A universal equation for calculating the energy gradient function in shear driven flows using the energy gradient theory

TL;DR

This paper introduces a universal equation based on the energy gradient theory to analyze flow stability in shear driven flows, applicable to various flow configurations.

Contribution

The paper derives a universal equation for the energy gradient function specific to shear driven flows, expanding the applicability of energy gradient theory.

Findings

The energy gradient function can be used as a local Reynolds number for stability analysis.

The method applies to parallel, curved, and complex shear driven flows.

A relationship between energy variation, work done, and energy dissipation is established.

Abstract

The energy gradient theory was proposed in our previous studies. The mechanism of flow instability is very different in shear driven flows from pressure driven flows. In present paper, the relationship for the energy variation, work done, and energy dissipation in unit volumetric fluid of incompressible flow is derived. A universal equation for calculating the energy gradient function in shear driven flows is presented. With the calculation of the energy gradient function which is a field variable and is considered as a local Reynolds number, the stability of a basic flow can be analyzed. The method can be applied to parallel flows, curved flows, and various complex flows.