(295b) Scaleout of Turbulent Drag Reduction From a Pipe to a Flat Plate

Drag reduction by wall-injected Polyox solutions was studied by axial pressure profile and flow visualization measurements at Reynolds numbers from 40000 to 140000 in an acrylic test pipe of ID 15.7 mm and L/D 430.  Friction factors for the deionized water solvent followed the Prandtl-Karman law to within 0.2 1/√f units.  The P309 Polyox, of MW ~ 8x10⁶, was injected in concentrated solutions, of C_inj 500, 1000 or 5000 wppm, through 6 equi-spaced circumferential ports to provided downstream polymer concentrations C_line from 0.1 to 100 wppm that exhibited  eventual fractional drag reductions DR_line from 0.15 to the asymptotic maximum drag reduction MDR ~ 0.80 possible at the present Re.  At low C_line < 1 wppm, flow enhancements S’_line = (1/√f_p – 1/√f_n)_Re√f  increased almost linearly with increasing C_line, with the highest intrinsic slip [S’] = lim _C→0 (S’/ C_line) ~ 8.0 wppm^-1, while at high C_line > 10 wppm the asymptotic maximum S’_MDR ~ 18 was approached.  Polymer dissolution into the flow was assessed both from the initial increase in fractional drag reduction towards the eventual downstream DR_line, which provided a characteristic development distance (L/D)_dr, and from the final disappearance of the red-dyed strands of injected solution, which provided a characteristic dissolution distance (L/D)_pv.  At all C_line and C_inj, the (L/D)_dr ~ 100 were generally less than (L/D)_pv ~ 100 to > 400.  Finally, pipe flow drag reduction observations were “scaled out” to flat plate boundary layers by assuming that Type B drag reduction prevails identically in both internal and external flows, with U_CL = U_o, the free-stream velocity, and R⁺ = du_τ/ν , with d thickness and u_τ friction velocity at the boundary layer trailing edge L.  Scaleout of the present data to the classical HMS Highburton Polyox W301 ejection trials of Canham et. al (1971) suggests that the present Polyox P309 might have provided their reported drag reductions at roughly 1/20 th their polymer expenditure rate per unit of hull wetted area.