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

Trushant K Patel; Steven A E Miller

doi:10.1121/1.5139216

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

J Acoust Soc Am. 2019 Dec;146(6):4339. doi: 10.1121/1.5139216.

Authors

Trushant K Patel¹, Steven A E Miller¹

Affiliation

¹ Department of Mechanical and Aerospace Engineering, University of Florida, P.O. Box 116250, Gainesville, Florida 32611, USA.

PMID: 31893692
DOI: 10.1121/1.5139216

Abstract

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 β=(|M_j ²-M_d 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.