Axial friction coefficient of turbulent spiral Poiseuille flows

Abstract

Direct numerical simulations of spiral Poiseuille flows in a narrow gap geometry are performed with the aim of identifying the mechanisms governing the dynamics of the axial friction coefficient. The investigation has explored a small portion of the Reynolds number–Taylor number phase space ( $600 \leq Re \leq 5766$ and $1500 \leq Ta \leq 5000$ ), for which reference experimental results are available. The study is focused on the mechanism leading to the enhancement of the axial friction coefficient with the Taylor number when the Reynolds number is kept constant. The analysis of the spatial distribution of the Reynolds stress tensor and of the turbulent energy budget has evidenced the key role of the pressure–strain correlation in the energy transfer from the azimuthal to the axial component. The latter eventually determines the increase of the axial friction coefficient through the enhanced radial mixing of axial momentum. Data have also shown that the flow dynamics is heavily dependent on the $Ta/Re$ ratio, and different regimes develop (ranging from laminar to turbulent), each with peculiar behaviours.