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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Data-driven linear time advance operators for the acceleration of plasma physics simulation

In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1985

Probabilistic Structural Analysis Theory Development

The objective of the Probabilistic Structural Analysis Methods (PSAM) project is to develop analysis techniques and computer programs for predicting the probabilistic response of critical structural components for current and future space propulsion systems. This technology will play a central role in establishing system performance and durability. The first year's technical activity is concentrating on probabilistic finite element formulation strategy and code development. Work is also in progress to survey critical materials and space shuttle mian engine components. The probabilistic finite element computer program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) is being developed. The final probabilistic code will have, in the general case, the capability of performing nonlinear dynamic of stochastic structures. It is the goal of the approximate methods effort to increase problem solving efficiency relative to finite element methods by using energy methods to generate trial solutions which satisfy the structural boundary conditions. These approximate methods will be less computer intensive relative to the finite element approach.

Burnside, O. H.↗
NASA NTRS2000

Numerical Calculation of the Drag Force Acting on an Insoluble Particle Moving in Front of a Solidifying Interface

The distribution of insoluble particles in a metal casting depends primarily on the interaction of the particles with the solid/liquid interface (SLI) during the solidification process. Whether a particle will be engulfed or continuously pushed by SLI is essentially determined by the balance of forces acting on the particle. An important component of this force balance is the drag force generated by the particle motion in front of the SLI. Previously developed mathematical models for particle/SLI interaction made use of steady-state solutions of this force provided by the lubrication theory. However, our numerical model based on the SLI tracking approach shows that not only the steady-state approach is inappropriate to model the interaction process but also that even at steady-state the theoretical solution underestimates the drag force. A regression analysis of steady-state numerical solutions for cylindrical particles moving normal to a flat SLI gave a relationship of the form F(sub d) (exp num) = (square root of 3) pi eta V(sub p)((R(sub p) / d) (exp 10 gamma/3)) as compared to the theoretical solution F(sub d) (exp theor) = 3 X (square root of 2) pi eta V(sub p)((R(sub p) / d) (exp 3/2)) where F(sub d) is the drag force, eta is the dynamic viscosity of the fluid, V(sub p) is the particle velocity, R(sub p) is the particle radius, gamma is Euler's constant (gamma is approximately equal to 0.577), and d is the width of the gap between the particle and the SLI. Model validation as well as the influence of the interface shape on the value of F(sub d) will also be discussed.

Catalina, Adrian V.↗
NASA NTRS1974

Theoretical and observational analysis of spacecraft fields

In order to investigate the dipolar and nondipolar contributions of spacecraft magnetic fields, a simple magnetic field model is proposed. This model consists of a number N of randomly oriented dipoles of strength M sub k in a given volume. Two sets of formulas are presented that give the rms multipole field components, first, for isotropic orientations of the dipoles at given positions and second, for isotropic orientations of the dipoles distributed uniformly throughout a cube or sphere. The statistical results for a cube (8 cu m in size) together with individual examples computed numerically show the following features. Beyond about 2- to 3-m distance from the center of the cube the field is dominated by an equivalent dipole. The magnitude of the magnetic moment of the dipolar part is approximated by N to the 1/2 power times M for equal magnetic moments or generally by the Pythagorean sum of the dipole moments. The radial component tend to be greater than either of the transverse components for the dipole portion as well as for the nondipolar field contributions.

Neubauer, F. M.↗
NASA NTRS1977

Velocity and temperature distributions of coal-slag layers on magnetohydrodynamic generators walls

Approximate analytical expressions are derived for the velocity and temperature distributions in steady state coal slag deposits flowing over MHD generator walls. Effects of slag condensation and Joule heating are included in the analysis. The transport conditions and the slag temperature at the slag-gas interface are taken to be known parameters in the formulation. They are assumed to have been predetermined either experimentally or from the slag properties and the gas dynamic calculations of the free stream flow. The analysis assumes a power law velocity profile for the slag and accounts for the coupling between the energy and momentum conservation equations. Comparisons are made with the more exact numerical solutions to verify the accuracy of the results.

Pian, C. C. P.↗
NASA NTRS1981

Manufacturing in space: Fluid dynamics numerical analysis

Natural convection in a spherical container with cooling at the center was numerically simulated using the Lockheed-developed General Interpolants Method (GIM) numerical fluid dynamic computer program. The numerical analysis was simplified by assuming axisymmetric flow in the spherical container, with the symmetry axis being a sphere diagonal parallel to the gravity vector. This axisymmetric spherical geometry was intended as an idealization of the proposed Lal/Kroes growing experiments to be performed on board Spacelab. Results were obtained for a range of Rayleigh numbers from 25 to 10,000. For a temperature difference of 10 C from the cooling sting at the center to the container surface, and a gravitional loading of 0.000001 g a computed maximum fluid velocity of about 2.4 x 0.00001 cm/sec was reached after about 250 sec. The computed velocities were found to be approximately proportional to the Rayleigh number over the range of Rayleigh numbers investigated.

Robertson, S. J.↗
NASA NTRS2010

Simple Check Valves for Microfluidic Devices

A simple design concept for check valves has been adopted for microfluidic devices that consist mostly of (1) deformable fluorocarbon polymer membranes sandwiched between (2) borosilicate float glass wafers into which channels, valve seats, and holes have been etched. The first microfluidic devices in which these check valves are intended to be used are micro-capillary electrophoresis (microCE) devices undergoing development for use on Mars in detecting compounds indicative of life. In this application, it will be necessary to store some liquid samples in reservoirs in the devices for subsequent laboratory analysis, and check valves are needed to prevent cross-contamination of the samples. The simple check-valve design concept is also applicable to other microfluidic devices and to fluidic devices in general. These check valves are simplified microscopic versions of conventional rubber- flap check valves that are parts of numerous industrial and consumer products. These check valves are fabricated, not as separate components, but as integral parts of microfluidic devices. A check valve according to this concept consists of suitably shaped portions of a deformable membrane and the two glass wafers between which the membrane is sandwiched (see figure). The valve flap is formed by making an approximately semicircular cut in the membrane. The flap is centered over a hole in the lower glass wafer, through which hole the liquid in question is intended to flow upward into a wider hole, channel, or reservoir in the upper glass wafer. The radius of the cut exceeds the radius of the hole by an amount large enough to prevent settling of the flap into the hole. As in a conventional rubber-flap check valve, back pressure in the liquid pushes the flap against the valve seat (in this case, the valve seat is the adjacent surface of the lower glass wafer), thereby forming a seal that prevents backflow.

Willis, Peter A.↗
NASA NTRS1990

Numerical derivative techniques for trajectory optimization

The adoption of robust numerical optimization techniques in trajectory simulation programs has resulted in powerful design and analysis tools. These trajectory simulation/optimization programs are widely used, and a representative list includes the GTS system, the POST program, and newer collocation methods such as OTIS and FONPAC. All of these programs rely on optimization algorithms which require objective function and constraint gradient data during the iteration process. However, most trajectory optimization problems lack simple analytical expressions for these derivatives. In the general case a function evaluation involves integrating aerodynamic, propulsive, and gravity forces over multiple trajectory phases with complex control models. With the newer collocation methods, the integration is replaced by defect constraints and cubic approximations for the state. While analytic gradient expressions can sometimes be derived for trajectory optimization problems, the derivation is cumbersome, time consuming, and prone to mistakes. Fortunately, an alternate method exists for the gradient evaluation, namely finite difference approximations. In this paper some finite difference gradient techniques developed for use with the GTS system are presented. These techniques include methods for computing first and second partial derivatives of single and multiple sets of functions. A key feature of these methods is an error control mechanism which automatically adjusts the perturbation size to obtain accurate derivative values.

Hallman, Wayne P.↗
NASA NTRS2022

Vicarious Calibration of the Long Near Infrared Band: Cross-Sensor Differences in Sensitivity

Numerous assumptions and approximations are employed when translating satellite-derived radiance to surface remote sensing reflectance (RRS) for ocean color applications. Among these is the vicarious calibration coefficient (g) of the ‘long’ near infrared band (NIRL) used for atmospheric correction. For this band, the pre-launch calibration has always been deemed sufficient [thus g(NIRL) = 1.00] as long as other bands are vicariously calibrated. Recent research, however, suggests that MODIS/Aqua RRS time series are quite sensitive to g(NIRL) (and associated vicarious gains in other bands). In this work, we assessed the sensitivity of VIIRS/SNPP RRS to NIRL calibration, and compared our results to previous MODIS/Aqua and SeaWiFS/OrbView2 analysis. In doing so, we note g(NIRL) sensitivities of mission-averaged RRS timeseries are lower for VIIRS and SeaWiFS, relative to MODIS. At the scale of monthly climatologies, however, all sensors show prominent g(NIRL) sensitivity, with that of SeaWiFS being the most substantial. These findings informed simulation analyses, whereby we identified signal-to-noise ratio (SNR) and radiant path geometry, as well as their interaction, as having notable impacts on g(NIRL) sensitivity. As such, g(NIRL) sensitivity is a necessary consideration for reflectance uncertainty budgets, especially for sensors with higher NIR SNR or particular prevailing radiant path geometries. Given the geometry components embedded within g(NIRL) sensitivity, such studies should be coupled with cross-sensor intercalibrations (e.g., using simultaneous same view measurements) toward minimizing NIRL errors between satellite instruments, but such efforts will not completely remediate remaining cross-sensor biases in RRS.

Brian B Barnes↗
DOE OSTI2021

Magnetic Field Reconstruction for a Realistic Multi-Point, Multi-Scale Spacecraft Observatory

Future in situ space plasma investigations will likely involve spatially distributed observatories comprised of multiple spacecraft, beyond the four and five spacecraft configurations currently in operation. Inferring the magnetic field structure across the observatory, and not simply at the observation points, is a necessary step towards characterizing fundamental plasma processes using these unique multi-point, multi-scale data sets. We propose improvements upon the classic first-order reconstruction method, as well as a second-order method, utilizing magnetometer measurements from a realistic nine-spacecraft observatory. The improved first-order method, which averages over select ensembles of four spacecraft, reconstructs the magnetic field associated with simple current sheets and numerical simulations of turbulence accurately over larger volumes compared to second-order methods or first-order methods using a single regular tetrahedron. Using this averaging method on data sets with fewer than nine measurement points, the volume of accurate reconstruction compared to a known magnetic vector field improves approximately linearly with the number of measurement points.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRSDate not supplied

Test and Analysis of a Composite Conical-Cylindrical Shell

Launch-vehicle shell structures, which can be comprised of both cylindrical and conical sections, are known to be susceptible to buckling due to their large radius-to-thickness ratios. The advancements in composite manufacturing and numerical methods have enabled designers to consider more nontraditional shapes, such as connecting the conical and cylindrical sections with a toroidal transition to create a single-piece conical-cylindrical shell. This single-piece construction eliminates the need for a heavy interface ring between sections and has the potential to save mass. To better understand the buckling behavior, a composite conical-cylindrical shell was designed, fabricated, and tested. Prior to test, a finite element model that included thickness variations and radial imperfections was created. The test article buckled elastically at 251.8 kN, approximately 8.8% higher than the predicted buckling load of 231.4 kN Continued research in conical-cylindrical structures has the potential to expand the design space for launch-vehicle structures and lead to improved designs and reduced weight.

Buckling↗
DOE OSTI2023

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators: correcting the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction–diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

On unifying randomized methods for inverse problems

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems with Gaussian priors by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a sample average approximation (SAA). More importantly, we are able to prove a single theoretical result that guarantees the asymptotic convergence for a variety of randomized methods. Additionally, viewing randomized methods as an SAA enables us to prove, for the first time, a single non-asymptotic error result that holds for randomized methods under consideration. Another important consequence of our unified framework is that it allows us to discover new randomization methods. Here, we present various numerical results for linear, nonlinear, algebraic, and PDE-constrained inverse problems that verify the theoretical convergence results and provide a discussion on the apparently different convergence rates and the behavior for various randomized methods.

42 ENGINEERING↗
DOE OSTI2023

CFL Optimized Forward–Backward Runge–Kutta Schemes for the Shallow-Water Equations

Abstract We present the formulation and optimization of a Runge–Kutta-type time-stepping scheme for solving the shallow-water equations, aimed at substantially increasing the effective allowable time step over that of comparable methods. This scheme, called FB-RK(3,2), uses weighted forward–backward averaging of thickness data to advance the momentum equation. The weights for this averaging are chosen with an optimization process that employs a von Neumann–type analysis, ensuring that the weights maximize the admittable Courant number. Through a simplified local truncation error analysis and numerical experiments, we show that the method is at least second-order in time for any choice of weights and exhibits low dispersion and dissipation errors for well-resolved waves. Further, we show that an optimized FB-RK(3,2) can take time steps up to 2.8 times as large as a popular three-stage, third-order strong stability-preserving Runge–Kutta method in a quasi-linear test case. In fully nonlinear shallow-water test cases relevant to oceanic and atmospheric flows, FB-RK(3,2) outperforms SSPRK3 in admittable time step by factors roughly between 1.6 and 2.2, making the scheme approximately twice as computationally efficient with little to no effect on solution quality. Significance Statement The purpose of this work is to develop and optimize time-stepping schemes for models relevant to oceanic and atmospheric flows. Specifically, for the shallow-water equations we optimize for schemes that can take time steps as large as possible while retaining solution quality. We find that our optimized schemes can take time steps between 1.6 and 2.2 times larger than schemes that cost the same number of floating point operations, translating directly to a corresponding speedup. Our ultimate goal is to use these schemes in climate-scale simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Rapid simulations of hyperspectral near-field images of three-dimensional heterogeneous surfaces – part II

The modeling of the near-field interaction in the scattering-type scanning near-field optical microscope (s-SNOM) is rapidly advancing, although an accurate yet versatile modeling framework that can be easily adapted to various complex situations is still lacking. In this work, we propose a time-efficient numerical scheme in the quasi-electrostatic limit to capture the tip-sample interaction in the near field. This method considers an extended tip geometry, which is a significant advantage compared to the previously reported method based on the point-dipole approximation. Using this formalism, we investigate, among others, nontrivial questions such as uniaxial and biaxial anisotropy in the near-field interaction, the relationship between various experimental parameters (e.g. tip radius, tapping amplitude, etc.), and the tip-dependent spatial resolution. The demonstrated method further sheds light on the understanding of the contrast mechanism in s-SNOM imaging and spectroscopy, while also representing a valuable platform for future quantitative analysis of the experimental observations.

Chen, Xinzhong (ORCID:0000000261033848)↗
NASA NTRS1950

Analysis of spanwise temperature distribution in three types of air-cooled turbine blade

Methods for computing spanwise blade-temperature distributions are derived for air-cooled hollow blades, air-cooled hollow blades with inserts, and air-cooled blades containing internal cooling fins. Individual and combined effects on spanwise blade-temperature distributions of cooling-air and radial heat conduction are determined. In general, the effects of radiation and radial heat conduction were found to be small and the omission of these variations permitted the construction of nondimensional charts for use in determining spanwise temperature distribution through air-cooled turbine blades. An approximate method for determining the allowable stress-limited blade-temperature distribution is included, with brief accounts of a method for determining the maximum allowable effective gas temperatures and the cooling-air requirements. Numerical examples that illustrate the use of the various temperature-distribution equations and of the nondimensional charts are also included.

Livingood, John N B↗
NASA NTRS1994

High-spatial-resolution passive microwave sounding systems

The principal contributions of this combined theoretical and experimental effort were to advance and demonstrate new and more accurate techniques for sounding atmospheric temperature, humidity, and precipitation profiles at millimeter wavelengths, and to improve the scientific basis for such soundings. Some of these techniques are being incorporated in both research and operational systems. Specific results include: (1) development of the MIT Microwave Temperature Sounder (MTS), a 118-GHz eight-channel imaging spectrometer plus a switched-frequency spectrometer near 53 GHz, for use on the NASA ER-2 high-altitude aircraft, (2) conduct of ER-2 MTS missions in multiple seasons and locations in combination with other instruments, mapping with unprecedented approximately 2-km lateral resolution atmospheric temperature and precipitation profiles, atmospheric transmittances (at both zenith and nadir), frontal systems, and hurricanes, (3) ground based 118-GHz 3-D spectral images of wavelike structure within clouds passing overhead, (4) development and analysis of approaches to ground- and space-based 5-mm wavelength sounding of the upper stratosphere and mesosphere, which supported the planning of improvements to operational weather satellites, (5) development of improved multidimensional and adaptive retrieval methods for atmospheric temperature and humidity profiles, (6) development of combined nonlinear and statistical retrieval techniques for 183-GHz humidity profile retrievals, (7) development of nonlinear statistical retrieval techniques for precipitation cell-top altitudes, and (8) numerical analyses of the impact of remote sensing data on the accuracy of numerical weather predictions; a 68-km gridded model was used to study the spectral properties of error growth.

Staelin, D. H.↗
DOE OSTI2021

Analysis of the Reactive CO 2 Surface Flux in Electrocatalytic Aqueous Flow Reactors

We study how the mass transfer of a chemical species in shear flow is suppressed by the production of a second species that partially reacts away the first species. The second species is produced at the surface with the first species as a reactant. Our work is directly motivated by electrochemical CO 2 reduction in aqueous flow reactors, where OH– molecules generated by the CO evolution reaction react away CO 2 molecules, ultimately inhibiting the mass transfer of CO 2 to the cathode surface. We derive a simple approximation of the Sherwood number, a dimensionless measure of the mass flux into the surface, as a function of the Péclet number, surface Damköhler number, and bulk Damköhler number, and we compare our approximation to numerical solutions of the governing equations. We find that in the diffusion-limited regime, the Sherwood number is well described by the classical Graetz-Lévêque result reduced by a reaction factor due to the competing bulk reaction; with the stoichiometry relevant to electrochemical CO 2 reduction, this reaction factor is 1/2. While the model problem we solve provides insight into how OH– production affects CO 2 mass transfer, experimental systems often involve more complex chemistry. We thus also show how a common buffered electrolyte, KHCO 3 , affects our results.

30 DIRECT ENERGY CONVERSION↗