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ABSTRACT The performance of aircraft engines can be significantly affected by the variety of foreign particles that are mixed into the air while operating under miscellaneous conditions. In particular, aircraft engines that operate in sandy or dusty conditions may fail within minutes of exposure to particle-laden flow due to foreign particle deposition on hot section components or erosion occurring on the compressor and turbine blades. For these reasons, the effect of sand ingestion on erosion, which may occur in the turbine and compressor blades, was studied in this master's thesis. In this master's thesis, the effect of sand ingestion on erosion on the M250 turboshaft engine's compressor blades will be investigated with the aid of numerical methods. In this study, we used the OpenFOAM software to solve the multiphase flow problem from the standpoint of finite control methods and the Eulerian-Lagrangian framework. The initial sand distribution conditions were taken from the Ph.D. thesis written by Olshefski, K. T. (2023) [1]. The compressor blade was modeled as 2D, which has a NACA 6510 profile shape, with a chord length of 63 mm. The results show that the leading edge and the suction side of the compressor, i.e. the upper half of the compressor, eroded more compared to the trailing edge, and the pressure side. Results also show that as the sand particle distribution becomes non-uniform the most eroded region shifts toward the trailing edge. In addition, for varying angles of attack, the region where the erosion occurs alters periodically. We observed that as the angle of attack increases, the eroded region shifts toward the trailing edge, but when the angle of attack is kept increasing the eroded region shifts back to the leading edge again. In conclusion, the non-uniformity of sand particle loading has a strong effect on the determination of the eroded regions. Furthermore, the variation of the angle of attack has a huge role in both the determination of eroded regions and the amount of eroded material. / Master of Science / GENERAL AUDIENCE ABSTRACT In this master's thesis, the effect of sand ingestion on compressor blade erosion was investigated with the help of numerical methods. The compressor is one of the vital parts of air-breathing engines such as turboshaft, turbofan, turbojet, and turboprop engines. Therefore, the erosion on the compressor blades may cause pressure surges, which could cause severe problems in the operation of aircraft or airplanes operating under dusty conditions. Historically, it is reported that a TransAmerican aircraft propelled by Alison T-56 engines lost two of its four engines after 3 to 4 minutes of exposure to volcanic ash while flying over Mt. St. Helens in 1980. Another example of the effects of sand ingestion is an MV-22 Osprey crash that happened during a training exercise in Hawaii, claiming the lives of two US Marines and injuring twenty other personnel in 2015. It was attributed that the cause of the fatal accident was the ingestion of dust that caused engine failure. Therefore, our intention in studying this field is to have an understanding of the regions of compressor blades that are vulnerable to erosion. In this master's thesis, numerical methods based on the finite volume method were used to obtain numerical solutions to estimate erosion on the compressor blade by utilizing OpenFOAM. We would like to recommend a nice OpenFOAM tutorial for those who are interested in applying numerical methods using OpenFOAM, taught by Jozsef Nagy accessible on YouTube, https://www.youtube.com/@OpenFOAMJozsefNagy. Also, for creating geometry and mesh generation of an airfoil for the use of OpenFOAM, we would like to recommend the tutorial presented by Ali Ikhsanul, accessible on YouTube via this link https://www.youtube.com/@aliikhsanul7982. These tutorial videos could help those who are interested in Openfoam but do not have much experience with Openfoam. The work in this master's thesis indicates that the leading edge of the compressor blade is more prone to be eroded than the trailing edge. In addition, it is shown that the eroded region distribution is highly dependent on the angle of attack of sand particles.

Modern microprocessors require low supply voltage (about 1V), but very high current (maximum current is 300A in servers, 100A in desktop PCs and 70A in notebook PCs), and tighter voltage regulation. However, the size of a CPU Voltage Regulator (VR) needs to be reduced. To achieve much higher power density with decent efficiency in VR design is a major challenge. Moreover, the CPU current rating can vary from 40A to 300A for different kinds of computers, and CPU power supply specifications change quickly even for the same type of computers. Since the maximum power rating of one channel converter is limited, the VR channel number may vary over a large range to meet VR specifications. Traditionally, VR design with different channel numbers needs different types of VR controllers. To reduce the developing cost of different control ICs, and to maximize the market share of one design, scalable phase design based on the same type of IC is a new trend in VR design. To achieve higher power density and at the same time to achieve scalable phase design, the concept of Monolithic Voltage Regulator Channel (MVRC) is introduced in this dissertation. MVRC is a power IC with one channel converter's power MOSFETs, drivers and control circuitries monolithically integrated based on lateral device technology and working at high frequency. It can be used alone to supply a POL (Point of Load). And without the need for a separate master controller, multiple MVRC chips can be paralleled together to supply a higher current load such as a CPU. To make MVRC a reality, the key is to develop a fully distributed control scheme and its associated analog IC circuitry, so that it can provide control functions required by microprocessors and the performance must be equal or better than a traditional a centralized VRM controller. These functions includes: multiphase interleaving, Adaptive Voltage Position (AVP) and current sharing. To achieve interleaving, this dissertation introduces a novel distributed interleaving scheme that can easily achieve scalable phase interleaving without channel number limitation. Each channel's interleaving circuitry can be monolithically integrated without any external components. The proposed scheme is verified by a hardware prototype. The key building block is a self-adjusting saw-tooth generator, which can produce accurate saw-tooth waveforms without trimming. The interleaving circuit for each channel has two self-adjusting saw-tooth generators. One behaves as a Phase Lock Loop to produce accurate phase delay, and the other produces carrier signals. To achieve Adaptive Voltage Position and current sharing, a novel distributed control scheme adopting the active droop control for each channel is introduced. Verified by hardware testing and transient simulations, the proposed distributed AVP and current sharing control scheme meets the requirements of Intel's guidelines for today and future's VR design. Monte Carlo simulation and statistics analysis show that the proposed scheme has a better AVP tolerance band than the traditional centralized control if the same current sensing scheme is used, and its current sharing performance is as good as the traditional control. It is critical for the current sensing to achieve a tight AVP regulation window and good current sharing in both the traditional centralized control scheme and the proposed distributed control scheme. Inductor current sensing is widely adopted because of the acceptable accuracy and no extra power loss. However, the Signal-to-Noise Ratio (SNR) of the traditional inductor current sensing scheme may become too small to be acceptable in high frequency VR design where small inductor with small DCR is often adopted. To improve the SNR, a novel current sensing scheme with an accurate V/I converter is proposed. To reduce the complexity of building an accurate V/I converter with traditional Opamps, an accurate monolithic transconductance (Gm) amplifier with a large dynamic range is developed. The proposed Gm amplifier can achieve accurate V/I conversion without trimming. To obtain further verification, above proposed control schemes are monolithically integrated in a dual channel synchronous BUCK controller using TSMC BiCMOS 0.5um process. Testing results show that all the proposed novel analog circuits work as expected. System testing results show good interleaving, current sharing and AVP performance. The silicon size of each channel is 1800×1000um². With proposed current sensing, interleaving, AVP and current sharing, as well as their associated analog IC implementations, the technical barriers to develop a MVRC are overcome. MVRC has the potential to become a generic power IC solution for today and future POL and CPU power management. The proposed distributed interleaving, AVP and current sharing schemes can also be used in any cellular converter system. The proposed analog building blocks like the self-adjusting saw-tooth generator and the accurate transconductance amplifier can be used as basic building blocks in any DC-DC controller. / Ph. D.

Future microprocessor poses many challenges to its dedicated power supplies, the voltage regulators (VRs), such as the low voltage, high current, fast load transient, etc. For the VR designs using multiphase buck converters, one of the results from these stringent challenges is a large amount of output capacitors, which is undesired from both a cost and a motherboard real estate perspective. In order to save the output capacitors, the control-loop bandwidth must be increased. However, the bandwidth is limited in the practical design. The influence from the switching frequency on the control-loop bandwidth has not been identified, and the influence from multiphase is not clear, either. Since the widely-used average model eliminates the inherent switching functions, it is not able to predict the converter's high-frequency performance. In this dissertation, the primary objectives are to develop the methodology of high-frequency modeling for the buck and multiphase buck converters, and to analyze their high-frequency characteristics. First, the nonlinearity of the pulse-width modulator (PWM) scheme is identified. Because of the sampling characteristic, the sideband components are generated at the output of the PWM comparator. Using the assumption that the sideband components are well attenuated by the low-pass filters in the converter, the conventional average model only includes the perturbation-frequency components. When studying the high-frequency performance, the sideband frequency is not sufficiently high as compared with the perturbation one; therefore, the assumption for the average model is not good any more. Under this condition, the converter response cannot be reflected by the average model. Furthermore, with a closed loop, the generated sideband components at the output voltage appear at the input of the PWM comparator, and then generate the perturbation-frequency components at the output. This causes the sideband effect to happen. The perturbation-frequency components and the sideband components are then coupled through the comparator. To be able to predict the converter's high-frequency performance, it is necessary to have a model that reflects the sampling characteristic of the PWM comparator. As the basis of further research, the existing high-frequency modeling approaches are reviewed. Among them, the harmonic balance approach predicts the high-frequency performance but it is too complicated to utilize. However, it is promising when simplified in the applications with buck and multiphase buck converters. Once the nonlinearity of the PWM comparator is identified, a simple model can be obtained because the rest of the converter system is a linear function. With the Fourier analysis, the relationship between the perturbation-frequency components and the sideband components are derived for the trailing-edge PWM comparator. The concept of multi-frequency modeling is developed based on a single-phase voltage-mode-controlled buck converter. The system stability and transient performance depend on the loop gain that is affected by the sideband component. Based on the multi-frequency model, it is mathematically indicated that the result from the sideband effect is the reduction of magnitude and phase characteristics of the loop gain. With a higher bandwidth, there are more magnitude and phase reductions, which, therefore, cause the sideband effect to pose limitations when pushing the bandwidth. The proposed model is then applied to the multiphase buck converter. For voltage-mode control, the multiphase technique has the potential to cancel the sideband effect around the switching frequency. Therefore, theoretically the control-loop bandwidth can be pushed higher than the single-phase design. However, in practical designs, there is still magnitude and phase reductions around the switching frequency in the measured loop gain. Using the multi-frequency model, it is clearly pointed out that the sideband effect cannot be fully cancelled with unsymmetrical phases, which results in additional reduction of the phase margin, especially for the high-bandwidth design. Therefore, one should be extremely careful to push the bandwidth when depending on the interleaving to cancel the sideband effect. The multiphase buck converter with peak-current control is also investigated. Because of the current loop in each individual phase, there is the sideband effect that cannot be canceled with the interleaving technique. For higher bandwidths and better transient performances, two schemes are presented to reduce the influence from the current loop: the external ramps are inserted in the modulators, and the inductor currents are coupled, either through feedback control or by the coupled-inductor structure. A bandwidth around one-third of the switching frequency is achieved with the coupled-inductor buck converter, which makes it a promising circuit for the VR applications. As a conclusion, the feedback loop results in the sideband effect, which limits the bandwidth and is not included in the average model. With the proposed multi-frequency model, the high-frequency performance for the buck and multiphase buck converters can be accurately predicted. / Ph. D.

The gasification of carbonaceous fuel materials offers significant potential for the production of both energy and chemical products. Advancement of gasification technologies may be expedited through the use of computational fluid dynamics, as virtual reactor design offers a low cost method for system prototyping. To that end, a series of numerical studies were conducted to identify a computational modeling strategy for the simulation of coal gasification in fluidized bed reactors. The efforts set forth by this work first involved the development of a validatable hydrodynamic modeling strategy for the simulation of sand and coal fluidization. Those fluidization models were then applied to systems at elevated temperatures and polydisperse systems that featured a complex material injection geometry, for which no experimental data exists. A method for establishing similitude between 2-D and 3-D multiphase systems that feature non-symmetric material injection were then delineated and numerically tested. Following the development of the hydrodynamic modeling strategy, simulations of coal gasification were conducted using three different chemistry models. Simulated results were compared to experimental outcomes in an effort to assess the validity of each gasification chemistry model. The chemistry model that exhibited the highest degree of agreement with the experimental findings was then further analyzed identify areas of potential improvement. / Ph. D.

As laptop mobile users expect more application features and long battery life, the processor current has to increase to response the demanding while the voltage has to decease to save the power loss. Therefore, it is necessary for a system designer to improve the efficiency of the voltage regulator converter (VRC) for the processor. Laptop processor architecture is more complicated than desktop because of different mode operations and their transitions. The laptop processor runs at different voltage levels for each operation mode to save the battery life. Therefore, the VRC needs to supply the correct and stable voltage to the processor. In this thesis, an analysis of power loss is derived to estimate the efficiency and switching frequency, three widely current sensing methods are discussed, two methods to compensate for the thermal resistance in loss less current sense methods are proposed, the tolerance of load line base on the component's tolerance in the converter is analyzed, the equation to estimate the output capacitance is derived, and the small signal analysis of multiphase synchronous buck converter with the droop current loop is derived. A hardware prototype was implemented base on 4-phase synchronous buck topology to provide high efficiency and lower cost solution. The results of load line meets the Intel specification in different modes of operation, provides the best transient responses, and meets the specification during the load transient. The control loop lab measurement is also matched with the analysis and simulation. / Master of Science

Creating effective models predicting particle entrainment behavior within axisymmetric turbulent jets is of significant interest to many areas of study. Research into multiphase flows within turbulent structures has primarily focused on specific geometries for a target application, with little interest in generalized cases. In this research, the entrainment characteristics of various particle sizes and densities were simulated by determining the distribution of particles across a surface after the particles had fallen out of entrainment within the jet core. The model was based on an experimental set-up created by Lieutenant Zachary Robertson, which consists of a particle injection system designed to load particles into a fully developed pipe [1]. This pipe flow then exits into an otherwise quiescent environment (created within a wind tunnel), creating an axisymmetric turbulent round jet. The particles injected were designed to test the effect of both particle size and density on the entrainment characteristics. The data generated by the model indicated that, for all particle types tested, the distribution across the bottom surface of the wind tunnel followed a standard Gaussian distribution. Experimentation yielded similar results, with the exception that some of the experimental trials showed distributions with significantly non-zero skewness. The model produced results with the highest correlation to experimentation for cases with the smallest Stokes number (small size/density), indicating that the trajectory of particles with the highest level of interaction with the flow were the easiest to predict. This was contrasted by the high Stokes number particles which appear to follow standard rectilinear motion. / Master of Science

The analysis of turbulent flows provides a unique scientific challenge whose solution remains central to unraveling the fundamental nature of all fluid dynamics. Measuring and predicting turbulent flows becomes even more difficult when considering a two-phase flow, which is a commonly encountered engineering problem across many disciplines. One such example, the ingestion of foreign debris into a gas turbine engine, provided the impetus for this study. Despite more than 40 years of research, operation with a particle-laden inlet flow remains a significant problem for modern turbomachines. The purpose, therefore, is to develop experimental methods for investigating multi-phase flows relevant to the cooling of gas turbine components. Initially, several generic components representing turbine cooling designs were evaluated with a particle-laden flow using a special high temperature test facility. The results of this investigation revealed that blockage was highly sensitive to the carrier flowfield as defined by the cooling geometry. A second group of experiments were conducted in one commonly used cooling design using a Time Resolved Digital Particle Image Velocimetry (TRDPIV) system that directly investigated both the carrier flowfield and particle trajectories. Traditional PIV processing algorithms, however, were unable to resolve the particle motions of the two-phase flow with sufficient fidelity. To address this issue, a new Particle Tracking Velocimetry (PTV) algorithm was developed and validated for both single-phase and two-phase flows. The newly developed PTV algorithm was shown to outperform other published algorithms as well as possessing a unique ability to handle particle laden two-phase flows. Overall, this work demonstrates several experimental methods that are well suited for the investigation of wall-bounded turbulent two-phase flows, with a special emphasis on a turbine cooling method. The studies contained herein provide valuable information regarding the previously unknown fluid and particle dynamics within the turbine cooling system. / Ph. D.

Fuel cells provide a clean and highly efficient energy source for power generation; however, in order to efficiently utilize the energy from fuel cells, a power conditioning system is required. Typical fuel cell systems for stand-alone and utility grid-tied stationary power applications are found mostly with low nominal output voltages around 24 V and 48 V, and power levels are found to be 3 to 10 kW [1][2]. A power conditioning system for such applications generally consists of a dc-dc converter and a dc-ac inverter, and the dc-dc converter for low-voltage, high-power fuel cells must deal with a high voltage step-up conversion ratio and high input currents. Although many dc-dc converters have been proposed, most deal with high input voltage systems that focus on step-down applications, and such dc-dc converters are not suitable for low-voltage, high-power fuel cell applications. Multiphase isolated dc-dc converters offer several advantages that are very desirable in low-voltage, high-power fuel cell applications. First, a multiphase is constructed with paralleled phases, which increase power rating and current handling capability for high input current. Second, an interleaving control scheme produces a high operating frequency with a low switching frequency, and the high operating frequency reduces size of passive components. Thirdly, use of a transformer provides electrical isolation and a high conversion ratio. Lastly, several multiphase converters are capable of soft-switching operation, which increases converter efficiency. This thesis examines two highly efficient, soft-switching dc-dc converters that are targeted for fuel cell applications. The thesis also describes the converters' basic operating principles and analyzes performance for low-voltage, high-power fuel cell applications. 5-kW prototypes for each converter are built and tested with a fuel cell simulator. Experimental switching waveforms and efficiency profiles are shown to support the described basic principles and the analysis. Major features and differences between these two converters are also discussed. / Master of Science