<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>

<p>Combustion instability, a complex phenomenon observed in combustion chambers is due to the coupling between heat release and other unsteady flow processes. Combustion instability has long been a topic of interest to rocket scientists and has been extensively investigated experimentally and computationally. However, to date, there is no computational tool that can accurately predict the combustion instabilities in full-size combustors because of the amount of computational power required to perform a high-fidelity simulation of a multi-element chamber. Hence, the focus is shifted to reduced fidelity computational tools which may accurately predict the instability by using the information available from the high-fidelity simulations or experiments of single or few-element combustors. One way of developing reduced fidelity computational tools involves using a reduced fidelity solver together with the flame transfer functions that carry important information about the flame behavior from a high-fidelity simulation or experiment to a reduced fidelity simulation.</p> <p> </p> <p>To date, research has been focused mainly on premixed flames and using acoustic solvers together with the global flame transfer functions that were obtained by integrating over a region. However, in the case of rockets, the flame is non-premixed and distributed in space and time. Further, the mixing of propellants is impacted by the level of flow fluctuations and can lead to non-uniform mean properties and hence, there is a need for reduced fidelity solver that can capture the gas dynamics, nonlinearities and steep-fronted waves accurately. Nonlinear Euler equations have all the required capabilities and are at the bottom of the list in terms of the computational cost among the solvers that can solve for mean flow and allow multi-dimensional modeling of combustion instabilities. Hence, in the current work, nonlinear Euler solver together with the spatially distributed local flame transfer functions that capture the coupling between flame, acoustics, and hydrodynamics is explored.</p> <p> </p> <p>In this thesis, the approach to extract flame transfer functions from high-fidelity simulations and their integration with nonlinear Euler solver is presented. The dynamic mode decomposition (DMD) was used to extract spatially distributed flame transfer function (FTF) from high fidelity simulation of a single element non-premixed flame. Once extracted, the FTF was integrated with nonlinear Euler equations as a fluctuating source term of the energy equation. The time-averaged species destruction rates from the high-fidelity simulation were used as the mean source terms of the species equations. Following a variable gain approach, the local species destruction rates were modified to account for local cell constituents and maintain correct mean conditions at every time step of the nonlinear Euler simulation. The proposed reduced fidelity model was verified using a Rijke tube test case and to further assess the capabilities of the proposed model it was applied to a single element model rocket combustor, the Continuously Variable Resonance Combustor (CVRC), that exhibited self-excited combustion instabilities that are on the order of 10% of the mean pressure. The results showed that the proposed model could reproduce the unsteady behavior of the CVRC predicted by the high-fidelity simulation reasonably well. The effects of control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size are also studied. The reduced fidelity model could reproduce the limit cycle amplitude within a few percent of the mean pressure. The successful constraints on the model include good spatial resolution and FTF with all modes up to at least one dominant frequency higher than the frequencies of interest. Furthermore, the reduced fidelity model reproduced consistent mode shapes and linear growth rates that reasonably matched the experimental observations, although the apparent ability to match growth rates needs to be better understood. However, the presence of significant heat release near a pressure node of a higher harmonic mode was found to be an issue. This issue was rectified by expanding the pressure node of the higher frequency mode. Analysis of two-dimensional effects and coupling between the local pressure and heat release fluctuations showed that it may be necessary to use two dimensional spatially distributed local FTFs for accurate prediction of combustion instabilities in high energy devices such as rocket combustors. Hybrid RANS/LES-FTF simulation of the CVRC revealed that it might be necessary to use Flame Describing Function (FDF) to capture the growth of pressure fluctuations to limit cycle when Navier-Stokes solver is used.</p> <p> </p> <p>The main objectives of this thesis are:</p> <p>1. Extraction of spatially distributed local flame transfer function from the high fidelity simulation using dynamic mode decomposition and its integration with nonlinear Euler solver</p> <p>2. Verification of the proposed approach and its application to the Continuously Variable Resonance Combustor (CVRC).</p> <p>3. Sensitivity analysis of the reduced fidelity model to control parameters such as the number of modes included in the FTF, the number of sampling points used in the Fourier transform of the unsteady heat release, and mesh size.</p> <p> </p> <p>The goal of this thesis is to contribute towards a reduced fidelity computational tool which can accurately predict the combustion instabilities in practical systems using flame transfer functions, by providing a path way for reduced fidelity multi-element simulation, and by defining the limitations associated with using flame transfer functions and nonlinear Euler equations for non-premixed flames.</p> <p> </p><br>