Acoustic Radiation in Hypersonic Turbulent Boundary Layers: Deciphering Linear Dynamics

This thesis is primarily concerned with hypersonic turbulent boundary layers and the unique features – present in them. This problem is studied in three levels of varying fidelity – by means of linear resolvent analysis, a blended resolvent estimation approach, and direct decomposition of a temporally-resolved dataset. This thesis then explores three complementary research directions: (i) quantification of how streamwise development influences acoustic radiation across various parameter regimes, (ii) development of a forcing model that enables acoustic radiation estimation using only near-wall measurements, and (iii) evaluation of these findings through comparison with data-driven analysis techniques. First, the resolvent analysis is performed on a turbulent hypersonic streamwise developing mean profile. It is shown that these (acoustically radiating) streamwise developing resolvent modes may be effectively modeled using resolvent modes around an assumed-parallel mean profile. Then this model is used to investigate the impact of streamwise development on acoustic radiation for varying bulk parameters. Second, the modeling of acoustic radiation from near-wall information is tackled. To achieve this, resolvent based estimation (RBE) is leveraged along with a small number of near-wall measurements. It is shown that RBE alone is insufficient to accurately predict the freestream power spectral density. Resolvent analysis around a streamwise developing mean profile is then analyzed by performing a Helmholtz decomposition, where it is shown that the solenoidal part of the resolvent forcing is primarily responsible for the linear amplification. This observation is used to develop an approximate forcing CSD method, which filters out any dilatational forcing, to supplement RBE. Using the approximate forcing with RBE shows significantly improved estimation of the freestream PSD. Finally, spectral proper orthogonal decomposition (SPOD) is applied to a 3-D temporally-resolved dataset resulting from a direct numerical simulation of a hypersonic streamwise developing turbulent boundary layer. It is shown that the SPOD of the fluctuations around a streamwise developing mean extracts modes with a constant streamwise wavenumber and shows high-rank behavior. By further transforming the data in the streamwise direction, an SPOD of the fluctuations around a 1-D mean profile uncovers low-rank behavior and similar structures are seen between the resolvent and SPOD modes.