The work is devoted to experimental and numerical study of aerodynamic structure of a swirl flow in isothermal model of a vortex burner device that is characterized by the fluid flow supply via two sequentially-mounted tangential swirlers. Depending on the way of the flow supply into the second-stage swirler, either co-swirl or counter-swirl of two flows can be realized. The effect of the second-stage supply direction on the resulting aerodynamic structure has been investigated. Using LDA measurement system the profiles of averaged axial and tangential velocity components were obtained. Experiments have shown that in the co-swirl case the flow inside the vortex burner model is characterized by strong non-uniformity, while in the counter-swirl regime a rapid mixing of the flows from the first and second stages occurs, resulting in a uniform distribution of the flow across the chamber section. Numerical simulation of 3D isothermal turbulent flow has been performed for the counter-swirl regime using the differential Reynolds stress model in the time-dependent formulation. Using the Q-criterion for the identification of vortices in numerical data arrays, the evolution of large-scale vortex structures of the swirl flow inside the vortex chamber has been visualized, indicating the presence of two spiral-shape vortex filaments in the vortex chamber. The periodic character of dynamics of these vortex structures has been revealed.