VELOCITY DISTRIBUTION AND FRICTION FACTORS 
IN FLOWS WITH DRAG REDUCTION 
Michael Poreh and Yona Dimant 
Technion - Israel Instttute of Technology 
Hatfa, Israel 
ABSTRACT 
A simple descriptive model, based on van Driest's 
mixing length L =ky [1 - exp (-y+/A*)] with a va- 
riable damping parameter At, is proposed to re- 
present the effect of linear macromolecules in di- 
lute solutions on the wall region in boundary layer 
flows. Measurements used to support an elastic 
sublayer model for drag reduction are shown to be 
in better agreement with the proposed model. A 
relation between At and parameters of the poly- 
mer solution and the flow identified by Virk (1971), 
is derived for the range where Virk's correlations 
are valid. The maximum drag reduction appears 
to be associated with an asymptotic value of At, 
INTRODUCTION 
The ability of minute quantities of high molecular weight poly- 
mers to reduce the turbulent skin friction and thus to decrease the drag 
of underwater bodies, has excited many investigations of the phenome- 
non of drag reduction. Theoretical efforts to explain the mechanism of 
drag reduction have not been very successful, probably because drag 
reduction is affected by an interaction between the molecules and the 
time-dependent, non-linear turbulent flow near the edge of the viscous 
sublayer. On the other-hand, experimental and semi-empirical studies 
have succeeded in documenting many features of simple drag reduction 
flows and describing them in approximate phenomenological models. 
The earlier descriptions of such flows employed a two-layer 
model to describe the mean velocity profile (Meyer 1966, Elata et al 
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