The laminar flow instability criterion and turbulence in pipe

TL;DR

This paper presents a new stability criterion for laminar-to-turbulent transition in pipe flow, modeling the flow as a flexible rod and incorporating physical factors like inlet geometry and flow velocity.

Contribution

It introduces a novel stability criterion based on a flexible rod analogy, accounting for various physical factors influencing flow stability in pipes.

Findings

Reynolds number is a key part of the stability criterion

The criterion considers inlet geometry, pipe length, and flow velocity

Applicable to both internal and external streamline flows

Abstract

The identification of stream in the straight pipe as a flexible rod has allowed to present the criterion expression for determination of transition of the laminar flow regime to the turbulent as a loss of stability of the rectilinear static structure of translational motion of stream in pipe and its transition to the flexural-vortical dynamic structure of translational motion, just as a flexible rod buckling. The introduced criterion allows to take into account an influencing of the inlet geometry, the pipe length, the flow velocity, and also of any physical factors on stability of the rectilinear flow structure. It is ascertained, that Reynolds number is the number of local hydrodynamic similarity and it is displayed that one is constituent part of the introduced stability criterion. The developed approach to a problem of stability is applicable for a problem solving on internal flow and external streamline.