Assimilating rough features: A data-driven framework to infer rough wall properties from sparse experimental data

TL;DR

This paper introduces a data assimilation framework that infers rough wall properties like the sand-grain roughness height from sparse experimental data by modifying smooth-wall RANS simulations, achieving high accuracy in velocity profiles and roughness predictions.

Contribution

It presents a novel data-driven approach to estimate rough wall parameters from limited data, bypassing the need for detailed measurements.

Findings

Reproduces velocity profiles within 1% accuracy

Predicts friction velocity within 1-6% of experimental data

Accurately infers sand-grain roughness height up to 1% error

Abstract

Surface roughness influences turbulent boundary layers (TBLs) primarily through the roughness function $\Delta U^+$ and the equivalent sand-grain roughness height \(k_s\). Direct determination of \(k_s\) typically requires detailed velocity and wall-shear stress measurements, which are often impractical. As an alternative, this study presents a data assimilation framework that modifies a smooth-wall Reynolds-Averaged Navier-Stokes (RANS) baseline to match sparse rough-wall particle image velocimetry (PIV) data in the fully rough regime. Through this approach, secondary variables such as the friction velocity, \(u_\tau\), and \(k_s\) can be inferred from the assimilated flow fields. The assimilated TBL reproduces experimental velocity profiles within 1\% and predicts friction velocity within 1-6\% of the experimental measurements. Furthermore, the \(k_s\) values inferred from the assimilation also match the experimental data up to 1\%. These results demonstrate the potential of data assimilation as a cost-effective alternative to high-fidelity methods and support the generalisation of the framework to model streamwise-varying roughness by treating \(k_s\) as a function of fetch length.