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.
Researchers focused on reduced emissions hydrocarbon fuel combustion systems have developed new high-efficiency furnace and gas turbine engine technologies that, unfortunately, regularly suffer from detrimental combustion instabilities. Engineering design tools developed to predict these instabilities in combustion systems frequently neglect nonlinear acoustic effects. However, boundaries and duct junctions, e.g., area changes, valves, and orifices, often exhibit nonlinear effects even at low acoustic pressure amplitudes. Experimental data of these nonlinear effects are required to accurately model engine and duct acoustics and to predict combustion instabilities. This experimental investigation focuses on understanding the nonlinear acoustic response of an orifice with and without steady flow. Various orifices were mounted in a multiple-microphone impedance tube and the acoustic impedance of the combination was used to measure the nonlinear acoustic response and impedance of the orifices at amplitudes from 114 to 190 dB and over frequencies from 100 to 1500 Hz. The preliminary results of the experimental study suggest that the impedance is dependent on the acoustic velocity amplitude. This indicates significant nonlinear effects. These experimental data will assist the development of nonlinear acoustic models of orifices in combustion systems.
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