvent properties, /zs is the solvent viscosity, D is the pipe diameter, F is the velocity in the pipe, and A is the fluid time constant (from the Carreau model fit of the viscosity curve). 

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Mechanochemical and chemical reaction engineering aspects in the break down of turbulent drag reduction of cationic surfactant solutions... 

H.J. Choi and M.S. Jhon, Polymer-induced turbulent drag reduction, Industrial Engineering Chemistry Research, 35(9) 2993-2998, January 1996. 

Armstrong R, Jhon MS (1984) A self-consistent theoretical approach to polymer induced turbulent drag reduction Chem Eng Commun 30 99... 

Balakrishnan C, Gordon RJ (1975) Influence of molecular conformation and intermolecular interactions on turbulent drag reduction J Appl Polym Sci, 19 909... 

Banijamali SH, Merrill EW, Smith KA, Peebles LH (1974) Turbulent drag reduction by polyacrylic acid AIChE J 20 824... 

Bewersdorff HW, Singh RP (1987) Turbulent drag reduction and relaminarisation by xanthan gum IUTAM-Symposium, Bangalore, India... 

Deshmukh SR, Chaturvedi PN, Singh RP (1985) The turbulent drag reduction by graft copolymers of guar gum and polyacrylamide J Appl Polym Sci 30 4013... 

Dschagarowa E, Mennig G (1977) Influence of molecular weight and molecular conformation of polymers on turbulent drag reduction Rheol Acta 16 309... 

Gordon RJ (1970) On the explanations and correlations of turbulent drag reduction in dilute macromolecular solutions J Appl Polym Sci 14 2097... 

Kim OK, Little RC, Ting RY (1973) Polymer structural effects in turbulent drag reduction AIChE Symp Series 69 39... 

Metzner AB, Kale DD (1976) Turbulent drag reduction in dilute fiber suspensions Mechanistic considerations AIChE J 22 669... 

Metzner AB (1977) Polymer solution and fiber suspension rheology and their relationship to turbulent drag reduction Phys Fluids 20 145... 

Stenberg LG, Lagerstedt T, Lindgren ER (1977) Polymer additives mixing and turbulent drag reduction Phys Fluids 20 276... 

Virk, P.S. Wagger, D.L. The effect of salinity on turbulent drag reduction by polyelectrolyte additives at high Reynolds numbers. Addendum to the Proceedings of the International Symposium on Seawater Drag Reduction, Newport, RI, Jul 22-23 Office of Naval Research Arlington VA, 1998. 

Over the past 60 years, a great deal of applied and theoretical research has been carried out on both polymer and surfactant DRAs because of their potential useful applications and the influence of the additives on both turbulent structure and rheology. Important results include the identification of maximum drag reduction asymptotes (MDRAs) both Virk s MDRA for polymer solutions [Virk et al., 1970 see Eq. (2.5)] and Zakin et al. s MDRA for surfactant solutions [Zakin et al., 1996 see Eq. (2.6)], relating solution nanostructures and rheological properties to macroscopic DR phenomena hypotheses on the influence of DRAs on turbulent structures, mechanisms for turbulent drag reduction, developing heat transfer enhancement techniques, and so on. 

Turbulent drag reduction in homogeneous flows by polymer or surfactant additives is a striking phenomenon with both theoretical and practical implications. On the theoretical side, it remains a challenge to fully understand the drag reduction mechanism and the interaction details between DRAs and the turbulent flow field. New methods, especially computational ones, have been developed to solve this problem, such as direct numerical simulations and stochastic simulations. On the application... 

Choi, H. J., Kim, C. A., Sohn, J.-L, and Jhon, M. S., An exponential decay function for polymer degradation in turbulent drag reduction, Polym. Degrad. Stabil., 69, 341-346... 

Kalashnikov, V. N., Degradation accompanying turbulent drag reduction by polymer additives, J. Non-Newtonian Fluid Mech., 103, 105-121 (2002). 

Kawaguchi, Y, Tawaraya, Y., Yabe, A., Hishida, K., and Maeda, M., Active control of turbulent drag reduction in surfactant solutions by wall heating, Proc. ASME Fluids Eng. Div., 237, 47-52 (1996). 

Liberatore, M. W., Baik, S., McHugh, A. J., and Hanratty, T. J., Turbulent drag reduction of polyacrylamide solutions effect of degradation on molecular weight distribution, J. Non-Newtonian Fluid Meek, 123, 175-183 (2004). 

Singh, R. P., Turbulent drag reduction by polymer-based mixtures and graft copolymers, Curr. ScL, 68, 736-739 (1995). 

Gramain P, Borreill J (1978) Influence of molecular weight and molecular structure of polystyrenes on turbulent drag reduction. Rheol Acta 17 303-311... 

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