<p dir="ltr">Neural operator learning is emerging as a prominent technique in scientific machine learn- ing for modeling complex nonlinear systems with multi-physics and multi-scale applications. A common drawback of such operators is that they are data-hungry and the results are highly dependent on the quality and quantity of the training data provided to the models. Moreover, obtaining high-quality data in sufficient quantity can be computationally prohibitive. Faster surrogate models are required to overcome this drawback which can be learned from datasets of variable fidelity and also quantify the uncertainty. In this work, we propose a Multi-Level Stacked Deep Operator Network (MLSDON) which can learn from datasets of different fidelity and is not dependent on the input function. Through various experiments, we demonstrate that the MLSDON can approximate the high-fidelity solution operator with better accuracy compared to a Vanilla DeepONet when sufficient high-fidelity data is unavailable. We also extend MLSDON to build robust confidence intervals by making conformalized predictions. This technique guarantees trajectory coverage of the predictions irrespective of the input distribution. Various numerical experiments are conducted to demonstrate the applicability of MLSDON to multi-fidelity, multi-scale, and multi-physics problems.</p>

<p dir="ltr">Powder Sprays such as Direct Energy Deposition and Cold Spray are rapidly growing and promising manufacturing methods in the Additive Manufacturing field, as they allow easy and localized delivery of powder to be fused to a substrate and consecutive layers. The relatively small size of nozzles allows for these methods to be mounted on CNC machines and Robotic Arms for the creation of complex shapes. However, these manufacturing methods are inherently stochastic, and therefore differences in powder size, shape, trajectory, and velocity can drastically affect whether they will deposit on a substrate. This variation results in an inherent reduction of deposition efficiency, leading to waste and the need for powder collection or recycling systems. The design of the nozzles can drastically affect the variation of powder trajectory and velocity on a holistic level, and thus understanding the gas-powder flow of these nozzles in respect to the features of said nozzles is crucial. This paper proposes and examines how changes in the nozzle geometry affect gas-powder flow and powder focusing for Direct Energy Deposition and Cold Spray. In addition, a new Pulsed Cold Spray nozzle design is proposed that will control the amount of gas and powder used by the nozzle via solenoid actuation. By making these changes to the nozzle, it is possible to improve deposition efficiency and reduce powder/gas waste in these processes, while also allowing for improved coating density. Furthermore, the research done in this thesis will also focus on novel applications to powder spray manufacturing methods, focusing on polymer metallization and part identification.</p>

<p dir="ltr">Interest in using detonation-based combustion cycles for use propulsion and power generation has gained considerable attention in the last 10 years or so. The rotating detonation engine (RDE), in particular, has garnered the most attention as a possible replacement for current generation combustion systems. RDEs are continuous flow devices that typically operate in a non-premixed fashion. Reactants are injected into an annular combustion chamber that is usually several millimeters wide. One or more detonation waves propagate azimuthally around the annulus, consuming the reactants. The products then expand out of the combustor where it can produce thrust or be passed into a turbine. The detonation wave front in RDEs travel at speeds between 1-3 km/s which poses additional complexity beyond traditional combustors. There are large gaps in the research community for RDEs that use one or more liquid based propellants. Questions regarding liquid breakup, atomization, breakup, recovery all remain unanswered both experimentally and numerically. This work seeks to understand these fundamental physical phenomena that drive these devices by applying advanced, high-speed laser and other optical diagnostics. </p><p dir="ltr"> A 120 mm nominal diameter rotating detonation combustor that operates on non-premixed hydrogen-air was modified to remove a hydrogen orifice and was replaced with a single liquid fuel injector. This simple, yet important, modification enables the study of a one-way coupling between a liquid fuel jet and a detonation wave at relevant spatio-temporal scales. Planar laser-induced fluorescence was performed at rates up to 1 MHz to quantify the quasi-steady jet dynamics and the recovery behavior of the single liquid jet. Long-duration PLIF imaging lasting 30-40 detonation periods at 300 kHz was also performed for statistical significance. A diesel liquid-in-crossflow injector was observed to breakup or be removed from the PLIF plane within only a few microseconds. After the detonation wave passes through the spray there is a significant dwell period can last between 20-40% of the detonation period before the new fuel is issued into the channel. The quasi-steady liquid jet trajectory was also compared to a jet-in-crossflow from literature and there is decent agreement in the jet near-field. </p><p dir="ltr"> The same hardware scheme with a different liquid fuel injector was tested in conjunction with an alternative imagine scheme. The first technique was able to capture details in the radial-axial plane but could not resolve any motion in the azimuthal direction. A volume-based illumination scheme was used for LIF to image a liquid fuel jet in the azimuthal-axial plane. For this experiment the location of the liquid fuel jet was moved into a different position and as a result experiences significantly different behavior than the jet in crossflow. The breakup and evaporation process takes place over a much longer period of time and there is no pause of liquid fuel injection. Similarly, LIF was performed at 300 kHz for 30 detonation cycles to enable sadistically quantification and phase averaging. Filtered OH* and CH* chemiluminescence imaging was also performed over the same field of view as the LIF imaging. Estimation of the velocity field was calculated using optical flow from the Jet-A LIF images. The velocity results agree well with the recovery analysis from the PLIF measurements.</p><p dir="ltr"> Using the same liquid fuel injection scheme, Jet-A droplet diameter and velocity was measured <i>in-situ</i> during a hot-fire experiment using phase Doppler interferometry (PDI). Although a point technique, PDI was used to measure thousands of droplets during a single test at multiple locations and with multiple conditions. As a means of comparison, cold flow experiments were performed with water in the exit plume. Droplet diameters were measured between 1-20 µs in both cases. PDI results were compared with the optical flow results and there is agreement in median velocities and some differences in the minimum and maximum velocity values. Possible sources of error in the diameter measurement are discussed as well.</p>

<p dir="ltr">The foundation of numerical codes used in engineering analyses of two-phase flows is the two-fluid model (TFM). However, the TFM codes use artificial regularization to remove the high frequency ill-posed instability in the numerical solution. This work demonstrates that incorporating variational inertial coupling terms to the numerical two-fluid model code, makes it more complete, objective and well-posed without the need for any regularization. The variational TFM is implemented in an industrial CFD code and the two-fluid Burgers problem is used to verify the numerical TFM against analytic solutions.</p>

<p dir="ltr">Positive displacement machines are used in various industries spanning the power spectrum, from industrial robotics to heavy construction equipment to aviation. These machines should be highly efficient, compact, and reliable. It is very advantageous for designers to use virtual simulations to design and improve the performance of these units as they significantly reduce cost and downtime. The recent trends of electrification and the goal to increase power density force these units to work at higher pressures and higher rotational speeds while maintaining their efficiencies and reliability. This push means that the simulation models need to advance to account for various aspects during the operation of these machines. </p><p dir="ltr">These machines typically have several bodies in relative motion with each other. Quantifying these motions and solving for their effect on the fluid enclosed are vital as they influence the machine's performance. The push towards higher rotational speeds introduces unwanted cavitation and aeration in these units. To model these effects, keeping the design evaluation time low is key for a designer. The lumped parameter approach offers the benefit of computational speed, but a major drawback that comes along with it is that it typically assumes fluid inertia to be negligible. These effects cannot be ignored, as quantifying and making design considerations to negate these effects can be beneficial. Therefore, this thesis addresses these key challenges of cavitation dynamics, body dynamics, and accounting for fluid inertia effects using a lumped parameter formulation.</p><p dir="ltr">To account for dynamics features related to cavitation, this thesis proposes a novel approach combining the two types of cavitation, i.e., gaseous and vaporous, by considering that both vapor and undissolved gas co-occupy a spherical bubble. The size of the spherical bubble is solved using the Rayleigh-Plesset equation, and the transfer of gas through the bubble interface is solved using Henry's Law and diffusion of the dissolved gas in the liquid. These equations are coupled with a novel pressure derivative equation. To account for body dynamics, this thesis introduces a novel approach for solving the positions of the bodies of a hydraulic machine while introducing new methods to solve contact dynamics and the application of Elasto Hydrodynamic Lubrication (EHL) friction at those contact locations. This thesis also proposes strategies to account for fluid inertia effects in a lumped parameter-based approach, taking as a reference an External Gear Machine. This thesis proposes a method to study the effects of fluid inertia on the pressurization and depressurization of the tooth space volumes of these units. The approach is based on considering the fluid inertia in the pressurization grooves and inside the control volumes with a peculiar sub-division. Further, frequency-dependent friction is also modeled to provide realistic damping of the fluid inside these channels.</p><p dir="ltr">To show the validity of the proposed dynamic cavitation model, the instantaneous pressure of a closed fluid volume undergoing expansion/compression is compared with multiple experimental sources, showing an improvement in accuracy compared to existing models. This modeling is then further applied to a gerotor machine and validated with experiments. Integrating this modeling technique with current displacement chamber simulation can further improve the understanding of cavitation in hydraulic systems. Formulations for body dynamics are tested on a prototype Gerotor and Vane unit. For both gerotor and vane units, comparisons of simulation results to experimental results for various dynamic quantities, such as pressure ripple, volumetric, and hydromechanical efficiency for multiple operating conditions, have been done. Extensive validation is performed for the case of gerotors where shaft torque ripple and the motion of the outer gear is experimentally validated. The thesis also comments on the distribution of the different torque loss contributions. The model for fluid inertia effects has been validated by comparing the lumped parameter model with a full three-dimensional Navier Stokes solver. The quantities compared, such as tooth space volume pressures and outlet volumetric flow rate, show a good match between the two approaches for varying operating speeds. A comparison with the experiments supports the modeling approach as well. The thesis also discusses which operating conditions and geometries play a significant role that governs the necessity to model such fluid inertia effects in the first place.</p>