Transition from laminar to turbulent pipe flow as a process of growing material instabilities

TL;DR

This paper introduces a modified Navier-Stokes model incorporating viscous fluid strength to better simulate the transition from laminar to turbulent pipe flow, aligning numerical results with experimental observations.

Contribution

The study develops and tests a modified NS theory that includes material instabilities, providing a more accurate simulation of flow transition phenomena.

Findings

Classical NS model shows stable laminar flow inconsistent with experiments.

Modified NS model with viscous strength exhibits flow instabilities and transition to turbulence.

Material instabilities are identified as the trigger for turbulence transition.

Abstract

In this work, we simulate the transition to turbulence in the pipe flow based on the modified NS theory incorporating the viscous fluid strength in the constitutive equations. The latter concept enriches theory by allowing for material instabilities in addition to the kinematic ones. We present results of comparative numerical simulations based on the classical NS model and the NS model enhanced with the finite viscous strength. As expected, simulations based on the classical NS model exhibit stable laminar flow in contrast to experimental observations. Conversely, simulations based on the modified NS model with viscous strength exhibit instabilities and transition to turbulence per experimental observations. The transition to turbulence is triggered by the growing material instabilities.