MSc (Mathematics) / Department of Mathematics and Applied Mathematics / See the attached abstract below

<div>The results of two experimental studies are presented in this document. The first is an investigation on the transient response of plain orifice liquid injectors to transverse detonation waves at elevated pressures of 414, 690, and 1,030 kPa (60, 100, and 150 psia). Detonations were produced using a predetonator which utilized hydrogen and</div><div>oxygen or ethylene and oxygen as reactants. For injectors of identical diameter, an increase in length correlated with a decrease in the maximum back-flow distance. A preliminary study using an injector of larger diameter suggested that for injectors of the same length under the same pressure drop, the larger injector was more resistant to back-flow. Refill time of the injectors was found to be inversely-proportional to detonation pressure ratio and injector stiffness, and a curve fit was produced to relate the three parameters.</div><div><br></div><div>The second experimental campaign was the hotfire testing of an RP-2-GOX rotating detonation engine. Total engine mass flow rates ranged from 0.8 to 3.5 kg/s (1.7 to 7.7 lbm/s) and static chamber pressures between 316 and 1,780 kPa (46 and 258 psia) were produced. In a majority of tests, between four and six co-rotating detonation waves were observed. Using an array of 36 embedded thermocouple probes, chamber outer wall heat fluxes between 2.8 and 8.3 MW/m² were estimated using an inverse heat transfer method of calculation. Performance of the RP-2 injector was assessed by relating to the information obtained in the prior injector response study.</div>

Chronic sensitization of dopamine D2/D3 receptors by agonist quinpirole (QNP) induces compulsive checking behaviour in rats, which is considered an animal model of obsessive-compulsive disorder (OCD). Previous study revealed deficit in cognitive flexibility in QNP sensitized rats. This thesis focused on determining if this cognitive flexibility deficit is ameliorated by co-administration of clomipramine (CMI), risperidone (RIS) or combination of both (CMI+RIS) to QNP treatment. Aversively motivated active place avoidance task on a Carousel maze with reversal was used. The number of entrances into a to-be-avoided shock sector was evaluated as measure of performance. Six treatment groups were used: control group, QNP group, CMI group, QNP/CMI combination, QNP/RIS combination and QNP/CMI/RIS combination. Surprisingly, when compared alone, significantly worse acquisition was observed for QNP group compared to control group. However, similarly to previous study, QNP group had a worse performance in a first reversal session compared to control group. When all groups were compared, only QNP/CMI group had worse initial learning compared to control group. In reversal learning, only QNP treated group had a significantly more entrances than control group in first reversal session. Results suggest that co-treatment...

<p>A series of experimental tests were performed to study the transient response of gas/liquid injectors exposed to transverse detonation waves. A total of four acrylic injectors were tested to compare the response between gas/liquid and liquid only injectors, as well as compare the role of various geometric features of the notional injector design. Detonation waves are produced through the combustion of ethylene and oxygen, at conditions to produce average wave pressures between 128 and 199 psi. The injectors utilize water and nitrogen to simulate the injection of liquid and gaseous propellants respectively. Quantification of injector refill times was possible through the use of a high-speed camera recording at a frame rate of 460,000 frames per second. High frequency pressure measurements in both the gaseous and liquid manifolds allow for quantification of the temporal pressure response of the injectors. Variations in simulant mass flow rates, measured through the use of sonic nozzles and cavitating venturis, produce pressure drops up to 262 psi across the injector. Injector refill times are found to be a strong function of the impulse delivered across the injector. Manifold acoustics were found to play a large role in injector response as manifolds that promote manifold over-pressurizations during the injector recovery period recover quicker than designs that limit this response.</p>

<div>Recently, researchers have pointed their attention toward Method of Moments (MoM)-based approaches to model low frequency magnetic devices (i.e. transformers and inductors). This has been prompted by the use of population-based design (PBD) methods wherein the performance of large numbers (on the order of millions) of candidate designs must be evaluated. MoM is attractive for such problems due to the fact that only the magnetic material is discretized. In addition, for the case in which the magnetic material is linear, only a surface mesh is required. In this research, point-matching and Galerkin-based MoM formulations are utilized for the design of electric machinery. In the formulations considered, the model inputs are the free currents of machine windings and the bound currents of permanent magnets. The unknowns are the magnetizations within the magnetic material which are used to compute winding inductance, electromagnetic torque, and core loss. </div><div><br></div><div>The proposed Galerkin formulation has been utilized in the PBD of a surface-mount permanent magnet machine with favorable results. Specifically, it is shown that a machine's performance can be evaluated on a time scale expected of a practical design tool. This is achieved in part through judicious exploitation of the periodic structure and excitation of machines to reduce the size of the system matrix. It is shown how the exploitation of periodic structure may be extended to the point-matching formulation for use in nonlinear analyses. Finally, alternative hybrid approaches that combine surface and volume meshing are explored for the analysis of an internal permanent magnet machine. It is shown that such a combination holds promise as a tool for rapid evaluation of machine performance.</div>

This student thesis aims to analyze the unbalance on rotating machinery by simulation and experimental. The machinery flywheel rotation is modelled as a Single Degree of Freedom (SDOF) and Multi Degree of Freedom (MDOF) system. The model rotation unbalance is simulated by MATLAB. Then the vibration measurement is taken by experimental. In addition, the tachometer is used to determine the flywheel speed calibration. Finally, the rotating unbalance reduction simulation is performed with different parameter value to determine an optimum level of machinery rotation vibration. Unbalance on rotating machinery causes a harmful influence on the environment and machinery. The root cause of rotating unbalance is determined by the simulation and experimental analysis. The analysis result is used as an indicator for predicting machinery breakdown and estimating the correct predictive maintenance action for the machinery. In this project, the simulation and experimental analysis were carried out on a rotating component of the KICKR Snap Bike Trainer. The simulation and numerical analysis are performed by MATLAB programme. On the experimental part, the vibration measurement method and results were discussed. The suggestion of unbalance reduction were recommended base on measurement and vibration analysis results.

Nowadays Snecma focuses on new engine architectures in order to meet the future demands in civil aviation. One of these considered concepts is aircrafts powered by counter rotating fan engines which aim at tackling both noise and polluting emissions. A powerful way to reduce the perceived noise is to reduce the fan rotating speeds, which requires to lower fan pressure ratio. This thesis continues a study on an innovative counter rotating fan architecture carried out by Snecma from 2005 to 2010 for VITAL (European Commission funded project). It is a way to meet the noise target while maintaining acceptable engine dimensions and matching installation constraints since each fan has a smaller diameter than the current ones, and an individual low pressure ratio. Therefore the drag is decreased and less fuel is burnt. In order to fulfill these ambitious objectives, the first step of this thesis is to use the code of the VITAL model developed with Janus (Snecma in-house code) in order to create a new code for the PROOSIS software. When modeling two counter rotating fans, the key point is to take into account the influence from the first stage on the second one.  Since the aft fan “sees” a perturbed flow by the inlet fan wake, its characteristic map is not the usual one anymore. One major challenge was the new design of a two separated flow and three-spool counter rotating engine driven by a gearbox which meets the very high bypass ratio target. The model finally turned out to be operational for a relevant set of initialization parameters and thus makes now possible more accurate studies on counter rotating turbofan engines in the R&amp;T unit.

The behavior of fibers suspended in a flow between two counter-rotating discs has been studied experimentally. This is inspired by the refining process in the papermaking process where cellulose fibers are ground between discs in order to change performance in the papermaking process and/or qualities of the final paper product. To study the fiber behavior in a counter-rotating flow, an experimental set-up with two glass discs was built. A CCD-camera was used to capture images of the fibers in the flow. Image analysis based on the concept of steerable filters extracted the position and orientation of the fibers in the plane of the discs. Experiments were performed for gaps of 0.1-0.9 fiber lengths, and for equal absolute values of the angular velocities for the upper and lower disc. The aspect ratios of the fibers were 7, 14 and 28. Depending on the angular velocity of the discs and the gap between them, the fibers were found to organize themselves in fiber trains. A fiber train is a set of fibers positioned one after another in the tangential direction with a close to constant fiber-to-fiber distance. In the fiber trains, each individual fiber is aligned in the radial direction (i.e. normal to the main direction of the train). The experiments show that the number of fibers in a train increases as the gap between the discs decreases. Also, the distance between the fibers in a train decreases as the length of the train increases, and the results for short trains are in accordance with previous numerical results in two dimensions.Furthermore, the results of different aspect ratios imply that there are three-dimensional fiber end-effects that are important for the forming of fiber trains.

<div>Rotating Detonation Engines (RDEs) provide a promising avenue for reducing greenhouse gas emissions from combustion-based propulsion and power systems by improving their thermodynamic efficiency through the application of pressure-gain combustion. However, the thermodynamic and systems-level advantages remain unrealized due to the challenge of harnessing the tightly coupled physics and nonlinear detonation dynamics inherent to RDEs, particularly for the less-detonable reactants characteristic of applications. Therefore, a RDE was developed to operate with natural gas and air as the primary reactants at elevated chamber pressures and air preheat temperatures, providing a platform to study RDEs with the less-detonable reactants and flow conditions representative of land-based power generation gas turbine engines. The RDE was tested with two injector configurations in a broad, parametric survey of flow conditions to determine the effect of operating parameters on the propagation of detonation waves in the combustor and delivered performance. Measurements of chamber wave dynamics were performed using high-frequency pressure transducers and high-speed imaging of broadband combustion chemiluminescence, while thrust measurements were used to characterize the work output potential.</div><div><br></div><div>The detonation dynamics were first studied to characterize RDE operability for the target application. Wave propagation speeds of up to 70% of the mixture Chapman-Jouguet detonation velocity and chamber pressure fluctuations greater than 4 times the mean chamber pressure were observed. Supplementing the air with additional oxygen, varying the equivalence ratio, and enriching the fuel with hydrogen revealed that combustor operability is sensitive to the chemical kinetics of the reactant mixture. While most test conditions exhibited counter-rotating detonation waves within the chamber, one injector design was able to support single wave propagation. A thermodynamic performance model was developed to aid analysis of RDE performance by making comparisons of net pressure gain for identical flow conditions. While the injector that supported a single wave operating mode better followed the trends predicted by the model, neither injector achieved the desire stagnation pressure gain relative to the reactant manifold pressure. Application of the model to a generic RDE revealed the necessity of normalizing any RDE performance parameter by the driving system potential and identified the area ratio between the exhaust and injection throats as the primary parameter affecting delivered pressure gain. A pair of test conditions with distinct wave dynamics were selected from the parametric survey to qualitatively and quantitatively analyze the exhaust flow using high-speed particle image velocimetry. A single detonation wave with an intermittent counter-rotating wave was characterized in the first test case, while a steady counter-rotating mode was studied in the second. The velocity measurements were phase averaged with respect to the instantaneous wave location to reveal contrasting flowfields for the two cases. The total pressure and temperature of flow exiting the combustor were computed using the phase-resolved velocity measurements along with the measured reactant flowrate and thrust to close the global balance of mass and momentum, providing an improved method of quantifying RDE performance. Finally, a reduced order model for studying RDE operability and mode selection was developed. The circumferential detonation wave dynamics are simulated and permitted to naturally evolve into the quasi-steady state operating modes observed in RDEs. Preliminary verification studies are presented and areas for further development are identified to enable the model to reach a broader level of applicability.</div><div><br></div><div>The experimental component of this work has advanced understanding of RDE operation with less-detonable reactants and developed improved methods for quantifying RDE performance. The accompanying modeling has elucidated the design parameters and flow conditions that influence RDE performance and provided a framework to investigate the factors that govern RDE mode selection and operability.<br></div>

<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>