Analysis of Roughness Correlations on Ice Geometries via Embedded Large-Eddy Simulation

This study uses embedded large-eddy simulations of a developing turbulent boundary layer over a heated flat plate with realistic ice roughness to assess local effects on velocity (Delta U+) and thermal (Delta Theta(+)) log-layer shifts. Validated against experimental data, the numerical setup is used to analyze the mean turbulent flow properties and ultimately assess a selection of equivalent sand-grain roughness k(s) correlations against computed roughness shifts. Several established models are taken into account that estimate equivalent sand-grain roughness distributions based on geometric properties of the nonuniform rough surfaces. The trend of Delta U+ and Delta Theta(+) is observed by employing the different correlations. The analysis is complemented with a brief assessment of Stanton-number-friction factor analogies resulting from the simulation outputs. Finally, a multivariate approach is employed to investigate possible cross-dependencies between roughness geometrical properties and shifts. The results indicate that some existing models capture the trends of velocity shifts accurately only in the fully rough regime for k(s)(+)>400, while for k(s)(+)<400, they generally struggle to correctly capture the expected trends. Thermal shifts show inconsistent trends across the tested models. The same gap appears in St estimates via friction analogies, showing no clear dependence on geometry features.