This paper presents a new formulation for trailing edge noise radiation from rotating blades based on an analytical solution of the convective wave equation. It accounts for distributed loading and the effect of mean flow and spanwise wavenumber. A commonly used theory due to Schlinker and Amiet predicts trailing edge noise radiation from rotating blades. However, different versions of the theory exist; it is not known which version is the correct one, and what the range of validity of the theory is. This paper addresses both questions by deriving Schlinker and Amiet's theory in a simple way and by comparing it with the new formulation, using model blade elements representative of a wind turbine, a cooling fan and an aircraft propeller. The correct form of Schlinker and Amiet's theory is identified. It is valid at high enough frequency, i.e. for a Helmholtz number relative to chord greater than one and a rotational frequency much smaller than the angular frequency of the noise sources.
An analytical model is presented for the wake interaction tones produced by a contra-rotating propeller. We re-cast the usual far-field radiation formulae as a double integral over a nominal propeller source annulus. Assuming that the number of blades on both propellers is large, we evaluate the integral asymptotically in terms of its leading-order contributions from interior stationary or boundary critical points which represent the specific locations on the propeller annulus that dominate the sound radiation. The asymptotic approach is powerful producing results in the form of one-line algebraic formulae that contain no integrals or special functions yet remain accurate. The asymptotics show that sweep is not necessarily beneficial and can cause the blade design to become critical for particular tones and directions in terms of a continuum of interior points distributed along a line on the propeller source annulus producing a higher-order result and thus an enhanced radiated sound field. The paper also shows how the interior points are completely consistent with the sub- or super-critical gust response of a swept blade. Tones with low and zero azimuthal mode order are treated as special cases and the asymptotics show that, as the mode order reduces, the radiated sound becomes concentrated around the flight axis where even higher-order solutions are possible, including rings and annuli of stationary points around the propeller annulus. Full numerical calculations confirm the accuracy of the asymptotic approach.
This paper presents broadband noise predictions from uninstalled contra-rotating open rotors (CRORs). CRORs are being increasingly investigated as an alternative to single propellers and turbofan engines for power plants on aircraft, since they yield a significant reduction in fuel burn for short-haul flights. However, there is the need to develop schemes by which CROR noise can be predicted and reduced.Using semi-analytical prediction schemes, the principal broadband noise source mechanisms (rotor trailing edge noise and rotor-rotor interaction noise) are investigated, leading to strategies for their mitigation. For the configuration considered, trailing-edge broadband noise is predicted to be dominant at low rotor loading conditions (typical of cruise and approach) whereas rotorrotor interaction broadband noise is predicted to be dominant at high rotor loading conditions (typical of take-off). A systematic parameter study is also presented in which the dependence of CROR broadband noise on the rotor-rotor gap, rotor speeds and blade numbers are investigated at constant engine power, torque split and solidity.
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