Numerical prediction of loudness metrics for N-waves and shaped sonic booms in kinematic turbulence.

The effects of a kinematic field of velocity fluctuations on the loudness metrics of two waveforms are examined with a three-dimensional one-way propagation solver. The waveforms consist of an N-wave and a simulated low-boom from NASA's X-59 QueSST aircraft. The kinematic turbulence is generated using a von Kármán composite spectrum, which is dependent on a root mean square (rms) velocity and outer scale of the turbulence. A length scale is proposed to account for the effect of the rms velocity and integral scale on the focusing and defocusing of the sonic boom waveform. The probability density function of the location of the first caustic attains a maximum value when the propagation distance is equal to the proposed length scale. Simulation results indicate that for small values of the nondimensional propagation distance, the standard deviation of the loudness metrics increases linearly. The loudness metrics follow a normal distribution within a given range of the nondimensional propagation distance. Results indicate the potential to parameterize the loudness metric distributions by the rms velocity and integral length scale.

Analysis of supersonic jet turbulence, fine-scale noise, and shock-associated noise from characteristic, bi-conic, faceted, and fluidic injection nozzles.

Fine-scale mixing noise (FSMN) and broadband shock-associated noise (BBSAN) are the dominant components of supersonic jet noise in the sideline and upstream directions. We use the previously developed statistical FSMN and BBSAN models to compare the noise radiated from three different nozzles, i.e., a method of characteristics nozzle, a bi-conic nozzle, and a faceted nozzle at different operating conditions. A numerical sensitivity analysis is performed using the models by perturbing various model parameters and conditions such as nozzle pressure ratio (NPR), total temperature ratio, area ratio, and boundary layer thickness. We observed that FSMN is most sensitive to NPR and BBSAN is most sensitive to area ratio. We also examine the changes in source statistics and corresponding correlations of the radiated noise using the fluidic injection noise reduction technique. Noise reduction predictions relative to the baseline cases are compared at different operating conditions and similar reduction as the experimental measurements were obtained at over-expanded conditions. Finally, we analyze the noise source locations for both components of jet noise in the sideline direction. The trends predicted in this study increase understanding of the changes in source statistics and radiated noise for different nozzles over a range of operating conditions.

Statistical sources for broadband shock-associated noise using the Navier-Stokes equations.

A decomposition of the Navier-Stokes equations is used to identify the equivalent source term for broadband shock-associated noise (BBSAN). An analytical closed-form model to predict BBSAN is developed using an acoustic analogy based on the Navier-Stokes equations. The field-variables are decomposed into the base flow, aerodynamic fluctuations, and acoustic fluctuations. The spectral densities of fluctuating acoustic quantities are obtained by convolving the vector Green's function with the source terms involving the two-point cross-correlation of the aerodynamic quantities. The scaling of the source term with the off-design parameter ß=(|Mj 2-Md 2|)1/2 is compared with experimental results. The base flow is obtained using a Reynolds-averaged Navier-Stokes solution, while the fluctuating statistical quantities are obtained using theoretical and experimental results. This paper identifies the equivalent source of BBSAN based on the scaling analysis and the physical mechanism of shock-associated noise. The identified source term resides within the Navier-Stokes equations without further rearrangement and correlates very highly with BBSAN. Predictions for BBSAN are made at multiple observer angles and nozzle pressure ratios using the identified source term, and these predictions compare favorably with the experimental results. Finally, identification of the source locations in the jet exhaust responsible for BBSAN at different Strouhal numbers is performed.