A Solution Method for the Reynolds-Averaged Navier-Stokes Equation

TL;DR

This paper introduces a new solution method for the Reynolds-Averaged Navier-Stokes equations using Lagrangian transport of momentum, validated with DNS data at high Reynolds numbers, and applicable to turbulent flow solutions.

Contribution

It presents a novel approach to express Reynolds stress via Lagrangian momentum balance, enabling improved turbulence modeling and flow predictions.

Findings

Validated the theory with DNS data at Re=1000 and 5200.

Derived key turbulence parameters such as von Karman constant and inner layer thickness.

Provided example solutions for turbulent channel and jet flows.

Abstract

Using the Lagrangian transport of momentum, the Reynolds stress can be expressed in terms of basic turbulence parameters. DNS data at higher Reynolds numbers (Re= 1000 and 5200) have been used to again validate this theory, where it is the Lagrangian momentum balance between u2 and pressure fluctuation forces that determine the Reynolds stress at these conditions. This approach can be used to obtain key parameters such as the von Karman constant, inner layer thickness and the Reynolds stress itself. This expression for the Reynolds stress can be combined with RANS for solutions for turbulent channel and jet flows. Examples of these solutions are presented.