Minimization Principle for Analytical Solution of Turbulent Flow in Channel

TL;DR

This paper introduces a minimization principle-based method to analytically solve turbulent flow in channels, combining laminar and turbulent solutions, and demonstrates good agreement with experimental data.

Contribution

It proposes a novel approach using the minimization principle to determine superposition coefficients for analytical turbulent flow solutions.

Findings

Analytical solutions align well with experimental data.

Superposition approach effectively models turbulent flow.

Minimization principle provides a systematic way to solve turbulence problems.

Abstract

The analytical solution for turbulent flow in channel presented in Fedoseyev (2023), described the mean turbulent flow velocity as a superposition of the laminar (parabolic) and turbulent (superexponential) solutions. In this study, the coefficients of superposition are proposed to obtain through the minimization principle, the principle of minimum viscous dissipation. The obtained analytical solutions agree well with the experimental data for turbulent flow.