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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Postirradiation characterization of palladium as an additive for fuel cladding chemical interaction mitigation in metallic fuel

This work describes the microstructural and elemental characterization of irradiated metallic fuels containing palladium as an additive. The use of additives has been proposed to control Fuel-Cladding Chemical Interaction (FCCI) and thus to promote higher fuel utilization (i.e., higher burnup). In this work, Pd has been investigated as a potential additive to metallic fuel to bind lanthanides, impeding their migration and attack on the cladding. The influence of Pd on the microstructure, chemistry and performance of metallic fuel has been characterized via scanning electron microscopy for two metallic fuel designs—namely, annular and solid fuel. Pd was observed to play an important role in the chemistry of the fuel. Indeed, the addition of Pd leads to the formation of new phases. Pd was detected to combine not only with the lanthanides, as intended, but also with Zr, a main element of the fuel matrix. While Pd proved to be effective in preventing lanthanide migration and their attack on the cladding, the Pd-Zr compound may potentially lead to other unexpected fuel-performance issues, such as the formation of low-melting point phases and increased unalloyed U available for FCCI interaction with Fe in the cladding. Even the increase of Zr to 13wt%. did not completely mitigate this adverse phenomenon generated by the Pd-Zr interaction. Furthermore, the efficacy of using this additive needs further investigation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Synergies between H, He and radiation damage in dual and triple ion irradiation of candidate fusion blanket materials

Three ferritic/martensitic alloys were studied to understand the synergistic effect between single ion beam (Fe 2+ ), dual ion beam (Fe 2+ +He 2+ and Fe 2+ +H + ), and triple ion beam (Fe 2+ +He 2+ +H + ) irradiations on cavity evolution. A commercial alloy, F82H, a castable nanostructured alloy, CNA3, and a high purity model alloy, Fe8Cr2W, were irradiated at 400°C to 600°C to a damage level of 50 dpa at a damage rate of 1 × 10 –3 dpa/s with He and H injection rates of 10 and 40 appm/dpa, respectively. Post-irradiation characterization via bright field transmission electron microscopy and high-angle annular dark-field scanning transmission electron microscopy was performed on all irradiated conditions to characterize the cavity size distribution and determine the effects of H/He injection on cavity microstructure. In all three alloys, hydrogen co-injection with helium resulted in an increased cavity number density and maximum cavity size, producing an increase in swelling over that from helium injection alone. Swelling in F82H appears to peak between 450°C and 500°C. At 600°C, swelling was minimal and cavities of high density and small size were confined to grain boundaries and dislocations while at 400°C, swelling is also low with a nearly homogeneous, high density, distribution of very small cavities throughout. Swelling was least in the commercial alloy F82H due to the high sink strength. The CNA3 alloy underwent dissolution of precipitates that lowered the sink strength and resulted in higher swelling than F82H, but less than the model alloy. Electron energy loss spectroscopy (EELS) elemental mapping revealed hydrogen forming a halo-like structure about the periphery of the cavities and helium residing within the cavities themselves. Finally, this observation suggests that hydrogen reduces the surface energy of helium-filled cavities which results in both increased cavity number density and cavity size in triple beam irradiation over dual beam irradiation.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Analysis of radially resolved thermal conductivity in high burnup mixed oxide fuel and comparison to thermal conductivity correlations implemented in fuel performance codes

The thermal diffusivity and thermal conductivity of high burnup (19 % FIMA) mixed oxide (U, Pu)O 2 nuclear fuel has been measured along the radial direction using a thermoreflectance-based method. Measured thermal conductivity exhibits a notable radial variation consistent with the expectations that a large temperature gradient across the annular fuel pellet leads to a heterogeneous microstructure. A common fuel performance model of thermal conductivity, the Lucuta-Inoue model, is used to analyze the measured thermal conductivity profile. Further, this model adequately captures the radial dependence of thermal conductivity except in the periphery. The analysis suggests that the characteristic radial shape of the thermal conductivity profile follows the burnup profile within the fuel pin. In the periphery, the high burnup structure is formed and the conductivity model, not capturing this effect, likely overestimates the thermal conductivity.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Understanding fission gas bubble distribution, lanthanide transportation, and thermal conductivity degradation in neutron-irradiated α-U using machine learning

U—10Zr based metallic nuclear fuel is the leading candidate for next-generation sodium-cooled fast reactors in the United States. US research reactors have used and tested this fuel type since the 1960s and accumulated considerable experience and knowledge about the fuel performance. Most of the knowledge, however, remains empirical. The lack of mechanistic understanding of fuel performance puts a large burden on proof through experimental verification for the qualification of U—10Zr fuel for commercial use. Further, this paper proposes an image data-driven machine learning approach, coupled with domain knowledge provided by advanced post irradiation examination, to provide unprecedented quantified insights into the morphology, size, density and the connectivity of fission gas bubbles and their effects on the fission product transportation and thermal conductivity. Specifically, we developed a method to automatically detect, extract statistics, and classify ~19,000 fission gas bubbles into different categories, and quantitatively link the data to lanthanide transportation through connected bubbles and degradation of thermal conductivity along the radial temperature gradient in a neutron irradiated U—10Zr annular fuel. Results indicate the approach can be modified to study other irradiation effects, such as secondary phase redistribution and gaseous fuel swelling in other irradiated nuclear fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Scanning transmission election microscopy observations of twisted epitaxial gold nanodiscs in twisted molybdenum disulfide bilayers

Atomic scale, scanning transmission electron microscopy (STEM) analysis of the moiré structures in twisted epitaxial gold nanodiscs encapsulated in twisted bilayer molybdenum disulfide is presented. High angle annular dark field STEM imaging reveals that the period of the moiré patterns between gold and molybdenum disulfide varies with different twist angles of the bilayer molybdenum disulfide, ranging from 1.80 nm (epitaxial alignment of gold) to 1.53 nm (twisted epitaxial alignment of gold). Additionally, bright field STEM imaging reveals a faint, larger "moiré of moiré" structure in cases where the bilayer molybdenum disulfide twist angle is small (~6°), arising from the overlapping three-layers, which is not visible in conventional transmission electron microscopy images. In conclusion, our experiments indicate that scanning transmission electron microscopy as a suitable tool for moiré analysis of twisted multilayer planar heterostructures, complementary to information provided by conventional transmission electron microscopy and diffraction.

Au↗
DOE OSTI2022

Atomically sharp jagged edges of chemical vapor deposition-grown WS 2 for electrocatalysis

Chemical vapor deposition (CVD)-grown 2D transition metal dichalcogenides can adopt faceted edges. To investigate how sharp these sites can be, we utilize aberration-corrected annular dark-field scanning transmission electron microscopy (ADF-STEM) to resolve the atomic structure of two-dimensional (2D) WS 2 domains that show jagged edges. Nanoscale triangular edge structures with S zigzag terminations are observed. Both the peak and valley regions exhibit near-atomic sharpness. The peaks are as sharp as two atoms in width. Highly ordered valley sites display a minimum width of three atoms, and prospective single-atom valleys appear as two-atom-wide sites in the ADF-STEM contrast. Regarding the kinetics, density-functional theory (DFT) calculations indicate that the 2-W-atom peak would not evolve into a single-W-atom peak even though the latter configuration is also stable with a high enough binding energy under the growth conditions. These results help deepen our understanding of the possible structuring at the nanoscale and the atomic-scale limits of peaks and valleys formed via intersection of two zigzag edges. The enriched edge sites lead to higher catalytic activities for the hydrogen evolution reaction (HER).

36 MATERIALS SCIENCE↗
DOE OSTI2022

A novel active veto prototype detector with an inner target for improved rare event searches

Here, we report the fabrication and performance of an annular, cryogenic, phonon-mediated veto detector that can host an inner target detector, allowing substantial reduction in radiogenic backgrounds for rare event search experiments. A germanium veto detector of mass ~500g with an outer diameter of 76 mm and an inner diameter of 28 mm was produced inside of which was mounted a 25 mm diameter germanium inner target detector of mass ~10g. The detector was designed using inputs from a GEANT4 based simulation, where it was modeled to be sandwiched between two germanium detectors. The simulation showed that the background rates (dominated by gamma interactions) could be reduced by >90%, and that such an arrangement is sufficient for aggressive background reduction needed for neutrino and dark matter search experiments. Operating at mK temperatures at the experimental site, the veto detector prototype achieved a baseline resolution of 1.24±0.02 keV while hosting a functional inner target detector. The baseline resolution of the inner target detector was 147±2 eV. The experimental results of an identical detector arrangement are in excellent agreement with the simulation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

CLARION2-TRINITY: A Compton-suppressed HPGe and GAGG:Ce-Si-Si array for absolute cross-section measurements with heavy ions

The design and performance of a new Compton-suppressed HPGe and charged-particle array, CLARION2-TRINITY, are described. The TRINITY charged-particle array is comprised of 64 Cerium-doped Gadolinium Aluminum Gallium Garnet (GAGG:Ce) crystals configured into five rings spanning 7–54 degrees, and two annular silicon detectors that can shadow or extend the angular coverage to backward angles with minimal $\gamma$-ray attenuation. GAGG:Ce is a non-hygroscopic, bright, and relatively fast scintillator with a light distribution well matched to SiPMs. Count rates up to 40 kHz per crystal are sustainable. Fundamental characteristics of GAGG:Ce are measured and presented, including light- and heavy-ion particle identification (PID) capability, pulse-height defects, radiation hardness, and emission spectra. The CLARION2 array consists of up to 16 Compton-suppressed HPGe Clover detectors (efficiency at 1 MeV) configured into four rings (eight HPGe crystal rings) using a non-Archimedean geometry that suppresses back-to-back coincident 511-keV gamma rays. The entire array is instrumented with 100- and 500-MHz (14 bit) waveform digitizers which enable triggerless operation, pulse-shape discrimination, fast timing, and pileup correction. Lastly, two examples of experimental data taken during the commissioning of the CLARION2-TRINITY system are given: a PID spectrum from 16 O + 18 O fusion-evaporation, and PID and Doppler-corrected -ray spectra from 48 Ti + 12 C Coulomb excitation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Design, assembly and operation of a Cosmic Ray Tagger based on scintillators and SiPMs

The Mu2e experiment at Fermilab aims to search for the SM forbidden μ – → e – conversion in Al muonic atoms. The signal signature consists of 104.96 MeV electrons, identified by a straw-tube tracker and a crystal calorimeter, made of two annular disks. Here, in order to calibrate the calorimeter disks with minimum ionizing particles (MIP) before the installation, we have realized a Cosmic Ray Tagger (CRT) at Laboratori Nazionali di Frascati (LNF) of INFN. The CRT consists of two planes of eight 2.5 x 1.5 x 160 cm 3 plastic scintillator (EJ-200) bars, coupled to SiPMs on both edges, so as to estimate longitudinal hit positions from time differences. 3D MIP tracking is achieved by reconstructing hit positions in the two planes, placed above and below the disks, and allows to calibrate the energy response, to align the time offsets, and to study the detector performances dependence along the crystals axis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

BlueSTEAl: A pair of silicon arrays and a zero-degree phoswich detector for studies of scattering and reactions in inverse kinematics

BlueSTEAl, the Blue (aluminum chamber of) Silicon TElescope Arrays for light nuclei, has been developed to study direct reactions in inverse kinematics, as well as scattering and breakup reactions using radioactive ion beams. It is a detector system consisting of a pair of annular silicon detector arrays and a zero-degree phoswich plastic scintillator. For typical binary reaction studies in inverse kinematics, light ions are detected by the Si array in coincidence with heavy recoils detected by the phoswich placed at the focal-plane of a zero-degree magnetic spectrometer. The Si array can also be used to detect light nuclei such as beryllium and carbon with clear isotope separation, while the phoswich can also be placed at zero degrees without a spectrometer and used as a high-efficiency beam counting monitor with particle identification capability at the rate of up to ~5 × 10 4 particles per second. This paper reports on the capabilities of BlueSTEAl as determined by recent experiments performed at the Texas A&M Cyclotron Institute. Furthermore, the device is also anticipated to be used in future experiments at other radioactive ion beam facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Simulation of natural circulation cartridge loop experiments and application to molten salt reactors

This work uses the TRAC/RELAP Advanced Computational Engine (TRACE) thermal hydraulics (TH) code to model natural circulation cartridge loop experiments previously conducted at Oak Ridge National Laboratory (ORNL) using water and compares the simulated and experimental results. TRACE is also used to characterize natural circulation in the cartridge loop vehicle using FLiNaK as the working fluid. The experimental vehicle is a buoyancy-aided, annular cartridge loop, referred to as a thermosyphon, and is designed to aid in qualifying liquid–fueled and/or liquid–cooled irradiation experiments for the Versatile Test Reactor (VTR), which is currently being designed in the United States. Out-of-pile water experiments have been conducted using the cartridge and the Thermosyphon Test Loop facility at ORNL, and future experiments are anticipated that would use other molten salt surrogates as the working fluid, followed by eventual insertion of a similar cartridge into VTR. Additionally, this work aims to determine how well TRACE can replicate the natural convection conditions that were observed experimentally; this serves as an initial step for validating the modeling tool for design and safety calculations to support future irradiation experiments in VTR. Initial predictions of potential experiments were made using FLiNaK as the natural circulation fluid to demonstrate the relevance of the cartridge design to molten salt reactors (MSRs). Results from this study indicate that TRACE can accurately capture natural convection phenomena in the thermosyphon and that several design changes to the current cartridge vehicle are necessary to achieve hydraulic conditions similar to those expected in MSRs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Fuel performance evaluation of two high burnup PWR core designs during normal operation, control rod withdrawal, and control rod ejection scenarios

There is interest among utilities to extend the current, 18-month operating cycle to 24 months. Economically, this extension would require greater than 5 % enrichment and peak rod average discharge burnup levels above 62 GWd/MTU. A notable challenge of increasing enrichment is the resulting additional excess reactivity encountered during the early stages of fuel life. To accommodate, burnable absorbers beyond soluble boron are introduced into the fuel system. In high burnup fuels, the possibilities of cladding lift-off and fuel melting increase due, in part, to increased rod internal pressures and limited fuel thermal conductivity, respectively. This work collaboratively employs PARCS, RELAP5-3D, and BISON to compare the fuel performance of two high burnup fuel candidates with higher than 5 % enrichment. Here, the fuel performance parameters were compared to current NRC guidance. The results demonstrate an annular fuel design with homogenously blended gadolinium as a burnable absorber operates with greater safety margins during normal operation, allowing for additional operational flexibility. During normal operation, the core design utilizing Integral Fuel Burnable Absorber pins contained fuel pins which reached plenum pressures above 15.5 MPa by the end of the first fuel cycle and fuel pins experienced cladding hoop strains above 1 %. In the Gd core design, only two observed pins experienced plenum pressures above 15.5 MPa and no pins exceeded 1 % cladding hoop strain. During the control rod withdrawal scenario, plenum pressures for pins in both designs marginally exceeded system pressure, however neither experienced excessive hoop strain. The Gd core design experienced a maximum fuel temperature of 2418 K, which is significantly higher than the Integral Fuel Burnable Absorber design at 2157 K, but still within regulatory guidance. We predicted that the fuel in both could return to service after the CRW event. We also predicted that cladding would not fail during the Control Rod Ejection in either core design. Generally, the Integral Fuel Burnable Absorber core design performed with greater safety margin with regards to temperature during normal operation and the transient events. However, the Gd core design performed with greater safety margin regarding plenum pressure and hoop strain limits during normal operation and both transient events.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Reactivity-initiated accidents in two pressurized water reactor high burnup core designs

Here, this paper presents a safety analysis of two proposed core loadings for 24-month Pressurized Water Reactor (PWR) fuel cycles. This analysis focuses on reactivity-initiated accidents (RIAs) and evaluates core safety performance impacts of rod-averaged burnup limits up to 75 GWD/MTU and less than 7 % enriched UO 2 . The capabilities of Polaris, PARCS, and RELAP5-3D are leveraged to evaluate the core neutronic and thermal–hydraulic behavior for normal-operation, uncontrolled control rod withdrawal (CRW) transients, and control rod ejection (CRE) accidents. The two core designs are compared to identify features of realistic high burnup/extended enrichment core design approaches which have significant safety impact, identify experimental data needs for high-fidelity predictive modeling, and provide recommendations for future high burnup core designs. The first core design evaluated in this study was developed by Southern Nuclear Company and used an ZrB 2 Integral Fuel Burnable Absorber (IFBA) and B 4 C Wet-Annular Burnable Absorber (WABA)-based burnable poison strategy. The second core design assessed in this work used a Gd 2 O 3 -doped UO 2 burnable poison, similar to that used in boiling water reactors or French PWRs. Results indicate that fuel thermal limits are maintained for limiting CRW and hot full power (HFP) CRE transients. Cladding failure is predicted for the highest energy deposition rods in each core during limiting hot zero power (HZP) CRE accidents (where maximum radially averaged enthalpy exceeds 120 cal/g), though licensing may be permissible with a limited number of failed rods. While concerns exist regarding high critical boron concentration during steady state for the IFBA core and large plenum pressures for the gadolinia core design, the analysis demonstrates adequate safety performance during limiting RIA accident scenarios for two representative high burnup core designs. Design changes limiting plenum pressures and implementation of accident tolerant fuel (ATF) cladding features which minimize hydriding and susceptibility to pellet-cladding mechanical interaction (PCMI) are recommended for future high burnup fuel concepts. To support the technical basis for burnup limit increases, high-fidelity fuel performance models are needed to address physical effects not considered in this analysis, and high burnup irradiated fuel tests are required to extend applicability of the fuel failure limits and validate existing and future models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Development and preliminary validation of a mechanistic multiscale model for fuel-cladding chemical interaction in metallic nuclear fuels

Despite decades of fuel rod material and design improvements, fuel-cladding chemical interaction (FCCI) remains the single-most lifetime-limiting behavior for modern metallic fuel rods. Constraining fuel lifetime increases operating costs, limiting the economic viability of commercializing metallic nuclear fuel technology. A mechanistic multiscale model utilizing the finite element method-based MARMOT and BISON codes was developed to more confidently predict cladding-side FCCI and its impact on fuel performance. The new BISON model incorporates mesoscale models for the effects of fuel microstructure evolution on the transport of wastage-inducing lanthanides through the fuel and for the kinetics of cladding wastage layer growth. The mesoscale models, in turn, build on lanthanide transport property data obtained from the atomistic scale. Preliminary validation studies using wastage thickness and cladding profilometry data from four fuel rods irradiated in Experimental Breeder Reactor II experiment X447 and one fuel rod from Fast Flux Test Facility experiment IFR1 show that the new model predicts cladding wastage and its effects on cladding deformation as well as existing empirical FCCI correlations. The new model is expected to aid in the design of new metallic fuel concepts, including fuel additives, cladding liners, and sodium-free annular fuel geometries. In conclusion, future work will focus on broader validation and refinement of the model’s treatment of different fuel alloys and cladding materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Recent advances in CO 2 hydrogenation to value-added products — Current challenges and future directions

Climate change, global warming, fossil fuel depletion and rising fuel prices have created great incentives to seek alternative fuel production technologies. CO 2 transformation to value-added products using renewable H 2 has proven to be an emerging solution to enable this goal. In this regard, three different promising processes, namely methane, methanol and hydrocarbon synthesis via CO 2 hydrogenation are thoroughly discussed. In addition, the influential factors affecting process efficiencies such as catalyst design and mechanistic insight, operating conditions as well as reactor types are investigated, with key pathways that dictate catalyst activity and selectivity of the most promising materials described. Furthermore, a brief overview of the reactor configuration and its crucial role in the improving process viability is analyzed. Accordingly, fixed-bed, fluidized-bed, annular and spherical reactors along with H 2 O/H 2 perm-selective membrane reactors are disscussed for hydrocarbon production. In addition, different reactor configurations are compared to assess the best one that is adjustable depending on the reaction mechanism. In conclusion, a corrugated-wall dual-type membrane reactor is proposed as an emerging alternative for CO 2 hydrogenation to value-added products.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A comprehensive review on the loss of wellbore integrity due to cement failure and available remedial methods

With the recent abrupt fluctuations in oil pricing and the need of complying with environmental and social requirements, nowadays it is an urgent call for the oil and gas industry to produce the hydrocarbon without any loss as well as in a safe manner. Cements are placed in the annular space of casing to provide zonal isolation in between wellbore and surface during the operational life cycle of the well or even after the abandonment. But this is not what happens most of the time. Cement degrades or loses its integrity through debonding either from the casing or formation and generates cracks or fractures due to varied reasons throughout the life of the well. Multiple causes contribute to the loss of wellbore integrity – either by physical, mechanical, or chemical processes. These failures lead to sustained casing pressure (SCP) and contamination of surrounding environment. To combat this issue or to restore the well integrity, multiple remedial actions have also been either implemented in the industry or proposed based on experimental research to prevent the damage or to seal the leakage in the cement sheath. Here, this paper will provide an extensive review of the underlying reasons of cement failure and the available remedial actions to minimize the loss of well integrity issue. These information are not only useful to know about the different corrective options available for us to implement in industry but also it will provide us a knowledge base regarding how we can enhance the performance of the exiting systems to battle the cement integrity problem more efficiently.

02 PETROLEUM↗
DOE OSTI2020

The effects of mixture preburning on detonation wave propagation

Pressure gain combustion in the form of continuous detonations can provide a significant increase in the efficiency of a variety of propulsion and energy conversion devices. In this regard, rotating detonation engines (RDEs) that utilize an azimuthally-moving detonation wave in annular systems are increasingly seen as a viable approach to realizing pressure gain combustion. However, practical RDEs that employ non- premixed fuel and oxidizer injection need to minimize losses through a number of mechanisms, including turbulence-induced shock-front variations, incomplete fuel-air mixing, and premature deflagration. In this study, a canonical stratified detonation configuration is used to understand the impact of preburning on detonation efficiency. It was found that heat release ahead of the detonation wave leads to weaker shock fronts, delayed combustion of partially-oxidized fuel-air mixture, and non-compact heat release. Furthermore, large variations in wave speeds were observed, which is consistent with wave behavior in full-scale RDEs. Peak pressures in the compression region or near triple points were considerably lower than the theoretically-predicted values for ideal detonations. Analysis of the detonation structure indicates that this deflagration process is parasitic in nature, reducing the detonation efficiency but also leading to heat release far behind the wave that cannot directly strengthen the shock wave. As a result, this parasitic combustion leads to commensal combustion (heat release far downstream of the wave), indicating that it is the root cause of combustion efficiency losses.

42 ENGINEERING↗
DOE OSTI2020

Modal dynamics of high-frequency transverse combustion instabilities

This paper investigates the modal dynamics of self-excited high frequency transverse instabilities in a multi-nozzle, swirl-stabilized can combustor. It utilizes results from multiple pressure sensors to decompose the disturbance into clockwise (CW) and counter-clockwise (CCW) waves, enabling a reconstruction of the pressure amplitude, phase, anti-nodal line location, and spin ratio. While these types of decompositions have been demonstrated on small scale combustors, particularly annular combustors, this is the first study to analyze these results for a high power, multi-nozzle can combustor. Its particular focus is in characterizing the system evolution in phase space and the nature of the system attractors under linearly unstable conditions; results are presented in spin ratio-phase difference space, so that limit cycle oscillations appear as fixed points. Results are shown for conditions where three different attractors dominate (standing, CW, and CCW) but are taken for very long time periods (~50,000 cycles) so that the system's interaction with these attractors can be observed. For the standing mode-dominated case, the phase portrait shows spiral trajectories converging to a single fixed point. For the spinning mode dominated cases, however, multiple fixed points and saddle points were observed, and the trajectories showed a more complicated structure. It was also shown that even though the CW mode is dominant, this mode intermittently switches to standing or CCW modes for short period. These results suggest that the strength of each attractor depends on test conditions and that random noise stochastically perturbs the system so that large regions of the phase space are explored. Lastly, one interesting observation is that the angular velocity of the anti-nodal line linearly varies with the spin ratio under standing-mode dominant conditions.

42 ENGINEERING↗