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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Pressure Gain Combustion (PGC) systems have gained significant focus in recent years due to its potential for increased thermodynamic efficiency over a constant pressure cycle (or Brayton cycle). A rotating detonation combustor (RDC) is a type of PGC system, which is thermodynamically more efficient than the conventional gas turbine combustor. One of the main aspects of the detonation process is the rapid burning of the fuel-oxidizer mixture, due to which there is not enough time for the pressure to equilibrate. Therefore, the process is thermodynamically closer to a constant volume process, which is thermodynamically more efficient than a constant pressure cycle. RDC, if integrated successfully with a turbine, can increase thermal efficiency and reduce carbon emissions, especially when hydrogen is introduced into the fuel stream. However, due to highly unsteady flow generated from RDC, a systematic approach to transition the flow exiting the RDC to supply steady, subsonic flow at the turbine inlet has not been developed so far. Numerical simulations serve as a valuable tool to provide insight into the flow physics and to optimize the RDE design. Numerical studies have explored RDC by utilizing high-fidelity 3D simulations. However, these CFD studies require significant computational resources, due to the large differences in length and time scales between the flow field and the chemical reactions involved. The motivation of this dissertation is to investigate these research gaps and to develop computationally efficient methods for RDC designs to be integrated with downstream turbine section. First, this research work develops a methodology to predict the unsteady flow field exiting an RDC using 2D reacting simulations and to validate the approach using experimental measurements. Next, computational techniques are applied to condition the flow within the annulus by strategically constricting the flow area. A design of experiment (DoE) study is used to optimize the area profiling of the combustor. Additionally, the performance of the profiled design is compared against the baseline and the conventional nozzle design used in the literature. However, these numerical works use a perfectly premixed condition, whereas, the actual setup consists of discrete fuel/oxidizer injectors providing a non-uniform mixture in the combustor. To eliminate the assumption of perfectly premixed conditions, a method is developed to model the dynamic injector response of fuel/oxidizer plenums. The goal of this approach is to provide an inhomogeneous mixture composition without having to resolve/mesh the individual injectors. This research work provides a robust and computationally efficient methods for minimizing unsteadiness, maximizing pressure gain, and modeling dynamic injector response of an RDC. / Doctor of Philosophy / Traditional gas turbine combustor utilizes deflagration combustion. In recent years, detonation-based combustion has been explored as an alternative to enhance the efficiency of a modern gas turbine combustor. Rotating Detonation Combustor (RDC) utilizes detonation-based combustion and is thermodynamically efficient compared to conventional gas turbine combustors. The RDC consists of a detonation wave front and an oblique shock wave, which travel towards the exit of the combustor. Thus, the flow exiting the RDC is highly unsteady. The turbine requires a relatively steady flow at the inlet guide vanes. Therefore, the flow exiting the RDC needs to be conditioned before integrating with a downstream turbine section to gain the thermodynamic benefits of RDC. Numerical simulation of an RDC provides additional flexibility over experiments in understanding the flow physics. In addition, simulations are vital in optimizing the RDC designs such that the flow exiting the combustor is relatively uniform without comprising the pressure gain benefits of RDC. However, one of the challenges is that the RDC simulations are computationally expensive. Therefore, computationally efficient methods are required to understand and optimize the RDC designs to minimize the unsteady flow behavior and maximize the pressure gain. The objective is to utilize 2D and 3D reacting simulations to understand the flow behavior and to develop an optimization workflow to condition the flow exiting the combustor. Additionally, the optimized design is evaluated against the baseline and the conventional design used previously in the literature. Moreover, in most RDCs, the fuel and oxidizer are injected using discrete injectors. Due to the discrete injection, the fuel/oxidizer mixture is never perfectly premixed and results in a localized variation in fuel-oxidizer composition in the combustor. A novel method is developed to model the dynamic injector response of discrete fuel/oxidizer injection. The goal is to provide an inhomogeneous mixture composition without having to resolve/mesh the individual injectors. The emphasis of this study is to provide insight into the importance of flow conditioning exiting the RDC and the development of efficient CFD methods to optimize RDC to seamlessly integrate with a downstream turbine section.

<p dir="ltr">A fast model of a Rotating Detonation Combustor (RDC) is developed based on the Method of Characteristics (MOC). The model provides a CFD-like solution of an unwrapped 2D RDC flow field in under 10 seconds with similar fidelity as 2D Reacting URANS simulations. Parametric studies are conducted using the simplified model, and the trends are analyzed to gain insight into the underlying physics of rotating detonation combustors. A methodology to assess the performance of operation with multiple waves is presented. The main effect of increasing waves is found to be the increase in the exit Mach number of the combustion chamber. The design process of a mixer component is also presented. The mixer lies downstream of a channel-cooled RDC with subsonic exit and upstream of a Rolls-Royce M250 helicopter engine in open-loop configuration. The mixer dilutes the RDC exhaust with approximately 250% air to condition the flow for the M250 turbine at steady state operation, while also acting as an isolator with a choked throat to prevent back propagation of pressure waves. The mixer aerodynamic design was completed using 2D axisymmetric RANS simulations, and the mechanical design was evaluated using Ansys Mechanical FEA and was found to be able to survive the high thermal stresses present both during the transient heating and steady state operating condition.</p>

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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.

The detonation-based engine has the key advantage of increased thermodynamic efficiency over the traditional constant pressure combustor. These detonation-based engines are also known as Pressure Gain Combustion systems (PGC) and Rotating Detonation Combustor (RDC) is a form of PGC, in which the detonation wave propagates azimuthally around an annular combustor. Prior researchers have performed a high fidelity 3-D numerical simulation of a rotating detonation combustor (RDC) to understand the flow physics such as detonation wave velocity, pressure profile, wave structure; however, performing these 3-D simulations is computationally expensive. 2-D simulations are a potential alternative to reduce computational cost. In most RDCs, fuel and oxidizer are injected discretely from separate plenums, and this discrete fuel/air injection results in inhomogeneous mixing within the domain. Due to the discrete fuel injection locations, fuel/oxidizer will stratify to form localized pockets of rich and lean mixtures. The motivation of the present study is to investigate the impact of unmixedness and stratification length scales on the performance of an RDC using a 2-D numerical approach. Unmixedness, which is defined as the standard deviation of equivalence ratio normalized by the mean global equivalence ratio, is a measure of the degree of fuel-oxidizer inhomogeneity. To model the effect of unmixedness in a 2-D domain, a lognormal distribution of the fuel mass fraction is generated with a mean equivalence ratio of 1 and varying standard deviations at the inlet boundary as a numerical source term. Moreover, to model the effects of stratification length scales, fuel mass fraction at the inlet boundary cells is bundled for a given length scale, and the mass fractions for these bundles are updated based on the lognormal distribution after every three-time steps. Using this methodology, 2-D numerical analyses are carried out to investigate the performance of an RDC for an H2-air mixture with varying unmixedness and stratification length scales. Results show that mean detonation velocity decreases and wave speed variation increases with an increase in unmixedness. However, with an increase in stratification length scale mean velocity remain relatively unchanged but variation in local velocity increases. The detonation wave front corrugation also increases with an increase in mixture inhomogeneity. The mean detonation cell size increases with an increase in unmixedness. The cell shape becomes more distorted and irregular with an increase in stratification length scale and unmixedness. The combined effect of unmixedness and stratification length scale leads to a decrease in pressure gain. Overall, this concept is able to elucidate the effects of varying unmixedness and stratification length scales on the performance of an RDC. / Master of Science / Pressure Gain Combustion (PGC) system has gained significant focus in recent years due to its increased thermodynamic efficiency over a constant pressure Brayton Cycle. Rotating Detonation Combustor (RDC) is a type of PGC system, which is thermodynamically more efficient than the conventional gas turbine combustor. One of the main aspects of the detonation process is the rapid burning of the fuel-oxidizer mixture, which occurs so fast that there is not enough time for pressure to equilibrate. Therefore, the process is thermodynamically closer to a constant volume process rather than a constant pressure process. A constant volume cycle is thermodynamically more efficient than a constant pressure Brayton cycle. In an RDC, a mixture of fuel and air is injected axially, and a detonation wave propagates continuously through the circumferential section. Numerical simulation of an RDC provides additional flexibility over experiments in understanding the flow physics, detonation wave structure, and analyzing the physical and chemical processes involved in the detonation cycle. Prior researchers have utilized a full-scale 3-D numerical simulation for understanding the performance of an RDC. However, the major challenge with 3-D analyses is the computational expense. Thus, to overcome this, an inexpensive 2-D simulation is used to model the flow physics of an RDC. In most RDCs, the fuel and oxidizer are injected discretely from separate plenums. Due to the discrete fuel injection, the fuel/air mixture is never perfectly premixed and results in a stratified flow field. The objective of the current work is to develop a novel approach to independently investigate the effects of varying unmixedness and stratification length scales on RDC performance using a 2-D simulation.

<p dir="ltr">Rotating detonation combustors are a developing technology with the potential to successfully integrate pressure gain combustion in to modern propulsion devices. Utilization of propagating detonation waves could increase combustion cycle efficiency and reduce combustor size, resulting in an overall increase in system range or payload-carrying capabilities. However, the sensitivity of rotating detonation combustor operation and performance to geometric features, such as injector configuration or chamber length, still needs to be characterized over a wide range of operating conditions. In addition, the hardware configuration that promotes easy ignition into a coherent detonation operating mode does not always maximize combustor performance, especially at low-loss conditions where feedback between chamber and manifold dynamics can exist. Therefore, a rotating detonation combustor with continuously variable geometry capabilities was designed in order to continuously vary any number of hardware design parameters during combustor testing. Not only does the variable geometry combustor enable rapid characterization of operability sensitivity with minimal hardware swaps, it also enables exploration of hysteresis in performance as the combustor is ignited in one configuration and transitioned to a different geometry while maintaining detonative operation.</p><p dir="ltr">The operability of the variable geometry rotating detonation combustor was first characterized with variable fuel injector location. Higher wave speeds were observed at injector locations closest to the oxidizer throat, with decreased wave speed and eventual transition to deflagrative operation occurring at locations farther downstream due to increasing momentum flux ratio. Variation in fuel injection location induced bifurcations in the number of waves, resulting in corresponding changes in wave speed and gross thrust. Hysteresis was observed in these quantities as the direction of injector translation was reversed. Active translation promoted detonative operation of the experiment at conditions and configurations that hitherto operated only in a deflagrative mode with fixed combustor geometry. </p><p dir="ltr">Sensitivity of rotating detonation combustor operation and performance to oxidizer injector pressure drop was characterized using continuous variation of the injector area during combustor operation. Propulsive performance of the combustor was evaluated using thrust and equivalent available pressure, relating them back to reactant supply pressures for assessment of combustor pressure gain. An effective reactant supply pressure was developed in order to combine contributions of both fuel and oxidizer manifold pressures to the total pressure of the system so that pressure gain could be accurately calculated. Pressure gain increased during a test as oxidizer injector area was increased and the corresponding manifold pressure was decreased. At larger injector areas, pressure gain decreased as the operating mode of the combustor transitioned from detonation to deflagration, concomitant with reduction of gross thrust. Modeling of injector recovery time revealed that the injector operated in both choked and unchoked regimes, which was used to explain detonation wave number transitions in the experiment. A broadened range of detonative operability enabled by active variation of combustor geometry resulted in higher performance with lower injector pressure drop.</p><p dir="ltr">Sensitivity of rotating detonation combustor operation and performance to combustor chamber length was characterized using continuous variation of the chamber length during combustor operation. Specific impulse of the combustor remained relatively constant as chamber length was decreased from its maximum values, proving the practicality of efficient packaging for rotating detonation combustors. A limiting chamber length at which combustion could not longer be supported within the chamber was found to exist for every operating condition, resulting in flame blow-out and performance degradation. Modeling of detonation fill height revealed that relatively low specific impulse measurements could be attributed to unburned reactants exiting the chamber, and a more efficient use of reactants was potentially the cause for improved performance at higher mass flow rates as detonation wave number increased and reactant residence time decreased.</p><p dir="ltr">This experiment and the associated analysis has helped further characterize rotating detonation combustor sensitivity to hardware design parameters. The continuously variable geometry capabilities enabled precise identification of geometric parameters that resulted in operating mode transitions. Analysis and modeling of the flow processes within the injector and chamber were used to help explain why these mode transitions occurred, and can be used for future rotating detonation combustor development.</p>