Recent experimental and computational investigations have provided a comprehensive phenomenological description of unsteadiness in nominally two-dimensional (2-D), spanwise homogeneous shock-wave/turbulent-boundary-layer interactions (STBLIs), including both the impinging-shock and compression-ramp configurations. However, a complete mechanistic description of unsteadiness from an objective dynamical systems perspective has been lacking. Furthermore, the STBLIs encountered in many aerospace applications are fundamentally three-dimensional (3-D), in which the separation structure and topology are profoundly different from those exhibited by 2-D interactions, rendering many of the conclusions derived for the latter inapplicable. This dissertation addresses the main knowledge gaps and advances the understanding of STBLI unsteadiness by providing: (1) an objective mechanistic description of unsteadiness in 2-D interactions, (2) a phenomenological description of unsteadiness in nominally 3-D interactions (swept interactions that are inherently not spanwise homogeneous), including the sharp-fin and swept-compression-ramp configurations, (3) an objective mechanistic description of unsteadiness in these 3-D interactions, and (4) a phenomenological description of unsteadiness in a representative compound 3-D interaction (a double-fin inlet/isolator configuration).
The approach employs high-fidelity large-eddy simulations of various 2-D and 3-D STBLIs in the high-supersonic (Mach 2-4) speed regime. Simulation accuracy is ensured through extensive comparison with experimental data obtained from concurrent experimental campaigns at partner institutions. The phenomenological description of unsteadiness is then compiled from various analyses of the resulting, spatiotemporally varying, turbulent flow. These include spectra of the unsteady fluctuations, band-isolated fluctuation dynamics obtained through temporal filtering, reduced-order representations, correlations, and other statistical analyses, which are assimilated to address each of the primary knowledge gaps. Several relevant time (and length) scales are detected, and each is associated with a primary physical process underlying the unsteadiness. The Strouhal number (Stδ = f δ / U∞) based on the incoming boundary layer thickness (δ) and freestream velocity (U∞) aids in describing these phenomena with respect to typical frequency bands of the broad range of flows examined, including: very-high-frequency (Stδ > 1) fine-scale turbulence, high-frequency (Stδ ∼ 1) integral-scale turbulence, mid-frequency (Stδ ∼ 0.1) shear-layer coherence, and low-frequency (Stδ <∼ 0.01) large-scale "breathing" of the interaction. Notably, the relevant length scale for the Strouhal numbers describing the mid- and low-frequency bands is not δ (length scales reflective of the shear layer thickness and size of the separation are more appropriate); however, Stδ provides a suitable unified scale to facilitate relative comparison of the different bands for the flows of interest in this work. Variation of the "appropriate" representative length scale for the Strouhal number has significant ramifications for differences in mid-frequency scaling between 2-D and 3-D interactions; the mid-frequency shear-layer scaling for 2-D interactions is consistent with that predicted by classical (2-D) free-interaction theory (spanwise homogeneous), whereas the mid-frequency shear-layer scaling for swept 3-D interactions exhibits aspects of both conical (3-D) free-interaction theory in the inner layer (not spanwise homogeneous) as well as classical (2-D) free-interaction theory in the outer layer. Most significantly, the low-frequency band that is prominent in 2-D interactions (with topologically closed separation) is relatively insignificant in simple (quasi-conical) 3-D interactions (with open separation); however, low-frequency dynamics again become significant for the representative compound 3-D interaction (with closed separation), highlighting the influence of separation structure and topology on the low-frequency dynamics.
The mechanistic description of unsteadiness is facilitated by the development of a new numerical method capable of objective identification of linear mechanisms in unsteady, 3-D, turbulent flows. The method extends several concepts from dynamical systems theory to the very-high-degree-of-freedom STBLI simulations, effectively identifying the spatiotemporal character of linear perturbations associated with the largest Lyapunov exponent of the discretized, chaotic, turbulent flows of interest; the linear mechanisms (the dynamic linear response of the flow to forcing) arise from the ensemble statistics of the linear perturbations. The method may be generalized in a straightforward manner to identify perturbations associated with additional Lyapunov exponents of the discrete Lyapunov spectrum. In application to the several, chaotic, supersonic flows of interest, the dynamic linear response distinguishes the quality of absolute versus convective instability; the supersonic turbulent boundary layer and simple (quasi-conical) 3-D STBLIs exhibit only convective instability (sustained by external forcing, behaving as an amplifier/filter), whereas the 2-D STBLI exhibits an absolute instability (self-sustaining, behaving as an internally driven oscillator) associated with the largest Lyapunov exponent. Analysis of the absolute instability of the 2-D STBLI indicates that the shock responds to linear restoring tendencies when displaced far from the mean position; however, the mean position does not coincide with the linearly stable position; rather, the linearly stable position is located upstream of the mean. The results of this analysis support the description of a mechanism for the low-frequency unsteadiness of 2-D STBLIs that results from competing linear mechanisms (objective) and nonlinear mass-depletion mechanisms (presumed from phenomenology); this new description unifies many of the existing mechanistic theories for low-frequency unsteadiness in 2-D STBLIs. Brief comments on the influence of linear mechanisms on the mid-frequency (shear layer) bands are also provided.