Shape factor

Abstract: Data from 14 previous experimental studies were used to develop an empirical equation that accounts for the effects of size, density, shape, and roundness on the settling velocity of natural sediment. This analysis was done in terms of four nondimensional parameters, namely, the dimensionless nominal diameter D*, the dimensionless settling velocity W*, the Corey shape factor, and the Powers roundness index. For high D* (large or dense particles), changes in roundness and shape factor have similar magnitude effects on settling velocity. Roundness varies much less for naturally occuring grains, however, and hence is a less important control than shape. For a typical coarse sand with a Powers roundness of 3.5 and a Corey shape factor of 0.7, the settling velocity is about 0.68 that of a sphere of the same D*, with shape and roundness effects contributing about equally to the settling velocity reduction. At low D* the reduction in settling velocity due to either shape or roundness is much less. Moreover, at low D*, low roundness causes a greater decrease in settling velocity at low shape factor values than at high shape factor values. This appears to be due to the increased surface drag on the flatter grains.

Abstract: Statistics obtained from seven different direct numerical simulations (DNSs) pertaining to a canonical turbulent boundary layer (TBL) under zero pressure gradient are compiled and compared. The considered data sets include a recent DNS of a TBL with the extended range of Reynolds numbers Reθ = 500–4300. Although all the simulations relate to the same physical flow case, the approaches differ in the applied numerical method, grid resolution and distribution, inflow generation method, boundary conditions and box dimensions. The resulting comparison shows surprisingly large differences not only in both basic integral quantities such as the friction coefficient cf or the shape factor H12, but also in their predictions of mean and fluctuation profiles far into the sublayer. It is thus shown that the numerical simulation of TBLs is, mainly due to the spatial development of the flow, very sensitive to, e.g. proper inflow condition, sufficient settling length and appropriate box dimensions. Thus, a DNS has to be considered as a numerical experiment and should be the subject of the same scrutiny as experimental data. However, if a DNS is set up with the necessary care, it can provide a faithful tool to predict even such notoriously difficult flow cases with great accuracy.