Large Eddy Simulations of Rough Turbulent Channel Flows Bounded by Irregular Roughness: Advances Toward a Universal Roughness Correlation

Abstract

The downward shift of the mean velocity profile in the logarithmic region, known as roughness function, $$\Delta U^+$$ , is the major macroscopic effect of roughness in wall bounded flows. This speed decrease, which is strictly linked to the friction Reynolds number and the geometrical properties which define the roughness pattern such as roughness height, density, shape parameters, has been deeply investigated in the past decades. Among the geometrical parameters, the effective slope (ES) seems to be suitable to estimate the roughness function at fixed friction Reynolds number, Re $$_{\tau }$$ . In the present work, the effects of several geometrical parameters on the roughness function, in both transitional and fully rough regimes, are investigated by means of large eddy simulation of channel flows characterized by different wall-roughness textures at different values of Re $$_{\tau }$$ up to 1000. The roughness geometry is generated by the superimposition of sinusoidal functions with random amplitudes and it is exactly resolved in the simulations. A total number of 10 cases are solved. With the aim to find a universal correlation between the roughness geometry and the induced roughness function, we analyzed the effect of more than a single geometrical parameter, including the effective slope, which takes into account both the roughness height and its texture. Based on data obtained from our simulations and a number of data points from the literature, a correlation between the ES and the root mean square of the roughness oscillation, as well as between ES and the mean absolute deviation of the roughness, satisfactorily predicts the roughness function.