The wind-shade roughness model for turbulent wall-bounded flows

TL;DR

This paper introduces a geometric model using the wind-shade factor to predict hydrodynamic roughness in turbulent boundary layer flows over rough surfaces, enabling efficient estimation from surface elevation data.

Contribution

The novel wind-shade roughness model estimates surface roughness solely from geometric information, incorporating sheltering and pressure drag effects with a rapid algorithm.

Findings

Model accurately predicts roughness heights across diverse surfaces.

Inclusion of viscous stress improves predictions for transitional roughness.

Efficient geometric evaluation enables practical applications in flow prediction.

Abstract

To aid in prediction of turbulent boundary layer flows over rough surfaces, a new model is proposed to estimate hydrodynamic roughness based solely on geometric surface information. The model is based on a fluid-mechanics motivated geometric parameter called the wind-shade factor. Sheltering is included using a rapid algorithm adapted from the landscape shadow literature, while local pressure drag is estimated using a piecewise potential flow approximation. Similarly to evaluating traditional surface parameters such as skewness or average slope magnitude, the wind-shade factor is purely geometric and can be evaluated efficiently from knowing the surface elevation map and the mean flow direction. The wind-shade roughness model is applied to over 100 different surfaces available in a public roughness database and some others, and the predicted sandgrain-roughness heights are compared to measured values. Effects of various model ingredients are analyzed, and transitionally rough surfaces are treated by adding a term representing the viscous stress component.