Scramjet-based, air-breathing propulsion systems are poised to enable development of hypersonic defense, high speed transport, and access-to-space aerospace vehicles. A particular variant of scramjet engine, the dual-mode scramjet, is capable of operating in subsonic- and supersonic-burning modes and is attractive for flight at or above Mach 5. Despite the relative geometric simplicity of such scramjet engines, the intense hypersonic flight environment presents challenges to routine, long-duration hypersonic flight in the form of shock-turbulence interactions, heat-transfer, and turbulent-combustion.
A critical component of dual-mode scramjets, the isolator, conditions the flow before it reaches the combustion zone and contains the Pre-Combustion Shock-Train (PCST) which forms in response to the pressure rise due to chemical heat release. When subjected to sufficiently large mechanically- or chemically-induced back-pressures, the isolator may unstart, resulting in the rapid ejection of the shock-train from the isolator, adversely affecting controllability and survivability of high-speed air-breathing vehicles.
To better anticipate and control for isolator unstart events, detailed understanding of the combustor dynamics is required.
In particular, the selection and placement of measurement sensors for ground and flight experiments is predicated on quantifying the dynamic response of the scramjet engine system. This dissertation computationally studies the isolator dynamics during a fuel-staging-induced unstart event. In this process, fuel flow rates are varied in time between two reference fueling states studied experimentally and characterized as aft-fueled and forward-fueled biased, respectively.
The dynamics of a rectangular cross-section scramjet combustor, in the presence of simulated inflow-distortion, are described and quantified with respect to combustion-induced unstart. Because of the high Reynolds number and multi-physics effects of mixing and combustion, a model-based, Unsteady Reynolds-Averaged Navier-Stokes (URANS) approach is employed to study the turbulent reacting flowfield. Before characterizing unstart phenomenology, solution sensitivities to model parameters and assumptions are quantified.
The primary analysis considers the dynamics of the PCST during the imposed fuel-staging transient. A wall-pressure-based shock sensor employed in experiments is used to track the response of the PCST to the heat release-induced back-pressure gradients. From this sensor, an incipient unstart condition is identified which delineates between slowly-varying, pre-unstart PCST motion and more rapid PCST unstart motion. Extending this one-dimensional sensor to the predicted two-dimensional wall field reveals strong spanwise gradients associated with side wall separation.
Rectangular combustors are particularly sensitive to corner flow, including shock-induced separation and secondary flow. Commensurately, side wall separation is identified as a principal component of the unstart dynamics in this rectangular combustor. Viscous effects associated with these separation zones are characterized in terms of the isolator confinement parameter employed in the literature, which suggests a shift from an oblique to normal shock-train structure. Secondary flow is also quantified in terms of streamwise vorticity variations along the combustor. A separation bubble on the upper wall of the isolator is also identified which modulates the shock-train structure near the isolator entrance. A bias in mixing and heat release zones near the side wall of the combustor is identified as the primary driver of the side wall separation dynamics which precede unstart, consistent with experimental measurements of steady-state combustor operation.
A secondary component of the analysis leverages Model Order Reduction (MOR) techniques to filter the high-dimensional flowfield into a low-dimensional basis of features called modes. Two popular MOR methods, namely, snapshot-based Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), are employed to isolate spatially coherent flow structures from the computational dataset via the extracted modes. These methods, which are typically applied to statistically stationary flowfields, require careful extension to the statistically unsteady unstart event. To anchor the MOR-based analysis, the Total Variation metric is adapted to quantify spatially-localized flowfield dynamics and provide a basis to verify that the extracted modes are representative of the non-stationary dynamics. From the dominant POD and DMD modes, as applied to selected analysis planes (spatial windows), flow structures related to upper and side wall separation zones are captured. Time-windowing the dataset provides an additional filter to isolate PCST structures at different phases of the fuel-staging transient.
The efficiency of the MOR-based representations of the combustor dynamics are evaluated in terms of the reconstruction error for a given level of data compression (order reduction). Importantly, two methods are proposed from which to infer higher-order dynamics using the reconstruction errors. The first method, relies directly on the reduced-order reconstruction to identify large-magnitude error regions indicative of higher-order dynamics. A second approach is presented in which the MOR-based filters are applied to the entire three-dimensional domain for which brute force computation of reconstruction error is computationally infeasible. DMD, in particular, is shown to encode information of the time-mean and higher-order dynamics within the dominant mode. Consequently, the difference between the time-mean field and DMD mode is shown to identify regions which feature non-linear temporal flowfield variations. The three-dimensional MOR analysis isolates spanwise gradients associated with isolator corner flow and shear layers developing downstream of the cavity and the backward-facing steps.
To facilitate MOR analysis of the full, three-dimensional simulation data, variables are partitioned into separate decompositions to mitigate computation cost. For DMD, it is shown that partitioning the observables of interest into separate MOR decompositions produces similar but not identical dynamics, as inferred from the DMD eigenspectra. This suggests caution when applying these techniques to high-dimensional three-dimensional datasets if the goal is to compare the low-order representations of different variables.
Finally, a time-local variant of the DMD method is applied to filter the statistically unsteady scramjet flowfield. The method shows improved reconstruction performance over standard DMD while still capturing the primary dynamic structure associated with upper wall separation. Such MOR decompositions are thus shown to provide a reasonable filter to the leading dynamics of the statistically unsteady combustor which may further facilitate control system development and optimal sensor selection and placement.