Acoustic scattering by an axially-segmented turbofan inlet duct liner at supersonic fan speeds

Fan noise is one of the principal noise sources in turbofan aero-engines. At supersonic fan speeds, fan tones are generated by the “rotor-alone” pressure field. In general, these tones can be well absorbed by an inlet duct acoustic liner, except at high supersonic fan speeds when the rotor-alone pressure field is well cut-on. In this article an axially segmented liner is proposed, which is predicted to improve the attenuation of tones at high supersonic fan speeds. The analysis is based on locally reacting cavity liners. The axially segmented liner is axisymmetric and consists of two circular sections of different linings joined together. The optimum design consists of two linings with the same face-sheet resistance, but with different cavity depths. The depth of the liner adjacent to the fan is very thin. This means that where the two liners are joined there is a wall impedance discontinuity that can cause acoustic scattering. Fan tones can be modelled in terms of spinning modes in a uniform circular-section duct. The liner is axisymmetric, so modal scattering will be only between different radial modes. The optimum design minimizes the acoustic energy scattered into the first radial mode. This improves the attenuation of fan tones at high supersonic fan speeds, because acoustic energy is scattered into high radial mode orders, which are better absorbed by the lining.