A direct connect, supersonic solid fuel combustor with a cavity is explored in the context of understanding characteristics related to ignition, regression rate, combustion, and flow fields for application in advancing solid fuel scramjet research. 3D printed, polymethylmethacrylate fuel grains are loaded into both fully enclosed and optically accessible combustors. The ignition characteristics are investigated by systematically varying the internal geometry of the fuel grain to develop a flammability map with respect to non-dimensional geometric parameters. Results reveal that a longer and larger flameholding cavity creates favorable conditions for ignition and sustained combustion. The inlet temperature is also systematically varied to extend the available literature on the supersonic combustion of solid fuels to lower temperature operating conditions and show that a higher inlet temperature is conducive to sustained combustion and higher regression rates. The regression rates of the fuel grains are measured to determine a concentration of regression in the flameholding cavity along the angle of the downstream side of the cavity. Ignition and sustained combustion rely heavily on the fuel in the flameholding cavity. A decreasing regression rate is observed as the fuel regresses by measuring the regression rate at discrete time intervals during a firing of the optical combustor. The optical combustor is also subject to various high-frequency imaging techniques. Shadowgraph imaging shows the changes in density of the flow field and finds a normal shock in the constant area section. CH* chemiluminescence imaging provides novel observations of the concentrated areas of combustion along the fuel grain wall by highlighting the heat release from combustion. A high intensity of CH* radicals is in the upstream section of the flameholding cavity. When considered in the context of the concentration of regression, this indicates that the recirculation zone pulls fuel from the downstream section of the cavity, combusts it in the upstream section of the flameholding cavity, then expels the higher enthalpy gas into the core flow. Additionally, observing the flow provides insight into the flow dynamics of opposing cavities in a supersonic flow field. The symmetry of the flow field is found to be reliant on the stability of the flameholding cavity length to depth ratio. / Master of Science / A solid fuel scramjet has the potential to be the simplest and most cost effective method of achieving hypersonic flight. A liquid fuel scramjet has been demonstrated in free flight, but liquid fuels present many issues involving safety and storage that can be eliminated by introducing solid fuels. Supersonic combustion, or burning fuel in an air flow moving faster than the speed of sound, is a complicated subject due to the irregularity of flow fields and the requirement of combustion to occur at a high rate. The research within this thesis presents many novel technologies that have never been presented in published literature in the context of the supersonic combustion of solid fuels. By conducting ground testing of a solid fuel scramjet, characteristics of the combustion can be studied to expand the available literature in the field to new fuel geometries and inlet conditions. The ignition and sustained combustion of a solid fuel scramjet is extremely reliant on the initial geometry of the fuel and the initial temperature of the flow. This research advances the field of supersonic combustion of solid fuels by developing an optically accessible combustor using quartz windows. These characteristics of supersonic combustion are investigated using highspeed video recording. The results of these techniques provide insight into favorable fuel geometries and inlet conditions. Additionally, patterns observed in the flow field explain concentrations of combustion and fuel consumption.

Cold flow inside a Solid Fueled Ramjet (SFRJ) is simulated using large eddy simulations (LES). A finite element method using a Discontinuous Galerkin bases has been implemented in the open-sourced multi-physics software SU2. Novel LES formulations of the fuel-gas boundary conditions and the heat release due to mixing are obtained using integration by parts over the discontinuous Galerkin bases. The Smagorisnki and wall-adapted subgrid stress model for the scalar variance have been implemented and investigated in twodimensions. Spectral Proper Orthogonal Decomposition is used to analyze CFD results to determine acoustic modes in the ramjet. Peak acoustic frequencies are compared between between numerical and experimental results. Comparisons are made between simulations performed with a 2D axisymmetric domain and full 3D domain. Cold-flow LES simulations show that there are two dominant acoustic modes (St ≡ f/f0 = {3, 18}) in the ramjet and their frequency appears to be invariant to the cavity configuration. The first peak corresponds to a longitudinal mode associated to the chamber fundamental oscillations (with length scale Lc). The second is characterized with radial fluctuations in the mixing chamber and features the maximum chamber radius of the ramjet as its scaling length. Mixed (radial and axial) modes in the intermediate frequency range reveal the effect of a slanted aft wall on the acoustics. Three-dimensional cold flow simulations predicted weak non-symmetric (azimuthal) modes. Hot-flow simulations show a substantial increase in the mean chamber pressure with the addition of the cavity, indicating that it enhances flame-holding in solid-fuel ramjets, in agreement with the experiments. The analysis of the ramjet acoustic modes shows the emergence of low frequency modes in the cavity cases, in agreement with the experiments. Using SPOD, these modes were associated with low frequency breathing of the recirculation region at the nozzle throat. Perturbations are localized in the throat region because of the Mach number pressure scaling. These modes do not seem to affect the pressure fluctuation and thus combustion in the chamber. Together with the emergence of low frequency vortical modes, the cavity supports a decrease in the high-wave number harmonics of the ramjet chamber acoustic mode. These fluctuations are supported by non-linear amplification of the fundamental mode, which is enhanced by the thermo-acoustic coupling. / Master of Science / Novel propulsion designs, such as solid fuel ramjets, present the opportunity of optimizing cavity shapes using additive manufacturing and three-dimensional printing to improve fuelair mixing and lowering the thermo-acoustic feedback. In this work a computational model for solid fuel ramjets is developed and applied to laboratory firing tests performed by Prof Young's group at the advanced propulsion laboratory at Virginia Tech. In order to capture the fine mixing scales a novel discretization of the reactive Navier-Stokes using discontinuous Galerkin bases is implemented in an open source CFD code popular with aerospace graduate students and researchers. Subgrid modelling is implemented to determine the effect of small scales on the PMMA combustion mechanism developed at Virginia Tech. Numerical methods are used to simulate the turbulent flow of air through an axisymmetric cavity.

Scramjets have been identified as a potential long-term replacement for rocket and ramjet propulsion systems due to their enhanced performance at high Mach numbers. The introduction of solid fuels in these scramjet systems allows for shaping of the solid fuel cavity by additive manufacturing and introduces the possibility of enhancing combustion rates and stability. The present investigation aims to develop a coupled, high-order computational model to study the combustion of solid fuel scramjets. The primary objectives are to identify the effects of changing geometry on combustion and to better characterize the combustion process and flow patterns within a solid fuel scramjet engine. The high-Mach number of the air inflow over a scramjet cavity introduces a strong coupling between fluid dynamics, combustion, and regression time scales. Existing models often use simplified treatments of melt-layer conditions and combustion models that over-predict experimental rates, along with highly dissipative numerical schemes that inhibit the study of thermo-acoustic interactions between coherent pressure waves and the burning walls of the cavity. These limitations in current models suggest the need for a Navier-Stokes solver based on a high-order, discontinuous Galerkin method, incorporating melt layer equations and enhanced combustion manifolds. These manifolds should account for the effects of pressure and high oxidizer temperatures on flamelet dynamics. The focus is on modeling the flow field with accurate chemical heat release and residence time, to better study the effects of heat flux on the solid surface and the resulting coupling. An investigation of solid fuel scramjets was performed, and the numerical methodology with which the problem was tackled is described. A novel combustion mechanism was developed using a counterflow burner to study the combustion and regression of solid model fuel polymethyl methacrylate (PMMA). The diffusion flame between the fuel and oxidizer was studied numerically using a solid fuel decomposition and melt layer model to simulate convection and pyrolysis of the material. This model was validated using new experimental data as well as previously published works. The foam layer parameters are critical to the success of the validation. Results showed that the increased residence time of the gas in the bubbles facilitates the fuel breakdown. Fully coupled fuel injection and solid fuel surface monitoring was implemented based on this counterflow model and was a function of heat flux. Fuel regression was handled using adaptive control points for a B-Spline basis that updates based on surface movement. This methodology was used due to its resilience against the creation of surface discontinuities likely to result from large temperature gradients during combustion. Fourth-order computational simulations of ramjet combustion without regressing fuel walls using an in-house Discontinuous Galerkin approach were performed with a fully conjugate solution for the thermal wave in the solid. Results in ramjet geometries showed the turbulent combustion strongly affects the heat feedback to the walls and thus increases both the regression and fuel injection rates. Scramjet geometries were also simulated using the flamelet-progress variable approach in two different oxidizer conditions. All of these simulations showed strong agreement with experimental data and helped to uncover flame holding characteristics of the scramjet cavities and the strong coupling between the recirculation region and pyrolysis of fuel. The analysis has led to a better understanding of the effects of solid fuel scramjet geometries on mixing, enhanced modeling of acoustic instabilities in solid fuel air-breathing propulsion, and improved fuel chemistry modeling. It has been shown that cavity design significantly influences heat transfer to the solid fuel in both ramjet and scramjet conditions. The presence and thickness of the melt layer will guide designs that aim to reduce or enhance mechanical removal of fuel. Additionally, ramjet results indicate that longer cavities can couple with acoustics to induce self-excited conditions, leading to increased heat transfer to the solid. The importance of self-sustained instability and its coupling with melt layer fuel injection will contribute to improved acoustic stability. Developing pressure/temperature-dependent manifolds and melt layer models will advance our understanding of solid fuel supersonic combustion and its effects on phenomena such as blowout, fuel residence time, and solid fuel dual-mode transition. / Doctor of Philosophy / Scramjets, a type of high-speed jet engine, could one day replace rockets due to their efficiency at very high speeds. By introducing solid fuels into these engines, researchers can use advanced manufacturing techniques to shape fuel cavities, potentially enhancing the engine's performance. This study focuses on developing a sophisticated computational model to understand how changes in engine geometry affect the combustion process in solid fuel scramjets. The research aims to better understand the complex interactions between airflow, combustion, and fuel consumption, with the ultimate goal of improving engine design. The findings from this research provide valuable insights into how different scramjet designs impact fuel combustion. For instance, the design of the fuel cavity can significantly affect heat transfer, influencing the efficiency and stability of the engine. The study also highlights the importance of understanding the interaction between airflow and fuel injection, which is critical for optimizing engine performance and ensuring reliable operation at high speeds. Overall, this research advances our understanding of solid fuel scramjets and contributes to the development of more efficient and stable high-speed propulsion systems. By improving our ability to model and predict the behavior of these engines, the findings will guide future designs, potentially leading to more effective and reliable scramjets for various applications, including space exploration and high-speed flight.

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