Modelling spanwise heterogeneous roughness through a parametric forcing approach

K Schäfer,B Frohnapfel,A Stroh,P Forooghi

doi:10.1017/jfm.2021.850

K Schäfer, B Frohnapfel + Show 2 more

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https://doi.org/10.1017/jfm.2021.850

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Abstract

Inhomogeneous rough surfaces in which strips of roughness alternate with smooth-wall strips are known to generate large-scale secondary motions. Those secondary motions are strongest if the strip width is of the order of the half-channel height and they generate a spatial wall shear stress distribution whose mean value can significantly exceed the area-averaged mean value of a homogeneously smooth and rough surface. In the present paper it is shown that a parametric forcing approach (Busse & Sandham, J. Fluid Mech., vol. 712, 2012, pp. 169–202; Forooghi et al., Intl J. Heat Fluid Flow, vol. 71, 2018, pp. 200–209), calibrated with data from turbulent channel flows over homogeneous roughness, can capture the topological features of the secondary motion over protruding and recessed roughness strips (Stroh et al., J. Fluid Mech., vol. 885, 2020, R5). However, the results suggest that the parametric forcing approach roughness model induces a slightly larger wall offset when applied to the present heterogeneous rough-wall conditions. Contrary to roughness-resolving simulations, where a significantly higher resolution is required to capture roughness geometry, the parametric forcing approach can be applied with usual smooth-wall direct numerical simulation resolution resulting in less computationally expensive simulations for the study of localized roughness effects. Such roughness model simulations are employed to systematically investigate the effect of the relative roughness protrusion on the physical mechanism of secondary flow formation and the related drag increase. It is found that strong secondary motions present over spanwise heterogeneous roughness with geometrical height difference generally lead to a drag increase. However, the physical mechanism guiding the secondary flow formation, and the resulting secondary flow topology, is different for protruding roughness strips and recessed roughness strips separated by protruding smooth surface strips.

Highlights

Turbulent flows over spatially inhomogeneous rough surfaces are present in a variety of engineering and environmental applications, whereas smooth surfaces are rather the exception
In numerical simulations idealized strip-type roughness conditions can be generated by alternating wall-normal velocity gradients at the wall (e.g. Willingham et al 2014; Chung et al 2018) while in experiments the smooth-wall region in between roughness strips can be elevated with the aim of avoiding offsets in the virtual origin between rough and smooth surfaces (Wangsawijaya et al 2020)
While results documenting the behaviour of secondary motions are often described in a time-averaged and, in the case of direct numerical simulation (DNS), often in a phase-averaged sense, Wangsawijaya et al (2020) point out that this averaging procedure masks a time-dependent meandering behaviour of the secondary motions that they found to be largest in the case of roughness strips with widths of the order of the boundary layer thickness

Summary

Introduction

Turbulent flows over spatially inhomogeneous rough surfaces are present in a variety of engineering and environmental applications, whereas smooth surfaces are rather the exception. Spanwise inhomogeneous rough surfaces have attracted increasing attention in research Such surfaces are known to generate secondary flows of Prandtl’s second kind (Prandtl 1931; Hinze 1967; Anderson et al 2015) that appear as large-scale vortical structures in the time-averaged flow field perpendicular to the main flow direction (Hinze 1967; Barros & Christensen 2014; Vanderwel et al 2019). Strip-type roughness is characterized by spanwise alternating wall shear stress conditions, where spanwise wall elevations are not present or negligibly small These surfaces produce large-scale secondary motions with upward motion above the lower stress patch and downward motion of the circulation above the high stress region if the spanwise wavelength of the surface structure is of the order of the boundary layer thickness (Chung et al 2018). While results documenting the behaviour of secondary motions are often described in a time-averaged and, in the case of direct numerical simulation (DNS), often in a phase-averaged sense, Wangsawijaya et al (2020) point out that this averaging procedure masks a time-dependent meandering behaviour of the secondary motions that they found to be largest in the case of roughness strips with widths of the order of the boundary layer thickness

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