An analysis based on the Townsend-Bakewell model of the eddies in the wall regions of turbulent shear flows shows that viscoelastic fluid properties must lead to significant reductions in the rate of production of turbulent energy. This analysis in turn leads to the proper form of the similarity laws for drag reducing fluids, heretofore deduced empirically.Measurements of the axial and radial turbulence intensities for flow through smooth round tubes are reported, as are measurements o f the time-averaged velocity profiles and the drag coefficients. These indicate that for solutions exhibiting drag reduction a t all Reynolds numbers the flow may be transitional to Reynolds numbers of the order of 105. This Design calculations based upon the present results suggest that in large diameter pipelines, or in boundary layers on large objects, drag reduction may not be attainable under conditions of practical interest until fluids having relaxation times an order of magnitude larger than those presently available, but with comparable viscosity levels, are developed or, alternately, until fluids exhibiting Weissenberg numbers which do not change with deformation rate, can be found.A growing number of studies have been undertaken cesses there. A recent detailed study of the Newtonian which aim to characterize or elucidate the physical asflow wit,hin this wall region (3) has shown that the large pects of drag reduction. Several of these (7, 14, 20, 24, eddies exist as counter-rotating pairs with their axes 35, 39, 46) include sufficient ranges of the primary varialong the mean flow direction. In the lateral direction a ables such as tube size, the polymeric additive used and diffuse influx of material occurs which is concentrated its concentration to illustrate the varied nature and extent between the two eddies and rapidly ejected from the of drag reduction and t,he difficulty of obtaining a genboundary layer region owing to the counter-rotation of era1 and quantitative understanding of the phenomenon. the eddy pair. The eddy pattern remains defined to the Although in several instances (10, 22, 24, 28, 39) drag outer edge of the sublayer and as these patterns may be reduction data have been correlated empirically and associated with about 50% of the total turbulent energy several theoretical analysis have been presented (11, 16, they must control to a large extent the radial momentum 41, 42) little consistent information, pertinent to the transport rates which exist in the wall region. From the processes involved in drag reduction, has evolved. Comstreamline patterns presented by Bakewell a graphical pounding this problem is the utility of measurements using analysis has shown (38) that the streamlines are adethe usual tools of research in turbulence, impact, and hotquately described by: wire probes, which has been severely questioned ( 2 , 15, 23, 25, 36) and remains in doubt for viscoelastic fluids. Thus the several experimental investigations in which such tools were employed ( 2 , 12, 13, 28, 44, 4 6 ) , though clea...

No abstract

An experimental study, based on streak photograph determination of instantaneous velocities, was directed at determining the turbulent flow velocity profiles of polymer solutions in circular pipes. The measurements resolve several discrepancies in interpretation of earlier velocity profile measurements in drag reducing systems. In particular, it is shown for dilute drag reducers that the semilogarithmic profile due to Prandtl with the same slope as for Newtonian fluids is quantitatively correct provided Bogue's empirical correction function is applied to the data. For a relatively concentrated solution, data serve to extent on earlier study which has shown the flow to be transitional at surprisingly high values of Reynolds number. he similarity laws for turbulent flow of drag re-

Stress levels in elongational flow of suspensions of long fibers have been determined experimentally using a jet thrust apparatus. Stress levels for fibers with an axis ratio of 340 and a volume fraction of 0.001 exhibit stresses nearly an order of magnitude above values for a pure Newtonian fluid. A recent theory by Batchelor is shown to give the correct dependence of stress on axis ratio and concentration, but the predicted magnitude of stress is generally lower than the experimental values.

Available drag reduction correlations are presented and their utility for engineering scale-up to a scale-up from a correlation based on friction velocity and the availability of some turbulent flow data with the process fluid of interest is compared. A further purpose is to investigate the consequences of polymer modification of the mean flow profile in the outer layer. Emphasis is placed on accuracy and ability to portray the drag reducing activity of complex systems. In the case of very dilute polymeric systems in large conduits, very accurate predictions may be needed to assess the performance of a particular additive. Similarly, equations capable of detailed predictions of observed behavior can provide needed insight into the mechanism of drag reduction. Inasmuch as the semi-logarithmic resistance law, e.g., the Seyer and Metzner model of turbulent viscoelastic flow, provides a scale-up criterion significantly more complicated to use than a number of other models, an engineering approximation to this model is described. It is shown that for accurate predictions to be made at modest levels of drag reduction activity, the model must be modified to compensate for thickening of the sublayer.