Summary
A link between the decoupling of the Reynolds stress and the temporal relaxation of turbulent fluctuations, controlled by a finite propagation of momentum at small spatial scales, has been developed for turbulent flow of a Maxwell fluid. A characteristic time between turbulent bursts from the wall region, a relaxation time for the velocity, space-time correlation, and the intensity of turbulent fluctuations normal to the mean flow govern the behavior of the Reynolds stress in the near wall region. The theory predicts quantitative extents of drag reduction in agreement with experiments and, more importantly, contains the familiar saturation and onset features of turbulent drag reduction.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Seyer, F. A. and A. B. Metzner; Turbulence Phenomena in Drag-Reducing Systems. AIChE J. 15 (1969) 426.
Logan, S. E.; Laser Velocimeter Measurement of Reynold’s Stress and Turbulence in Dilute Polymer Solutions. AIAA J. 10 (1972) 962.
Ruckenstein, E; On the Mechanism of Drag Reduction in Turbulent Flow of Viscoelastic Liquids. Chem. Eng. Sci. 26 (1971) 1075.
Einstein, H. A. and H. Li; The Viscous Sublayer Along a Smooth Boundary, Proc. Am. Soc. Civil Engrs., J. Eng. Mech. Div., 82, 293 (1956).
Monin, A. S. and A. M. Yaglom; Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 1. Cambridge: The MIT Press 1971.
Tennekes, H. and J. L. Lumley; A First Course in Turbulence. Cambridge: The MIT Press 1972.
Astarita, G. and G. Marrucci; Principles of Non-Newtonian Fluid Mechanics. New York: McGraw-Hill 1974.
Lumley, J. L.; Drag Reduction by Additives. Ann. Rev. Fluid Mech. 1 (1969) 367.
Armstrong, R. and M. S. Jhon; A Self-Consistent Theoretical Approach to Polymer Induced Turbulent Drag Reduction. Dept. Chem. Eng., Carnegie-Mellon University (personal communication) 1984.
Hershey, H. C. and J. L. Zakin; Existence of Two Types of Drag Reduction in Pipe Flow of Dilute Polymer Solutions. Ind. Eng. Chem. Fund. 6 (1967) 381.
Patterson, G. K. and J. L. Zakin; Prediction of Drag Reduction with a Viscoelastic Model. AIChE J. 14 (1968) 434.
Virk, P. S.; Drag Reduction Fundamentals. AIChE J. 21 (1975) 625.
Snellenberger, R. W. and C. A. Petty; Estimates of Average Mass Transfer Rates Using An Approximate Hydrodynamic Green’s Function. Chem. Eng. Commun. 20 (1983) 311
Hill, J. C. and C. A. Petty; A Statistical Theory of Turbulent Mass Transfer Induced By a Mean Concentration Gradient. PACHEC III, Seoul, Korea, May 8–11, 1983.
Morse, P. M. and H. Feshbach; Methods of Theoretical Physics, Part I. New York: McGraw-Hill 1953.
Berman, N. S.; Drag Reduction by Polymers. Ann. Rev. Fluid Mech. 10 (1978) 47.
Schummer, P. and W. Thielen; Structure of Turbulence in Viscoelastic Fluids. Chem. Eng. Commun. 4 (1980) 593.
Lee, W. K., R. C. Vaseleski, and A. B. Metzner; Turbulent Drag Reduction in Polymeric Solutions Containing Suspended Fibers. AIChE J. 20 (1974) 128.
Fortuna, G. and T. J. Hanratty; The Influence of Drag-Reducing Polymers on Turbulence in the Viscous Sublayer. J. Fluid Mech. 53 (1972) 575.
Achia, B. V., and D. W. Thompson; Structure of the Turbulent Boundary in Drag-Reducing Pipe Flow. J. Fluid Mech. 81 (1977) 439.
Yao, H. T.; The Application of Turbulent Relaxation Models To Mass Transfer Near Interfaces At High Molecular Schmidt Numbers. Ph.D. Dissertation, Michigan State University 1982.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer, Berlin Heidelberg
About this paper
Cite this paper
Lyons, S., Petty, C.A. (1985). Predictions of Turbulent Drag Reduction for a Linear Viscoelastic Fluid. In: Gampert, B. (eds) The Influence of Polymer Additives on Velocity and Temperature Fields. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82632-0_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-82632-0_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-82634-4
Online ISBN: 978-3-642-82632-0
eBook Packages: Springer Book Archive