Buzzsaw Noise Predictions for Modern Turbofans

Abstract

During typical airplane takeoff conditions with high bypass ratio jet engines buzzsaw noise is being created as each fan operates at supersonic tip speeds. In the tip region of the fan blade a weak shock is spiraling upstream in a helical fashion against the convective mean flow. Earlier studies revealed that slight variations in blade tip stagger angle create significant variations in shock strengths. The relative velocity for each shock can be related to the instantaneous pressures on either side of the discontinuity. As the shocks are decaying, these initially equally (regular) spaced shocks are continuously evolving to an unevenly (irregular) spaced set of shocks. The steady rotation of the complete set of shocks remains locked to the rotor with the periodicity being preserved once per revolution and each multiple pure tone (MPT) is a harmonic of the shaft frequency. A F ourier decomposition of the system of shocks near the fan face shows that most of the acoustic energy lies in the blade passage frequency and harmonics only by virtue of being regularly spaced. The remaining acoustic energy at the fan face will be distributed over frequencies at engine orders that follow a prescribed azimuthally varying shock strength distribution. At the end of the inlet the rotating system of shocks will have evolved into a highly irregularly spaced pressure pattern that will radiate to the far field or to the fuselage sidewall. The noise that is frequently heard in the passenger cabin consists of a multitude of MPTs giving it a very unusual characteristic. During a series of engine tests, unsteady pressure measurements were acquired in the inlet at various axial locations. The unsteady pressure signals were recorded along with a once per revolution synchronizing signal from the rotor shaft. Utilizing the method of pulse synchronous averaging, refined periodic pressure waveforms were obtained. These measured waveforms were then compared with predictions. Finally, these measurements from the location closest to the fan were used as an initial distribution and propagated over sufficiently large distances to study the emergence and decay of the high frequency buzzsaw spectral characteristics. The effects of lining and cut-off are not included in this model. NOMENCLATURE ao undisturbed sound velocity atot sound velocity based on total temperature k k=(γ+1)/ γ us mean shock speed r relative position of shock r relative position of shock normalized by λo t time z axial distance from fan tip leading edge V + maximum fluid velocity near discontinuity V - minimum fluid velocity near discontinuity A area of symmetric duct cross-section A* throat area B number of fan blades D diameter of fan EO engine order MFF fan face axial Mach number Mrel relative Mach number of fan Mrot tangential Mach number of fan Mx axial Mach number of flow Po undisturbed static pressure P