Non-linear duct acoustics and its application to fan noise

Quite often the scalar Helmholtz equation is assumed to be the fundamental equation of duct acoustics and various relations are derived from it. An investigation is, therefore, conducted regarding the underlying assumptions leading to the Helmholtz equation. It is found that serious errors, even well below 186 dB, are possible if the assumption of linearity were to be made. In duct acoustics these errors are highest near the cutoff points and in the case of ducts with transonic flow. It is pointed out that serious errors could arise if a nonlinear problem is analyzed by linear methods. At times, an entire phenomenon remains unpredictable by linear methods. Attention is given to the characteristics of nonlinear systems, the phenomenon of multiple pure tones in the case of noise from the aircraft engine fans, the limitations of the conventional acoustics equation, duct shape and nonlinearity, and the numerical simulation of a fan with 8 blades.