<p dir="ltr">Instantaneous fuel regression rate within a solid fuel ramjet combustor was characterized using X-ray radiography and ultrasonic transducer measurements. Experiments were performed with cylindrical, center-perforated hydroxyl-terminated polybutadiene (HTPB) fuel grains at three mass fluxes (407-561 kg/m2-s) with consistent inlet total temperatures and chamber pressures. Ultrasonic transducer measurements demonstrated changes of web thickness ranging from 7.50-9.85 mm and regression rate measurements ranging from 1.35-1.74 mm/s. Local maxima of change in web thickness due to flow reattachment and erosive burning were consistently measured with the ultrasonic transducers. Changes in port radius on the order of 8-9 mm and regression rates of approximately 1.25 mm/s were deduced from the X-ray radiography images. Structure of the flow reattachment region was evident in measurements from the X-ray radiography images captured near the combustor entrance while images captured at the mid-length of the combustor exhibited more uniform fuel regression profiles. Ultrasonic measurements of change in web thickness were consistently greater in magnitude relative to X-ray radiography measurements. X-ray radiography imaging allowed for the more accurate measurement of fuel regression with the greatest axial spatial resolution while ultrasonic transducer measurements yielded the greatest radial spatial resolution. The change in web thickness calculated with weight-based techniques yielded smaller magnitude measurements of change in web thickness relative to X-ray radiography.</p><p dir="ltr">Time-dependent measurements of web thickness and regression rate along the port of aluminum-loaded and boron carbide-loaded, hydroxyl-terminated polybutadiene (HTPB) fuel grains were measured in a solid fuel ramjet combustor with X-ray radiography. The combustor was operated at three mass flux conditions, ranging from 397-532 kg/m2-s, with consistent chamber pressures and upstream-of-combustor total temperatures of 1313 kPa and 748 K, respectively. A cross-correlation-based edge detection scheme was used to extract the fuel grain edges within X-ray radiography images collected at 15 Hz. Cross-section photographs of the post-combustion fuel grain surfaces exhibited evidence of flow reattachment and large aft-end regression. Aluminized fuel grains exhibited average weight-based regression rates of 1.29-1.48 mm/s, and boron carbide-loaded fuel grains yielded average regression rates of 1.21-1.38 mm/s. Head-end X-ray measurements of change in port radius indicated flow reattachment, particularly for the bottom (theta = 180) edge of the fuel grain. The absolute maximum of change in port radius, which ranged between 8.56-10.31 mm for aluminized fuel grains and 8.22-9.40 mm for boron carbide-containing fuel grains, did not always coincide with the flow reattachment location. Time-averaged regression rate profiles measured with X-ray radiography were relatively uniform along the port axis but smaller in magnitude compared to the weight-based measurements; 1.17-1.35 mm/s for the aluminum-loaded fuel grains and 1.07-1.24 mm/s for the boron carbide-loaded fuel grains. Pre-ignition fuel regression, on the order of 1.5 mm, was determined to be the cause of the over-prediction of regression rate by weight-based measurements compared to X-ray measurements.</p><p dir="ltr">The weight-based average regression rates measured in tests conducted with the axisymmetric solid fuel ramjet test article in its various configurations were compared to quantify the effects of average port air mass flux, bypass air addition, carbon black addition, and metal particle addition on regression rate. Baseline tests without an aft-mixing section or bypass air addition fuel grains containing carbon black yielded a regression rate coefficient of a = 5.33E-2 and an exponent of n = 0.50 for p4 = 1179-1298 kPa. Including an aft-mixing section without bypass air addition yielded regression rates of 0.94-1.04 mm/s due to the increased residence time. Bypass air addition of 14\% bypass ratio reduced the regression rate to 0.83-0.92 mm/s, and 30% bypass ratio reduced the regression rate to 0.80-0.82 mm/s. For otherwise equal tests, adding carbon black to the fuel grain increased the regression rates from 0.76-0.78 mm/s to 0.83-0.92 mm/s (6-21%). Aluminized fuel grains exhibited an increase in regression rate coefficient over the baseline fuel grains from a = 5.33E-2 to a = 6.30E-2 (18%), but the regression rate exponent remained at n = 0.50. Boron carbide (B4C) addition reduced the regression rate exponent to n = 0.46 but increased the regression rate coefficient to a = 7.55E-2; a 42% increase.</p><p dir="ltr">A simplified solid fuel ramjet combustion model which includes (1) turbulent heat convection, (2) radiation, (3) radiation-coupled surface blowing, (4) unsteady sub-surface heat conduction, (5) solid fuel regression, (6) gas-phase combustion, and (7) fuel port hydrodynamics was developed for regression rate prediction over a range of combustor geometries and operating conditions. Turbulent convection was modeled with empirical correlations relating non-dimensional boundary layer transport numbers. Radiative heat transfer was estimated using modified empirical correlations for radiation in a slab hybrid rocket combustor. Hybrid rocket combustion theory was used to model surface blowing. The condensed-phase heat transfer was modeled by solving the unsteady, variable thermophysical property, regressing surface heat equation with an explicit time-integration, finite volume scheme on a non-uniform grid. A general Arrhenius expression was used to estimate the fuel regression rate. Chemical equilibrium calculations for a stoichiometric HTPB/air diffusion flame were used to model the gas-phase combustion. The port gas dynamics were modeled with compressible flow ordinary differential equations. The results of these individual physical processes were examined in detail for a high mass flux (G_air = 561 kg/m2-s) case. Experiments performed in the axisymmetric solid fuel ramjet combustor were simulated in the model, which yielded a lower regression rate versus mass flux exponent of n = 0.39 compared to the experimentally-obtained n = 0.50. A larger parameter sweep of the model yielded a mass flux exponent of n_1 = 0.30, a pressure exponent of n_2 = 0.04, and an inflow total temperature exponent of n_3 = 0.39. These exponents are less than those observed in other works, but the model successfully captured the relative influence of mass flux, chamber pressure, and inflow total temperature.</p><p dir="ltr">A combustion diagnostic consisting of X-ray radiography and thermocouples embedded within the fuel grain was successfully applied and demonstrated in a solid fuel ramjet slab combustor. One representative test condition with an air mass flowrate of 1 kg/s, an upstream-of-combustor static pressure of 560 kPa, and an upstream-of-combustor total temperature of 639 K was examined. Changes in web thickness of approximately 4 mm and steady-state regression rates of 0.35 mm/s were measured at the thermocouple locations. Condensed-phase temperature measurements yielded fuel grain surface temperatures of 820 K and temperature profiles which were compared to theoretical Michelson profiles. The Michelson profile closely matched the thermocouple-measured temperature profile at one axial location. Sub-surface conductive heat fluxes of 0.35 MW/m2, heat fluxes required to vaporize solid fuel of 0.60 MW/m2$, and surface heat fluxes of 0.95 MW/m2$ were estimated using the condensed-phase temperature profiles.</p>

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.

<p dir="ltr">This dissertation describes efforts in the development of an optically-accessible solid fuel ramjet combustion experiment and the application, and requisite modifications, of multiple laser-based diagnostics. These measurements target the characterization of the complex turbulent reacting flow physics in a multi-phase combustion environment representative of conditions within a solid fuel ramjet.</p><p dir="ltr"><br>First, dynamic flow-flame interactions were investigated in an optically-accessible solid fuel ramjet combustor. Experiments were performed with a single hydroxyl-terminated polybutadiene fuel slab located downstream of a backward-facing step in a rectangular chamber. To emulate flight-relevant combustor conditions, unvitiated heated air was directed through the combustion chamber with an inlet temperature of ∼655 K, chamber pressures of 450–690 kPa, and port Reynolds number of ∼500,000. 20 kHz OH∗-chemiluminescence and 10 kHz particle imaging velocimetry measurements were used to characterize the heat-release distribution and velocity field. Comparison between the mean OH∗ chemiluminescence images acquired at three flow conditions indicates reduction in flame height above the grain with increasing air mass flow rate. Dominant heat-release coherent structures in the statistically stationary flow are identified using the spectral proper orthogonal decomposition technique implemented on time-series of instantaneous images. The spatial mode shapes of the chemiluminescence and velocity field measurements indicated that the flow-flame interactions were dominated by vortex shedding generated at the backward facing step in the combustor, at Strouhal numbers of 0.06 – 0.10.</p><p dir="ltr"><br>Following this effort, a coherent anti-Stokes Raman scattering (CARS) laser system was assembled and aligned for measurements of the Q-branch ro-vibrational energy level structure of nitrogen using a coannular phase-matching scheme and frequency-shifted probe beam. These measurements were demonstrated in the model SFRJ combustion chamber operated with an inlet air temperature of 690 K and pressure of 0.59 MPa. Over 300 single-shot spectra were collected and fit for temperatures ranging from the core air flow to the combustion gases with a probe location situated above the redeveloping boundary layer region diffusion flame. A skewed temperature distribution was reported at the probe location, as expected from a region only intermittently exposed to hot combustion gases. Temperatures of 500-2000 K were fit to theory, indicating a requirement for high dynamic range measurements.</p><p dir="ltr"><br>A handful of shortcomings were identified in the application of the shifted-CARS technique to the luminous SFRJ flow-field and thus modifications were made to the CARS system for improved dynamic range, signal-to-noise ratio and signal-to-interference ratio. A dual-pump system provided simultaneous measurements of the Q-branch ro-vibrational energy level structure of nitrogen and pure-rotational energy level structure of nitrogen and oxygen. These spectra possessed ample features for accurate comparison to theory at temperatures of 600-2500 K, a typical range at flame locations within the highly dynamic SFRJ reacting flow. Additionally, an electro-optical shutter (EOS), comprised of a Pockels cell located between crossed-axis polarizers, was integrated into the CARS system. The use of the EOS enabled thermometry measurements in high luminosity flames through significant reduction of the background resulting from broadband flame emission. Temporal gating ≤100 nanoseconds along with an extinction ratio >10,000:1 was achieved using the EOS. Integration of the EOS enabled the use of an unintensified CCD camera for signal detection, improving upon the signal-to-noise ratio achievable with inherently noisy microchannel plate intensification processes, previously employed for short temporal gating.<br></p><p dir="ltr">Using this system, temperature and relative oxygen concentration scalar fields were measured in an optically accessible solid fuel ramjet (SFRJ) combustion chamber using coherent anti-Stokes Raman scattering (CARS). Additionally, planar laser-induced fluorescence measurements of the hydroxyl radical (OH-PLIF) were performed to spatially characterize flame location and provide context to the temperature measurements. The combustion chamber was operated with an inlet air temperature of 670 K, mass flowrate of 1.14 kg/s, and pressure of 0.57 MPa, conditions relevant to practical device operation. The dual-pump CARS system provided simultaneous measurements of the Q-branch ro-vibrational energy level structure of nitrogen and pure-rotational energy level structure of nitrogen and oxygen. These spectra possessed ample features for accurate comparison to theory at temperatures of 600-2500 K, a typical range at flame locations within the highly dynamic SFRJ reacting flow<br>and inherently track the relative oxygen concentration within the measurement volume. A skewed temperature distribution was reported at various probe locations, as expected from stochastic probing of dynamic reacting vortex structures. Comparison between CARS and OH-PLIF measurements within the flow impingement region indicated that the high temperature regions closely align with regions of high OH-PLIF intensity while the temperature standard deviation better matches the flame-surface density. The signal intensity distribution within instantaneous OH-PLIF images indicates transport of combustion products toward the grain, supported by the near-wall peak temperatures. This process is critical for the transport of energy to the grain such that additional fuel can be volatilized and mix with the air to support the flame.</p><p dir="ltr"><br>Finally, an ultra-fast CARS system has been designed and aligned for 1 kHz one-dimensional measurements of temperature by targeting the ro-vibrational Q-branch transitions of nitrogen. This effort seeks to develop a technique that can capture the hydrodynamics that drive the combustion in SFRJ and provide an intuition for the energy transport near the solid fuel wall of the SFRJ combustor through capturing instantaneous temperature profiles. The designed system utilized a 9 W high-energy regenerative amplifier with 30 fs duration pulses.<br>For the CARS measurement, the 4 W 800 nm output from the external compressor is used as the Stokes beam and a 0.5 W, 675 nm ouput from the TOPAS optical parametric amplifier (OPA) split to and used as the pump and probe beams. A chirping rod placed in the beam path of the probe beam was used to generate the picosecond pulse. Preliminary measurements have been acquired within room air and a laminar H2-Air nonpremixed flame. A discussion of the experimental challenges and remaining work is presented in this document.</p>