A theoretical investigation of the nonlinear acoustic response of abrupt area contractions

Acoustic instabilities are frequently the culprit for engine failure. To mitigate these instabilities, an accurate model of the nonlinear acoustic pressure profile of the system is necessary. This study develops a nonlinear model for the acoustic response of an area-contraction. The derivation begins with the unsteady Bernoulli equation which is formed into the pressure drop across the area-contraction. Each acoustic variable is assumed to be time-harmonic and is written as the sum of a steady and fundamental term. Using a Fourier transformation, nonlinear expressions for the pressure drop and impedance are derived as functions of the steady and acoustic velocity. These expressions capture the nonlinearity of the acoustic response when the flow can reverse out of the orifice, i.e., the amplitude of the mean velocity is less than the amplitude of the oscillating acoustic velocity. This impedance model is verified by archive quality acoustic response data from a previous study.