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.

<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>

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>      Rotating detonation combustion has been investigated since the 1960s and has gained much attention in the past decade due to its promise of pressure gain. In theory, the pressure gain can provide higher power output at inlet total temperatures similar to those of Brayton cycle engines, leading to increased efficiency and decreased engine size. However, complexities presented by detonative combustion have prevented it from becoming widely adopted, especially for turbomachinery applications. A rotating detonation combustor with a transonic or supersonic exhaust imposes rapid fluctuations in pressure, temperature, and flow angle at the inlet of the turbine. To account for these fluctuations, ad hoc turbine designs have been proposed over the last few years, including supersonic bladed and bladeless variants. Computational fluid dynamics simulations have shown that it is possible to extract a meaningful amount of work from these turbines, but dedicated experimental test rigs are needed to validate these designs at relevant conditions in long-duration tests.</p> <p>     Toward this goal, this thesis focuses on three research elements. The first element is the design of a cooled rotating detonation combustor with a downstream turbine that can operate for long durations. The cooled combustor is accomplished in a two-part procedure: (1) repurposing Purdue University’s Turbine-integrated High-pressure Optical Rotating detonation engine (THOR) and (2) designing a lightweight, gaseous film-cooled combustor shroud with ample configurations for pressure, temperature, and optical measurements.</p> <p>     The second element is the design of three supersonic turbines for use in RDEs: an axial-flow bladed turbine, an axial-flow bladeless turbine, and an axial-inflow/radial-outflow bladed turbine. Each turbine is designed for cold flow testing, and provisions for mounting the axial-flow bladed turbine downstream of the cooled combustor are proposed. Supplemental turbine hardware is also designed to provide precise and repeatable conditions for the turbine tests.</p> <p>     The third element is the construction of an energy absorption dynamometer to measure the power output of the different supersonic turbines. Four types of dynamometers are explored, including hydraulic brakes, electromagnetic brakes, electric generator brakes, and airbrakes. Although the literature declares the electromagnetic brake to be more accurate, the most cost-effective solution is to utilize the compressor side of a donated turbocharger. Combining all research elements yields a new test rig for this new class of supersonic turbines.</p>

<p>In rotating detonation engines the turbine inlet conditions may be transonic with unprecedented unsteady fluctuations, very different from those in conventional high-pressure turbines. To ensure an acceptable engine performance, the turbine passages must be unchoked at subsonic and started at supersonic conditions. Additionally, to maximize the aerodynamic performance potential, ad-hoc designs are required, suited for the oscillations in Mach number and flow angle. This manuscript focuses on designing and characterizing diffusive turbine vanes that can operate downstream of a transonic rotating detonation combustor.  </p> <p><br></p> <p>First, the phenomenon of unstarting is presented, concentrating on the effect of pressure loss on the accurate prediction of the starting limit. Afterward, a multi-objective optimization with steady Reynolds Averaged Navier Stokes simulations, including the endwall and 3D vane design, is performed. The results are discussed, highlighting the impact of the throat-to-inlet area ratio on the pressure loss and the geometric features of the top-performing designs. Compared to previous  research on stator passages with contoured endwalls, considerable reductions in pressure loss and stator-induced rotor forcing are obtained, with an extended operating range and preserving high turning.  </p> <p><br></p> <p>Subsequently, the influence of the inlet boundary layer thickness on the vane performance is evaluated, inducing remarkable increases in pressure loss and downstream pressure distortion. Employing an optimization with a thicker inlet boundary layer, specific endwall design recommendations are found, providing a notable improvement in both objective functions. The impact of the geometry variations on flow detachment is assessed as well.</p> <p><br></p> <p>Finally, the impact of the inlet flow angle on the vane design is studied through a multi-point, multi-objective optimization with different inlet angles. The effect of incidence on the flow field and vane performance is evaluated first. Then, by comparing the optimized geometries with those optimized for axial inflows, several design guidelines are identified </p>