On the role of secondary motions in turbulent square duct flow

TL;DR

This study uses DNS data to quantify the impact of secondary motions in turbulent square duct flow, revealing their significant role in friction and turbulence regulation, and introduces a generalized FIK identity for analysis.

Contribution

It introduces a generalized FIK identity to quantify secondary motions' effects and demonstrates their role in turbulence regulation and flow universality in square duct flow.

Findings

Secondary motions contribute about 6% of total friction.

They act as a self-regulating mechanism for turbulence.

Suppressing secondary motions alters flow dynamics, highlighting their importance.

Abstract

We use a direct numerical simulations (DNS) database for turbulent flow in a square duct up to bulk Reynolds number $\Rey_b=40000$, to quantitatively analyze the role of secondary motions on the mean flow structure. For that purpose we derive a generalized form of the identity of Fukagata, Iwamoto and Kasagi (FIK), which allows to quantify the effect of cross-stream convection on the mean streamwise velocity, wall shear stress and bulk friction coefficient. Secondary motions are found to contribute for about $6\%$ of total friction, and to act as a self-regulating mechanism of turbulence whereby wall shear stress nonuniformities induced by corners are equalized, and universality of the wall-normal velocity profiles is established. We also carry out numerical experiments whereby the secondary motions are artificially suppressed, in which case their equalizing role is partially taken by the turbulent stresses.