Development of local turbulent drag reduction due to nonuniform polymer concentration

Abstract

Turbulent drag reduction produced by injection of polymer at the centerline of a pipe flow was found to increase with streamwise distance from the injection point. This was due to radial dispersion of the injected polymer. A tentative relationship between the two is proposed.

Drag Reduction by Polymer Additives

“…It is appropriate to inteject here that the observation that a critical wall Reynolds stress must be exceeded for drag reduction to result is closely related to the time criterion expressed by Equation (1)(2)(3)(4)(5)(6)(7)(8)(9). This is easily seen by noting that for wall flows, the maximal eddy shearing rate is which defines a critical wall Reynolds stress varying inversely with R and which is independent of solvent density, viscosity and pipe radius.…”

“…A dependence of a,, on polymer gyration radius (defined in Section 1.2) RG of the form a',,, RGja is observed, with 2 < a < 3. The gyration radius RG is virtually always significantly smaller than the dissipation scales of turbulent flows of Reynolds numbers Re < 106. There are also experiments [5] which monitor the friction factor as a function of the distance downstream from a point in the center of the pipe where the drag reducing agent is injected. Some drag reduction appears even before significant amounts of additive have had time to diffuse to the wall.…”

“…N's (1)(2)(3)(4)(5)(6) kBT where q/, is the solvent viscosity. The important time scale r. is called the "Zimm time" and is of order milliseconds for PEO with N = 10i monomer units.…”

“…Rg Pe AM; (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) here n is the number of nodes in a branched polymer or tethered surface, and a' is proportional to m 3 '/ where m is the average number of monomers per nodes (inn ; N). The exponent, v, is approximately, 0.5 for branched polymers [10], and 0.4 for polymerized surfaces [9].…”

“…Here i' is the external velocity field evaluated at the center-of-mass position, and we have expanded i' --2 in gradients of the velocity field at this point to get Equation (3)(4)(5).…”