A numerical investigation of a propeller with swirl recovery vanes, for which experimental data exist, is performed. A second swirl recovery vane geometry, with shorter vanes to avoid the impingement of the propeller tip vortices, is also investigated. For the baseline swirl recovery vanes, the efficiency of the propulsive system increases by 2.4% with respect to the isolated propeller. This is obtained by converting angular momentum in axial momentum. A reduction of the swirl angle in the near wake by 48% is found. Most of the thrust is generated at the root of the vanes. Leading-edge impingement noise is the dominant source. The vanes cause noise to increase by 20 dB with respect to the isolated propeller in the axial direction, where noise from the propeller vanishes. In the axial direction, sound pressure level spectra show tonal peaks at harmonics of the second blade passing frequency, while in the other directions, peaks are present at harmonics of the first blade passing frequency. However, the overall isolated propeller noise is 23 dB higher than the noise generated by the swirl recovery vanes. Shortening the vane length causes a 13% reduction of the thrust generated by the vanes with respect the baseline case but no variation of the far-field noise.