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At least 577 records · Page 32

Microgravity research in NASA ground-based facilities

An overview of reduced gravity reasearch performed in NASA ground-based facilities sponsored by Microgravity Science and Applications Program of the NASA Office of Space Science and Applications is presented. A brief description and summary of the operations and capabilities of each of these facilities along with an overview of the historical usage of them is included. The goals and program elements of the Microgravity Science and Applications programs are described and the specific programs that utilize the low gravity facilities are identified. Results from two particular investigations in combustion (flame spread over solid fuels) and fluid physics (gas-liquid flows at microgravity conditions) are presented.

Lekan, Jack↗

Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade Superalloys

High Cycle Fatigue (HCF) induced failures in aircraft gas-turbine engines is a pervasive problem affecting a wide range of components and materials. HCF is currently the primary cause of component failures in gas turbine aircraft engines. Turbine blades in high performance aircraft and rocket engines are increasingly being made of single crystal nickel superalloys. Single-crystal Nickel-base superalloys were developed to provide superior creep, stress rupture, melt resistance and thermomechanical fatigue capabilities over polycrystalline alloys previously used in the production of turbine blades and vanes. Currently the most widely used single crystal turbine blade superalloys are PWA 1480/1493 and PWA 1484. These alloys play an important role in commercial, military and space propulsion systems. PWA1493, identical to PWA1480, but with tighter chemical constituent control, is used in the NASA SSME (Space Shuttle Main Engine) alternate turbopump, a liquid hydrogen fueled rocket engine. Objectives for this paper are motivated by the need for developing failure criteria and fatigue life evaluation procedures for high temperature single crystal components, using available fatigue data and finite element modeling of turbine blades. Using the FE (finite element) stress analysis results and the fatigue life relations developed, the effect of variation of primary and secondary crystal orientations on life is determined, at critical blade locations. The most advantageous crystal orientation for a given blade design is determined. Results presented demonstrates that control of secondary and primary crystallographic orientation has the potential to optimize blade design by increasing its resistance to fatigue crack growth without adding additional weight or cost.

Arakere, Nagaraj K.↗

Characterization of Deficiencies in the Frequency Domain Forced Response Analysis Technique for Supersonic Turbine Bladed Disks

Turbine blades in rocket and jet engine turbomachinery experience enormous harmonic loading conditions. These loads result from the integer number of upstream and downstream stator vanes as well as the other turbine stages. Assessing the blade structural integrity is a complex task requiring an initial characterization of whether resonance is possible and then performing a forced response analysis if that condition is met. The standard technique for forced response analysis in rocket engine turbines is to decompose a computational fluid dynamics (CFD).generated flow field into its harmonic components, and to then perform a frequency response analysis at the problematic natural frequencies using cyclically symmetric structural dynamic models. Recent CFD analysis and water-flow testing at NASA/MSFC, though, indicates that this technique may miss substantial harmonic and non ]harmonic excitation sources that become present in complex flows. This complex content can only be captured by a CFD flow field encompassing at least an entire revolution. A substantial development effort to create a series of software programs to enable application of the 360 degree forcing function in a frequency response analysis on cyclic symmetric models has been completed (to be described in a future paper), but the question still remains whether the frequency response analysis itself is capable of capturing the excitation content sufficiently. Two studies comparing frequency response analysis with transient response analysis, therefore, of bladed-disks undergoing this complex flow environment have been performed. The first is of a bladed disk with each blade modeled by simple beam elements and the disk modeled with plates (using the finite element code MSC/NASTRAN). The focus of this model is to be representative of response of realistic bladed disks, and so the dimensions are roughly equivalent to the new J2X rocket engine 1st stage fuel pump turbine. The simplicity of the model allows the CFD load to be able to be readily applied, along with analytical and experimental variations in both the temporal and spatial fourier components of the excitation. In addition, this model is a first step in identifying response differences between transient and frequency forced response analysis techniques. The second phase assesses this difference for a much more realistic solid model of a bladed-disk in order to evaluate the effect of the spatial variation in loading on blade dominated modes. Neither research on the accuracy of the frequency response method when used in this context or a comprehensive study of the effect of test-observed variation on blade forced response have been found in the literature, so this research is a new contribution to practical structural dynamic analysis of gas turbines. The primary excitation of the upstream nozzles interacts with the blades on fuel pump of the J2X causes the 5th Nodal diameter modes to be excited, as explained by Tyler and Sofrin1, so a modal analysis was first performed on the beam/plate model and the 5ND bladed-disk mode at 40167 hz was identified and chosen to be the one excited at resonance (see figure 1). The first forced response analysis with this model focuses on identifying differences between frequency and transient response analyses. A hypothesis going into the analysis was that perhaps the frequency response was enforcing a temporal periodicity that did not really exist, and so therefore it would overestimate the response. As high dynamic response was a considerable source of stress in the J2X, examining this concept could potentially be beneficial for the program.

Brown, Andrew M.↗

Decision-Aiding and Optimization for Vertical Navigation of Long-Haul Aircraft

Most decisions made in the cockpit are related to safety, and have therefore been proceduralized in order to reduce risk. There are very few which are made on the basis of a value metric such as economic cost. One which can be shown to be value based, however, is the selection of a flight profile. Fuel consumption and flight time both have a substantial effect on aircraft operating cost, but they cannot be minimized simultaneously. In addition, winds, turbulence, and performance vary widely with altitude and time. These factors make it important and difficult for pilots to (a) evaluate the outcomes associated with a particular trajectory before it is flown and (b) decide among possible trajectories. The two elements of this problem considered here are: (1) determining what constitutes optimality, and (2) finding optimal trajectories. Pilots and dispatchers from major u.s. airlines were surveyed to determine which attributes of the outcome of a flight they considered the most important. Avoiding turbulence-for passenger comfort-topped the list of items which were not safety related. Pilots' decision making about the selection of flight profile on the basis of flight time, fuel burn, and exposure to turbulence was then observed. Of the several behavioral and prescriptive decision models invoked to explain the pilots' choices, utility maximization is shown to best reproduce the pilots' decisions. After considering more traditional methods for optimizing trajectories, a novel method is developed using a genetic algorithm (GA) operating on a discrete representation of the trajectory search space. The representation is a sequence of command altitudes, and was chosen to be compatible with the constraints imposed by Air Traffic Control, and with the training given to pilots. Since trajectory evaluation for the GA is performed holistically, a wide class of objective functions can be optimized easily. Also, using the GA it is possible to compare the costs associated with different airspace design and air traffic management policies. A decision aid is proposed which would combine the pilot's notion of optimality with the GA-based optimization, provide the pilot with a number of alternative pareto-optimal trajectories, and allow him to consider unmodelled attributes and constraints in choosing among them. A solution to the problem of displaying alternatives in a multi-attribute decision space is also presented.

Patrick, Nicholas J. M.↗

Decision-Aiding and Optimization for Vertical Navigation of Long-Haul Aircraft

Most decisions made in the cockpit are related to safety, and have therefore been proceduralized in order to reduce risk. There are very few which are made on the basis of a value metric such as economic cost. One which can be shown to be value based, however, is the selection of a flight profile. Fuel consumption and flight time both have a substantial effect on aircraft operating cost, but they cannot be minimized simultaneously. In addition, winds, turbulence, and performance x,ary widely with altitude and time. These factors make it important and difficult for pilots to (a) evaluate the outcomes associated with a particular trajectory before it is flown and (b) decide among possible trajectories. The two elements of this problem considered here are (1) determining, what constitutes optimality, and (2) finding optimal trajectories. Pilots and dispatchers from major U.S. airlines were surveyed to determine which attributes of the outcome of a flight they considered the most important. Avoiding turbulence-for passenger comfort topped the list of items which were not safety related. Pilots' decision making about the selection of flight profile on the basis of flight time, fuel burn, and exposure to turbulence was then observed. Of the several behavioral and prescriptive decision models invoked to explain the pilots' choices, utility maximization is shown to best reproduce the pilots' decisions. After considering more traditional methods for optimizing trajectories, a novel method is developed using a genetic algorithm (GA) operating on a discrete representation of the trajectory search space. The representation is a sequence of command altitudes, and was chosen to be compatible with the constraints imposed by Air Traffic Control, and with the training given to pilots. Since trajectory evaluation for the GA is performed holistically, a wide class of objective functions can be optimized easily. Also, using the GA it is possible to compare the costs associated with different airspace design and air traffic management policies. A decision aid is proposed which would combine the pilot's notion of optimility with the GA-based optimization, provide the pilot with a number of alternative pareto-optimal trajectories, and allow him to consider un-modelled attributes and constraints in choosing among them. A solution to the problem of displaying alternatives in a multi-attribute decision space is also presented.

Patrick, Nicholas J. M.↗

Advances in cryogenic foam insulations.

Description of a discretely oriented thread-reinforced polyurethane foam thermal insulation system for liquid hydrogen fuel tanks. The 3-D foam and glass liner composite is designed to be adhesively bonded to the inside surface of the tank wall and to be in direct contact with liquid hydrogen. All elements of this insulation composite are capable of sustaining the loads and environmental conditions imposed by testing under simulated Space Shuttle vehicle requirements at temperatures between -423 and +350 F.

Lemons, C. R.↗

Prospects of thermionic power systems

Potential thermionic power systems for space or terrestrial applications are described so that the development goals can be clearly identified. The thermionic power systems considered are a space nuclear power system, a fossil-fuel thermionic topping steam power system, a solar thermionic topping steam power system, and advanced systems. Attention is given to a discussion of the current status of technology development in thermionic converters and associated elements in power systems. Future prospects of thermionic power systems are also discussed. It is concluded that thermionic conversion has a great potential for a variety of applications.

Shimada, K.↗

Probabilistic simulation of uncertainties in thermal structures

Development of probabilistic structural analysis methods for hot structures is a major activity at Lewis Research Center. It consists of five program elements: (1) probabilistic loads; (2) probabilistic finite element analysis; (3) probabilistic material behavior; (4) assessment of reliability and risk; and (5) probabilistic structural performance evaluation. Recent progress includes: (1) quantification of the effects of uncertainties for several variables on high pressure fuel turbopump (HPFT) blade temperature, pressure, and torque of the Space Shuttle Main Engine (SSME); (2) the evaluation of the cumulative distribution function for various structural response variables based on assumed uncertainties in primitive structural variables; (3) evaluation of the failure probability; (4) reliability and risk-cost assessment, and (5) an outline of an emerging approach for eventual hot structures certification. Collectively, the results demonstrate that the structural durability/reliability of hot structural components can be effectively evaluated in a formal probabilistic framework. In addition, the approach can be readily extended to computationally simulate certification of hot structures for aerospace environments.

Chamis, Christos C.↗

Probabilistic simulation of uncertainties in thermal structures

Development of probabilistic structural analysis methods for hot structures is a major activity at NASA-Lewis, and consists of five program elements: (1) probabilistic loads, (2) probabilistic finite element analysis, (3) probabilistic material behavior, (4) assessment of reliability and risk, and (5) probabilistic structural performance evaluation. Attention is given to quantification of the effects of uncertainties for several variables on High Pressure Fuel Turbopump blade temperature, pressure, and torque of the Space Shuttle Main Engine; the evaluation of the cumulative distribution function for various structural response variables based on assumed uncertainties in primitive structural variables; evaluation of the failure probability; reliability and risk-cost assessment; and an outline of an emerging approach for eventual hot structures certification. Collectively, the results demonstrate that the structural durability/reliability of hot structural components can be effectively evaluated in a formal probabilistic framework. In addition, the approach can be readily extended to computationally simulate certification of hot structures for aerospace environments.

Chamis, C. C.↗

Chemiluminescence Measurements in a Combustor Using a 7-Point Lean Direct Injector Array Configuration for Gas Turbine Engine Applications

This paper reports results for a 7-point lean direct injector (LDI) array for a particular configuration. The LDI configuration in this study used a 60 degrees center pilot swirler and 52.5 degrees on the six outer swirlers. Chemiluminescence images of C2 and CH were collected at a frame rate of 25 Hz using an intensified CCD camera. Narrow bandwidth filters were coupled with the CCD camera in order to spectrally isolate C2 and CH signals. C2 was captured at 515 nm, and the CH signal was acquired at 430 nm. Six inlet conditions were considered in this study, all with the same inlet pressure, 75 psia, and same inlet temperature, 800 degcrees Fahrenheit. These conditions aimed to observe the effect of equivalence ratio, fuel staging, and reference velocity on C2 and CH emissions. Based on the chemiluminescence images, the changes in the inlet conditions was evident in both the pilot and outers. Additionally, the pilot (center injector element) appeared well isolated from the six outer elements under all test conditions.

lean direct injection↗

Mars rover RTG study

The paper describes the design and analysis of radioisotope thermoelectric generators (RTGs) for powering the Mars rover vehicle, which is a critical element of the unmanned Mars Rover and Sample Return mission (MRSR). A brief description is given of a reference mission scenario, an illustrative rover design and activity pattern on Mars, power system requirements, and environmental constraints, including the RTG cooling requirements during transit to Mars. The key RTG design problem, i.e. venting the helium generated by the fuel's alpha decay without intrusion of the Martian atmosphere into the RTG, is identified and a design approach to solve that problem is proposed. The study's primary objective is to quantify the performance improvements achievable in new successfully developed technologies, to estimate the required time, effort, success probability, and programmatic risk in developing these new technologies, and thus to help identify the best strategy for meeting the MRSR system goals. Finally, the paper compares the RTGs' specific powers for different power levels (250W vs 125W), different thermoelectric element designs (standard vs short unicouples vs multicouples), and different thermoelectric figures of merit (0.00058K to the -1 to 0.00140K to the -1).

Schock, A.↗

Laser Ablation Increases PEM/Catalyst Interfacial Area

An investigational method of improving the performance of a fuel cell that contains a polymer-electrolyte membrane (PEM) is based on the concept of roughening the surface of the PEM, prior to deposition of a thin layer of catalyst, in order to increase the PEM/catalyst interfacial area and thereby increase the degree of utilization of the catalyst. The roughening is done by means of laser ablation under carefully controlled conditions. Next, the roughened membrane surface is coated with the thin layer of catalyst (which is typically platinum), then sandwiched between two electrode/catalyst structures to form a membrane/ele c t - rode assembly. The feasibility of the roughening technique was demonstrated in experiments in which proton-conducting membranes made of a perfluorosulfonic acid-based hydrophilic, protonconducting polymer were ablated by use of femtosecond laser pulses. It was found that when proper combinations of the pulse intensity, pulse-repetition rate, and number of repetitions was chosen, the initially flat, smooth membrane surfaces became roughened to such an extent as to be converted to networks of nodules interconnected by filaments (see Figure 1). In further experiments, electrochemical impedance spectroscopy (EIS) was performed on a pristine (smooth) membrane and on two laser-roughened membranes after the membranes were coated with platinum on both sides. Some preliminary EIS data were interpreted as showing that notwithstanding the potential for laser-induced damage, the bulk conductivities of the membranes were not diminished in the roughening process. Other preliminary EIS data (see Figure 2) were interpreted as signifying that the surface areas of the laser-roughened membranes were significantly greater than those of the smooth membrane. Moreover, elemental analyses showed that the sulfur-containing molecular groups necessary for proton conduction remained intact, even near the laser-roughened surfaces. These preliminary results can be taken as indications that laser-roughened PEMs should function well in fuel cells and, in particular, should exhibit current and power densities greater than those attainable by use of smooth membranes.

Whitacre, Jay↗

Finite Element Analysis of MEMS Devices

A side-slide actuator and a corrugated diaphragm actuator will be analyzed and optimized this summer. Coupled electrostatic and fluid analyses will also be initiated. Both the side-slide actuator and the corrugated diaphragm actuator will be used to regulate the flow of fuel in a jet engine. Many of the side-slide actuators will be placed on top of a fuel injector that is still in the developmental stage as well. The corrugated diaphragm actuator will also be used to regulate the flow of fuel in fuel injectors. A comparative analysis of the performance matrix of both actuators will be conducted. The side-slide actuator uses the concept of mechanical advantage to regulate the flow of fuel using electrostatic forces. It is made from Nickel, Silicon Carbide, and thin layers of Oxide. The slider will have a hole in the middle that will allow fuel to pass through the hole underneath it. The goal is to regulate the flow of fuel through the inlet. This means that the actuator needs to be designed so that when a voltage is applied to the push rod, the slider will deflect in the x-direction and be able to completely block the inlet and no fuel can pass through. Different voltage levels will be tested. The parameters that are being optimized are the thickness of the diaphragm, what kind of corrugation the diaphragm should have, the length, width, and thickness of the push rod, and what design should be used to return the slider. The current possibilities for a return rod are a built in spring on the slider, a return rod that acts like a spring, or a return rod that is identical to the push rod. The final actuator design should have a push rod that has rotational motion and no translation motion, a push rod thickness that prevents warping due to the slider, and a large ratio of the displacement on the bottom of the push rod to displacement on the top of the push rod. The corrugated diaphragm actuator was optimized last winter and this summer will be spent completing the optimization of the coupled electrostatic and fluid flow parameters. It was found that Nickel is the best material to use for the diaphragm because it has a higher yield strength and allows for a larger stress, deflection and applied pressure. The parameters that were optimized were the wavelength and thickness of the diaphragm.

Corrigan, Jennifer↗

Nanophase Nickel-Zirconium Alloys for Fuel Cells

Nanophase nickel-zirconium alloys have been investigated for use as electrically conductive coatings and catalyst supports in fuel cells. Heretofore, noble metals have been used because they resist corrosion in the harsh, acidic fuel cell interior environments. However, the high cost of noble metals has prompted a search for less-costly substitutes. Nickel-zirconium alloys belong to a class of base metal alloys formed from transition elements of widely different d-electron configurations. These alloys generally exhibit unique physical, chemical, and metallurgical properties that can include corrosion resistance. Inasmuch as corrosion is accelerated by free-energy differences between bulk material and grain boundaries, it was conjectured that amorphous (glassy) and nanophase forms of these alloys could offer the desired corrosion resistance. For experiments to test the conjecture, thin alloy films containing various proportions of nickel and zirconium were deposited by magnetron and radiofrequency co-sputtering of nickel and zirconium. The results of x-ray diffraction studies of the deposited films suggested that the films had a nanophase and nearly amorphous character.

Narayanan, Sekharipuram↗

Orbiter Capability for Providing Water to the International Space Station according to the Most Probable Flight Attitudes

Water to be generated by, delivered to, and processed by the International Space Station (ISS) is a critical Environmental Control and Life Support (ECLS) element, especially for the early ISS missions. A significant portion of the water required by the ISS shall be provided by the Shuttle Transportation System (STS) Orbiter. The balance of water generated by the Orbiter Fuel Cells (FC), minus that water consumed by the Orbiter Flash Evaporator System (FES) and crew, is available for transfer to the ISS. During later missions, crew respired and perspired water, as well as effluent water from the Orbiter LiOH canisters, will be collected as condensate and available for transfer to the ISS. Orbiter radiator performance provides the most variance in determining the amount of net Orbiter water available for transfer to the ISS. As radiator performance decreases, the dependence upon the FES (and FC water) increases for rejecting Orbiter waste heat. Generally, radiator performance decreases as the ISS assembly size increases (especially as solar arrays are added), and also as beta angle increases. ISS solar array deployment necessitates the use of models with articulating solar arrays (for Earth local-vertical attitudes), as array position dramatically affects Orbiter radiator performance. Recent developments in the relaxation of beta angle limitations have also increased the complexity and difficulty of providing water to the ISS. Other factors that may hinder the ability to transfer water are the number of empty Contingency Water Containers (CWCs) available, duration of open-hatch time, crew activity timeline, and full CWC storage capability. A parametric study has been accomplished that provides a quick-reference table for determining expected water generation rates for ISS missions 2A.2 through 7A.1. An hourly Orbiter water generation rate is reported according to a matrix that consists of: (1) (six) significant changes in ISS assembly configuration; (2) (four) beta angles (0 deg. , +37 deg., +53 deg. , and +75 deg.); (3) the (three) most representative ISS attitudes (XPOP-O, XPOP-180 and +XVV); (4) (four) Orbiter radiator configurations (both stowed, starboard deployed, port deployed, and both deployed) and (5) the (two) conditions (radiator inlet temperatures and fuel cell power) most consistent with sleep and wake periods. Those permutations of higher probability of occurrence than others have been identified. Another parametric study has been accomplished that provides a quick-reference table for determining expected water generation rates for ISS assembly complete missions. An hourly Orbiter water generation rate is reported according to a matrix that consists of: (1) (seven) beta angles (-75 deg., -60 deg., -30 deg., 0 deg., +30 deg., +60 deg., and +75 deg.); (2) the (nine) PYR angles that define the corners of the envelope; (3) (four) Orbiter radiator configurations (both stowed, starboard deployed, port deployed, and both deployed) and (4) the (two) conditions (radiator inlet temperatures and fuel cell power) most consistent with sleep and wake periods.

Dunaway, Brian↗

Shuttle Program Loads Integration: Going From Concept to Operations and Staying Successful

From the beginning of the Shuttle Program to its end, integrated loads and dynamics analyses and tests have been critical in shaping the vehicle design and operational decisions for NASA and its customers. Starting with scaled models and simple mathematical simulations of the structural dynamics, engineers defined the required structural stiffness and predicted the limit loads for each element of the system. Early structural tests provided reasonable confidence that the models and predictions were good. The first launch of the Space Shuttle brought surprises, though, when the ignition overpressure event caused a forward fuel tank support strut to buckle, among several unexpected effects. The launch pad and other ground equipment became an integral part of the system integration, especially where the acoustic and pressure environments of ignition and lift-off were concerned. Following the Challenger accident, operating limits were changed in response to new understandings of how the integrated system performed. Controlling loads while maximizing performance was a key tenet of the Performance Enhancement design process, which enabled construction of the International Space Station. During the return to flight after the Columbia accident, engineers grew to understand that loads during the roll maneuver were also important to the vehicle s structural margin and life. At this point the crawler transport from the Vehicle Assembly Building to the launch pad also became a part of the integrated loads analysis. Even in the last years of the Space Shuttle Program, new data still provided interesting insights into this complicated and fascinating spaceship. This paper will present some examples of the important findings by the team of specialists that supported the Integrated Loads and Dynamics Panel for the Space Shuttle Program.

Bernstein, Karen↗

Probabilistic Structural Analysis and Reliability Using NESSUS With Implemented Material Strength Degradation Model

This project included both research and education objectives. The goal of this project was to advance innovative research and education objectives in theoretical and computational probabilistic structural analysis, reliability, and life prediction for improved reliability and safety of structural components of aerospace and aircraft propulsion systems. Research and education partners included Glenn Research Center (GRC) and Southwest Research Institute (SwRI) along with the University of Texas at San Antonio (UTSA). SwRI enhanced the NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) code and provided consulting support for NESSUS-related activities at UTSA. NASA funding supported three undergraduate students, two graduate students, a summer course instructor and the Principal Investigator. Matching funds from UTSA provided for the purchase of additional equipment for the enhancement of the Advanced Interactive Computational SGI Lab established during the first year of this Partnership Award to conduct the probabilistic finite element summer courses. The research portion of this report presents the cumulation of work performed through the use of the probabilistic finite element program, NESSUS, Numerical Evaluation and Structures Under Stress, and an embedded Material Strength Degradation (MSD) model. Probabilistic structural analysis provided for quantification of uncertainties associated with the design, thus enabling increased system performance and reliability. The structure examined was a Space Shuttle Main Engine (SSME) fuel turbopump blade. The blade material analyzed was Inconel 718, since the MSD model was previously calibrated for this material. Reliability analysis encompassing the effects of high temperature and high cycle fatigue, yielded a reliability value of 0.99978 using a fully correlated random field for the blade thickness. The reliability did not change significantly for a change in distribution type except for a change in distribution from Gaussian to Weibull for the centrifugal load. The sensitivity factors determined to be most dominant were the centrifugal loading and the initial strength of the material. These two sensitivity factors were influenced most by a change in distribution type from Gaussian to Weibull. The education portion of this report describes short-term and long-term educational objectives. Such objectives serve to integrate research and education components of this project resulting in opportunities for ethnic minority students, principally Hispanic. The primary vehicle to facilitate such integration was the teaching of two probabilistic finite element method courses to undergraduate engineering students in the summers of 1998 and 1999.

Bast, Callie C.↗

Analysis of the STS-126 Flow Control Valve Structural-Acoustic Coupling Failure

During the Space Transportation System mission STS-126, one of the main engine's flow control valves incurred an unexpected failure. A section of the valve broke off during liftoff. It is theorized that an acoustic mode of the flowing fuel, coupled with a structural mode of the valve, causing a high cycle fatigue failure. This report documents the analysis efforts conducted in an attempt to verify this theory. Hand calculations, computational fluid dynamics, and finite element methods are all implemented and analyses are performed using steady-state methods in addition to transient analysis methods. The conclusion of the analyses is that there is a critical acoustic mode that aligns with a structural mode of the valve

Jones, Trevor M.↗