TURBULENCE IN VISCOELASTIC FLUIDS 



F. A. Seyer and A. B. Metzner 



University of Delaware 



Newark, Delaware 



INTRODUCTION 



Recent analyses and experimental studies dealing with turbulence and with 

 unsteady flows of dilute polymeric solutions will be considered. Emphasis will 

 be placed on those contributions which lead to proper descriptions of the rele- 

 vant fluid properties and the interactions between these properties and the flow 

 field, to yield mechanistic interpretations of the turbulent characteristics of 

 these materials. 



This paper will show that while the large-scale portion of the turbulent 

 spectrum appears to be similar to that of Newtonian systems, major decreases 

 in the energy levels are predicted at high wavenumbers. These predictions find 

 some experimental support, but a major obstacle to research in this area ap- 

 pears to be a rather general inapplicability of the experimental devices nor- 

 mally used to study turbulent velocity fields. As a result only a few detailed 

 measurements are available, and of these some are probably either in error or 

 of restricted generality. Methods for overcoming these deficiencies will be 

 considered, but no ready solutions of direct and easy applicability will be noted. 



Interest in the area of turbulent flow of dilute polymeric solutions has been 

 motivated by the important observation that the drag coefficients of such sys- 

 tems in turbulent flow may be significantly lower than those of Newtonian or 

 other purely viscous fluids. Most available evidence suggests this effect to be 

 due to the viscoelastic properties of these systems, though, as will be seen, few 

 really definitive results are available with which to test this hypothesis rigor- 

 ously. Few results are available owing to the difficulty of studying both the de- 

 tailed turbulent motion in these systems and their physical properties; results 

 obtained using conventional experimental techniques may be subject to serious 

 error. Thus the hypothesis concerning the importance of viscoelasticity, while 

 tentatively accepted and used herein, remains in need of much more rigorous 

 tests than have been carried out to date. Comments concerning its limitations 

 are available elsewhere (Refs. 45 and 51). 



The format of this paper is as follows: 



1. Continuum properties of polymeric solutions, and the relationships of 

 these to the turbulent behavior of these systems. 



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