Turbulent drag reduction, flow development, and degradation of aqueous polyethyleneoxide solutions was studied by axial pressure profile measurements in a smooth, segmented, pipe with electro-polished bore of ID 4.58 mm and overall L/D 180. The test pipe assembly, of 6 identical segments, each of L/D 30 with a 0.38 mm ID pressure tap 2.4 L/D from its downstream end, was placed in a single-pass progressive cavity pump-driven flow system fed from two 180 liter tanks that held premixed polymer solutions. A polyethyleneoxide polymer, Polyox N60K of MW 3.2x106, was used at concentrations C from 1 to 500 wppm in deionized water DW solvent.
Individual friction factors for DW solvent at any fixed flowrate were constant to within 1.2% for all tap pairs, and all DW friction factors adhered to the Prandtl-Karman law 1/√f = 4.0 log Re√f - 0.4 within ±0.2 1/√f units for 300 < Re√f < 6000. Thus the present solvent flows were all fully-developed by the time they reached the first tap pair 1&2 at mean L/D = 42, that is, solvent “entrance lengths” were Le,n/D < 42, in accord with established results of Le,n/D = 25 to 40 for turbulent Newtonian pipe flow.
Drag reduction by polymer solutions, quantitatively described by the flow enhancement S’ = (1/√fp – 1/√fn)Re√f, varied over the entire possible range 0 < S’ < S’mdr, from S’ ~ 0, near onset on the Prandtl-Karman law, to S’ ~ 17, close to the maximum drag reduction asymptote 1/√f = 19.0 log Re√f - 32.4. Three kinds of S’ vs L/D behavior, described by examples, could be discerned. (i) At low C and low Re√f, example C = 1 wppm and Re√f < 2500, S’ was essentially independent of L/D, with flow development akin to solvent, Le,p/D ~ Le,n/D. (ii) At low C and high Re√f, example C = 1 wppm and Re√f > 2500, S’ was highest initially (L/D = 42) and decreased monotonically with increasing L/D, reflecting polymer degradation beyond a “falloff point” at Re√f^ ~2500. (iii) At high C and all Re√f, example C = 200 and 500 wppm and 600 < Re√f < 2500, S’ was lowest initially, increased with increasing L/D, and asymptotically attained a constant S’ ~ S’mdr. A normalized summary of the preceding, (S’/S’mdr) = (0.70, 0.93, 0.97, 1.00, 1.00) at L/D = (42, 72, 102, 132, 162) suggest an entrance length of Le,mdr /D ~ 102 at maximum drag reduction, (S’/S’mdr) → 1.