In the present study numerical results of simulations, using RANS and LES, of the non-reacting flow in a swirl-stabilized burner are presented. The burner was developed for lean premixed combustion with high fuel flexibility at low emissions. An important challenge for a fuel-flexible, low emission combustor is the prevention of flashback for fuels of high reactivity, such as hydrogen, without compromising on lean blow out safety and mixing quality. Flashback safety can be increased by a sufficiently high and uniform axial velocity at the end of the mixing tube. In the investigated combustor the velocity deficit in the center of the mixing tube, which results from the swirl, is prevented by a non-swirling axial jet. In a parametric study the effect of different amounts of axial injection on the flow field is investigated. The results are validated with experimental data, gained from PIV measurements in a vertical water tunnel. It is shown that the mean flow field can be well captured by steady-state RANS simulations using a realizable k-ε turbulence model. The most suitable geometry is identified and, subsequently, transient LES simulations are conducted. The dynamic flow field characteristics are investigated. It was found that in spite of the high swirl, the flow field is quite stable and no dominating frequency is detected. The flow field of the swirling flow in the combustion chamber can be captured well using LES. Furthermore, the mixing quality is compared to the experiments, which are performed in a water tunnel. In contrast to the RANS simulation, the LES can qualitatively capture the spatial unmixedness observed from experimental data. All simulations were conducted using water as fluid.