A correlation between drag and an integral property of the wake

TL;DR

This paper introduces an integral property linking wake characteristics to drag in two-dimensional flows, providing a new way to correlate drag data across various geometries and flow conditions.

Contribution

It defines a novel integral quantity relating wake energy and vorticity to drag, applicable to different shapes and flow regimes, enhancing understanding of drag mechanisms.

Findings

The new quantity correlates drag with flow speed and boundary mass flow rate.

Drag is proportional to the flow speed and the mass flow in the wake boundary.

The integral property suggests drag can become unbounded with finer vortices, absent quantization.

Abstract

An integral quantity is presented that relates the wake of a body in nominally two-dimensional flow to its drag, for Reynolds numbers ranging from 9,000 to 144,000. It is defined as the ratio of the kinetic energy to the vorticity in the fluid boundary and, for the special case of laminar flow, is proportional to the angular momentum in the wake bubble. The new quantity is useful for correlating drag data for circular and rectangular cylinders, wedges, v-gutters, and normal flat plates with and without splitter plates. The correlation indicates that the drag force is proportional to the flow speed and the mass flow rate stored in the boundary of the fluid, where the fluid boundary is defined so as to include the wake bubble. Order-of-magnitude arguments indicate that, absent any quantization of vortex size, this mass flow rate, and hence the drag force, can become unbounded as the vortices contained in the wake becomes finer.