A simple model for drag reduction

TL;DR

This paper introduces a simple 1D model of the FENE-P equations to analytically understand turbulent drag reduction caused by dilute polymeric additives, capturing key phenomena observed in experiments.

Contribution

A novel simplified 1D model of the FENE-P equations that explains the core mechanisms of turbulent drag reduction analytically.

Findings

Demonstrates drag reduction in the simple model

Shows reduction of velocity gradients at fixed throughput

Shows increase of throughput at fixed dissipation

Abstract

Direct Numerical Simulations established that the FENE-P model of viscoelastic flows exhibits the phenomenon of turbulent drag reduction which is caused in experiments by dilute polymeric additives. To gain analytic understanding of the phenomenon we introduce in this Letter a simple 1-dimensional model of the FENE-P equations. We demonstrate drag reduction in the simple model, and explain analytically the main observations which include (i) reduction of velocity gradients for fixed throughput and (ii) increase of throughput for fixed dissipation.