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Progress in conventional rocket engine technologies, based on constant pressure combustion, has plateaued in the past few decades. Rotating detonation engines (RDEs) are of particular interest to the rocket propulsion community as pressure gain combustion may provide improvements to specific impulse relevant to booster applications. Despite recent significant investment in RDE technologies, little research has been conducted to date into the effect of nozzle design on rocket application RDEs. Proper nozzle design is critical to capturing the thrust potential of the transient pressure ratios produced by the thrust chamber. A computational fluid dynamics study was conducted based on hotfire conditions tested in the Purdue V1.3 RDE campaign. Three geometries were investigated: nozzleless/blunt body, internal-external expansion (IE-) aerospike, and flared aerospike. The computational study found the RDE's dynamic exhaust plume enhances the ejection physics beyond that of a typical high pressure device. For the nozzleless geometry, the base pressure was drawn down below constant pressure estimates, increasing the base drag on the engine. For the aerospike geometries, the occurrance of flow separation on the plug was delayed, which has ramifications on nozzle design for operation at a range of pressure altitudes. The flared aerospike design, which has the ability to achieve much higher area ratios, was shown to have potential performance benefits over the limited IE-aerospike geometry. A new test campaign with the Purdue RDE V1.4 was designed with instrumentation to capture static pressures on the nozzleless and aerospike surfaces. These results were used to validate the results from the computational study. The computational and experimental studies were used to identify new flow physics associated with a rocket RDE important to future nozzle design work. Future computational work is necessary to explore the effect of different parameters on the nozzle performance. More testing, including with an altitude simulation chamber, would help quantify the possible benefit of new aerospike nozzle designs, including the flared aerospike geometry.

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<p>  The wave dynamics within a rotating detonation engine were investigated using a combustor where the fuel injector was varied continuously relative to the oxidizer throat. Both natural gas and a hydrocarbon fuel blend containing the major components of a "cracked" kerosene fuel were characterized using high speed imaging, pressure sensors, and photomultiplier tubes. Major detonation features were visualized with high-speed cameras through a 360 optical outerbody. The detonation region, oblique shock, contact surface where fresh reactants mixed with products of a previous wave, and burning above the fuel injectors in a stratified zone beneath the detonation wave were studied as fuel conditions and fuel injector position were changed. As the inner body of the engine was translated away from the oxidizer throat, or started at a position far from the oxidizer throat, the combustor was not able to support coherent detonation behavior. At these points, the region of highest heat release remained close to the fuel injectors, and there was very little heat release processed behind the front edge of the wave compared to the level of deflagrative combustion occurring inside the chamber. The surrogate hydrocarbon blend is more representative of a composition that high speed vehicles would use, so the operability limits of the fuel and the fuel with nitrogen dilution were characterized using a metal and an optical outerbody on the combustor. With a larger amount of ethylene in the fuel composition compared to the amount of methane, the chamber tended towards slower waves and higher wave modes, and the combustor was able to sustain a coherent detonative mode with up to 40% nitrogen. When all chosen fuel blend components were present in the fuel except ethane, the combustion kinetics of the fuel was slowed significantly, and there was a measured decrease in thrust. No fuel tested was able to support coherent detonative modes with 50% nitrogen in the oxidizer.  </p>

Detonation cycles are identified as an efficient alternative to the Brayton cycles used in power and propulsion applications. Rotating Detonation Engine (RDE) operating on a detonation cycle works by compressing the working fluid across a detonation wave, thereby reducing the number of compressor stages required in the thermodynamic cycle. Numerical analyses of RDEs are flexible in understanding the flow field within the RDE, however, three-dimensional analyses are expensive due to the differences in time-scale required to resolve the combustion process and flow-field. The alternate two-dimensional analyses are generally modeled with perfectly premixed fuel injection and do not capture the effects of improper mixing arising due to discrete injection of fuel and oxidizer into the chamber. To model realistic injection in a 2-D analysis, the current work uses an approach in which, a Probability Density Function (PDF) of the fuel mass fraction at the chamber inlet is extracted from a 3-D, cold-flow simulation and is used as an inlet boundary condition for fuel mass fraction in the 2-D analysis. The 2-D simulation requires only 0.4% of the CPU hours for one revolution of the detonation compared to an equivalent 3-D simulation. Using this method, a perfectly premixed RDE is comparing with a non-premixed case. The performance is found to vary between the two cases. The mean detonation velocities, time-averaged static pressure profiles are found to be similar between the two cases, while the local detonation velocities and peak pressure values vary in the non-premixed case due to local pockets fuel rich/lean mixtures. The mean detonation cell sizes are similar, but the distribution in the non-premixed case is closer due to stronger shock structures. An analytical method is used to check the effects of fuel-product stratification and heat loss from the RDE and these effects adversely affect the local detonation velocity. Overall, this method of modeling captures the complex physics in an RDE with the advantage of reduced computational cost and therefore can be used for design and diagnostic purposes. / Master of Science / The conventional Brayton cycle used in power and propulsion applications is highly optimized, at cycle and component levels. In pursuit of higher thermodynamic efficiency, detonation cycles are identified as an efficient alternative and gained increased attention in the scientific community. In a Rotating Detonation Engine (RDE), which is based on the detonation cycle, the compression of gases occurs across a shock wave. This method of achieving high compression ratios reduces the number of compressor stages required for operation. In an RDE (where combustion occurs between two coaxial cylinders), the fuel and oxidizer are injected axially into the combustion chamber where the detonation is initiated. The resultant detonation wave spins continuously in the azimuthal direction, consuming fresh fuel mixture. The combustion products expand and exhaust axially providing thrust/mechanical energy when coupled with a turbine. Numerical analyses of RDEs are flexible over experimental analysis, in terms of understanding the flow physics and the physical/chemical processes occurring within the engine. However, three-dimensional numerical analyses are computationally expansive, and therefore demanding an equivalent, efficient two-dimensional analysis. In most RDEs, fuel and oxidizer are injected from separate plenums into the chamber. This type of injection leads to inhomogeneity of the fuel-air mixture within the RDE which adversely affects the performance of the engine. The current study uses a novel method to effectively capture these physics in a 2-D numerical analysis. Furthermore, the performance of the combustor is compared between perfectly premixed injection and discrete, non-premixed injection. The method used in this work can be used for any injector design and is a powerful/efficient way to numerically analyze a Rotating Detonation Engine.

<div>Rotating detonation engines (RDE) have the potential to significantly advance the efficiency of chemical propulsion. They are approximately one order of magnitude shorter than constant pressure engines, a savings benefit that is especially important for upper stage engines. There are many challenges to advancing their technological readiness level, but one area this thesis attempts to help mitigate is the understanding of heat loads and the viability of regenerative jacket cooling.<br></div><div> A one-dimensional, steady-state heat transfer and regenerative cooling model for the upper stage RL10A-3-3A (RL10) engine is developed in MATLAB. This model considers forced convection in the boundary layer between the combustion product gases and the hot-gas-side wall, conduction through the wall, and forced convection in the boundary layer between the hydrogen coolant and coolant-side wall. Variable gas and coolant transport properties are utilized to increase physical accuracy. The model also quantifies pressure drop through the cooling channels due to wall friction. This allows for overall heat flux, and consequently hot-gas-side and coolant-side wall temperatures to be predicted along the length of the engine. Properties of the coolant can also be predicted including the jacket outlet temperature and pressure. These cooling circuit final parameters, temperature rise and pressure drop, were matched to a more detailed, three-dimensional, transient RL10 system model developed by NASA, thereby anchoring this model.</div><div> An RDE is designed to notionally meet the thrust level of RL10. Model design decisions are documented and explained, and a detailed comparison of the two engine geometries is made. The regenerative cooling model is adapted for the RDE considering such unique aspects as detonative heat flux and the centerbody/plug nozzle. Steady state heating and cooling analysis is performed on the RDE and the results are compared to RL10. Investigation into the effects of the RDE’s differing cooling jacket output conditions on the turbine are calculated and discussed.</div><div> Appendix analyses consider more realistic detonative heat flux approximations according to recent RDE calorimetry studies and the effect of altering detonation chamber heat flux.</div><div> Even with the conservative assumption of throat-level heat flux everywhere in the RDE’s annular combustion chamber, regenerative jacket cooling shows promise as a means of thermal survival. Wall temperatures are reasonable, coolant temperature rise is lower, and coolant pressure drop is lower. The reduced temperature rise presents the new challenge of correctly powering the turbine since the incoming coolant is less energized. Further studies should also look at channel optimization specific to the RDE to maximize cooling performance and ease of system integration.<br></div>

<div>Gas turbine engines have operated on the Brayton cycle for decades, each decade only gaining approximately one to two percent in thermal efficiency as a result of efforts</div><div>to improve engine performance. Pressure-gain combustion in place of constant-pressure combustion in a Brayton cycle could provide a drastic step-change in the thermal efficiency of these devices, leading to reductions in fuel consumption and emissions production. Rotating Detonation Engines (RDEs) have been widely researched as a viable option for pressure-gain combustion. Due to the extremely high frequencies associated with operation of an RDE, the development and application of high-speed diagnostics techniques for RDEs is necessary to further understand and</div><div>develop these devices.</div><div><br></div><div>An application of high-speed diagnostic techniques in a natural gas-air RDE at conditions relevant to land-based power generation is presented. Diagnostics included high-frequency chamber pressure measurements, chemiluminescence imaging of the annulus, and Particle Image Velocimetry (PIV) measurements at the exit plane of the RDE. Results from a case with two detonation waves rotating clockwise (aft looking forward) in the combustor annulus are presented. Detonation surface plots are created from chemiluminescence images and allow for the extraction of properties such as dominant frequency modes and wave number, speed, and direction. The chamber frequency for the case with two co-rotating waves in the chamber is found to be 3.46 kHz and corresponds to average individual wave speeds of 68% Chapman-Jouguet (CJ) velocity. Dynamic Mode Decomposition (DMD) is applied and indicates the presence of two strong detonation waves rotating clockwise and periodically intersecting with weaker, counter-rotating waves in the annulus at certain times during operation. Singular-Spectrum Analysis (SSA) is used to isolate modes corresponding to the detonation frequency in the signals of velocity components obtained from PIV, maintaining instantaneous phase information. Axial and azimuthal components of velocity are observed to remain nearly 180 degrees out of phase. Lastly, approximate angles for the trailing oblique shocks in the combustion chamber are calculated.</div>

<div>The results of two experimental studies are presented in this document. The first is an investigation on the transient response of plain orifice liquid injectors to transverse detonation waves at elevated pressures of 414, 690, and 1,030 kPa (60, 100, and 150 psia). Detonations were produced using a predetonator which utilized hydrogen and</div><div>oxygen or ethylene and oxygen as reactants. For injectors of identical diameter, an increase in length correlated with a decrease in the maximum back-flow distance. A preliminary study using an injector of larger diameter suggested that for injectors of the same length under the same pressure drop, the larger injector was more resistant to back-flow. Refill time of the injectors was found to be inversely-proportional to detonation pressure ratio and injector stiffness, and a curve fit was produced to relate the three parameters.</div><div><br></div><div>The second experimental campaign was the hotfire testing of an RP-2-GOX rotating detonation engine. Total engine mass flow rates ranged from 0.8 to 3.5 kg/s (1.7 to 7.7 lbm/s) and static chamber pressures between 316 and 1,780 kPa (46 and 258 psia) were produced. In a majority of tests, between four and six co-rotating detonation waves were observed. Using an array of 36 embedded thermocouple probes, chamber outer wall heat fluxes between 2.8 and 8.3 MW/m² were estimated using an inverse heat transfer method of calculation. Performance of the RP-2 injector was assessed by relating to the information obtained in the prior injector response study.</div>

<p>A series of experimental tests were performed to study the transient response of gas/liquid injectors exposed to transverse detonation waves. A total of four acrylic injectors were tested to compare the response between gas/liquid and liquid only injectors, as well as compare the role of various geometric features of the notional injector design. Detonation waves are produced through the combustion of ethylene and oxygen, at conditions to produce average wave pressures between 128 and 199 psi. The injectors utilize water and nitrogen to simulate the injection of liquid and gaseous propellants respectively. Quantification of injector refill times was possible through the use of a high-speed camera recording at a frame rate of 460,000 frames per second. High frequency pressure measurements in both the gaseous and liquid manifolds allow for quantification of the temporal pressure response of the injectors. Variations in simulant mass flow rates, measured through the use of sonic nozzles and cavitating venturis, produce pressure drops up to 262 psi across the injector. Injector refill times are found to be a strong function of the impulse delivered across the injector. Manifold acoustics were found to play a large role in injector response as manifolds that promote manifold over-pressurizations during the injector recovery period recover quicker than designs that limit this response.</p>

<div>Rotating Detonation Engines (RDEs) provide a promising avenue for reducing greenhouse gas emissions from combustion-based propulsion and power systems by improving their thermodynamic efficiency through the application of pressure-gain combustion. However, the thermodynamic and systems-level advantages remain unrealized due to the challenge of harnessing the tightly coupled physics and nonlinear detonation dynamics inherent to RDEs, particularly for the less-detonable reactants characteristic of applications. Therefore, a RDE was developed to operate with natural gas and air as the primary reactants at elevated chamber pressures and air preheat temperatures, providing a platform to study RDEs with the less-detonable reactants and flow conditions representative of land-based power generation gas turbine engines. The RDE was tested with two injector configurations in a broad, parametric survey of flow conditions to determine the effect of operating parameters on the propagation of detonation waves in the combustor and delivered performance. Measurements of chamber wave dynamics were performed using high-frequency pressure transducers and high-speed imaging of broadband combustion chemiluminescence, while thrust measurements were used to characterize the work output potential.</div><div><br></div><div>The detonation dynamics were first studied to characterize RDE operability for the target application. Wave propagation speeds of up to 70% of the mixture Chapman-Jouguet detonation velocity and chamber pressure fluctuations greater than 4 times the mean chamber pressure were observed. Supplementing the air with additional oxygen, varying the equivalence ratio, and enriching the fuel with hydrogen revealed that combustor operability is sensitive to the chemical kinetics of the reactant mixture. While most test conditions exhibited counter-rotating detonation waves within the chamber, one injector design was able to support single wave propagation. A thermodynamic performance model was developed to aid analysis of RDE performance by making comparisons of net pressure gain for identical flow conditions. While the injector that supported a single wave operating mode better followed the trends predicted by the model, neither injector achieved the desire stagnation pressure gain relative to the reactant manifold pressure. Application of the model to a generic RDE revealed the necessity of normalizing any RDE performance parameter by the driving system potential and identified the area ratio between the exhaust and injection throats as the primary parameter affecting delivered pressure gain. A pair of test conditions with distinct wave dynamics were selected from the parametric survey to qualitatively and quantitatively analyze the exhaust flow using high-speed particle image velocimetry. A single detonation wave with an intermittent counter-rotating wave was characterized in the first test case, while a steady counter-rotating mode was studied in the second. The velocity measurements were phase averaged with respect to the instantaneous wave location to reveal contrasting flowfields for the two cases. The total pressure and temperature of flow exiting the combustor were computed using the phase-resolved velocity measurements along with the measured reactant flowrate and thrust to close the global balance of mass and momentum, providing an improved method of quantifying RDE performance. Finally, a reduced order model for studying RDE operability and mode selection was developed. The circumferential detonation wave dynamics are simulated and permitted to naturally evolve into the quasi-steady state operating modes observed in RDEs. Preliminary verification studies are presented and areas for further development are identified to enable the model to reach a broader level of applicability.</div><div><br></div><div>The experimental component of this work has advanced understanding of RDE operation with less-detonable reactants and developed improved methods for quantifying RDE performance. The accompanying modeling has elucidated the design parameters and flow conditions that influence RDE performance and provided a framework to investigate the factors that govern RDE mode selection and operability.<br></div>