The paper presents numerical investigations of decelerated swirling flows specific to hydraulic turbines draft tube cone, within the framework of axisymmetric flow models. First, we investigate the behaviour of a Burgers vortex in a diffuser as the swirl intensity is increased. We show that first a steady vortex breakdown occurs, with a central stagnation region, then the flow becomes highly unsteady with vortex rings convected downstream. Our main result proves that the vortex breakdown and the unsteadiness can be removed by slighlty altering the inlet axial velocity profile. A rather weak water jet injected at the axis in the inlet section, recovers a steady breakdown-free flow configuration. Second, we validate and assess the accuracy of the turbulent axisymmetric flow model in comparison with velocity and turbulent kinetic energy measurements in a model Francis turbine draft tube cone.