Scaling of secondary flows with surface parameters: a linear approach

TL;DR

This study investigates how surface ridge geometry influences secondary turbulent flows using a linear RANS model, revealing that flow strength scales with ridge height and shape effects emerge in complex geometries.

Contribution

It introduces a linear modeling approach to analyze the impact of ridge shape on secondary flows, highlighting conditions where shape effects are negligible or significant.

Findings

Secondary flow strength scales with mean ridge height.

Flow organization is similar across small, isolated ridges regardless of shape.

Tertiary flows appear in complex geometries like trapezoidal ridges.

Abstract

Secondary flows are generated when a lateral variation of the topography, such as streamwise aligned ridges, is imposed to a turbulent wall-bounded flow. In this case, the flow field is characterized by vortical structures developing along the streamwise direction known as Prandt's vortices of the second kind (Prandtl 1965). As demonstrated in previous experimental and numerical works, the strength and flow organization of these turbulent structures depend on the ridge shape. In this paper, the effect of the ridge geometry on the generation of secondary currents is investigated using the linearised RANS-based model proposed by Zampino (2022). Here, symmetric channels with rectangular, triangular and elliptical ridges are studied and the secondary flows are compared in order to highlight the main differences and similarities. The analogies of the flow organisation between the three geometries suggest that the secondary currents do not depend on the ridge shape when the ridges are small and isolated, and the strength of secondary flows collapses when properly scaled with the mean ridge height. Finally, the generation of secondary flows and the effect of the ridge shape on the flow organisation is studied in detail for the complex geometries. In particular, for trapezoidal ridges, we observed that tertiary flows emerge for the ridges where the scaling behaviour does not hold.