Drag reduction in pipe flow by optimal forcing

TL;DR

This paper investigates optimal flow forcing to reduce turbulence drag in pipe flow, demonstrating significant energy savings and over 12% drag reduction with minimal input energy, verified through simulations.

Contribution

It identifies the most effective azimuthal forcing mode for drag reduction and demonstrates practical energy-efficient control strategies.

Findings

Over 12% drag reduction achieved with minimal energy input.

The m=1 azimuthal mode is most effective for flow response.

Large scale modes show significant response and control potential.

Abstract

In most settings, from international pipelines to home water supplies, the drag caused by turbulence raises pumping costs many times higher than if the flow were laminar. Drag reduction has therefore long been an aim of high priority. In order to achieve this end, any drag reduction method must modify the turbulent mean flow. Motivated by minimization of the input energy this requires, linearly optimal forcing functions are examined. It is shown that the forcing mode leading to the greatest response of the flow is always of m=1 azimuthal symmetry. Little evidence is seen of the second peak at large m (wall modes) found in analogous optimal growth calculations, which may have implications for control strategies. The model's prediction of large response of the large length-scale modes is verified in full direct numerical simulation of turbulence ($Re=5300$, $Re_\tau\approx 180$). Further, drag reduction of over 12% is found for finite amplitude forcing of the largest scale mode, m=1. Significantly, the forcing energy required is very small, being less than 2% of that by the through pressure, resulting in a net energy saving of over 10%.