Date of Award

8-22-2025

Date Published

September 2025

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mechanical and Aerospace Engineering

Advisor(s)

Yiyang Sun

Subject Categories

Aerospace Engineering | Engineering

Abstract

Coherent structures play a key role in uncovering and predicting the underlying physics of complex turbulent flows. This dissertation employs data-driven and operator-based techniques to investigate spatiotemporal correlated structures of a complex supersonic multi-stream rectangular jet. The nozzle configuration comprises three primary shear layers: (i) an upper shear layer (USL) formed by the flow on the upper single-sided expansion ramp stream and the freestream, (ii) a splitter plate shear layer (SPSL) generated by the mixing of a core Mach 1.23 stream with a bypass Mach 1 stream at the splitter plate trailing edge (SPTE) and (iii) a lower shear layer (LSL) formed downstream of the aft-deck plate as it mixes with the freestream flow. The configuration produces a dominant high-frequency resonant tone that arises from the SPSL and persists throughout the flow field. To establish a fundamental understanding of the dominant tone, the SPSL is first examined in isolation using a combination of large-eddy simulations (LES) and linear operator-based input-output analysis. Spectral proper orthogonal decomposition (SPOD) identifies the Kelvin–Helmholtz (KH) mode as the most energetic coherent structure at the dominant frequency. Resolvent analysis of the time-averaged flow also shows peak gain at the dominant frequency, indicating the KH instability as the primary energy amplification mechanism. Bispectral mode decomposition (BMD) is used to investigate the nonlinear energy cascade within the turbulent shear layer. A componentwise input-output analysis, in which forcing is restricted in space and state variables, identifies the SPTE as the most receptive regions for introducing perturbations. Two-dimensional forced simulations demonstrate remarkable similarities between pressure modes obtained through dynamic mode decomposition and those predicted from linear input-output analysis. Leveraging the insights gained, the resolvent analysis is extended to the center plane of the jet flow. A wide range of frequencies and spanwise wavenumbers is examined, showing the energy amplification peaks near the dominating KH frequency for optimal and first-suboptimal modes. The optimal resolvent mode appears in the different shear layers depending on the input frequency–wavenumber pair. An intriguing shift phenomenon is observed where the optimal and suboptimal gain distributions crossover; these events are associated with switching the most receptive regions across the three shear layers. Comparison between the resolvent model and SPOD shows that sub-optimal resolvent modes better align with the leading SPOD modes, suggesting over-optimization by the linear operator in complex multi-stream jet flow. Subsequent input–output analyses with state-variable and spatial restrictions offer further insights into componentwise amplification of the jet flow response. The study is further extended to three-dimensional SPOD and resolvent analysis to account for the complete spatiotemporal dynamics of the jet. SPOD reveals a tonal two-dimensional KH mode in the SPSL, consistent with earlier findings, whereas broadband low frequencies three-dimensional structures govern USL and LSL. Tri-global resolvent analysis of the USL and LSL regions exhibits a similar trend to SPOD. The resolvent modes also reveal the self-sustaining production of streamwise vortices, which contribute to axis-switching behavior observed in rectangular jets. The insights gained from this study serve as a basis for future efforts to model and control shear layer dynamics in complex supersonic jet configurations.

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