This paper is concerned with the numerical simulation of unsteady turbulent flows behind sudden expansions without inlet swirl. Time dependent simulations have been carried out using the VLES approach with the standard k-ε model. The expansion ratio investigated is in the range from 1.96–6.0. The simulations show that the flows in axisymmetric sudden expansions are inherently unstable when the expansion ratio is above a critical value. The precessing phenomenon, which features self-sustained precession of the global flowfield around the expansion centerline, is predicted successfully using CFD, with simulated oscillation frequencies that are in general agreement with reported data. For the case of expansion ratios from 3.5–6.0, a combination of a precession motion and a flapping motion in a rotating frame of reference is predicted in terms of the jet movement. Large-scale structures are identified in the downstream flowfield. Other important phenomena, such as the transition of the oscillation patterns, have also been predicted.