<p dir="ltr">Improving launch vehicle and satellite propulsion system performance directly correlates to the delivery of more mass (or quantity) on orbit from launch vehicles, longer duration satellite missions, and longer ranges for missiles/interceptors. Alternative propulsion devices such as rotating detonation engines (RDEs) offer the potential for significant performance gains but their operability has only been demonstrated on “battle hardened” laboratory devices for rocket applications. The objective of this research was to demonstrate cooling and structural approaches that mature rotating detonation rocket engines (RDREs) to flight like maturation levels.</p><p dir="ltr">Multiple 1.6”/4.1 cm diameter RDE combustors were designed, fabricated, and tested. The RDE tested the most accumulated 309 seconds of hot fire testing and 118 starts/shutdowns. Long duration testing was completed to characterize heat flux and high cycle fatigue (HCF) loading. Large quantities of short duration tests were completed to evaluate thermal cycling impacts to the combustor structure and evaluate low cycle fatigue (LCF) loading. The hardware experienced 118 LCF loadings on the combustor cooling passages, equivalent to the amount of thermal cycle starts and shutdowns. An endurance test was completed at 60 seconds in duration, demonstrating operation well beyond thermal steady state. Additionally, ~3.7 million HCF loadings were placed on the combustor cooling passages, equivalent to the approximate amount of detonation wave passes present for all of the WC 2.0 testing.</p><p dir="ltr">Predicted operating pressures ranged from 5 to 15 atm. The highest-pressure conditions resulted in hot gas wall temperatures exceeding 1000°F on the outerbody of the combustor and injector face temperatures peaking at 350°F. Water calorimetry was used to compute heat fluxes, which were then compared to traditional rocket engine throat level heat fluxes calculated using Bartz equations under average operating conditions. The outerbody heat fluxes reached up to 3.7 kW/cm², while injector face heat fluxes reached a maximum of 1.6 kW/cm². When compared to Bartz throat level values, the outer-body heat fluxes varied from 0.9 to 1.6 times the throat level values, and injector heat fluxes ranged from 0.3 to 0.5 times the throat level values.</p><p dir="ltr">A combined thermal and pressure loading fatigue assessment was completed that took into consideration mean stresses and cumulative damage from the spectrum of loading events. Traditional rocket combustor life is typically limited by the thermal cycles that can be placed on the cooling channel hot wall. The fatigue analysis results highlight the reduction in available low cycle fatigue life as RDE's experience larger thermal loads when compared to traditional rocket combustors. Low cycle fatigue life will become especially challenging in higher chamber pressure combustors where thermal environments are more extreme, and the ability keep hot wall temperatures within acceptable levels is more challenging.</p><p dir="ltr">The study also highlights that the passing detonation wave provides a high cycle fatigue (HCF) failure mechanism that is not present in traditional rocket combustors. This failure mechanism is the result of the pressure pulse provided by the passing detonation wave causing a variable load on the hot wall. This variable load is applied at frequencies commonly in the 10's of kHz, resulting in large quantities of loading cycles when operated at rocket like durations (>60 sec). This HCF failure mechanism is most impactful at larger chamber pressures where the detonation pressure ratio causes peak pressures to be elevated, resulting in larger cyclic stresses and strains in the hot wall. The results indicate that high chamber pressure combustors may experience HCF life exceedances within seconds of operation.</p>

<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>

A total number of 849 tests were conducted to investigate the transient response of liquid injectors with various geometries including different taper angles, injection angles and orifice lengths. High-speed videos were analyzed to characterize refill times and back-flow distances of nine different injector geometries subjected to a ethylene-oxygen detonation wave. Water was used as the working fluid and experiments were performed at two different vessel pressure settings (60 and 100 psia). Although a minimal difference was found between plain and angled injectors due to having constant orifice diameter geometry, introduction of taper angle resulted in more agile injectors with less sensitivity to ambient and feed pressures. Several attempts were made to normalize refill times and obtain a general trend for transient response of liquid injectors.

<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>

<p>The interaction and behavior of detonation waves propagating in a linear detonation combustor (LDC) were studied to identify the coupled thermoacoustic-chemical phenomenon responsible for self-generated and self-sustained detonation waves. The LDC was operated with natural gas and gaseous oxygen over a wide range of equivalence ratios and optically observed with OH*-chemiluminescence, schlieren, and broadband imaging in addition to high-frequency pressure transducers and photomultiplier tubes. Counter-propagating, self-sustained detonation waves were observed in the semi-bounded combustor to accelerate and amplify consistently from the closed-boundary to the open-boundary. The incident waves then reflect off of the open-boundary and transition into weaker waves that propagate acoustically relative to the burned products before being reflected by the closed-boundary and accelerating to dominancy once again. The combustor was then modified to have symmetric boundary conditions with both ends closed. For closed cases, the detonation waves experienced similar acceleration and amplification processes. The incident waves accelerate until they are reflected by a closed boundary into a flow field for which the fuel-injectors have yet to recover. For this reason, the reflected waves propagate through burned products until they encounter fresh reactants and accelerate again. The closed boundary conditions also caused the direction of dominance to periodically alternate. This study indicates that the local mixing field between open and closed boundary conditions affects the strength and speed of the reflected wave and demonstrates the impact of combustor geometry on coupled thermoacoustic-chemical phenomenon in RDEs.</p>

No description available.

<p dir="ltr">Rotating detonation engines (RDEs) are a promising technology by which to increase the efficiency of propulsion and power generation systems. Self-sustained, rotating detonation waves within the combustion chamber provide a means for combustion to occur at elevated local pressures, theoretically resulting in hotter temperature product gas than a constant pressure combustion process could provide at equivalent operating conditions. Despite theoretical advantages of RDEs, the thermodynamic benefit has yet to be achieved in experimental applications. Additionally, much of the experimental work to date has been conducted at mean operating pressures lower than industrial applications will require, especially for rocket or gas turbine combustion environments. The sensitivity of these devices to operating pressure has made clear the importance of chemical reaction rates on the successful operation of these combustors. This work addresses critical risks associated with implementing this technology at flight-relevant conditions by advancing the understanding of deflagrative loss mechanisms on delivered performance and by investigating the coupling between chemical kinetic timescales and operating modes produced by the combustor.</p><p dir="ltr">A novel pressure measurement technique was developed in which the stagnation pressure of exhausting gas produced by the RDC is measured through quantification of the under-expanded exhaust plume divergence angle at megahertz-rates. Time-averaged stagnation pressure measurements obtained with this technique are shown to be within 1.5% of the equivalent available pressure (EAP) measured. Time-resolved stagnation pressure measurements produced by this technique provide a means to quantify the detonation cycle pressure ratio. It was shown that increasing the total mass flow rate through the combustor, therefore increasing the mean operating pressure, results in a decrease in both detonation wave velocities and detonation cycle stagnation pressure ratios.</p><p dir="ltr">Numerical modeling of detonations was conducted to understand the coupling of stagnation pressure ratios and wave speeds to deflagrative modes of combustion within rotating detonation combustors. Using the experimental measurements, it is shown that significant amounts of propellant combusts as a result of deflagration prior to (i.e., preburning) and after (i.e., afterburning) the detonation wave. Increasing the RDC operating pressure by 4x is shown to increase the amount of preburned propellant by 4.5x. Relevant chemical kinetic reaction rates of the conditions tested are modeled to increase by 4.5x as well, indicating that the increase in reactant preburning is the result of faster chemical kinetic timescales associated with higher pressure combustion. Results from this testing suggest an operating pressure upper limit for this combustor exists around 20 bar. At these conditions, chemical kinetic rates would be fast enough that deflagration would be the primary mode of combustion and the detonation would not exist. It is suggested that different injector or combustor designs might be able to extend operating limits, however it is unclear if there is a chemical kinetic limit at which no design would be able to overcome.</p><p dir="ltr">Despite significant amounts of deflagrative combustion within the RDC, the vacuum specific impulse produced by the RDC was shown to be between 95.0% and 98.5% of what an ideal deflagrative combustor could produce for most conditions. Given conventional rocket combustors typically operate at specific impulse efficiencies in the range of 90%-99%, it is noted that the RDC tested in this work has demonstrated, at the very least, equal performance to the current state of the art for rocket propulsion combustors while utilizing an effective combustor length (L*) of only 63 mm (2.5 inches). A detailed RDC performance model was developed which considered losses associated with deflagration (both preburning and afterburning) and incomplete combustion. Using measurements obtained from the experiment it is determined that incomplete combustion contributes a larger performance loss than the deflagration which occurs within the combustor.</p><p dir="ltr">A total of 17 parametric studies were conducted experimentally to evaluate the response of the RDC specifically to changes in the propellant chemical reaction timescales. Detonation wave arrival times ranged between 10 microseconds and 178 microseconds as a result of testing at ranges of operating pressures, equivalence ratios, and utilizing nine unique propellant combinations. It was shown that the wave arrival time is primarily a function of chemical kinetic timescales and injector mixing processes. A model using the injector momentum ratio and modeled deflagrative preheat times is shown to be able to closely predict experimentally obtained detonation wave arrival times.</p>