Scaling relations for the velocity profile and circulation time, which can be used in design and scale-up, are of great importance in rotating drums. We conducted simulations by discrete element method at various operating conditions (which covers both rolling and cascading regimes) for spherical and non-spherical particles. New scaling relations were proposed for evaluating and fully characterize velocity profile and circulation time in both rolling and cascading regimes. Using dynamic angle of repose, effect of shape was included in these correlations to extend them to spherical and non-spherical particles. Simulation results can satisfactorily reproduce experimental measurements. Visual results show that transition from rolling to cascading regime depends not only on Froude number, fill level and particle size, but also on the particle shape. The surface velocity is scaled with peak velocity and half chord length and its profile is asymmetric with the maximum occurring after the mid-chord position for all simulations. We obtained a correlation for the peak velocity based on our simulations as well as available experimental data in literature. We also found the velocity profiles along the bed depth in active and passive layers. Our results show that the circulation time of particles follow a log-normal distribution. The mean circulation time decreases with rotation speed and drum diameter and increases with fill ratio. This value is greater for spherical particles compared to non-spherical particles. Correlations are also proposed for mean and standard deviation of the circulation time. (C) 2015 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.