Direct numerical simulations (DNS) are performed to study acoustic radiation in a quasi-two-dimensional nozzle with two independents spatially evolving turbulent boundary layers with an edge Mach number of 6. The emphasis of this work is to compare the radiated pressure fluctuations in a geometrically confined environment with those radiated from a single wall in an unconfined setting. The boundary-layer profile of the rms pressure fluctuation scaled by the mean shear stress at the wall is found to be in good agreement with prior flat-plate calculations at similar conditions. However, the normalized rms pressure fluctuation within the freestream p region is significantly higher than that in the unconfined case, by a factor that is approximately equal to 2. The application of two different compressibility transformations to the computed mean velocity profiles indicates that, in comparison with the van Driest transformation, the Trettel and Larsson transformation provides a better collapse with flat-plate simulations over a broad range of Mach numbers. The DNS data also reveal that, in spite of displaying a strongly non-Gaussian behavior inside the boundary layer, the radiated acoustic fluctuations in all thermodynamic variables have a skewness of approximately 0.3, indicating a minor deviation with respect to Gaussian behavior. Surface pressure fluctuations along the nozzle walls are not significantly impacted by the acoustic waves radiating from the opposite wall.


Mechanical and Aerospace Engineering


Office of Naval Research, Grant N00014-17-1-2347

International Standard Serial Number (ISSN)

1533-385X; 0001-1452

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2023 American Institute of Aeronautics and Astronautics, All rights reserved.

Publication Date

01 Jan 2022