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An overview is presented of experimental and theoretical work conducted at the Naval Research Laboratory on the reduction of hydrodynamic drag. The work establishes the effectiveness of certain chemical additives in reducing drag and defines the character of laminar, transitional, and turbulent flows when such additives are present. A variety of new additives for reducing drag have been developed during the program, and their unique properties are also summarized. Finally, the theoretical work is used as a basis for assessing the relative merits of proposed explanations for the drag reduction phenomenon.

Early turbulence has for the first time been observed in the flow of very dilute polymer solutions in tubes larger than capillary size. Flow rate-wall shear stress measurements were conducted in 0.553 and 0.660 cm. diameter pipes. Polyethylene oxide samples of two molecular weights were employed, ditsolved in water-glycerine mixtures with viscosities ranging from 0.0261 to 0.160 poise. The flow rate-wall shear stress relationship for these solutions corresponded to Poiseuille's Law below a well-defined onset wall shear stress, at which the Reynolds number was less than the transition value for Newtonian fluids. As the flow rate was increased from the onset condition, however, the wall shear stress became progessively larger than that predicted by the Poiseuille relationship. The onset wall shear stress for the phenomenon increased linearly with solvent viscosity. I t s relationship to polymer concentration was dependent on the solvent viscosity. An explanation for early turbulence is suggested on the basis of these results, and the relationship of the phenomenon to turbulent flow drag reduction is discussed.The nowNewtonian character of very dilute polymer solutions under turbulent flow conditions has been well documented in numerous experimental studies (1 ) . Recently, the flow of dilute polymer solutions in capillary tubes has also been characterized by a marked departure from Newtonian behavior under conditions of steady laminar shear (2, 3 ) . This behavior, which shall be termed early turbulence in the present work, has the following characteristics: 1. it exists only above some well-defined critical wall shear stress characteristic of a given polymer solution; 2. this critical wall shear stress varies with polymer concentration and molecular weight (the effect of solvent viscosity has not been heretofore investigated); 3. at shear stresses above the critical wall shear stress, the drag exerted by the polymer solution exceeds that for the laminar flow of a Newtonian fluid at the same flow rate; 4. the familiar laminar-to-turbulent transition is replaced by a continuous change from early turbulence to turbulent flow with reduced drag as the flow rate increases. It has recently been suggested (through use of a simple relation involving Reynolds number, viscosity, density, and wall shear stress) that early turbulence will be observed in highly dilute drag-reducing aqueous polymer solutions if the pipe diameter used is of the order of 0.20 cm. or less ( 2 ) . Apart from Hoyt's work ( 4 ) -d o n e at a single flow rate-measurements of dilute Polyox polymer solutions (nominally of the same viscosity as water) have been done exclusively at larger pipe diameters. However, this same simple relation suggested that the early turbulence phenomenon could be observed in much larger pipes provided the solvent viscosity were increased to an appropriate degree. The present work explores the relationship of TO, the critical wall shear stress for early turbulence, to the solvent viscosity over a range of polymer concentration...

synopsisStructural turbulence has been detected in dilute aqueous solutions of Polyox Coagulant (also known to be a highly effective drag-reducing agent). The flow line which characterizes structural turbulence from its onset in the laminar region passes well into the fully turbulent region (Reynolds turbulence) with virtually no change in slope, implying that the same molecular oscillations or segmental motions responsible for structural turbulence are now operative in drag reduction. The persistence of structural turbulence a t very low concentrations is rationalized on the basis of Busse's explanation of the role of polymer entanglements in viscosity and elastic turbulence.