Application and validation of sediment erosion models to time dependent wall shear stresses around a wall-mounted circular cylinder

The prediction of erosion rates by several popular erosion models is critically assessed for the case of initial scouring of a cylindrical bridge pier in a sand bed at subcritical conditions. The erosion models are applied to local wall shear stress data obtained by a high resolution Large Eddy Simulation (LES) of the flow around a wall-mounted cylinder at a Reynolds number of Re_D = 39000 based on the diameter of the cylinder D and the bulk velocity. The resulting erosion rates are compared to measured ones of an experiment at the same conditions thus being able to evaluate both qualitative and quantitative prediction capabilities of the various models. We consider erosion models based on pick-up function formulation (Einstein (1950); Yalin (1977); Fernandez Luque & Beek (1976)) and bed load functions (Meyer-Peter & Müller (1949)). These models have been applied to time averaged wall shear stress data computed by the LES. Comparing the shape of the eroded areas to experimental data gives a good impression of the applicability of the structural basis of these models to the underlying flow situation. The pick-up function model gives qualitatively better predictions of the erosion around the cylinder. Comparing the magnitude and the shape of the erosion helped choosing specific model versions and adjusting model parameters. In addition it is argued that wall shear stress fluctuations can be many times higher than the averaged ones. Formulations taking into account these fluctuations (e.g. Zanke (2001)) could give a better prediction of erosion in such flows. This statement is supported by a comparison of probability distribution functions (pdf) of the wall shear stress around the cylinder, which enlightens the differences between this measured pdf and pdfs based on a modeled approach.