On The Critical Reynolds Number For Transition From Laminar To Turbulent Flow

TL;DR

This paper investigates the transition from laminar to turbulent flow in pipes, proposing a method to determine the critical Reynolds number based on the asymptotic behavior of the viscous flow layer.

Contribution

It introduces a novel approach to identify the critical Reynolds number using the normalized viscous layer thickness and its asymptotic value.

Findings

The normalized viscous flow layer reaches an asymptotic value at transition.

The physical thickness of the viscous layer decreases exponentially after transition.

A simple method to calculate the critical Reynolds number from flow visualization data.

Abstract

In this visualisation, the transition from laminar to turbulent flow is characterised by the intermittent ejection of wall fluid into the outer stream. The normalised thickness of the viscous flow layer reaches an asymptotic value but the physical thickness drops exponentially after transition. The critical transition pipe Reynolds number can be obtained simply by equating it with the asymptotic value of the normalised thickness of viscous flow layer. Key words: Transition, critical stability Reynolds number, critical transition Reynolds number, non-Newtonian pipe flow