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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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NASA NTRS2002

VEXT: A Virtual Observatory Exploration Toolkit

This final report consists of two main parts. The first is taken from a paper by the PiCA (Pittsburgh Computational Astrostatistics) Group which describes our ongoing work in fast computation of n-point correlation functions. We present here a new algorithm for the fast computation of N-point correlation functions in large astronomical data sets. The algorithm is based on kd-trees which are decorated with cached sufficient statistics thus allowing for orders of magnitude speed-ups over the naive non-tree-based implementation of correlation functions. We further discuss the use of controlled approximations within the computation which allows for further acceleration. In summary, our algorithm now makes it possible to compute exact, all-pairs, measurements of the two, three and four-point correlation functions for cosmological data sets like the Sloan Digital Sky Survey and the next generation of Cosmic Microwave Background experiments. The second part summarizes the progress made by the PiCA Group in this area through the AISR grant.

Schneider, Jeff↗
DOE OSTI2023

Iterated Gauss-Seidel GMRES

The GMRES algorithm of Saad and Schultz [SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869] is an iterative method for approximately solving linear systems Ax = b, with initial guess x0 and residual r0 = b Ax0. The algorithm employs the Arnoldi process to generate the Krylov basis vectors (the columns of Vk ). It is well known that this process can be viewed as a QR factorization of the matrix Bk = [r0, AVk] at each iteration. Despite an O (..epsilon..)..kappa.. (Bk ) loss of orthogonality, for unit roundoff ..epsilon..and condition number ..kappa.. , the modified Gram-Schmidt formulation was shown to be backward stable in the seminal paper by Paige et al. [SIAM J. Matrix Anal.Appl., 28 (2006), pp. 264-284]. We present an iterated Gauss-Seidel formulation of the GMRES algorithm (IGS-GMRES) based on the ideas of Ruhe [Linear Algebra Appl., 52 (1983), pp. 591-601] and Swirydowicz et al. [Numer. Linear Algebra Appl., 28 (2020), pp. 1-20]. IGS-GMRES maintains orthogonality to the level O (..epsilon..)..kappa.. (Bk ) or O (..epsilon..), depending on the choice of one or two iterations; for two Gauss-Seidel iterations, the computed Krylov basis vectors remain orthogonal to working accuracy and the smallest singular value of Vk remains close to one. The resulting GMRES method is thus backward stable. We show that IGS-GMRES can be implemented with only a single synchronization point per iteration, making it relevant to large-scale parallel computing environments. We also demonstrate that, unlike MGS-GMRES, in IGS-GMRES the relative Arnoldi residual corresponding to the computed approximate solution no longer stagnates above machine precision even for highly nonnormal systems.

Arnoldi-QR↗
NASA NTRS1947

Scale effect and optimum relations for sea surface planning

From the general dimensional and mechanical similarity theory it follows that a condition of steady motion of a given shape\bottom with constant speed on the surface of water is determined by four nondimensional parameters. By considering the various systems of independent parameters which are applied in theory and practice and special tests, there is determined their mutual relations and their suitability as planning characteristics. In studying the scale effect on the basis of the Prnndtl formula for the friction coefficient for a turbulent condition the order of magnitude is given of the error in applying the model data to full scale in the case of a single-step bottom For a bottom of complicated shape it is shown how from the test data of the hydrodynamic characteristics for one speed with various loads, or one load with various speeds, there may be obtained by simple computation with good approximation the hydrodynamic characteristics for a different speed or for a different load. (These considerations may be of use in solving certain problems on the stability of planning.) This permits extrapolating the curve of resistance against speed for large speeds inaccessible in the tank tests or for other loads which were not tested. The data obtained by computation are in good agreement with the test results. Problems regarding the optimum trim angle or the optimum width in the case of planning of a flat plate are considered from the point of view of the minimum resistance for a given load on the water and planning speeds. Formulas and graphs are given for the optimum value of the planning coefficient and the corresponding values of the trim angle and width of the flat plate.

Sedov, L.↗
DOE OSTI2024

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗
DOE OSTI2018

Differential formulation of the viscous history force on a particle for efficient and accurate computation

It is well known that the computation of the Basset-like history force is very demanding in terms of CPU and memory requirements, since it requires the evaluation of a history integral. We use the recent rational theory of Beylkin & Monzón ( Appl. Comput. Harmon. Anal. , vol. 19, 2005, pp. 17–48) to approximate the history kernel in the form of exponential sums to reformulate the viscous history force in a differential form. This theory allows us to approximate the history kernel in terms of exponential sums to any desired order of accuracy. This removes the need for long-time storage of the acceleration histories of the particle and the fluid. The proposed differential form approximation is applied to compute the history force on a spherical particle in a synthetic turbulent flow and a wall-bounded turbulent channel flow. Particles of various diameters are considered, and results obtained using the present technique are in reasonable agreement with those achieved using the full history integral.

Mechanics↗
DOE OSTI2016

Extent of hydrogen coverage of Si(001) under chemical vapor deposition conditions from ab initio approaches

The extent of hydrogen coverage of the Si(001) c(4 × 2) surface in the presence of hydrogen gas has been studied with dispersion corrected density functional theory. Electronic energy contributions are well described using a hybrid functional. The temperature dependence of the coverage in thermodynamic equilibrium was studied computing the phonon spectrum in a supercell approach. As an approximation to these demanding computations, an interpolated phonon approach was found to give comparable accuracy. The simpler ab initio thermodynamic approach is not accurate enough for the system studied, even if corrections by the Einstein model for surface vibrations are considered. The on-set of H{sub 2} desorption from the fully hydrogenated surface is predicted to occur at temperatures around 750 K. Strong changes in hydrogen coverage are found between 1000 and 1200 K in good agreement with previous reflectance anisotropy spectroscopy experiments. These findings allow a rational choice for the surface state in the computational treatment of chemical reactions under typical metal organic vapor phase epitaxy conditions on Si(001).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Assessing parallel path cooling tower performance via artificial neural networks

Real-time monitoring of a research nuclear reactor, a system in which all generated power is dissipated to the environment, can be performed via analysis of the heat rejection from the cooling system. Given an inlet water temperature and flow rate, the reactor power can be well-approximated from the outlet water temperature; however, the instrumentation to measure outlet conditions may not be robust or accurate. If we know how a cooling tower performs from historical data, but cannot measure the outlet temperature, a mathematical representation of the system can be inverted to obtain the outlet water temperature that describes the cooling capacity. Unfortunately, model inversion processes are computationally expensive. To address this, an artificial neural network (ANN) is implemented to assess the performance of a multi-cell cooling tower for a nuclear reactor. This approach leverages the Merkel model to obtain an extensive data set describing performance of the cooling tower cells throughout a wide array of potential operating conditions. The Merkel model is expressed as a function of four parameters: the inlet and outlet water temperatures, inlet air wet bulb temperature, and ratio of liquid-to-gas mass flow rates (L/G), which together provide a non-dimensional number indicative of cooling tower performance, called the Merkel integral. Computing a 4-dimensional data structure that describes finite combinations of the Merkel integral, an inverse model is then generated using an ANN to determine the cell outlet water temperature from the other three model parameters along with the computed Merkel integral. Compared to traditional model inversion methods, the ANN reduces the computational time by approximately 4 orders of magnitude, with effectively no sacrifice to solution accuracy, and could be applied for different cooling towers in the event the performance curve is known. Finally, three use cases of the ANN are then reviewed: (1) determining the cell outlet water temperatures when gas flow at rated conditions (GFRC) is known, (2) performing the prior case without knowledge of the GRFC, and (3) assessing performance differences between the individual tower cells.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Accelerated iterative beam angle selection in IMRT

Purpose: Iterative methods for beam angle selection (BAS) for intensity-modulated radiation therapy (IMRT) planning sequentially construct a beneficial ensemble of beam directions. In a naïve implementation, the nth beam is selected by adding beam orientations one-by-one from a discrete set of candidates to an existing ensemble of (n − 1) beams. The best beam orientation is identified in a time consuming process by solving the fluence map optimization (FMO) problem for every candidate beam and selecting the beam that yields the largest improvement to the objective function value. This paper evaluates two alternative methods to accelerate iterative BAS based on surrogates for the FMO objective function value. Methods: We suggest to select candidate beams not based on the FMO objective function value after convergence but (1) based on the objective function value after five FMO iterations of a gradient based algorithm and (2) based on a projected gradient of the FMO problem in the first iteration. The performance of the objective function surrogates is evaluated based on the resulting objective function values and dose statistics in a treatment planning study comprising three intracranial, three pancreas, and three prostate cases. Furthermore, iterative BAS is evaluated for an application in which a small number of noncoplanar beams complement a set of coplanar beam orientations. This scenario is of practical interest as noncoplanar setups may require additional attention of the treatment personnel for every couch rotation. Results: Iterative BAS relying on objective function surrogates yields similar results compared to naïve BAS with regard to the objective function values and dose statistics. At the same time, early stopping of the FMO and using the projected gradient during the first iteration enable reductions in computation time by approximately one to two orders of magnitude. With regard to the clinical delivery of noncoplanar IMRT treatments, we could show that optimized beam ensembles using only a few noncoplanar beam orientations often approach the plan quality of fully noncoplanar ensembles. Conclusions: We conclude that iterative BAS in combination with objective function surrogates can be a viable option to implement automated BAS at clinically acceptable computation times.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

The optical, vibrational, structural and elasto-optic properties of Zn{sub 0.25}Cd{sub 0.75}S{sub y}Se{sub 1-y} quaternary alloys

The optical, vibrational, structural and elasto-optic properties of quaternary II-VI alloys Zn{sub 0.25}Cd{sub 0.75}S{sub 0.25}Se{sub 0.75}, Zn{sub 0.25}Cd{sub 0.75}S{sub 0.50}Se{sub 0.50} and Zn{sub 0.25}Cd{sub 0.75}S{sub 0.75}Se{sub 0.25} are presented. Within the empirical pseudopotential method (EPM) the disorder effects are modeled via modified virtual crystal approximation (MVCA). The computed bandgaps and the refined form factors are utilized to evaluate optical, vibrational, structural and elasto-optic properties. The refractive index (n), static (ε{sub 0}) and high frequency dielectric (ε{sub ∞}) constants are calculated to reveal optical behavior of alloys. The longitudinal ω{sub LO}(0) and transverse ω{sub TO}(0) optical frequencies are obtained to see vibrational characteristics. Moreover, the elastic constants (c{sub ij}) and bulk moduli (B) are computed by combining the EPM with Harrison bond orbital model. The elasto-optic nature of alloys is examined by computing the photo-elastic constants. These values are significant with regard to the opto-electronic applications especially when no experimental data are available on this system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1992

The dimension of attractors underlying periodic turbulent Poiseuille flow

A lower bound on the Liapunov dimenison, D-lambda, of the attractor underlying turbulent, periodic Poiseuille flow at a pressure-gradient Reynolds number of 3200 is calculated, on the basis of a coarse-grained (16x33x8) numerical solution, to be approximately 352. Comparison of Liapunov exponent spectra from this and a higher-resolution (16x33x16) simulation on the same spatial domain shows these spectra to have a universal shape when properly scaled. On the basis of these scaling properties, and a partial exponent spectrum from a still higher-resolution (32x33x32) simulation, it is argued that the actual dimension of the attractor underlying motion of the given computational domain is approximately 780. It is suggested that this periodic turbulent shear flow is deterministic chaos, and that a strange attractor does underly solutions to the Navier-Stokes equations in such flows.

Keefe, Laurence↗
DOE OSTI2020

Dirac's equation and its implications for density functional theory based calculations of materials containing heavy elements

Electronic structure calculations based on density functional theory (DFT) give quantitatively accurate predictions of properties of most materials containing light elements. For heavy materials, and in particular for f -electron systems, DFT based methods can fail both qualitatively and quantitatively for two distinct reasons: their failure to describe confinement effects arising from localized f -electron behavior and their incomplete or approximate treatment of relativity. In addition, different methods for incorporating relativistic effects, which give identical results in most light materials, can give different predictions in heavy elements. In order to develop a quantitative capability for calculating the properties of these materials, it is essential to separate the predictions of the underlying equations from the uncertainty introduced in approximations used in computation. Working toward that goal, here we have developed a code, called dirac-fp , which is based directly on solving the Dirac-Kohn-Sham equations and uses the full-potential linear muffin-tin orbital (FP-LMTO) approach to electronic structure. In order to assess the performance of dirac-fp , we perform calculations on three different face-centered cubic materials using different approximate treatments of relativity: the scalar relativistic (SR) approach commonly used in most solid-state DFT codes, the scalar relativistic plus spin-orbit coupling corrections (SR+SO) approach which includes spin-orbit coupling self-consistently using the SR states inside the muffin tins, and the Dirac-Kohn-Sham (Dirac) approach implemented in dirac-fp . Performing calculations on thorium, in which relativistic effects should be strong, aluminum, in which relativistic effects should be negligible, and gold, in which relativistic effects play an intermediate role, we find that the Dirac approach is able to provide theoretically consistent results in the electronic structure and ground-state properties across all three materials.

3-dimensional systems↗
DOE OSTI2016

Ab-initio study of electronic structure and elastic properties of ZrC

The electronic and elastic properties of ZrC have been investigated using the linear combination of atomic orbitals method within the framework of density functional theory. Different exchange-correlation functionals are taken into account within generalized gradient approximation. We have computed energy bands, density of states, elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, lattice parameters and pressure derivative of the bulk modulus by calculating ground state energy of the rock salt structure type ZrC.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1987

Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.

Liou, J.↗
NASA NTRS2016

Numerical Evaluation of an Ejector-Enhanced Resonant Pulse Combustor with a Poppet Inlet Valve and a Converging Exhaust Nozzle

A computational investigation of a pressure-gain combustor system for gas turbine applications is presented. The system consists of a valved pulse combustor and an ejector, housed within a shroud. The study focuses on two enhancements to previous models, related to the valve and ejector components. First, a new poppet inlet valve system is investigated, replacing the previously used reed valve configuration. Secondly, a new computational approach to approximating the effects of choked turbine inlet guide vanes present immediately downstream of the Ejector-Enhanced Resonant Pulse Combustor (EERPC) is investigated. Instead of specifying a back pressure at the EERPC exit boundary (as was done in previous studies) the new model adds a converging-diverging (CD) nozzle at the exit of the EERPC. The throat area of the CD nozzle can be adjusted to obtain the desired back pressure level and total mass flow rate. The results presented indicate that the new poppet valve configuration performs nearly as well as the original reed valve system, and that the addition of the CD nozzle is an effective method to approximate the exit boundary effects of a turbine present downstream of the EERPC. Furthermore, it is shown that the more acoustically reflective boundary imposed by a nozzle as compared to a constant pressure surface does not significantly affect operation or performance.

Computational Fluid Dynamics (CFD↗
NASA NTRS1992

Radiation transport around axisymmetric blunt body vehicles using a modified differential approximation

A moment method for computing 3D radiative transport in axisymmetric thermochemical nonequilibrium flows is developed. The method uses the P-1 approximation to reduce the governing system of integro-differential equations to a coupled set of partial differential equations. The numerical solution of these equations for realistic variations of the radiation properties is discussed. Representative results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.

Hartung, Lin C.↗
DOE OSTI2021

Towards Realistic Models of Heterogeneous Catalysis: Simulations of Oxidation Catalysis from First Principles

Among the most significant developments in heterogeneous catalysis in the last 20 years is the emergence of microkinetic models, often parameterized from density functional theory (DFT) calculations, used to quantify observed catalyst performance and to guide the discovery of new catalytic materials. While DFT directly reports binding energies and elementary step activation energies, the free energies that enter into microkinetic models must be computed from additional approximations. Frequently these free energy approximations assume ideal behavior—that adsorbates do not interact with one another, or that adsorbates are immobile or vibrate harmonically about a binding site. These assumptions can and do have an impact on predicted catalyst performance and potentially even on predicted trends. Our work relates to three categories of non-idealities, explored in the context of nitrogen oxidation and reduction catalysis on metal surfaces. One component relates to adsorbate translational free energy, the contribution least well described by conventional models, in which we develop modeling approaches that improve accuracy with limited increase in computational expense. A second component relates adsorbate-adsorbate interactions, in which we develop benchmark on-lattice interaction models and compare kinetic predictions with conventional mean-field models, in an effort to develop more robust coverage-dependent mean field modeling approaches. The last relates the most fundamental assumption of all—that of energy equipartition—in an effort to rationalize and guide plasma-enhanced catalysis.

99 GENERAL AND MISCELLANEOUS↗
NASA NTRS2018

Computational Component Build-Up for the X-57 Distributed Electric Propulsion Aircraft

A computational study of the wing for the distributed electric propulsion X-57 Maxwell airplane configuration at cruise and takeoff/landing conditions was completed. Three unstructured-mesh, Navier-Stokes computational fluid dynamics methods, FUN3D, USM3D and Kestrel, were used to predict the performance buildup of components to the full X-57 configuration. The goal of the X-57 wing and distributed electric propulsion system design was to meet or exceed the required lift coefficient of 3.95 for a stall speed of 58 knots. The X-57 Maxwell airplane was designed with a small, high aspect ratio cruise wing that was designed for a high cruise lift coefficient of 0.75 at a cruise speed of 150 knots and altitude of 8,000 ft, with an angle of attack of approximately 0deg. The computational data indicates that the X-57 full aircraft drag would meet the cruise drag goal with a 25 count drag margin. The cruise configuration maximum lift coefficient is 2.07 and without including the stabilator is 1.86 at an angle of attack of 14 deg, predicted with the USM3D flow solver using the Spalart-Allmaras turbulence model. The maximum lift coefficient for the high-lift wing (with the 30deg flap deflection) without the stabilator contribution is 2.60 at an angle of attack of 13 deg. For high-lift blowing conditions with 13.7 hp/prop, the maximum lift coefficient excluding the stabilator is 4.426 at (alpha) = 13 deg. Therefore, the lift augmentation from the high-lift propellers is 1.7 and the total lift augmentation from the high-lift system (30 deg flap deflection and the high-lift blowing) is 2.38. The drag for the high-lift wing with 30 deg flap deflection is much higher than the cruise wing configuration, but the high-lift system is used only during a small portion of the flight envelope. The pitching moment is relatively constant for both blown and unblown conditions when the stabilator is excluded. Modeling the full geometry has indicated some adverse effects from the fuselage on the wing and stabilator. At high angles of attack, the solutions with the USM3D flow solver using the Spalart-Allmaras turbulence model indicates large flow separation on the wing upper surface between the two high-lift nacelles near the fuselage, and also a reduction in sectional lift on the stabilator in the first 50 percent of the stabilator semispan. However, the large flow separation near the fuselage is mostly eliminated in the solutions predicted with two codes, USM3D and Kestrel, using Hybrid Reynolds-averaged Navier Stokes/Large Eddy Simulation turbulence models.

Deere, Karen A.↗
DOE OSTI2024

Unconventional Error Cancellation Explains the Success of Hartree–Fock Density Functional Theory for Barrier Heights

Energy barriers, which control the rates of chemical reactions, are seriously underestimated by computationally efficient semilocal approximations for the exchange-correlation energy. The accuracy of a semilocal density functional approximation is strongly boosted for reaction barrier heights by evaluating that approximation non-self-consistently on Hartree–Fock electron densities, which has been known for ~30 years. Here, the conventional explanation is that the Hartree–Fock theory yields the more accurate density. This work presents a benchmark Kohn–Sham inversion of accurate coupled-cluster densities for the reaction H 2 + F → HHF → H + HF and finds a strong, understandable cancellation between positive (excessively overcorrected) density-driven and large negative functional-driven errors (expected from stretched radical bonds in the transition state) within this Hartree–Fock density functional theory. This confirms earlier conclusions (Kaplan, A. D., et al. J. Chem. Theory Comput. 2023, 19, 532–543) based on 76 barrier heights and three less reliable, but less expensive, fully nonlocal density functional proxies for the exact density.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗