A theoretical and experimental investigation of the nonlinear acoustic response of acoustic insertion elements.

In a previous paper, a model was developed for the nonlinear acoustic resistance for compact insertion elements. Within the model, two loss coefficients are used to tune the model for each type of element, and data were used to empirically determine these coefficients for an area contraction. This paper extends the nonlinear model, developing expressions based on physical principles for the forward and reverse loss coefficients for both an area contraction and orifice. In addition, experimental data for the acoustic resistance of both elements was taken using an impedance tube. Utilizing the expressions developed, the model compares favorably with the experimental data.

An experimental validation of a nonlinear acoustic resistance model for an acoustically compact area contraction with steady mean flow.

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.

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.