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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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Stability and convergence analysis of the harmonic balance method for a Duffing oscillator with freeplay nonlinearity.
Abstract not provided.
Nonlinear Analysis of a Tapered Impact Damper using the Method of Harmonic Balance.
Abstract not provided.
High-harmonic generation from artificially stacked 2D crystals
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Black Start of Unbalanced Microgrids Harmonizing Single- and Three-Phase Grid-Forming Inverters: Preprint
As power systems are transforming with increasing penetrations of inverter-based resources (IBRs), system restoration using IBRs has drawn attention. Using distributed grid-forming (GFM) assets located near critical loads, either three-phase or single-phase, to establish microgrid voltages in the absence of a bulk grid, a distribution system could obtain high system survivability. For swift and secure recovery of a critical load in a single-phase lateral, local single-phase GFM inverters can form a microgrid, and then it can be combined with a neighbouring grid with the inverters remaining in GFM mode for voltage and frequency regulation until the bulk grid comes online. It leads to dynamic interoperation of single-phase GFM inverters with three-phase ones in the black start process. This paper studies the novel approach with electromagnetic transient (EMT) simulations. To evaluate the potential and the technical challenges of the heterogeneous IBR-driven black start, three-phase and single-phase GFM inverter models are developed, including negative-sequence control for voltage balance and a phase-by-phase current limiter (three-phase) and current magnitude limiter (single-phase). To examine dynamic aspects of the black-start process, the EMT simulation also models transformer and motor dynamics emulating their inrush and startup behavior as well as network dynamics. Involvement of grid-following assets to facilitate the black-start process is also modeled. By allowing multiple GFM inverters to collectively black start without leader-follower coordination, regardless of phases, a system can achieve extreme resilience. An inverter-driven black start of a heavily unbalanced 2-MVA distribution feeder using 1 three-phase and 3 single-phase GFM inverters is demonstrated. The simulation shows the heterogeneous system can maintain stability with the single-phase GFM dynamics coupled with the three-phase one.
Generalized Analytical and Numerical Modeling of Optical Second Harmonic Generation in Anisotropic Crystals and Complex Heterostructures Using #SHAARP Package
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Nonlinear Multi-Harmonic Phase Resonance Simulations of High-Fidelity Finite Element Models.
Abstract not provided.
On the Harmonic Balance Method Augmented with Non-Smooth Basis Functions for Contact/Impact Problems.
Abstract not provided.
Harmonic balance based methodology for reduced order modeling to predict response of nonlinear structures
Conference paper for ISMA 2024
How structural differences influence cross-model consistency: An electric sector case study
Multiple models are often employed to describe a range of possible outcomes for one or more scenarios, yielding insights into causal relationships and their uncertainties. Electric sector capacity expansion scenarios are a common topic of such efforts due to the economic influence of the electric sector, but model results typically span a broad solution space despite efforts to harmonize input assumptions, making decision implications difficult to discern. This study investigates the relationship between input harmonization and cross-model scenario consistency under disparate electric sector scenarios. We compare cross-model consistency between two state-of-the-art electric sector capacity expansion models (GCAM-USA and ReEDS) for six electric sector scenarios comprising alternate assumptions about fossil fuel resource availability, technology innovation, and long-term economy-wide transitions under four harmonization configurations varying model representations of electricity demand, fuel prices, renewable resources, and capacity retirements. These comparisons reveal that cross-model consistency can vary across scenarios under a given harmonization configuration, suggesting that harmonization efforts must often be scenario-specific if comparable cross-model consistency is desired. Model structural differences can hinder consistency, and the impact of these differences can depend on the scenario. Ultimately, thorough harmonization can reveal insights into cross-model consistency, which can be used to tighten uncertainty bounds and improve the decision-making implications of multi-model activities.
Revisiting the Global Patterns of Seasonal Cycle in Sea Surface Salinity
Argo profiling floats and L-band passive microwave remote sensing have significantly improved the global sampling of sea surface salinity (SSS) in the past 15 years, allowing the study of the range of SSS seasonal variability using concurrent satellite and in situ platforms. Here, harmonic analysis was applied to four 0.25° satellite products and two 1° in situ products between 2016 and 2018 to determine seasonal harmonic patterns. The 0.25° World Ocean Atlas (WOA) version 2018 was referenced to help assess the harmonic patterns from a long-term perspective based on the 3-year period. The results show that annual harmonic is the most characteristic signal of the seasonal cycle, and semiannual harmonic is important in regions influenced by monsoon and major rivers. The percentage of the observed variance that can be explained by harmonic modes varies with products, with values ranging between 50% and 72% for annual harmonic and between 15% and 19% for semiannual harmonic. The large spread in the explained variance by the annual harmonic reflects the large disparity in nonseasonal variance (or noise) in the different products. Satellite products are capable of capturing sharp SSS features on meso- and frontal scales and the patterns agree well with the WOA 2018. These products are, however, subject to the impacts of radiometric noises and are algorithm dependent. The coarser-resolution in situ products may underrepresent the full range of high-frequency small scale SSS variability when data record is short, which may have enlarged the explained SSS variance by the annual harmonic.
Optimum wavelengths for two color ranging
The range uncertainties associated with the refractive atmosphere can be mitigated by the technique of two color, or dual wavelength, ranging. The precision of the differential time of flight (DTOF) measurement depends on the atmospheric dispersion between the two wavelengths, the received pulsewidths and photoelectron counts, and on the amount of temporal averaging. In general, the transmitted wavelengths are not independently chosen but instead are generated via nonlinear optics techniques (harmonic crystals, Raman scattering, etc.) which also determine their relative pulsewidths. The mean received photoelectrons at each wavelength are calculated via the familiar radar link equation which contains several wavelength dependent parameters. By collecting the various wavelength dependent terms, one can define a wavelength figure of merit for a two color laser ranging system. In this paper, we apply the wavelength figure of merit to the case of an extremely clear atmosphere and draw several conclusions regarding the relative merits of fundamental-second harmonic, fundamental-third harmonic, second-third harmonic, and Raman two color systems. We find that, in spite of the larger dispersion between wavelengths, fundamental-third harmonic systems have the lowest figure of merit due to a combination of poor detector performance at the fundamental and poor atmospheric transmission at the third harmonic. The fundamental-second harmonic systems (approximately 700 nm and 350 nm) have the highest figure of merit, but second-third harmonic systems, using fundamental transmitters near 1000 nm, are a close second. Raman-shifted transmitters appear to offer no advantage over harmonic systems because of the relatively small wavelength separation that can be achieved in light gases such as hydrogen and the lack of good ultrashort pulse transmitters with an optimum fundamental wavelength near 400 nm.
Characterizing Current THD’s Dependency on Solar Irradiance and Supraharmonics Profiling for a Grid-Tied Photovoltaic Power Plant
The rapidly increasing distributed energy resources (DERs) in power systems are now getting interconnected to set community grid structures, where power quality will be a major concern. The grid-to-grid (G2G) bidirectional power transfer among the distribution microgrid will not be considered commercially feasible unless the upstream harmonics are under the limits. The aggregation of such harmonics, measured as total harmonic distortion (THD), is feared to be beyond tolerable limits with the progression of rooftop grid-tied PV-like installations. Hence, this THD needs to be characterized with DER generation end variables. In this work, the photovoltaic (PV) DERs’ dependency on environment variables such as irradiance was profiled in the context of generating and injecting harmonics into the grid. A mathematical model of a grid-tied three-phase PV DER was developed as part of this correlation characterization, matching the fundamental unit structure of a 1.4 MW solar canopy located on the Florida International University (FIU) Miami campus. To determine the qualitative association with produced THD patterns, the model was evaluated with various irradiance settings. A real-time digital simulation (RTDS) platform was used to verify it. Following this confirmation, sets of data from power quality meters at the point of common coupling and FIU field sensors were utilized to validate further the correlation model. The results showed that the grid current’s THD exhibited a high correlation with the irradiance profile and its variation over time. The early morning and late afternoon periods of the day, associated with a low irradiance, constantly had higher harmonics generated from the PV DER. The midday THD was rather rational with partial shadings, hence a geolocation-dependent factor. These findings were verified by an RTDS and validated by real field data. In quantifying the THD injected by a single DER at a high-frequency (2–150 kHz) supraharmonics (SH) level, a 3% peak increment in magnitude was observed from the high-fixed to the low-fixed irradiance profile. The correlation characteristics depicted that the hybrid microgrid suffered from a daytime-dependent harmonic insertion from the grid-tied DER. This is a global problem unless specific measures are taken to mitigate the harmonics. The electrically notorious higher-frequency SH was found to increase proportionally. The G2G power transfer can be limited because of the higher THD in the early morning and late afternoon, which will also worsen because the numbers of grid-tied PV DERs (i.e., rooftop solar and industrial solar) are likely to increase rapidly soon. The community grid structure can thus have a controlled harmonics filtration setup purposefully designed to address the findings of this work, which also fall within the scope of our future research.
Rates of change of the earth's magnetic field measured by recent analyses
Typical rates of change of the earth's magnetic field are presented as a function of the earth's spherical harmonics. Harmonics up to the eight degree are analyzed. With the increase in the degree of the harmonics an increase in the relative rate of change can be observed. For higher degrees, the rate of change can be predicted. This enables a differentiation between harmonics originating in the core and harmonics caused by crustal magnetization. The westward drift of the magnetic field depends on the longitudinal gradient of the field. In order to determine the longitudinal motions, harmonics up to degree 20 can be utilized. The average rate of secular acceleration increases with the degree of harmonics from 0.001 deg/sq yr for a dipole term to an average of 0.05 deg/sq yr for degree eight harmonics.
Coupled 2-dimensional cascade theory for noise and unsteady aerodynamics of blade row interaction in turbofans. Volume 1: Theory development and parametric studies
Typical analytical models for interaction between rotor and stator in a turbofan analyze the effect of wakes from the rotor impinging on the stator, producing unsteady loading, and thereby generating noise. Reflection/transmission characteristics of the rotor are sometimes added in a separate calculation. In those models, there is a one-to-one relationship between wake harmonics and noise harmonics; that is, the BPF (blade passing frequency) wake harmonic causes only the BPF noise harmonic, etc. This report presents a more complete model in which flow tangency boundary conditions are satisfied on two cascades in relative motion for several harmonics simultaneously. By an extension of S.N. Smith's code for two dimensional flat plate cascades, the noise generation/frequency scattering/blade row reflection problem is solved in a single matrix inversion. It is found that the BPF harmonic excitation of the stator scatters considerable energy in the higher BPF harmonics due to relative motion between the blade rows. Furthermore, when swirl between the rotor and stator is modeled, a 'mode trapping' effect occurs which explains observations on fans operating at rotational speeds below BFP cuton: the BPF mode amplifies between blade rows by multiple reflections but cannot escape to the inlet and exit ducts. However, energy scattered into higher harmonics does propagate and dominates the spectrum at two and three times BPF. This report presents the complete derivation of the theory, comparison with a previous (more limited) coupled rotor/stator interaction theory due to Kaji and Okazaki, exploration of the mode trapping phenomenon, and parametric studies showing the effects of vane/blade ratio and rotor/stator interaction. For generality, the analysis applies to stages where the rotor is either upstream or downstream of the stator and to counter rotation stages. The theory has been coded in a FORTRAN program called CUP2D, documented in Volume 2 of this report. It is concluded that the new features of this analysis - unsteady coupling, frequency scattering, and flow turning between rotor and stator - have a profound effect on noise generation caused by rotor/stator interaction. Treating rotors and stators as isolated cascades is not adequate for noise analysis and prediction.
Reaction Wheel Disturbance Model Extraction Software - RWDMES
The RWDMES is a tool for modeling the disturbances imparted on spacecraft by spinning reaction wheels. Reaction wheels are usually the largest disturbance source on a precision pointing spacecraft, and can be the dominating source of pointing error. Accurate knowledge of the disturbance environment is critical to accurate prediction of the pointing performance. In the past, it has been difficult to extract an accurate wheel disturbance model since the forcing mechanisms are difficult to model physically, and the forcing amplitudes are filtered by the dynamics of the reaction wheel. RWDMES captures the wheel-induced disturbances using a hybrid physical/empirical model that is extracted directly from measured forcing data. The empirical models capture the tonal forces that occur at harmonics of the spin rate, and the broadband forces that arise from random effects. The empirical forcing functions are filtered by a physical model of the wheel structure that includes spin-rate-dependent moments (gyroscopic terms). The resulting hybrid model creates a highly accurate prediction of wheel-induced forces. It accounts for variation in disturbance frequency, as well as the shifts in structural amplification by the whirl modes, as the spin rate changes. This software provides a point-and-click environment for producing accurate models with minimal user effort. Where conventional approaches may take weeks to produce a model of variable quality, RWDMES can create a demonstrably high accuracy model in two hours. The software consists of a graphical user interface (GUI) that enables the user to specify all analysis parameters, to evaluate analysis results and to iteratively refine the model. Underlying algorithms automatically extract disturbance harmonics, initialize and tune harmonic models, and initialize and tune broadband noise models. The component steps are described in the RWDMES user s guide and include: converting time domain data to waterfall PSDs (power spectral densities); converting PSDs to order analysis data; extracting harmonics; initializing and simultaneously tuning a harmonic model and a wheel structural model; initializing and tuning a broadband model; and verifying the harmonic/broadband/structural model against the measurement data. Functional operation is through a MATLAB GUI that loads test data, performs the various analyses, plots evaluation data for assessment and refinement of analysis parameters, and exports the data to documentation or downstream analysis code. The harmonic models are defined as specified functions of frequency, typically speed-squared. The reaction wheel structural model is realized as mass, damping, and stiffness matrices (typically from a finite element analysis package) with the addition of a gyroscopic forcing matrix. The broadband noise model is realized as a set of speed-dependent filters. The tuning of the combined model is performed using nonlinear least squares techniques. RWDMES is implemented as a MATLAB toolbox comprising the Fit Manager for performing the model extraction, Data Manager for managing input data and output models, the Gyro Manager for modifying wheel structural models, and the Harmonic Editor for evaluating and tuning harmonic models. This software was validated using data from Goodrich E wheels, and from GSFC Lunar Reconnaissance Orbiter (LRO) wheels. The validation testing proved that RWDMES has the capability to extract accurate disturbance models from flight reaction wheels with minimal user effort.
Magnetic-Field-Response Measurement-Acquisition System
A measurement-acquisition system uses magnetic fields to power sensors and to acquire measurements from sensors. The system alleviates many shortcomings of traditional measurement-acquisition systems, which include a finite number of measurement channels, weight penalty associated with wires, use limited to a single type of measurement, wire degradation due to wear or chemical decay, and the logistics needed to add new sensors. Eliminating wiring for acquiring measurements can alleviate potential hazards associated with wires, such as damaged wires becoming ignition sources due to arcing. The sensors are designed as electrically passive inductive-capacitive or passive inductive-capacitive-resistive circuits that produce magnetic-field-responses. One or more electrical parameters (inductance, capacitance, and resistance) of each sensor can be variable and corresponds to a measured physical state of interest. The magnetic-field- response attributes (frequency, amplitude, and bandwidth) of the inductor correspond to the states of physical properties for which each sensor measures. For each sensor, the measurement-acquisition system produces a series of increasing magnetic-field harmonics within a frequency range dedicated to that sensor. For each harmonic, an antenna electrically coupled to an oscillating current (the frequency of which is that of the harmonic) produces an oscillating magnetic field. Faraday induction via the harmonic magnetic fields produces an electromotive force and therefore a current in the sensor. Once electrically active, the sensor produces its own harmonic magnetic field as the inductor stores and releases magnetic energy. The antenna of the measurement- acquisition system is switched from a transmitting to a receiving mode to acquire the magnetic-field response of the sensor. The rectified amplitude of the received response is compared to previous responses to prior transmitted harmonics, to ascertain if the measurement system has detected a response inflection. The "transmit-receive-compare" of sequential harmonics is repeated until the inflection is identified. The harmonic producing the amplitude inflection is the sensor resonant frequency. Resonant frequency and response amplitude are stored and then correlated to calibration data.
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 engines is to decompose a CFD-generated flow field into its harmonic components, and to then perform a frequency response analysis at the problematic natural frequencies. 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. A substantial effort has been made to account for this denser spatial Fourier content in frequency response analysis (described in another paper by the author), 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. Six loading cases were generated by varying a baseline harmonic excitation in different ways based upon cold-flow testing from Heritage Fuel Air Turbine Test. It was hypothesized that the randomness and other variation from the standard harmonic excitation would reduce the blade structural response, but the results showed little reduction. The second study was of a realistic model of a bladed-disk excited by the same CFD used in the J2X engine program. It was hypothesized that enforcing periodicity in the CFD (inherent in the frequency response technique) would overestimate the response. The results instead showed that the transient analysis results were up to 10% higher for "clean" nodal diameter excitations and six times larger for "messy" excitations, where substantial Fourier content around the main harmonic exists. Because the bulk of resonance problems are due to the "clean" excitations, a 10% underprediction is not necessarily a problem, especially since the average response in the transient is similar to the frequency response result, and so in a realistic finite life calculation, the life would be same. However, in the rare cases when the "messy" excitations harmonics are identified as the source of potential resonance concerns, this research does indicate that frequency response analysis is inadequate for accurate characterization of blade structural capability.