Abstract: Mean momentum equation based analysis of polymer drag-reduced channel flow is performed to evaluate the redistribution of mean momentum and the mechanisms underlying the redistribution processes. Similar to channel flow of Newtonian fluids, polymer drag-reduced channel flow is shown to exhibit a four layer structure in the mean balance of forces that also connects, via the mean momentum equation, to an underlying scaling layer hierarchy. The self-similar properties of the flow related to the layer hierarchy appear to persist, but in an altered form (different from the Newtonian fluid flow), and dependent on the level of drag reduction. With increasing drag reduction, polymer stress usurps the role of the inertial mechanism, and because of this the wall-normal position where inertially dominated mean dynamics occurs moves outward, and viscous effects become increasingly important farther from the wall. For the high drag reduction flows of the present study, viscous effects become non-negligible across the entire hierarchy and an inertially dominated logarithmic scaling region ceases to exist. It follows that the state of maximum drag reduction is attained only after the inertial sublayer is eradicated. According to the present mean equation theory, this coincides with the loss of a region of logarithmic dependence in the mean profile.
Abstract: A re-examination of the logarithmic dependence of the mean velocity distribution in polymer drag reduced flows shows that drag reducing polymers modify the von Kármán coefficient and, in channel flow, eradicate the log-layer at high drag reductions. It is also found that the “ultimate profile,” corresponding to the state of maximum drag reduction is not logarithmic.