Data-driven high-fidelity prediction of the equivalent sand-grain height of rough surfaces

This work addresses a long standing question about roughness: what is the equivalent sand-grain height, given the roughness topography? Deep Neural Network (DNN) and Gaussian Process Regression (GPR) machine learning approaches are used to develop a high-fidelity prediction approach of the Nikuradse (1933) equivalent sand-grain height $k_s$ for turbulent flows over a wide variety of different rough walls. To this end, 45 surface geometries are generated and simulated at $Re_\tau=1000$. The surfaces geometry differ widely in moments of surface height fluctuations, effective slope, average inclination, porosity and degree of randomness. When combined with 15 fully rough experimental data sets, courtesy of Flack et al (2016, 2018 and 2019), the DNN and GPR methods predict $k_s$ with an rms error of less than 10\% and a maximum error of less than 30\%, which appears to be significantly more accurate than existing correlations applied to the present database.

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