Laminar and Turbulent Flow in Wavy Pipes under Strong Wall Modulations

TL;DR

This study uses direct numerical simulations to analyze laminar, transitional, and turbulent flows in wavy pipes with strong wall modulations, revealing effects like flow reversal, subcritical transition to turbulence, and limitations of classical flow models.

Contribution

It introduces the effective hydraulic radius and sandgrain roughness as hydrodynamic concepts to better understand flow behavior in wavy pipes with strong wall fluctuations.

Findings

Flow reversal occurs at low Reynolds numbers due to wall amplitude.

Subcritical transition to turbulence is triggered between Re 500-1000.

Flow in turbulent regime is fully rough, dominated by inertial effects.

Abstract

We study laminar, transitional and turbulent flow in wavy pipes using direct numerical simulations for bulk Reynolds numbers between 1-5300. Flow behaviors are analyzed in terms of the friction factor f and mean velocity statistics for strong sinusoidal wall fluctuations in axial direction. Depending on the wall amplitude k, flow reversal may appear at bulk Reynolds numbers as small as 25, inducing local recirculation zones significantly increasing friction in the laminar regime. These effects are not captured by classical models based on bulk geometric parameters, but require the definition of an effective hydraulic radius Rh as a hydrodynamic concept. Furthermore, wall modulations trigger subcritical transitions to turbulence in a Reynolds range between 500 and 1000, well below the classical threshold for smooth pipes. The DNS data suggest an upper bound for laminar persistence with a critical Reynolds number that scales as a power-law with the wall amplitude, consistent with finite amplitude transition scenarios. In the turbulent regime, flow is found to be fully rough, dominated by inertial separation and wall-induced disturbances independent of Re. Using the hydraulic radius as the characteristic length scale, the wall amplitude provides a robust estimator for the equivalent sandgrain roughness, also a hydrodynamic concept. The impact of strong wall fluctuations on laminar and turbulent friction laws, as quantified by hydraulic radius and sandgrain roughness , and the amplitude dependence of critical Reynolds number, emphasise the limitations of the Moody diagram for the flow quantification in conduits with strong wall fluctuations across all flow regimes.