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NASA NTRS2002

Multigrid Solution of the Navier-Stokes Equations at Low Speeds with Large Temperature Variations

Multigrid methods for the Navier-Stokes equations at low speeds and large temperature variations are investigated. The compressible equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. Three implicit smoothers have been incorporated into a common multigrid procedure. Both full coarsening and semi-coarsening with directional fine-grid defect correction have been studied. The resulting methods have been tested on four 2D laminar problems over a range of Reynolds numbers on both uniform and highly stretched grids. Two of the three methods show efficient and robust performance over the entire range of conditions. In addition none of the methods have any difficulty with the large temperature variations.

Sockol, Peter M.↗

DOE OSTI2019

Development of the Local (Site) Symmetry Method in the Supercell Model for a Crystal with an Impurity

Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classification over k-vector (Brillouin zone folding) are discussed. When considering a point defect in a crystal in the supercell model, it is necessary to take into account the symmetry of the one-electron states of the original crystal at the top of the valence band and at the bottom of the conduction band. The selected supercell should reproduce these states. Each specific selection of a supercell corresponds to a specific splitting of the Wyckoff positions of the original crystal and, as a result, the possibility to place a defect in positions with different point symmetry and to perform a calculation without taking into account the point symmetry of the crystal with a defect at all (site symmetry method). By the results of the calculation of a crystal with a defect in the supercell model, taking into account site symmetry, it is possible to determine the real symmetry of the crystal with a defect, which is essential for the interpretation of experimental data. A copper impurity in a lithium node in a LiCl crystal retains the cubic symmetry of the atom being replaced; the impurity of an iron atom in a titanium site with cubic local symmetry in a SrTiO{sub 3} crystal lowers the symmetry to tetragonal; and the H site in the CsPbI{sub 3} crystal is characterized by the complete removal of point symmetry with the formation of an I{sub 2}{sup −} ion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Adaptive mesh refinement for steady flows in Nek5000

Adaptive mesh refinement is performed in the framework of the spectral element method augmented by approaches to error estimation and control. The h-refinement technique is used for adapting the mesh, where selected grid elements are split by a quadtree (2D) or octree (3D) structure. Continuity between parent-child elements is enforced by high-order interpolation of the solution across the common faces. Parallel mesh partitioning and grid management respectively, are taken care of by the external libraries ParMETIS and p4est. Two methods are considered for estimating and controlling the error of the solution. The first error estimate is local and based on the spectral properties of the solution on each element. This method gives a local measure of the L-2-norm of the solution over the entire computational domain. The second error estimate uses the dual-weighted residuals method - it is based on and takes into account both the local properties of the solution and the global dependence of the error in the solution via an adjoint problem. The objective of this second approach is to optimize the computation of a given functional of physical interest. The simulations are performed by using the code Nek5000 and three steady-state test cases are studied: a two-dimensional lid-driven cavity at Re = 7, 500, a two-dimensional flow past a cylinder at Re = 40, and a three-dimensional lid-driven cavity at Re = 2,000 with a moving lid tilted by an angle of 30 degrees. Finally, the efficiency of both error estimators is compared in terms of refinement patterns and accuracy on the functional of interest. In the case of the adjoint error estimators, the trend on the error of the functional is shown to be correctly represented up to a multiplicative constant.

42 ENGINEERING↗

DOE OSTI2020

Shaping attosecond pulses by controlling the minima in high-order harmonic generation through alignment of CO 2 molecules

In this paper, we report a simple method for generating shaped attosecond pulses by using a CO 2 molecule. Unlike most other molecules, owing to its unique energy and angle dependence and the presence of deep minima in the photoionization transition dipole moment, the shape of harmonic spectra, especially the position and depth of minima, can be readily controlled by tuning the degree of alignment. The sensitive alignment dependence of the minima is due to the coherent interference of a laser-induced dipole from each molecule when CO 2 molecules are moderately aligned, but not when they are well aligned or when they are isotropically distributed. Such a sensitivity offers a simple way of controlling the spectral amplitude and phase of the generated harmonics and thus shaping the generated attosecond pulses, for example, producing structured attosecond pulses by splitting a single burst into two. We illustrate how such pulses are generated and how to characterize them. This method offers a simple way to shape attosecond pulses at the generation step. It can be easily implemented experimentally to generate attosecond pulses with strong phase variations for unique applications.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Numerical Optimization of Spray-Guided Spark Assistance for Cold Idle Operation in a Heavy-Duty Gasoline Compression Ignition Engine

This article describes the results of a response surface model (RSM)-based numerical optimization campaign for spray-guided spark assistance at cold operations in a heavy-duty gasoline compression ignition (GCI) engine. On the basis of an earlier work on spark-assisted GCI cold combustion, a space-filling design of experiments (DoE) method was first undertaken to investigate a multitude of hardware design variables and engine operating parameters. The main design variables included the number of injector nozzles, fuel split quantities and injection timings, and spark timing. The objective variables were engine combustion efficiency (ŋ c ), maximum pressure rise rate (MPRR), and engine-out nitrogen oxide (NO x ) emissions. A total of 150 design candidates were automatically generated using the Sobol sequence method provided by the commercial software package, CAESES. Then, closed-cycle computational fluid dynamic (CFD) spark-assisted GCI simulations under cold idling operations were performed. The outcomes from the CFD-DoE design campaign were utilized to construct high-fidelity RSMs that allowed for further design optimization of the spark plug- and fuel injector-related design variables, along with fuel injection strategy parameters. A merit function with respect to objective variables was formulated with an appropriate weight assignment on each objective variable. Finally, the best design candidate was identified from the RSM-based optimization process and further validated in the CFD analysis. The best design candidate showed the potential to significantly improve combustion efficiency (ŋ c > 90%) over the baseline at cold idle while satisfying MPRR and NOx emissions constraints (MPRR < 5 bar/CAD and NO x < 4.5 g/kWh).

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2022

A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

58 GEOSCIENCES↗

DOE OSTI2019

Development of the FASPAX IC for a high burst rate X-ray imager with very high dynamic range ( 1 0 5 ) capability in small pixels

Development of the FASPAX IC for a high burst rate X-ray imager with very high dynamic range (10 5 ) capability in small pixels. The technique of current splitting is presented as part of an integrated circuit development for an X-ray imager. This method enables integration of charge signals of unprecedented magnitude in small pixels, achieving a dynamic range of 10 5 . Results from two front end prototypes are given and a final optimized design is proposed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Photocatalytic water splitting

With the goal of achieving large-scale H 2 production from renewable resources, water splitting into H 2 and O 2 using semiconductor photocatalysts (sometimes called artificial photosynthesis) has been studied for five decades. Unfortunately, the lack of rigour and reproducibility in the data collection and analysis of experimental results has hindered progress in the field. This Primer provides a comprehensive overview of proper characterization and evaluation of photocatalysts for overall water splitting. In particular, the Primer covers various pitfalls in photocatalysis research, best practices for reproducibility and reliable methods for conducting rigorous experiments. As a result, the recommendations are intended to reduce false positives in the literature and to promote progress towards a practical technology for producing H 2 from water by using sunlight.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Gas Permeability Test Protocol for Ion-Exchange Membranes

The membrane-based electrolysis of water is a growing topic of interest due to the advantages of employing membranes in hydrogen production efficiency and system safety over the traditional alkaline water electrolysis. Ion-exchange membranes with low gas permeability are highly desirable for stable and safe operation of membrane-based water-splitting technologies, hence gas permeability through ion-exchange membranes needs to be properly assessed with standardized methods. We addressed three methods to measure gas permeability of ion-exchange membranes, a pressure permeation cell, chronoamperometry microelectrodes, and in situ testing of the membrane electrode assembly, and provide a guideline for choosing the appropriate method for the targeted operating conditions of the water electrolyzers.

08 HYDROGEN↗

DOE OSTI2022

Ch3MS-RF: a random forest model for chemical characterization and improved quantification of unidentified atmospheric organics detected by chromatography–mass spectrometry techniques

Abstract. The chemical composition of ambient organic aerosols plays a critical role in driving their climate and health-relevant properties and holds important clues to the sources and formation mechanisms of secondary aerosol material. In most ambient atmospheric environments, this composition remains incompletely characterized, with the number of identifiable species consistently outnumbered by those that have no mass spectral matches in the literature or the National Institute of Standards and Technology/National Institutes of Health/Environmental Protection Agency (NIST/NIH/EPA) mass spectral databases, making them nearly impossible to definitively identify. This creates significant challenges in utilizing the full analytical capabilities of techniques which separate and generate spectra for complex environmental samples. In this work, we develop the use of machine learning techniques to quantify and characterize novel, or unidentifiable, organic material. This work introduces Ch3MS-RF (Chemical Characterization by Chromatography–Mass Spectrometry Random Forest Modeling), an open-source, R-based software tool, for efficient machine-learning-enabled characterization of compounds separated in chromatography–mass spectrometry applications but not identifiable by comparison to mass spectral databases. A random forest model is trained and tested on a known 130 component representative external standard to predict the response factors of novel environmental organics based on position in volatility–polarity space and mass spectrum, enabling the reproducible, efficient, and optimized quantification of novel environmental species. Quantification accuracy on a reserved 20 % test set randomly split from the external standard compound list indicates that random forest modeling significantly outperforms the commonly used methods in both precision and accuracy, with a median response factor percent error of −2 %, for modeled response factors, compared to > 15 %, for typically used proxy assignment-based methods. Chemical properties modeling, evaluated on the same reserved 20 % test set and an extrapolation set of species identified in ambient organic aerosol samples collected in the Amazon rainforest, also demonstrate robust performance. Extrapolation set property prediction mean absolute errors for carbon number, oxygen to carbon ratio (O : C), average carbon oxidation state (OSc‾), and vapor pressure are 1.8, 0.15, 0.25, and 1.0 (log(atm)), respectively. Extrapolation set out-of-sample R2 for all properties modeled are above 0.75, with the exception of vapor pressure. While predictive performance for vapor pressure is less robust compared to the other chemical properties modeled, random-forest-based modeling was significantly more accurate than other commonly used methods of vapor pressure prediction, decreasing the mean vapor pressure prediction error to 0.24 (log(atm)) from 0.55 (log(atm)) (chromatography-based vapor pressure prediction) and 1.2 (log(atm)) (chemical formula-based vapor pressure prediction). The random forest model significantly advances an untargeted analysis of the full scope of chemical speciation yielded by two-dimensional gas chromatography (GCxGC-MS) techniques and can be applied to gas chromatography coupled with electron ionization mass spectrometry (GC-MS) as well. It enables the accurate estimation of key chemical properties commonly utilized in the atmospheric chemistry community, which may be used to more efficiently identify important tracers for further individual analysis and to characterize compound populations uniquely formed under specific ambient conditions.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1965

Superconductive magnetic-field-trapping device

An apparatus which enables the establishment of a magnetic field in air that has the same intensity as the ones in ferromagnetic materials is described. The apparatus is comprised of a core of ferromagnetic material and is surrounded by a cylinder made of a material that has superconducting properties when cooled below a critical temperature. A method is provided for producing a magnetic field through the ferromagnetic core. The core can also be split and pulled apart when it is required that the center of the cavity be left empty.

Hildebrandt, A. F.↗

NASA NTRS1982

Studies of implicit and explicit solution techniques in transient thermal analysis of structures

Studies aimed at an increase in the efficiency of calculating transient temperature fields in complex aerospace vehicle structures are reported. The advantages and disadvantages of explicit and implicit algorithms are discussed and a promising set of implicit algorithms with variable time steps, known as GEARIB, is described. Test problems, used for evaluating and comparing various algorithms, are discussed and finite element models of the configurations are described. These problems include a coarse model of the Space Shuttle wing, an insulated frame tst article, a metallic panel for a thermal protection system, and detailed models of sections of the Space Shuttle wing. Results generally indicate a preference for implicit over explicit algorithms for transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures). The effects on algorithm performance of different models of an insulated cylinder are demonstrated. The stiffness of the problem is highly sensitive to modeling details and careful modeling can reduce the stiffness of the equations to the extent that explicit methods may become the best choice. Preliminary applications of a mixed implicit-explicit algorithm and operator splitting techniques for speeding up the solution of the algebraic equations are also described.

Adelman, H. M.↗

NASA NTRS1983

Navigation of the Galileo mission

An overview of the navigation of the Galileo mission is given. Predicted navigation performance for the various mission phases is discussed with particular emphasis given to the tour phase. Orbit determination strategies and resulting accuracies are discussed for various data types. In particular, the results of combining a new Very Long Baseline Interferometry (VLBI) data type called Differential One-Way Range (DOR) with conventional radio and optical data types are presented. Maneuver strategy results include the effects of maneuver placement and various targeting methods on propellant consumption and delivery accuracy. Emphasis is placed on new results obtained using asymptote and split targeting.

Miller, L. J.↗

NASA NTRS1998

The Wavelet Element Method: Realization and Additional Features in 2D and 3D - Part 2

The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interelement boundaries, a globally continuous biorthogonal wavelet basis on the general domain is obtained. This construction does not uniquely define the basis functions but rather leaves some freedom for fulfilling additional features. In this paper we detail the general construction principle of the WEM to the 1D, 2D and 3D cases. We address additional features such as symmetry, vanishing moments and minimal support of the wavelet functions in each particular dimension. The construction is illustrated by using biorthogonal spline wavelets on the interval.

Canuto, Claudio↗

NASA NTRS2003

Internal Flow Thermal/Fluid Modeling of STS-107 Port Wing in Support of the Columbia Accident Investigation Board

As part of the aero-thermodynamics team supporting the Columbia Accident Investigation Board (CAB), the Marshall Space Flight Center was asked to perform engineering analyses of internal flows in the port wing. The aero-thermodynamics team was split into internal flow and external flow teams with the support being divided between shorter timeframe engineering methods and more complex computational fluid dynamics. In order to gain a rough order of magnitude type of knowledge of the internal flow in the port wing for various breach locations and sizes (as theorized by the CAB to have caused the Columbia re-entry failure), a bulk venting model was required to input boundary flow rates and pressures to the computational fluid dynamics (CFD) analyses. This paper summarizes the modeling that was done by MSFC in Thermal Desktop. A venting model of the entire Orbiter was constructed in FloCAD based on Rockwell International s flight substantiation analyses and the STS-107 reentry trajectory. Chemical equilibrium air thermodynamic properties were generated for SINDA/FLUINT s fluid property routines from a code provided by Langley Research Center. In parallel, a simplified thermal mathematical model of the port wing, including the Thermal Protection System (TPS), was based on more detailed Shuttle re-entry modeling previously done by the Dryden Flight Research Center. Once the venting model was coupled with the thermal model of the wing structure with chemical equilibrium air properties, various breach scenarios were assessed in support of the aero-thermodynamics team. The construction of the coupled model and results are presented herein.

Sharp, John R.↗

NASA NTRS2007

Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations

A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.

Nark, Douglas M.↗

NASA NTRS1992

Calculation of fully three-dimensional separated flow with an unsteady viscous-inviscid interaction method

Three previous papers have shown that the viscous inviscid numerical methods were capable of calculating separated turbulent flows. The 'Semi-inverse method' and the models of the first author allow the computation of massive separations, stalled flows, and shock wave-boundary layer interactions, in two-dimensional or quasi-three-dimensional conditions, from low speeds to supersonic speeds. The 'Semi-implicit' method for time-consistent coupling allows for the computation of time-accurate transonic separated flow and buffer computations in two-dimensions. The present paper shows that the viscous-inviscid interaction approach is also able to compute the fully three-dimensional flow separation phenomena. The method is based on a thin-layer approximation of the theory of 'Defect-Formulation' that provides the viscous-inviscid splitting of the Navier-Stokes equations. A parametric analytical modelling of the 3D-turbulent velocity profiles is involved. Numerically, the 3D-velocity profiles are discretized in the normal z-direction and driven by parametric integral 3D-equations in direct or inverse modes in the x-direction. The viscous-inviscid coupling is fully 3D and solved the time-consistency problem with an extension of the 'Semi-implicit' method previously suggested in two-dimensions. A 3D inviscid subroutine with TSP approximation is used. Results are obtained for transonic steady flows over wings with shock-induced transonic separation. The method provides results for highly three-dimensional flow separations, such as induced by a three-dimensional through at the wall of a flat plate. The 3D viscous-inviscid coupling and the 3D model of the velocity field provide three-dimensional instantaneous skin-friction lines whose patterns exhibit the same complex topology as Navier-Stokes solvers, with foci, nodes, and saddle-points.

Leballeur, J. C.↗

NASA NTRS1990

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

The compressible Navier-Stokes equations are solved for a variety of two-dimensional inviscid and viscous problems by preconditioned conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. The system of linear equations which arises out of the linearization of a fully implicit scheme is solved iteratively by the well known methods of GMRES (Generalized Minimum Residual technique) and Chebyschev iteration. Incomplete LU factorization and block diagonal factorization are used as preconditioners. The resulting algorithm is competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

Venkatakrishnan, V.↗