Money versus Time: Evaluation of Flow Control in Terms of Energy Consumption and Convenience

TL;DR

This paper introduces a framework to evaluate flow control techniques by balancing energy consumption and convenience, providing a practical perspective on drag reduction strategies for internal and external flows.

Contribution

It develops two dimensionless parameters to quantify energy and time costs, enabling a comprehensive assessment of drag reduction methods in real-world applications.

Findings

Re-evaluation of existing drag reduction strategies within the new framework

Identification of optimal balance between energy use and flow convenience

Extension of the framework to external flow scenarios

Abstract

Flow control with the goal of reducing the skin friction drag on the fluid-solid interface is an active fundamental research area, motivated by its potential for significant energy savings and reduced emissions in the transport sector. Customarily, the performance of drag reduction techniques in internal flows is evaluated under two alternative flow conditions, i.e. at constant mass flow rate or constant pressure gradient. Successful control leads to reduction of drag and pumping power within the former approach, whereas the latter leads to an increase of the mass flow rate and pumping power. In practical applications, however, money and time define the flow control challenge: a compromise between the energy expenditure (money) and the corresponding convenience (flow rate) achieved with that amount of energy has to be reached so as to accomplish a goal which in general depends on the specific application. Based on this idea, we derive two dimensionless parameters which quantify the total energy consumption and the required time (convenience) for transporting a given volume of fluid through a given duct. Performances of existing drag reduction strategies as well as the influence of wall roughness are re-evaluated within the present framework; how to achieve the (application-dependent) optimum balance between energy consumption and convenience is addressed. It is also shown that these considerations can be extended to external flows.