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Recently, novel experimental evidence of continuous rotating detonations for gaseous H2/O2 propellants with a rotating detonation rocket engine (RDRE) was attained on the 3-inch Air Force Research Laboratory (AFRL) Distribution A RDRE, with the fuel and oxidizer injectors modified for H2/O2 gas propellants. Evident in previous experiments, detonation instabilities arising from upstream deflagration, from recirculation zones, and from insufficient gas mixing challenged resolution of detonation wave behavior from back-end imaging with the available optical equipment. Images were often over-illuminated from both the high amount of deflagration in the plume and the higher density of detonation waves in the annulus coupled with the small detonation cell size for H2/O2 gas propellants. Additionally, conventional optical systems attenuate the ultraviolet (UV) emission range (~308-320 nm wavelength) from the primary combustion species. To overcome these challenges are two methodologies that still utilize optical back-end imaging: (1) CH* chemiluminescence with fuel doping, and (2) OH* chemiluminescence. The first methodology utilizes doping CH4 into the H2/O2 gas mixture at a relatively small concentration of up to 5% by total mass flow rate to leverage CH* chemiluminescence at 409 ± 32 nm wavelength. The second methodology utilizes the combination of an OH* bypass filter for 308–320 nm wavelength to filter other emissions and an intensifier to amplify the detonation wave OH* emission. As of the present research, the first methodology was investigated across a regime of operating conditions, with planned future testing outlined to facilitate comparable data acquisition utilizing the second methodology.

Optimal trajectory design has been extensively studied across multiple disciplines adopting different techniques for implementation and execution. It has been utilized in past space trajectory missions to either optimize the amount of fuel spent or minimize the time of flight to meet mission requirements. Coupled Radial Basis Functions (CRBFs) are a new way to solve these optimal control problems, and this thesis applies CRBFs to spacecraft trajectory optimization design problems. CRBFs are real-valued radial basis functions (RBFs) that utilize a conical spline while also not being affected by the value of the shape parameter. The CRBF approach is applied to nonlinear optimal control problems. We adopt the indirect formulation so that the necessary and boundary conditions are derived from the system dynamical equations. As a result, a set of nonlinear algebraic equations (NAEs) is generated. The NAEs are then solved using a standard solver in MATLAB and the results are produced. CRBFs do not rely heavily on initial extensive analysis of the problem, which makes it very intuitive to use. The states, control, and co-states are defined as the equations to be solved and approximated using CRBFs. The results show that CRBFs can be applied to space trajectory optimization problems to produce accurate results across state and costate variables on uniform user defined nodes across the simulation time.

To model and examine the thermal fluid phenomena involved in high-pressure, multi-nozzle spray cooling, a testbed is developed which includes a heating subsystem and an accumulator to pressurize common rail based piezoelectric injectors. Compared to conventional platforms, the implemented testbed allows for an abundance of layout arrangements and settings that provide a greater range of functionality. The volumetric flow rate of the testbed is modeled by a recurrent neural network trained from time-sequential obtained through experiments. The fidelity of the model, as well as the testbed's hardware, software, functionalities, and shortcomings are discussed.

In the past few decades, Kessler syndrome (named after Donald J. Kessler) has become a point of concern in the field of Space Situational Awareness and the future of space missions. It refers to a scenario, where space debris in Earth's orbits collides and creates an exponential increase in space debris numbers leading to more collisions and more debris. In order to handle the resulting challenges like conjunction analysis, tracking, and probability of collisions, the State Transition Matrix (STM) and Tensors (STTs) of the orbit problem play a significant role. In addition, STM and STTs are ubiquitous in spaceflight dynamics, guidance, navigation, and control applications. Several methods exist in the literature for computing the STM and the STTs of the orbit problem; however, all these methods are either restricted by a simplified gravity model, computational accuracy or computational efficiency. In this dissertation, an adaptive Analytic Continuation is studied as a procedure for computing the STM and STTs of the perturbed Two-body problem. Analytic Continuation is a Taylor series based semi-analytic integration method that utilizes recursions of high-order time derivatives and the Leibniz rule to produce a solution with arbitrary accuracy at a fraction of the computational cost of finite difference methods. In this work, the method is used to compute the STM and the second order STT for the perturbed two-body problem. An adaptation technique is developed for keeping a balance between the number of higher order time derivatives and the time-step to achieve prescribed tolerances. Analytic Continuation is also adopted in a high-fidelity estimation framework (AC-EKF) to provide accurate orbit estimation results for a space-based space surveillance network of observers. Test cases on LEO, MEO, GTO and HEO show machine precision accuracy in the symplectic nature of the gravity perturbed STM and STT irrespective of the number of orbital revolutions. Gravity and atmospheric drag perturbed STM shows at least 3 times more accurate results when compared to finite difference methods in the initial error propagation of the trajectories in a span of 10 orbit periods. Furthermore, by incorporating second order STT, the error propagation results are improved by 2 - 4 orders of magnitude. Finally, results from AC-EKF show the utility of the method to accurately predict the error covariance in the absence of sensor coverage. As future work, Analytic Continuation will be expanded to compute arbitrarily high-order STTs with applications in orbit prediction and trajectory design.

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