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DOE OSTI2025

Discrete fracture network model benchmarks developed and applied in a DECOVALEX-2023 repository performance assessment study

This study presents newly developed benchmarks for modeling flow and transport within discrete fracture networks (DFNs) and useful methods for analyzing the results. The new benchmarks are designed to test modeling approaches for use in probabilistic performance assessment models of deep geologic repositories in fractured rock. The benchmarks simulate flow and transport through a 1 km 3 block of fractured rock. The first simulates migration of a short pulse of tracer through a simple network of four intersecting fractures. The second adds 1089 stochastically generated fractures. The third changes the pulse to a continuous point source. Evaluation of model performance relies on moment analysis and comparison of the results of different models. The expected nondimensional first moment of the conservative tracer for each benchmark is 1. The benchmarks were simulated by teams from Canada, Czechia, Germany, Korea, Sweden, Taiwan, and the United States as part of a DECOVALEX-2023 study (decovalex.org). The teams used various approaches, including explicit DFN modeling, DFN upscaling to an equivalent continuous porous medium (ECPM), and a combination of both methods. Transport mechanisms are modeled using either the advection-dispersion equation or particle tracking. Results demonstrate strong agreement among the models in breakthrough behavior up to the 75th percentile. Significant deviations in first moments and well-clustered outputs led to the identification of inaccuracies in several models. Such findings exemplify the benefit of exercising these benchmarks and using the presented methods to test DFN flow and transport models.

Benchmark↗

NASA NTRS1984

Statistical tests of additional plate boundaries from plate motion inversions

The application of the F-ratio test, a standard statistical technique, to the results of relative plate motion inversions has been investigated. The method tests whether the improvement in fit of the model to the data resulting from the addition of another plate to the model is greater than that expected purely by chance. This approach appears to be useful in determining whether additional plate boundaries are justified. Previous results have been confirmed favoring separate North American and South American plates with a boundary located beween 30 N and the equator. Using Chase's global relative motion data, it is shown that in addition to separate West African and Somalian plates, separate West Indian and Australian plates, with a best-fitting boundary between 70 E and 90 E, can be resolved. These results are generally consistent with the observation that the Indian plate's internal deformation extends somewhat westward of the Ninetyeast Ridge. The relative motion pole is similar to Minster and Jordan's and predicts the NW-SE compression observed in earthquake mechanisms near the Ninetyeast Ridge.

Stein, S.↗

NASA NTRS1992

Evolution of a magnetic flux tube in two-dimensional penetrative convection

Highly supercritical compressible convection is simulated in a two-dimensional domain in which the upper half is unstable to convection while the lower half is stably stratified. This configuration is an idealization of the layers near the base of the solar convection zone. Once the turbulent flow is well developed, a toroidal magnetic field B sub tor is introduced to the stable layer. The field's evolution is governed by an advection-diffusion-type equation, and the Lorentz force does not significantly affect the flow. After many turnover times the field is stratified such that the absolute value of B sub tor/rho is approximately constant in the convective layer, where rho is density, while in the stable layer this ratio decreases linearly with depth. Consequently most of the magnetic flux is stored in the overshoot layer. The inclusion of rotation leads to travelling waves which transport magnetic flux latitudinally in a manner reminiscent of the migrations seen during the solar cycle.

Jennings, R. L.↗

DOE OSTI2022

Improving Common PV Module Temperature Models by Incorporating Radiative Losses to the Sky

PV module operating temperature is the second-most important factor influencing PV system yield–after irradiance–and a substantial contributor to uncertainty in energy system yield predictions. Models commonly used to predict operating temperature in system simulations are based on a simplified energy balance that lumps together different heat loss mechanisms–including radiation–and assumes an overall linear behavior. Radiative heat loss to the sky is usually substantial, but modeling it accurately requires additional information about down-welling long-wave radiation or sky temperature and increases the complexity of temperature model equations. In this work we show how radiative losses to the sky can be separated into two parts to improve the accuracy of modeling without additional complexity. We also predict and demonstrate the variation of these losses at different tilt angles and show that the effective view factor is reduced by the non- isotropic distribution of down-welling long-wave radiation. Finally, we demonstrate substantial reduction in bias (MBE) and scatter (RMSE) when the new radiative loss term is added to the Faiman model using one year of measurements at Sandia National Labs.

14 SOLAR ENERGY↗

NASA NTRS1984

Error analysis and correction of discrete solutions from finite element codes

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

Thurston, G. A.↗

DOE OSTI2021

MoorPy (Quasi-Static Mooring Analysis in Python)

MoorPy is a quasi-static mooring model and a suite of associated functions for mooring system analysis. The core model supports quasi-static analysis of moored floating systems including any arrangement of mooring lines and floating platforms. It solves the distributed position and tension of each mooring line segment using standard catenary equations. Floating platforms can be represented with linear hydrostatic characteristics. MoorPy automatically computes a floating system's equilibrium state and can be queried to identify a mooring system's nonlinear force-displacement relationships. Linearized stiffness matrices are efficiently computed using semi-analytic Jacobians. MoorPy also includes plotting functions and a library of mooring component property and cost coefficients. MoorPy can be used directly from Python scripts to perform mooring design and analysis tasks, or it can be coupled with other tools to compute quasi-static mooring reactions as part of a larger simulation.

Hall, Mathew↗

NASA NTRS2011

Assessing the Age of an Asteroid's Surface with Data from the International Rosetta Mission

Rosetta is an international mission led by the European Space Agency (ESA) with key support and instrumentation from the National Aeronautics and Space Administration (NASA). Rosetta is currently on a ten-year mission to catch comet 67P/Churyumov-Gerasimenko (C-G); throughout its voyage, the spacecraft has performed flybys of two main belt asteroids (MBA): Steins and Lutetia. Data on the physical, chemical, and geological properties of these asteroids are currently being processed and analyzed. Accurate interpretation of such data is fundamental in the success of Rosetta's mission and overall objectives. Post-flyby data analyses strive to correlate the size, shape, volume, and rotational rate of Lutetia, in addition to interpreting its multi-color imagining, albedo, and spectral mapping. Although advancements in science have contributed to the examination of celestial bodies, methods to analyze asteroids remain largely empirical, not semi-empirical, nor ab initio. This study aims to interpret and document the scientific methods currently utilized in the characterization of asteroid (21) Lutetia in order to render these processes and methods accessible to the public. Examples include a standardized technique for assessing the age of an asteroid surface, complete with clickable reference maps, methodology of grouping surface characteristics together, and a standardized power law equation for the age. Other examples include determining the density of an object. Context for what both density and age mean is a bi-product of this study. Results of the study will aid in the development of pedagogical material on asteroids for public use, and in creation of an academic database for selected targets that might be used as a reference.

asteriods↗

NASA NTRS2013

Approach to Integrate Global-Sun Models of Magnetic Flux Emergence and Transport for Space Weather Studies

The Sun lies at the center of space weather and is the source of its variability. The primary input to coronal and solar wind models is the activity of the magnetic field in the solar photosphere. Recent advancements in solar observations and numerical simulations provide a basis for developing physics-based models for the dynamics of the magnetic field from the deep convection zone of the Sun to the corona with the goal of providing robust near real-time boundary conditions at the base of space weather forecast models. The goal is to develop new strategic capabilities that enable characterization and prediction of the magnetic field structure and flow dynamics of the Sun by assimilating data from helioseismology and magnetic field observations into physics-based realistic magnetohydrodynamics (MHD) simulations. The integration of first-principle modeling of solar magnetism and flow dynamics with real-time observational data via advanced data assimilation methods is a new, transformative step in space weather research and prediction. This approach will substantially enhance an existing model of magnetic flux distribution and transport developed by the Air Force Research Lab. The development plan is to use the Space Weather Modeling Framework (SWMF) to develop Coupled Models for Emerging flux Simulations (CMES) that couples three existing models: (1) an MHD formulation with the anelastic approximation to simulate the deep convection zone (FSAM code), (2) an MHD formulation with full compressible Navier-Stokes equations and a detailed description of radiative transfer and thermodynamics to simulate near-surface convection and the photosphere (Stagger code), and (3) an MHD formulation with full, compressible Navier-Stokes equations and an approximate description of radiative transfer and heating to simulate the corona (Module in BATS-R-US). CMES will enable simulations of the emergence of magnetic structures from the deep convection zone to the corona. Finally, a plan will be summarized on the development of a Flux Emergence Prediction Tool (FEPT) in which helioseismology-derived data and vector magnetic maps are assimilated into CMES that couples the dynamics of magnetic flux from the deep interior to the corona.

Mansour, Nagi N.↗

DOE OSTI2024

Efficient Modeling of Floating Wind Arrays Including Current Loads and Seabed Bathymetry

Capabilities for modeling the effects of seabed bathymetry and current drag loads on a floating wind farm are now available in an open-source model for quasi-static analysis. In this model, mooring lines and dynamic cables are represented by a quasi-static solver that can quickly represent complex mooring/cabling arrangements and arrays of floating bodies. To account for seabed bathymetry, we expand the model to include a surface mesh that captures changes in water depth over a rectangular grid. We formulate modifications to the catenary equations that capture a mooring line's profile and tensions when contacting a slope seabed. To account for current drag loads on mooring lines and dynamic cables, we formulate a novel technique that rotates the reference frame so that the vector sum of the the weight and the current force are used in the catenary equations, while accounting for the seabed orientation. To complete the system, current drag loads on floating substructures are handled by inclusion of strip-theory drag calculations. These new capabilities are verified by comparing with results from the established offshore dynamics models MoorDyn and OrcaFlex in equivalent steady-state scenarios. The results show very good agreement for both sloped seabeds and current loads. With computation times of the quasi-static model typically under one second, the model additions are a useful capability toward rapidly evaluating a floating wind array's response to environmental loads under realistic site conditions.

bathymetry↗

DOE OSTI2024

Efficient Modeling of Floating Wind Arrays Including Current Loads and Seabed Bathymetry: Preprint

Capabilities for modeling the effects of seabed bathymetry and current drag loads on a floating wind farm are now available in an open-source model for quasi-static analysis. In this model, mooring lines and dynamic cables are represented by a quasistatic solver that can quickly represent complex mooring/cabling arrangements and arrays of floating bodies. To account for seabed bathymetry, we expand the model to include a surface mesh that captures changes in water depth over a rectangular grid. We formulate modifications to the catenary equations that capture a mooring line's profile and tensions when contacting a slope seabed. To account for current drag loads on mooring lines and dynamic cables, we formulate a novel technique that rotates the reference frame so that the vector sum of the the weight and the current force are used in the catenary equations, while accounting for the seabed orientation. To complete the system, current drag loads on floating substructures are handled by inclusion of strip-theory drag calculations. These new capabilities are verified by comparing with results from the established offshore dynamics models MoorDyn and OrcaFlex in equivalent steady-state scenarios. The results show very good agreement for both sloped seabeds and current loads. With computation times of the quasi-static model typically under one second, the model additions are a useful capability toward rapidly evaluating a floating wind array's response to environmental loads under realistic site conditions.

bathymetry↗

NASA NTRS1998

Structure and Dynamics of the Solar Chromosphere

The problem of chromospheric dynamics and heating consists of two problems: one, concerning the magnetic network on the boundary of supergranulation cells (CB), where the oscillation period is seven minutes, and the other, concerning the cell interior (CI), where the oscillation period is three minutes. The observational data on the oscillations and the emission of radiation can be used to determine the structure and dynamics of the atmosphere provided answers are known to three critical questions, concerning: the nature of the waves powering the bright points, the origin of the observed oscillation periods and the mechanism of chromospheric heating. The recent modeling of the dynamics of the CI, which combines a sophisticated treatment of gas dynamics and radiative transfer in a one-dimensional model with empirical velocity input from the observations, answered the first of these questions: the waves powering K(sub 2upsilon), bright points are propagating acoustic waves. This firm conclusion declares invalid the model of Leibacher & Stein, which explains the observed period with standing acoustic waves in a chromospheric cavity. On the third question, the heating of the chromosphere in the CI, their model predicts that the temperature in the chromosphere is declining in the outward direction up to a height of at least I Mm most of the time, so even the time-average temperature is dropping monotonically in the outward direction, implying that lines formed in the chromosphere up to a height of at least 1 Mm appear in absorption most of the time and everywhere in the CI. The problem of the CI can be resolved with a two-component model, which combines a model for K(sub 2upsilon), bright points with a model for the background. The bright point model has the same aims as the CS94 model, except that the empirical driving from the LRK93 observations is replaced by impulsive excitation, as suggested by the properties of the Klein-Gordon equation.

Kalkofen, Wolfgang↗

NASA NTRS1978

Application of a trigonometric finite difference procedure to numerical analysis of compressive and shear buckling of orthotropic panels

A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.

Stein, M.↗

DOE OSTI2021

New Perspectives on the Exoplanet Radius Gap from a Mathematica Tool and Visualized Water Equation of State

Recent astronomical observations obtained with the Kepler and TESS missions and their related ground-based follow-ups revealed an abundance of exoplanets with a size intermediate between Earth and Neptune (1 R ⊕ ≤ R ≤ 4 R ⊕ ). A low occurrence rate of planets has been identified at around twice the size of Earth (2 × R ⊕ ), known as the exoplanet radius gap or radius valley. We explore the geometry of this gap in the mass–radius diagram, with the help of a Mathematica plotting tool developed with the capability of manipulating exoplanet data in multidimensional parameter space, and with the help of visualized water equations of state in the temperature–density (T–ρ) graph and the entropy–pressure (s–P) graph. We show that the radius valley can be explained by a compositional difference between smaller, predominantly rocky planets (<2 × R ⊕ ) and larger planets (>2 × R ⊕ ) that exhibit greater compositional diversity including cosmic ices (water, ammonia, methane, etc.) and gaseous envelopes. In particular, among the larger planets (>2 × R ⊕ ), when viewed from the perspective of planet equilibrium temperature (T eq ), the hot ones (T eq ≳ 900 K) are consistent with ice-dominated composition without significant gaseous envelopes, while the cold ones (T eq ≲ 900 K) have more diverse compositions, including various amounts of gaseous envelopes.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1993

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

This paper presents work performed on the generation and physics of acoustic waves in the solar atmosphere. The investigators have incorporated spatial and temporal turbulent energy spectra in a newly corrected version of the Lighthill-Stein theory of acoustic wave generation in order to calculate the acoustic wave energy fluxes generated in the solar convective zone. The investigators have also revised and improved the treatment of the generation of magnetic flux tube waves, which can carry energy along the tubes far away from the region of their origin, and have calculated the tube energy fluxes for the sun. They also examine the transfer of the wave energy originated in the solar convective zone to the outer atmospheric layers through computation of wave propagation and dissipation in highly nonhomogeneous solar atmosphere. These waves may efficiently heat the solar atmosphere and the heating will be especially significant in the chromospheric network. It is also shown that the role played by Alfven waves in solar wind acceleration and coronal hole heating is dominant. The second part of the project concerned investigation of wave propagation in highly inhomogeneous stellar atmospheres using an approach based on an analytic tool developed by Musielak, Fontenla, and Moore. In addition, a new technique based on Dirac equations has been developed to investigate coupling between different MHD waves propagating in stratified stellar atmospheres.

Musielak, Z. E.↗

NASA NTRS1994

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

This paper presents work performed on the generation and physics of acoustic waves in the solar atmosphere. The investigators have incorporated spatial and temporal turbulent energy spectra in a newly corrected version of the Lighthill-Stein theory of acoustic wave generation in order to calculate the acoustic wave energy fluxes generated in the solar convective zone. The investigators have also revised and improved the treatment of the generation of magnetic flux tube waves, which can carry energy along the tubes far away from the region of their origin, and have calculated the tube wave energy fluxes for the sun. They also examine the transfer of the wave energy originated in the solar convective zone to the outer atmospheric layers through computation of wave propagation and dissipation in highly nonhomogeneous solar atmosphere. These waves may efficiently heat the solar atmosphere and the heating will be especially significant in the chromospheric network. It is also shown that the role played by Alfven waves in solar wind acceleration and coronal hole heating is dominant. The second part of the project concerned investigation of wave propagation in highly inhomogeneous stellar atmospheres using an approach based on an analytic tool developed by Musielak, Fontenla, and Moore. In addition, a new technique based on Dirac equations has been developed to investigate coupling between different MHD waves propagating in stratified stellar atmospheres.

Musielak, Z. E.↗

NASA NTRS1985

Effects of transverse shearing on cylindrical bending, vibration, and buckling of laminated plates

The displacements for cylindrical bending and stretching of laminated and thick plates are expressed through-the-thickness by a few algebraic terms and a complete set of trigonometric terms. Only a few terms of this series are needed to get sufficiently accurate results for laminated and thick plates. Equations of equilibrium based on a sufficient number of terms of this series for displacements are determined using variational theorems from three-dimensional elasticity. Several examples are worked out. The displacements and stresses are obtained for simply supported isotropic and layered beams with a rectangular cross section and a sinusoidal lateral load distribution. These results are compared to an exact elasticity solution. Results for several approximations are obtained for a simply supported and a clamped beam with a rectangular cross section loaded at the center and results are compared to experimental results. Results are also obtained for isotropic and layered beams with a rectangular cross section for several approximations for the lowest natural frequency and buckling load.

Stein, M.↗

DOE OSTI2022

Long-term impact of light- and elevated temperature-induced degradation on photovoltaic arrays

Low levelized cost of electricity (LCOE) has been identified as critical for widespread adoption of photovoltaics (PV) without subsidies. Maintaining decades-long high-energy production is often an under-recognized opportunity in meeting cost goals because component lifetimes are not fully quantified at the time of manufacture. Whereas certain standardized tests minimize risk of early failure, there is little guidance to quantitatively predict degradation (or lack thereof) over decades, based on accelerated tests. In this article, we move toward bridging the understanding between indoor accelerated tests and outdoor performance data, with the goal of predicting energy yield with enough accuracy to inform financial decisions. Light- and elevated temperature-induced degradation (LETID) in p-type Si modules is analyzed in terms of impact on long-term module performance and thus LCOE. A method to predict the progression of LETID, using fixed kinetic constants and a numerical solution to the basic reaction rate equations, is detailed. Predictions are compared against both published data and that new to this study. These data include both indoor accelerated tests and fielded modules. We use the results in financial models to derive LCOE of modules in different climates with varying amounts of LETID, including uncertainty. Cost models based on the predictions indicate that LETID has a significant and climate-dependent impact on LCOE. Finally, we show that - even given the uncertainties identified in the study - these financial calculations can provide useful guidance to quantify risk based on accelerated test results. The analysis serves as an example of developing a predictive approach to PV reliability using physics of failure.

14 SOLAR ENERGY↗

NASA NTRS1947

Critical stress of thin-walled cylinders in axial compression

Empirical design curves are presented for the critical stress of thin-walled cylinders loaded in axial compression. These curves are plotted in terms of nondimensional parameters of small-deflection theory and are compared with theoretical curves derived for the buckling of cylinders with simply supported and clamped edges. An empirical equation is given for the buckling of cylinders having a length-radius ratio greater than about 0.75. The test data obtained from various sources follow the general trend of the theoretical curve for cylinders with clamped edges, agreeing closely with the theory in the case of short cylinders, but falling considerably below the theoretical results for long cylinders. The discrepancy in the case of long cylinders increases with increasing values of the ratio of radius to wall thickness. Plotting curves for different values of this ratio reduces the scatter in the test data and a certain degree of correlation with theory is achieved. Advantage is taken of this correlation to obtain estimated design curves for cylinders with simply supported edges, for which little experimental information is available. (author)

Batdorf, S B↗