Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “nonlinear term basis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

90 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations

Considerable progress over the past thirty years has been made in the development of large-scale computational fluid dynamics (CFD) solvers for the Euler and Navier-Stokes equations. Computations are used routinely to design the cruise shapes of transport aircraft through complex-geometry simulations involving the solution of 25-100 million equations; in this arena the number of wind-tunnel tests for a new design has been substantially reduced. However, simulations of the entire flight envelope of the vehicle, including maximum lift, buffet onset, flutter, and control effectiveness have not been as successful in eliminating the reliance on wind-tunnel testing. These simulations involve unsteady flows with more separation and stronger shock waves than at cruise. The main reasons limiting further inroads of CFD into the design process are: (1) the reliability of turbulence models; and (2) the time and expense of the numerical simulation. Because of the prohibitive resolution requirements of direct simulations at high Reynolds numbers, transition and turbulence modeling is expected to remain an issue for the near term. The focus of this paper addresses the latter problem by attempting to attain optimal efficiencies in solving the governing equations. Typically current CFD codes based on the use of multigrid acceleration techniques and multistage Runge-Kutta time-stepping schemes are able to converge lift and drag values for cruise configurations within approximately 1000 residual evaluations. An optimally convergent method is defined as having textbook multigrid efficiency (TME), meaning the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in the discretized system of equations (residual equations). In this paper, a distributed relaxation approach to achieving TME for Reynolds-averaged Navier-Stokes (RNAS) equations are discussed along with the foundations that form the basis of this approach. Because the governing equations are a set of coupled nonlinear conservation equations with discontinuities (shocks, slip lines, etc.) and singularities (flow- or grid-induced), the difficulties are many. This paper summarizes recent progress towards the attainment of TME in basic CFD simulations.

Brandt, Achi↗
DOE OSTI2020

A hybrid calibration approach to Hertz-type contact parameters for discrete element models

This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. Here, the proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.

Constitutive law↗
NASA NTRS2013

An Exposition on the Nonlinear Kinematics of Shells, Including Transverse Shearing Deformations

An in-depth exposition on the nonlinear deformations of shells with "small" initial geometric imperfections, is presented without the use of tensors. First, the mathematical descriptions of an undeformed-shell reference surface, and its deformed image, are given in general nonorthogonal coordinates. The two-dimensional Green-Lagrange strains of the reference surface derived and simplified for the case of "small" strains. Linearized reference-surface strains, rotations, curvatures, and torsions are then derived and used to obtain the "small" Green-Lagrange strains in terms of linear deformation measures. Next, the geometry of the deformed shell is described mathematically and the "small" three-dimensional Green-Lagrange strains are given. The deformations of the shell and its reference surface are related by introducing a kinematic hypothesis that includes transverse shearing deformations and contains the classical Love-Kirchhoff kinematic hypothesis as a proper, explicit subset. Lastly, summaries of the essential equations are given for general nonorthogonal and orthogonal coordinates, and the basis for further simplification of the equations is discussed.

Nemeth, Michael P.↗
DOE OSTI2021

Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pressure head), and these equations are coupled to one another by transfer terms. On its own, Richards equation is already a nonlinear partial differential equation, and it is exceedingly difficult to solve numerically due to the extra nonlinear dependencies involving the soil water. To deal with multiple scales, our strategy is that starting from a microscopic scale, we upscale the coupled system of dual-continuum Richards equations via homogenization by the two-scale asymptotic expansion, to obtain a homogenized system, at an intermediate scale (level). Based on a hierarchical approach, the homogenization’s effective coefficients are computed through solving the arising cell problems. Furthermore, to tackle the nonlinearity, after time discretization, we use Picard iteration procedure for linearization of the homogenized Richards equations. At each Picard iteration, some degree of multiscale still remains from the intermediate level, so we utilize the generalized multiscale finite element method (GMsFEM) combining with a multi-continuum approach, to upscale the homogenized system to a macroscopic (coarse-grid) level. This scheme involves building uncoupled and coupled multiscale basis functions, which are used not only to construct coarse-grid solution approximation with high accuracy but also (with the coupled multiscale basis) to capture the interactions among continua. These prospects and convergence are demonstrated by several numerical results for the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

In Situ UV–vis Quantification of Chlorobasicity in Binary Molten Chlorides

Optical basicity measurements provide a basis for determining the relative chlorobasicity of a given molten salt composition. This study uses Bi3+ as a spectroscopic probe to investigate optical basicity across three binary molten chloride systems (LiCl-KCl, MgCl2–KCl, and ZnCl2–KCl) through in situ UV–vis spectroscopy measurements of the 1S0→3P1 transition. LiCl-KCl systems exhibit the highest optical basicity with minimal compositional dependence, while both divalent systems show stronger, yet nonlinear, dependence that is reminiscent of acid–base titration curves. The influence of cation electronegativity and polarizing power (Li+ < Mg2+ < Zn2+) directly reflects the basicity curves, with ZnCl2–KCl displaying the steepest gradients and lowest basicity values. Nonlinear dependencies in divalent systems indicate formation of chloride-bridged network structures with coordination states dictated by the amount of KCl in a salt composition, which was further investigated and validated by molecular dynamics simulations of polymeric structures formed in ZnCl2 and MgCl2-based salts using machine learning force fields. The temperature dependence of chlorobasicity in terms of optical basicity was investigated, and a loose, positive correlation between the two was revealed. These findings establish Bi3+ as a sensitive probe for understanding electronic environments in molten chloride systems and provide insights for predicting the chemical behavior of molten salts for use in high-temperature environments.

Buttice, Kailee [Department of Nuclear Engineering↗
DOE OSTI2020

Data-driven recovery of hidden physics in reduced order modeling of fluid flows

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Furthermore, our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

42 ENGINEERING↗
DOE OSTI2023

Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures

Quantum mechanical calculations for material modeling using Kohn–Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for N smallest eigenvector-eigenvalue pairs, with N proportional to the number of electrons in the material system. Here, these calculations are computationally demanding and have asymptotic cubic scaling complexity with the number of electrons. Large-scale matrix eigenvalue problems arising from the discretization of the Kohn–Sham DFT equations employing a systematically convergent basis traditionally rely on iterative orthogonal projection methods, which are shown to be computationally efficient and scalable on massively parallel computing architectures. However, as the size of the material system increases, these methods are known to incur dominant computational costs through the Rayleigh–Ritz projection step of the discretized Kohn–Sham Hamiltonian matrix and the subsequent subspace diagonalization of the projected matrix. This work explores the potential of polynomial expansion approaches based on recursive Fermi-operator expansion as an alternative to the subspace diagonalization of the projected Hamiltonian matrix to reduce the computational cost. Subsequently, we perform a detailed comparison of various recursive polynomial expansion approaches to the traditional approach of explicit diagonalization on both multi-node central processing unit and graphics processing unit architectures and assess their relative performance in terms of accuracy, computational efficiency, scaling behavior, and energy efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1991

Robust and real-time control of magnetic bearings for space engines

Currently, NASA Lewis Research Center is developing magnetic bearings for Space Shuttle Main Engine (SSME) turbopumps. The control algorithms which have been used are based on either the proportional-intergral-derivative control (PID) approach or the linear quadratic (LQ) state space approach. These approaches lead to an acceptable performance only when the system model is accurately known, which is seldom true in practice. For example, the rotor eccentricity, which is a major source of vibration at high speeds, cannot be predicted accurately. Furthermore, the dynamics of a rotor shaft, which must be treated as a flexible system to model the elastic rotor shaft, is infinite dimensional in theory and the controller can only be developed on the basis of a finite number of modes. Therefore, the development of the control system is further complicated by the possibility of closed loop system instability because of residual or uncontrolled modes, the so called spillover problem. Consequently, novel control algorithms for magnetic bearings are being developed to be robust to inevitable parametric uncertainties, external disturbances, spillover phenomenon and noise. Also, as pointed out earlier, magnetic bearings must exhibit good performance at a speed over 30,000 rpm. This implies that the sampling period available for the design of a digital control system has to be of the order of 0.5 milli-seconds. Therefore, feedback coefficients and other required controller parameters have to be computed off-line so that the on-line computational burden is extremely small. The development of the robust and real-time control algorithms is based on the sliding mode control theory. In this method, a dynamic system is made to move along a manifold of sliding hyperplanes to the origin of the state space. The number of sliding hyperplanes equals that of actuators. The sliding mode controller has two parts; linear state feedback and nonlinear terms. The nonlinear terms guarantee that the systems would reach the intersection of all sliding hyperplanes and remain on it when bounds on the errors in the system parameters and external disturbances are known. The linear part of the control drives the system to the origin of state space. Another important feature is that the controller parameter can be computed off-line. Consequently, on-line computational burden is small.

Sinha, Alok↗
DOE OSTI2021

A domain wall-magnetic tunnel junction artificial synapse with notched geometry for accurate and efficient training of deep neural networks

Inspired by the parallelism and efficiency of the brain, several candidates for artificial synapse devices have been developed for neuromorphic computing, yet a nonlinear and asymmetric synaptic response curve precludes their use for backpropagation, the foundation of modern supervised learning. Spintronic devices—which benefit from high endurance, low power consumption, low latency, and CMOS compatibility—are a promising technology for memory, and domain-wall magnetic tunnel junction (DW-MTJ) devices have been shown to implement synaptic functions such as long-term potentiation and spike-timing dependent plasticity. In this work, we propose a notched DW-MTJ synapse as a candidate for supervised learning. Using micromagnetic simulations at room temperature, we show that notched synapses ensure the non-volatility of the synaptic weight and allow for highly linear, symmetric, and reproducible weight updates using either spin transfer torque (STT) or spin–orbit torque (SOT) mechanisms of DW propagation. We use lookup tables constructed from micromagnetics simulations to model the training of neural networks built with DW-MTJ synapses on both the MNIST and Fashion-MNIST image classification tasks. Accounting for thermal noise and realistic process variations, the DW-MTJ devices achieve classification accuracy close to ideal floating-point updates using both STT and SOT devices at room temperature and at 400 K. Our work establishes the basis for a magnetic artificial synapse that can eventually lead to hardware neural networks with fully spintronic matrix operations implementing machine learning.

42 ENGINEERING↗
NASA NTRS2005

Advanced Small Perturbation Potential Flow Theory for Unsteady Aerodynamic and Aeroelastic Analyses

An advanced small perturbation (ASP) potential flow theory has been developed to improve upon the classical transonic small perturbation (TSP) theories that have been used in various computer codes. These computer codes are typically used for unsteady aerodynamic and aeroelastic analyses in the nonlinear transonic flight regime. The codes exploit the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The new ASP theory was developed methodically by first determining the essential elements required to produce full-potential-like solutions with a small perturbation approach on the requisite Cartesian grid. This level of accuracy required a higher-order streamwise mass flux and a mass conserving surface boundary condition. The ASP theory was further developed by determining the essential elements required to produce results that agreed well with Euler solutions. This level of accuracy required mass conserving entropy and vorticity effects, and second-order terms in the trailing wake boundary condition. Finally, an integral boundary layer procedure, applicable to both attached and shock-induced separated flows, was incorporated for viscous effects. The resulting ASP potential flow theory, including entropy, vorticity, and viscous effects, is shown to be mathematically more appropriate and computationally more accurate than the classical TSP theories. The formulaic details of the ASP theory are described fully and the improvements are demonstrated through careful comparisons with accepted alternative results and experimental data. The new theory has been used as the basis for a new computer code called ASP3D (Advanced Small Perturbation - 3D), which also is briefly described with representative results.

Batina, John T.↗
DOE OSTI2023

Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration

The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a controllable way, but unfavorable combinatorics often defeats this in practice and applications with n ≥ 4 are rare. Here, we outline an algorithm to overcome this combinatorial bottleneck, based on a bottom-up approach to energy-based screening. This is implemented within a new open-source software application (“Fragme∩t”), which is integrated with a lightweight semi-empirical method that is used to cull subsystems, attenuating the combinatorial growth of higher-order terms in the graph that is used to manage the calculations. This facilitates applications of unprecedented size, and we report four-body calculations in (H2O)64 clusters that afford relative energies within 0.1 kcal/mol/monomer of the supersystem result using less than 10% of the unique subsystems. We also report n-body calculations in (H2O)20 clusters up to n = 8, at which point the expansion terminates naturally due to screening. These are the largest n-body calculations reported to date using ab initio electronic structure theory, and they confirm that high-order n-body terms are mostly artifacts of basis-set superposition error.

Chemistry↗
DOE OSTI2024

Robust Tensor Hypercontraction of the Particle–Particle Ladder Term in Equation-of-Motion Coupled Cluster Theory

One method of representing a high-rank tensor as a (hyper-)product of lower-rank tensors is the tensor hypercontraction (THC) method of Hohenstein et al. This strategy has been found to be useful for reducing the polynomial scaling of coupled-cluster methods by representation of a four-dimensional tensor of electron-repulsion integrals in terms of five two-dimensional matrices. Pierce et al. have already shown that the application of a robust form of THC to the particle–particle ladder (PPL) term reduces the cost of this term in couple-cluster singles and doubles (CCSD) from O(N 6 ) to O(N 5 ) with negligible errors in energy with respect to the density-fitted variant. In this work, we have implemented the least-squares variant of THC (LS-THC) which does not require a nonlinear tensor factorization, including the robust form (R-LS-THC), for the calculation of the excitation and electron attachment energies using equation-of-motion coupled cluster methods EOMEE-CCSD and EOMEA-CCSD, respectively. We have benchmarked the effect of the R-LS-THC-PPL approximation on excitation energies using the comprehensive QUEST database and the accuracy of electron attachment energies using the NAB22 database. Here, we find that errors on the order of 1 meV are achievable with a reduction in total calculation time of approximately 5x.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2004

Numerical Simulation of Waves Driven by Plasma Currents Generated by Low-Frequency Alfven Waves in a Multi-Ion Plasma

When multi-ion plasma consisting of heavy and light ions is permeated by a low-frequency Alfven (LFA) wave, the crossed-electric-and-magnetic field (E x B), and the polarization drifts of the different ion species and the electrons could be quite different. The relative drifts between the charged-particle species drive waves, which energize the plasma. Using 2.5-dimensional (2.5-D) particle-in-cell simulations, we study this process of wave generation and its nonlinear consequences in terms of acceleration and heating plasma. Specifically, we study the situation for LFA wave frequency being lower than the heavy-ion cyclotron frequency in a multi-ion plasma. We impose such a wave to the plasma assuming that its wavelength is much larger than that of the waves generated by the relative drifts. For better understanding, the LFA-wave driven simulations are augmented by those driven by initialized ion beams. The driven high-frequency (HF) wave modes critically depend on the heavy ion density nh; for small values of nh, the lower hybrid (LH) waves dominate. On the other hand, for large nh a significantly enhanced level of waves occurs over a much broader frequency spectrum below the LH frequency and such waves are interpreted here as the ion Bernstein (IB) mode near the light ion cyclotron harmonics. Irrespective of the driven wave modes, both the light and heavy ions undergo significant transverse acceleration, but for the large heavy-ion densities, even the electrons are significantly accelerated in the parallel direction by the waves below the LH frequency. Even when the LFA wave drive is maintained, the ion heating leads to the cessation of HF wave excitation just after a few cycles of the former wave. On the basis of marginal stability seen in the simulations, an empirical relation for LFA wave amplitude, frequency and ion temperature is given.

Singh, Nagendra↗
NASA NTRS2009

Performance of MODIS Thermal Emissive Bands On-orbit Calibration Algorithms

Two nearly identical copies of the Moderate Resolution Imaging Spectroradiometer (MODIS) are currently operated on-board the Terra and Aqua spacecrafts, launched in December 1999 and May 2002, respectively. Together, they have produced an unprecedented amount of science data products, which are widely used for the studies of changes in the Earth's system of land, oceans, and atmosphere. MODIS is a cross-track scanning radiometer, which uses a two-sided scan mirror and collects data continuously over a wide scan angle range (+/-55 degree relative to the instrument nadir) each scan of 1.47 seconds. It has 36 spectral bands with wavelengths ranging from visible (VIS) to long-wave infrared (LWIR). MODIS bands 1-19 and 26 are the reflective solar bands (RSB) and bands 20-25 and 27-36 are the thermal emissive bands (TEB). MODIS was developed and designed with improvements made over its heritage sensors (such as AVHRR and Landsat) and, in particular, with more stringent calibration requirements. Because of this, MODIS was built with a set of state-of-art on-board calibrators (OBC), which include a solar diffuser (SD), a solar diffuser stability monitor (SDSM), a blackbody (BB), a spectroradiometric calibration assembly (SRCA), and a space view (SV) port. With the exception of view angle differences, MODIS OBC measurements and the Earth View (EV) observations are made via the same optical path. MODIS TEB have a total of 160 individual TEB detectors (10 per band), which are located on two cold focal plane assemblies (CFPA). For nominal on-orbit operation, the CFPA temperature is controlled at 83K via a passive radiative cooler. For the TEB, the calibration requirements at specified typical scene radiances are less than or equal to 1% with an exception for the fire detection (low gain) band. MODIS TEB on-orbit calibration is performed on a scan-by-scan basis using a quadratic calibration algorithm, and data collected from sensor responses to the onboard BB and SV. The BB serves as the thermal calibration source and the SV provides measurements for the sensor's background and offsets. MODIS on-board BB is a v-grooved plate with its temperature measured using 12 platinum resistive thermistors (PRT) uniformly embedded in the BB substrate. All the BB thermistors were characterized pre-launch with reference to the NIST temperature standards. Unlike typical BB operations in many heritage sensors, which have no temperature control capability, the MODIS on-board BB can be operated at any temperatures between instrument ambient (about 270K) and 315K and can also be varied continuously within this range. This feature has significantly enhanced the MODIS' capability of tracking and updating the TEB nonlinear calibration coefficients over its entire mission. Following a brief description of MODIS TEB on-orbit calibration methodologies and its onboard BB operational activities, this paper provides a comprehensive performance assessment of MODIS TEB quadratic calibration algorithm. It examines the scan-by-scan, orbit-by-orbit, daily, and seasonal variations of detector responses and associated impact due changes in the CFPA and instrument temperatures. Specifically, this paper will analyze the contribution by each individual thermal emissive source term (BB, scan cavity, and scan mirror), the impact on the Level 1 B data product quality due to pre-launch and on-orbit calibration uncertainties. A comparison of Terra and Aqua TEB on-orbit performance, lessons learned, and suggestions for future improvements will also be made.

Xiong, Xiaoxiong↗
NASA NTRS2010

Universal Decoder for PPM of any Order

A recently developed algorithm for demodulation and decoding of a pulse-position- modulation (PPM) signal is suitable as a basis for designing a single hardware decoding apparatus to be capable of handling any PPM order. Hence, this algorithm offers advantages of greater flexibility and lower cost, in comparison with prior such algorithms, which necessitate the use of a distinct hardware implementation for each PPM order. In addition, in comparison with the prior algorithms, the present algorithm entails less complexity in decoding at large orders. An unavoidably lengthy presentation of background information, including definitions of terms, is prerequisite to a meaningful summary of this development. As an aid to understanding, the figure illustrates the relevant processes of coding, modulation, propagation, demodulation, and decoding. An M-ary PPM signal has M time slots per symbol period. A pulse (signifying 1) is transmitted during one of the time slots; no pulse (signifying 0) is transmitted during the other time slots. The information intended to be conveyed from the transmitting end to the receiving end of a radio or optical communication channel is a K-bit vector u. This vector is encoded by an (N,K) binary error-correcting code, producing an N-bit vector a. In turn, the vector a is subdivided into blocks of m = log2(M) bits and each such block is mapped to an M-ary PPM symbol. The resultant coding/modulation scheme can be regarded as equivalent to a nonlinear binary code. The binary vector of PPM symbols, x is transmitted over a Poisson channel, such that there is obtained, at the receiver, a Poisson-distributed photon count characterized by a mean background count nb during no-pulse time slots and a mean signal-plus-background count of ns+nb during a pulse time slot. In the receiver, demodulation of the signal is effected in an iterative soft decoding process that involves consideration of relationships among photon counts and conditional likelihoods of m-bit vectors of coded bits. Inasmuch as the likelihoods of all the m-bit vectors of coded bits mapping to the same PPM symbol are correlated, the best performance is obtained when the joint mbit conditional likelihoods are utilized. Unfortunately, the complexity of decoding, measured in the number of operations per bit, grows exponentially with m, and can thus become prohibitively expensive for large PPM orders. For a system required to handle multiple PPM orders, the cost is even higher because it is necessary to have separate decoding hardware for each order. This concludes the prerequisite background information. In the present algorithm, the decoding process as described above is modified by, among other things, introduction of an lbit marginalizer sub-algorithm. The term "l-bit marginalizer" signifies that instead of m-bit conditional likelihoods, the decoder computes l-bit conditional likelihoods, where l is fixed. Fixing l, regardless of the value of m, makes it possible to use a single hardware implementation for any PPM order. One could minimize the decoding complexity and obtain an especially simple design by fixing l at 1, but this would entail some loss of performance. An intermediate solution is to fix l at some value, greater than 1, that may be less than or greater than m. This solution makes it possible to obtain the desired flexibility to handle any PPM order while compromising between complexity and loss of performance.

Moision, Bruce E.↗
DOE OSTI2025

Investigating the Role of Accident Tolerant Cladding on Source Term Reduction for High-Burnup PWRs Using MELCOR

The use of accident tolerant fuel (ATF) cladding can increase coping times during and beyond design basis accidents. While such gains may be incremental, they provide a margin that can potentially be recovered to enable high-burnup (HBU) operation. Realizing such a margin requires demonstrating that the combination of HBU and ATF has not led to an overall increase in source term. This study investigates the influence of cladding technology (Zr-based, Cr-coated Zr, and FeCrAl) and fuel cycle length (18 and 24 months) on radiological dose at the boundary of the exclusion zone for a four-loop pressurized water reactor to investigate whether ATF claddings can provide such benefits. We analyze a recovered large break loss-of-coolant accident scenario to investigate the impact of transient timescale on the benefits of such coping time increases. The simulations have been performed using the MELCOR and MELCOR Accident Consequence Code System codes. For the cases analyzed, increased fuel cycle length did not necessarily increase radionuclide release and hydrogen generation, as these were found to be sensitive to the core power distribution. Similarly, off-site dose consequence is dominated by short-lived radionuclides that tend to saturate earlier in the burnup, so higher burnup operation did not necessarily increase the source term for the phenomena and transients analyzed here. Delays in recovery of the lowpressure safety injection system increase hydrogen production and radionuclide release, especially between 780 s and 1620 s, due to the nonlinear oxidation and core degradation behavior. Results show that Cr-coated Zr enhances safety by delaying heatup and gap release. Here, when uncertainty propagation on oxidation properties is considered, FeCrAl exhibits the lowest overall radionuclide release and off-site dose throughout the spectrum. However, while the considered “base model” performance is superior under delayed injection scenarios, upper-bound cases display hydrogen generation risk comparable to the Zr-based cladding.

Accident Tolerant Fuel↗
NASA NTRS1995

Upper Thermosphere Winds and Temperatures in the Geomagnetic Polar Cap: Solar Cycle, Geomagnetic Activity, and Interplanetary Magnetic Field Dependencies

Ground-based Fabry-Perot interferometers located at Thule, Greenland (76.5 deg. N, 69.0 deg. W, lambda = 86 deg.) and at Sondre Stromfjord, Greenland (67.0 deg. N, 50.9 deg. W, lambda = 74 deg.) have monitored the upper thermospheric (approx. 240-km altitude) neutral wind and temperature over the northern hemisphere geomagnetic polar cap since 1983 and 1985, respectively. The thermospheric observations are obtained by determining the Doppler characteristics of the (OI) 15,867-K (630.0-nm) emission of atomic oxygen. The instruments operate on a routine, automatic, (mostly) untended basis during the winter observing seasons, with data coverage limited only by cloud cover and (occasional) instrument failures. This unique database of geomagnetic polar cap measurements now extends over the complete range of solar activity. We present an analysis of the measurements made between 1985 (near solar minimum) and 1991 (near solar maximum), as part of a long-term study of geomagnetic polar cap thermospheric climatology. The measurements from a total of 902 nights of observations are compared with the predictions of two semiempirical models: the Vector Spherical Harmonic (VSH) model of Killeen et al. (1987) and the Horizontal Wind Model (HWM) of Hedin et al. (1991). The results are also analyzed using calculations of thermospheric momentum forcing terms from the Thermosphere-ionosphere General Circulation Model TGCM) of the National Center for Atmospheric Research (NCAR). The experimental results show that upper thermospheric winds in the geomagnetic polar cap have a fundamental diurnal character, with typical wind speeds of about 200 m/s at solar minimum, rising to up to about 800 m/s at solar maximum, depending on geomagnetic activity level. These winds generally blow in the antisunward direction, but are interrupted by episodes of modified wind velocity and altered direction often associated with changes in the orientation of the Interplanetary Magnetic Field (IMF). The central polar cap (greater than approx. 80 magnetic latitude) antisunward wind speed is found to be a strong function of both solar and geomagnetic activity. The polar cap temperatures show variations in both solar and geomagnetic activity, with temperatures near 800 K for low K(sub p) and F(sub 10.7) and greater than about 2000 K for high K(sub p) and F(sub 10.7). The observed temperatures are significantly greater than those predicted by the mass spectrometer/incoherent scatter model for high activity conditions. Theoretical analysis based on the NCAR TIGCM indicates that the antisunward upper thermospheric winds, driven by upstream ion drag, basically 'coast' across the polar cap. The relatively small changes in wind velocity and direction within the polar cap are induced by a combination of forcing terms of commensurate magnitude, including the nonlinear advection term, the Coriolis term, and the pressure gradient force term. The polar cap thennospheric thermal balance is dominated by horizontal advection, and adiabatic and thermal conduction terms.

Killeen, T. L.↗
NASA NTRS2003

Preliminary Planar Formation: Flight Dynamics Near Sun-Earth L2 Point

NASA's Goddard Space Flight Center is planning a series of missions in the vicinity of the Sun-Earth L2 libration point. Some of these projects will involve a distributed space system of telescope spacecraft acting together as a single telescope for high-resolution. The individual telescopes will be configured in a plane, surrounding a hub, where the telescope plane can be aimed toward various astronomical targets of interest. In preparation for these missions, it is necessary to develop an improved understanding of the dynamical behavior of objects in a planar configuration near L2. The classical circular restricted three body problem is taken as the basis for the analysis. At first order, the motion of such a telescope relative to the hub is described by a system of linear second order differential equations. These equations are identical to the circular restricted problem's linear equations describing the hub motion about L2. Therefore, the fundamental frequencies, both parallel to and normal to the ecliptic plane, are the same for the relative telescope motion as for the hub motion. To maintain the telescope plane for the duration necessary for the planned observations, a halo-type orbit of the telescopes about the hub is investigated. By using a halo orbit, the individual telescopes remain in approximately the same plane over the observation duration. For such an orbit, the fundamental periods parallel to and normal to the ecliptic plane are forced to be the same by careful selection of the initial conditions in order to adjust the higher order forces. The relative amplitudes of the resulting oscillations are associated with the orientation of the telescope plane relative to the ecliptic. As in the circular restricted problem, initial conditions for the linearized equations must be selected so as not to excite the convergent or divergent linear modes. In a higher order analysis, the telescope relative motion equations include the effects of the position of the hub relative to L2. In this paper, the differential equations are developed through second order in the distance of the hub from the libration point. A modified Lindstedt-Poincad perturbation method is employed to construct the solution of these differential equations through that same order of magnitude. In the course of the solution process, relationships are determined between the initial conditions of the telescopes, selected in order to avoid resonance excitation. As the differential equations include the hub position, it is necessary to simultaneously develop the solution for the hub. As has been done in past analyses of the circular restricted problem, the hub position is written in a power series formulation in terms of its distance from L2. Then, in order to be included in the telescope equations, the hub solution is cast in terms of the nonlinear frequency of the relative telescope motion. In the course of the analysis, it is determined that the hub should also maintain a halo orbit - about L2. Additionally, relationships are formed between the initial conditions of the telescopes and the hub. These relationships may be used to associate sets of initial conditions with particular orientations of the telescope plane. The accuracy of the analytical solution is verified through various simulations and comparison to numerical integration of the differential equations. The results of the simulations are presented, along with a graphical representation of the relationships between the initial conditions of the telescopes and hub.

Segerman, Alan M.↗