On the Use of Inverse Methods to Parameter Estimation in Turbulent Pipe Flows of Drag Reducing Polymers

Abstract

This article investigates the applicability of inverse methods in estimating the best values to be assigned to certain parameters which appear in turbulent flow studies of dilute polymer solutions in circular pipes. These parameters naturally arise when the Nagano-Hishida low-Re, k-e model is combined with a special form of the Generalized Newtonian Fluid model modified in such a way that it could account for the elasticity of dilute polymer solutions. This multi-objective problem is treated by a positively weighted convex sum of the objectives. Then the procedure is followed by a well-known Gauss-Newton nonlinear optimization method for optimizing model parameters in order to better predict the drag reduction phenomenon using polymeric additives. Parameter optimization relies on the availability of experimental data for the velocity profiles, friction factor, and turbulence kinetic energy for at least one concentration of a given polymer. It is shown that using these optimized parameters, it is possible to predict with more accuracy the amount of drag reduction achievable using a given polymeric additive. It is also shown that these parameters may neither work for other concentrations of the same polymer nor necessarily for any concentration of any other polymer, inferring that for non-Newtonian fluids these parameters are not at all universal.