(321i) Turbulent Drag Reduction, Flow Development, and Degradation of Polyox U310 Solutions in a Smooth Pipe

Turbulent drag reduction, flow development, and degradation of Polyox U310 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 210. The test pipe assembly, of 7 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 a 200 liter tank that held premixed polymer solution. The U310 Polyox, MW ~10x10⁶, was studied at concentrations C = 0.1 to 10 wppm in deionized water DW solvent.

At any fixed flowrate, individual friction factors for DW solvent were constant to within 1.2% for all tap pairs; and all DW friction factors adhered to the Prandtl-Karman law, 1/â??f = 4.0 log Reâ??f - 0.4, within ±0.2 1/â??f units for 500 < Reâ??f < 3000. Thus the present solvent flows were all fully-developed by the first tap pair 1&2 at mean L/D = 42, in accord with established entrance lengths of 25 â?? 40 L/D for Newtonian turbulent pipe flow.

Drag reduction by U310 solutions, described by flow enhancements aka â??slipâ? Sâ?? = (1/â??f_p â?? 1/â??f_n)_Reâ??f , varied over almost the entire possible range 0 < Sâ?? < Sâ??_mdr, from Sâ?? ~ 1 for C = 0.1 wppm at low Reâ??f ~ 500 in the polymeric regime to Sâ?? ~ 15 for C = 10 wppm at high Reâ??f ~ 2500, close to the maximum drag reduction asymptote, 1/â??f = 19.0 log Reâ??f - 32.4. Two distinct kinds of Sâ?? vs L/D behaviour, described by examples, were discerned:  (i) At low C and high Reâ??f, example C = 0.1 wppm and Reâ??f > 1000, Sâ?? was highest initially (L/D = 42) and decreased monotonically with increasing L/D to the end (L/D = 192), likely reflecting polymer degradation with increasing downstream distance, and yielding an apparent degradation rate constant kdeg ~ 4 1/s at wall shear stress Tw ~ 100 Pa. (ii) At high C and all Reâ??f, example C = 10 wppm and 500 < Reâ??f < 2500, Sâ?? was lowest initially (L/D = 42), increased with increasing L/D, and asymptotically attained a constant Sâ?? ~ Sâ??_mdr for L/D > 132, which likely represents the entrance length required for fully developed turbulent flow at maximum drag reduction.