A significant portion of the worldwide electrical energy consumption is connected to the operation of low-pressure rotor-only axial fans in e.g. air conditioning and ventilation applications. A characteristic property of such fans is the installation without outlet guide vanes due to cost or space constraints, resulting in a strong swirl component of the flow discharging directly into a free atmosphere. Through inertial forces, the swirl component yields a sub-atmospheric static pressure in the discharge immediately downstream of the trailing edge. In the free atmosphere, the swirl component is degrading through dissipation and the static pressure approaches the atmospheric level, resembling a static pressure recovery. For rotor-only low-pressure fans in a freely discharging configuration, the total-to-atmospheric pressure increase is of central interest and is directly impacted by this natural static pressure recovery. Previous analytical investigations have identified a significant impact of the vortex-design of the fan on the static pressure recovery, which is still to be demonstrated for actual fan designs. For this, three fans with varying radial work distribution have been designed with an in-house design tool and were manufactured. In this work, the fans have been experimentally investigated by means of five-hole-probe-, PIV- and hot-wire-measurements. The experimental investigation results in an extensive data base for the validation of numerical simulations. This data base is then compared to the results of numerical simulations of varying fidelity from industry-standard RANS simulations to non-zonal delayed detached eddy simulations (DDES). The comparison shows that RANS simulations are not capable of depicting the free shear layers present in the freely discharging outflow of the fans. The delayed detached eddy simulations on the other hand show significantly better agreement with the experimental data while only moderately increasing the computational effort.