Theory of Concentration Dependence in Drag Reduction by Polymers and of the MDR asymptote

Abstract

A simple model of the effect of polymer concentration on the amount of drag reduction in turbulence is presented, simulated and analyzed. The qualitative phase diagram of drag coefficient vs. Reynolds number (Re) is recaptured in this model, including the theoretically elusive onset of drag reduction and the Maximum Drag Reduction (MDR) asymptote. The Re-dependent drag and the MDR are analytically explained, and the dependence of the amount of drag on material parameters is rationalized.

References in corpus (3)

• An optimal shell model of turbulence
• Drag Reduction by Polymers in Turbulent Channel Flows: Energy Redistribution Between Invariant Empirical Modes
• Shell Model for Drag Reduction with Polymer Additive in Homogeneous Turbulence

Cited by in corpus (8)

• Colloquium: Theory of Drag Reduction by Polymers in Wall Bounded Turbulence
• Polymers in Fluid Flows
• The importance of bubble deformability for strong drag reduction in bubbly turbulent Taylor-Couette flow
• Drag Reduction by Polymer Additives in Decaying Turbulence
• Drag Reduction in Homogeneous Turbulence by Scale-Dependent Effective Viscosity
• Delay of Disorder by Diluted Polymers
• Shell Model of Two-dimensional Turbulence in Polymer Solutions
• Multiscale modelling strategy using the lattice Boltzmann method for polymer dynamics in a turbulent flow