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.
In a previously published paper, a model for the nonlinear acoustic response of an area contraction including bias flow was presented. The model's prediction for the zero-driving resistance grew progressively worse as the steady-flow Mach number increased. This trend suggests that the forward loss coefficients should depend on the steady Mach number. This letter provides an empirical fitting of this Mach number dependence, along with additional validation data for the model. These additional validation data corroborate the model's prediction that the nonlinear impedance is frequency independent. This letter additionally provides an experimental methodology for determining the characteristic length with sample results.
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