A New Algorithm for Nonlinear Propagation of Broadband Jet Noise

Open Access
Saxena, Swati
Graduate Program:
Aerospace Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
Committee Members:
  • Philip John Morris, Thesis Advisor
  • shock
  • Burgers equation
  • nonlinear acoustics
  • broadband jet noise
  • power spectral density
Nonlinear wave propagation is observed in the noise created by many sources such as fighter jet aircraft, explosions, gun fire, sonic booms etc. The wave acquires nonlinearity which becomes more pronounced with distance when the fluctuations in the state variables are high enough when compared to the ambient values. In the present work, a frequency domain nonlinear noise propagation algorithm (NLFDA) is presented. Noise propagation of the sound generated by high-speed jets, as mentioned, experiences nonlinear propagation. This nonlinear behavior, which includes the transfer of energy to high frequencies from central and lower frequencies, is captured in the present algorithm. The generalized nonlinear Burgers equation, which includes atmospheric absorption and dissipation, is solved for the pressure signal in the frequency domain. The results are then obtained as a function of time by inverting the signal back from frequency domain. A test case of a pure tone sinusoidal wave is considered, and the results are verified with the existing analytical Blackstock Bridging Function (BBF), Fubini and Fay solutions. The predicted results of the sinusoidal wave case agree fairly well with the analytical results. Scaled jet nozzle data collected at the anechoic chambers of the Boeing Low Speed Aeroacoustic Facility (LSAF) and Penn State Jet Acoustic Facility are used for the broadband noise prediction. The experiments include both heated subsonic and supersonic jet cases. The experimental and predicted Power Spectral Density (PSD) plots are compared for the measurements made by microphones located at different radial distances. The predicted results are in good agreement with the experimental results at all the microphone locations, and the PSD plots show a lift at high frequencies due to the nonlinear steepening of the waves. The skewness of the experimental and predicted signal is discussed. NLFDA comparisons are also done with full scale F/A-18E engine tie-down tests and the differences in the results are discussed. All the nonlinear PSD plots are also compared with the linear predictions to better visualize the differences in linear and nonlinear propagation. A ground reflection formulation is then described. The Boeing LSAF heated supersonic and F/A-18E engine data are propagated using the nonlinear algorithm with the ground effects are included to study the effective noise pattern due to the sound reflected from the ground. Morfey-Howell nonlinearity parameter, normalized quad-spectral density is calculated for the Boeing heated supersonic case and F/A-18E engine test case and the energy transfer to high frequencies from low frequencies is explained with its help. To conclude, the NLFDA algorithm presented in the thesis accurately captures the nonlinear affects in broadband high-speed jet noise and can be extended further in more than one dimension.