Theoretical conditions of pipe flow transition: new approach to the old problem

TL;DR

This paper presents a new theoretical approach to understanding the laminar-to-turbulent transition in pipe flow, deriving conditions for transition and validating them against experimental data.

Contribution

It introduces a novel theoretical framework and an expression for the critical Reynolds number based on disturbance mechanisms in pipe flow.

Findings

Derived an expression for the critical Reynolds number.

Achieved qualitative agreement with experimental data.

Analyzed the transition mechanism involving wall disturbances.

Abstract

For Hagen-Poiseuille flow the mechanism of laminar-to-turbulent transition originated from the deceleration of disturbed streams on the pipe wall is analyzed. An expression for the critical Reynolds number and the disturbance in the form of ring obstacle is derived. The good qualitative agreement between the theoretical results and published experimental data is demonstrated