A numerical investigation of a propeller with swirl recovery vanes (SRVs), for which experimental data exist, is performed. A second SRV geometry, with shorter vanes to avoid the impingement of the propeller tip vortices, is also investigated. For the baseline SRVs, the efficiency of the propulsive system increases of 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 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 (BPF) while, in the other directions, peaks are present at harmonics of the first BPF. However, the overall isolated propeller noise is 23 dB higher than the noise generated by the SRVs. Shortening the vane length causes 13% reduction of the thrust generated by the vanes with respect the baseline case, but no variation of the far-field noise. Nomenclature c = chord [m] C T = thrust coefficient [-] D = propeller diameter [m] J = advance ratio [-] n = rotational velocity [rev/s] P = power [W] r = local blade radius [m]