Observations of early turbulence in the pipe flow of drag reducing polymer solutions

Abstract

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...

Linear instability of viscoelastic pipe flow

“…While the pioneering work by Virk (1975b) found transition in pipe flow of dilute polymer solutions to occur roughly at the same Re as the Newtonian transition, there have been reports of a delayed transition (Giles & Pettit 1967;Castro & Squire 1968;White & McEligot 1970). Significantly, there have also been several reports of 'early turbulence', wherein transition is reported at a Re as low as 500 (Goldstein et al 1969;Forame et al 1972;Hansen et al 1973;Hansen & Little 1974;Hoyt 1977;Zakin et al 1977), although these early experimental efforts were not corroborated and followed up in a systematic manner. The conflicting conclusions of delayed or early transition could perhaps be attributed to poor characterization of the polymer solutions used.…”

Laminar–turbulent transition in pipe flow for Newtonian and non-Newtonian fluids

“…To complicate matters even further, transition Reynolds numbers have been found that are smaller than the Newtonian minimum of approximately 2300 and for this phenomenon the term 'early turbulence' has been coined. For instance, transition Reynolds numbers as low as 500 have been reported (Forame, Hansen & Little 1972;Zakin, Ni & Hansen 1977;Li & McCarthy 1995). Another result is given by Paterson & Abernathy (1972) who found that for a pipe inlet with squared corners polymers do not change the transition Reynolds number.…”

Phase separation in flowing polymer solutions

“…From birefringence, shear recovery, or normal stress measurements, we can evaluate GS, the stored free energy/cc of homogeneous flowing solutions ( 6 3 , Treating this as an added contribution to the free energy of mixing, we obtain an estimate for the free energy of mixing in flow AG'm = AG, t GS (1)…”

“…How the flow will perturb these relationships is not obvious. One approach to the problem would be to assume that equilibrium relationships apply with the free energy of mixing given by (1). This would lead to relationships among partial derivatives of AG, and G S which could be tested by experiment.…”