Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Convergence analysis”

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.

At least 1,585 records · Page 88

The solution of linear systems of equations with a structural analysis code on the NAS CRAY-2

Two methods for solving linear systems of equations on the NAS Cray-2 are described. One is a direct method; the other is an iterative method. Both methods exploit the architecture of the Cray-2, particularly the vectorization, and are aimed at structural analysis applications. To demonstrate and evaluate the methods, they were installed in a finite element structural analysis code denoted the Computational Structural Mechanics (CSM) Testbed. A description of the techniques used to integrate the two solvers into the Testbed is given. Storage schemes, memory requirements, operation counts, and reformatting procedures are discussed. Finally, results from the new methods are compared with results from the initial Testbed sparse Choleski equation solver for three structural analysis problems. The new direct solvers described achieve the highest computational rates of the methods compared. The new iterative methods are not able to achieve as high computation rates as the vectorized direct solvers but are best for well conditioned problems which require fewer iterations to converge to the solution.

Poole, Eugene L.↗

Euler Technology Assessment program for preliminary aircraft design employing SPLITFLOW code with Cartesian unstructured grid method

This report documents results from the Euler Technology Assessment program. The objective was to evaluate the efficacy of Euler computational fluid dynamics (CFD) codes for use in preliminary aircraft design. Both the accuracy of the predictions and the rapidity of calculations were to be assessed. This portion of the study was conducted by Lockheed Fort Worth Company, using a recently developed in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages for this study, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaptation of the volume grid during the solution convergence to resolve high-gradient flow regions. This proved beneficial in resolving the large vortical structures in the flow for several configurations examined in the present study. The SPLITFLOW code predictions of the configuration forces and moments are shown to be adequate for preliminary design analysis, including predictions of sideslip effects and the effects of geometry variations at low and high angles of attack. The time required to generate the results from initial surface definition is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.

Finley, Dennis B.↗

Structural Modeling of a Five-Meter Thin Film Inflatable Antenna/Concentrator With Rigidized Support Struts

Dynamic characterization of a non-rigidized thin film inflatable antenna/solar concentrator structure with rigidized composite support struts is described in detail. A two-step finite element modeling approach in MSC/NASTRAN is utilized, consisting of: (1) a nonlinear static pressurization procedure used to obtain the updated stiffness matrix, and (2) a modal "restart" eigen solution that uses the modified stiffness matrix. Unique problems encountered in modeling of this large 5-m lightweight inflatable are identified, including considerable difficulty in obtaining convergence in the nonlinear pressurization solution. It was found that the extremely thin polyimide film material (.001 in or I mil) presents tremendous problems in obtaining a converged solution when internal pressure loading is applied. It was concluded that the ratios of film thickness to other geometric dimensions such as torus cross-sectional and ring diameter and lenticular diameter are the critical parameters for convergence of the pressurization procedure. Comparison of finite element predictions for frequency and mode shapes with experimental results indicated reasonable agreement considering the complexity of the structure, the film-to-air interaction, and the nonlinear material properties of the film. It was also concluded that analysis should be done using different finite element to codes to determine if a more robust and stable solution can be obtained.

Smalley, Kurt B.↗

Evolutionary convergence in lignin-degrading enzymes

The resurrection of ancestral enzymes of now-extinct organisms (paleogenetics) is a developing field that allows the study of evolutionary hypotheses otherwise impossible to be tested. In the present study, we target fungal peroxidases that play a key role in lignin degradation, an essential process in the carbon cycle and often a limiting step in biobased industries. Ligninolytic peroxidases are secreted by wood-rotting fungi, the origin of which was recently established in the Carboniferous period associated with the appearance of these enzymes. These first peroxidases were not able to degrade lignin directly and used diffusible metal cations to attack its phenolic moiety. The phylogenetic analysis of the peroxidases of Polyporales, the order in which most extant wood-rotting fungi are included, suggests that later in evolution these enzymes would have acquired the ability to degrade nonphenolic lignin using a tryptophanyl radical interacting with the bulky polymer at the surface of the enzyme. Here, we track this powerful strategy for lignin degradation as a phenotypic trait in fungi and show that it is not an isolated event in the evolution of Polyporales. Using ancestral enzyme resurrection, we study the molecular changes that led to the appearance of the same surface oxidation site in two distant peroxidase lineages. By characterization of the resurrected enzymes, we demonstrate convergent evolution at the amino acid level during the evolution of these fungi and track the different changes leading to phylogenetically distant ligninolytic peroxidases from ancestors lacking the ability to degrade nonphenolic lignin.

59 BASIC BIOLOGICAL SCIENCES↗

Analysis of a Pneumatic Probe for Measuring Exhaust-Gas Temperatures with Some Preliminary Experimental Results

A pneumatic probe based on continuity of mass flow through two restrictions separated by a cooling chamber was constructed to measure gas temperature at and beyond the limit of thermocouples. This probe consisted of a subsonic flat-plate orifice for the first restriction and a sonic-flow converging-diverging nozzle for the second restriction. The effect of variation in gas constants on the calibration is examined for common engine-exhaust gases. A high-temperature wind tunnel that allowed calibration of the probe at temperatures up to 2000 deg R and. Mach numbers up to 0.8 is described. Agreement to better than 30 deg R between pneumatic probe indication and the indication of a rake of radiation shielded thermocouples indicates that extrapolation of the calibration to higher temperatures is possible with fair accuracy

Scadron, Marvin D.↗

Numerical Modeling of a Vortex Stabilized Arcjet

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased. The technique was used to predict the flow through a typical arcjet thruster geometry. Results indicate swirl and viscosity play an important role in the complex geometry of an arcjet.

Pawlas, Gary E.↗

Automated ICRF heating surrogate modeling via machine learning

This work introduces automated machine learning workflows that address critical bottlenecks in surrogate model development for Ion Cyclotron Range of Frequencies (ICRF) heating applications. The automated framework includes data analysis tools that transform raw datasets into actionable insights in seconds, replacing weeks of manual exploratory effort and ensuring consistent, reproducible dataset characterization. By integrating advanced hyperparameter optimization (HPO) methods including Bayesian optimization via BoTorch and Tree-structured Parzen Estimators (TPE), the framework significantly reduces model development time from weeks to hours, decreasing computational cost and required expertise, while enabling high-accuracy surrogate models. Compared to traditional hyperparameter scanning (HPS) techniques such as methodical, randomized, and grid searches, HPO methods achieve superior convergence and predictive performance, even when compared to already well-tuned reference models. On NSTX High Harmonic Fast Wave (HHFW) heating datasets, both Random Forest Regressor (RFR) and neural network surrogates demonstrate improved accuracy, achieving R 2 values beyond 0.97 and 0.98, respectively. The results show that while HPO gains are modest for robust architectures like RFR, they become essential for more sensitive models such as neural networks, highlighting the trade-offs across optimization strategies. Through automated workflows that eliminate manual hyperparameter tuning and require minimal ML expertise, this work enables widespread adoption of high-fidelity surrogate models across the fusion community for real-time plasma control, uncertainty quantification, rapid experimental scenario development, and integrated system optimization.

Sanchez-Villar, Alvaro [Princeton Plasma Physics L↗

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗

Designing a Stochastic Adaptive Impulsive Observer for Stochastic Linear and Nonlinear Impulsive Systems

State observation (estimation) is a very important issue in system analysis and control. This paper develops a new observer called Stochastic Adaptive Impulsive Observer (SAIO) for the state estimation of impulsive systems. The proposed observer is applicable to linear and nonlinear stochastic impulsive systems. In addition, the effect of parametric uncertainty is considered and unknown parameters of the system are estimated by suitable adaptation laws. Impulsive system theory, particularly stochastic Lyapunov-like function, is used to analyze the stability and convergence of the state estimations. The main advantages of the proposed observer are: 1) it gives continuous estimation from discrete time measurements of the system output, and 2) it is useful for state estimation when continuous measurements are impossible or expensive. Simulation results show the effectiveness of the proposed observer and we believe that it has many applications in control and estimation theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Construction of a Code Verification Matrix for Heat Conduction With Finite Element Code Applications

When establishing the pedigree of a simulation tool, code verification is used to ensure that the implemented numerical algorithm is a faithful representation of its underlying mathematical model. During this process, numerical results on various meshes are systematically compared to a reference analytic solution. The selection of analytic solutions can be a laborious process, as it is difficult to establish adequate code confidence without performing redundant work. In this report we address this issue by applying a physics-based process that establishes a set of reference problems. In this process, code simulation options are categorized and systematically tested, which ensures that gaps in testing are easily identified and addressed. The resulting problems are primarily intended for code verification analysis but may also be useful for comparison to other simulation codes, troubleshooting activities, or training exercises. The process is used to select fifteen code verification problems relevant for the one-dimensional steady-state heat conduction equation. These problems are applicable to a wide variety of simulation tools, but, in this work, a demonstration is performed using the finite element-based nuclear fuel performance code BISON. Convergence to the analytic solution at the theoretical rate is quantified for a selection of the problems, which establishes a baseline pedigree for the code. Not only can this standard set of conduction solutions be used for verification of other codes, but also the physics-based process for selecting problems can be utilized to quantify and expand testing for any simulation tool.

42 ENGINEERING↗

A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms

Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. Here we show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. Finally, the rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.

97 MATHEMATICS AND COMPUTING↗

Studying the Collective Functional Response of a Receptor in Alchemical Ligand Binding Free Energy Simulations with Accelerated Solvation Layer Dynamics

Ligand binding free energy simulations (LB-FES) that involve sampling of protein functional conformations have been longstanding challenges in research on molecular recognition. Particularly, modeling of the conformational transition pathway and design of the heuristic biasing mechanism are severe bottlenecks for the existing enhanced configurational sampling (ECS) methods. Inspired by the key role of hydration in regulating conformational dynamics of macromolecules, this report proposes a novel ECS approach that facilitates binding-associated structural dynamics by accelerated hydration transitions in combination with the lambda-exchange of free energy perturbation (FEP). Further, two challenging protein-ligand binding processes involving large configurational transitions of the receptor are studied, with hydration transitions at binding sites accelerated by Hamiltonian-simulated annealing of the hydration layer. Without the need for pathway analysis or ad hoc barrier flattening potential, LB-FES were performed with FEP/lambda-exchange molecular dynamics simulation at a minor overhead for annealing of the hydration layer. The LB-FES studies showed that the accelerated rehydration significantly enhances the collective conformational transitions of the receptor, and convergence of binding affinity calculations is obtained at a sweet-spot simulation time scale. Alchemical LB-FES with the proposed ECS strategy is free from the effort of trial and error for the setup and realizes efficient on-the-fly sampling for the collective functional response of the receptor and bound water and therefore presents a practical approach to high-throughput screening in drug discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The full squeezed CMB bispectrum from inflation

The small-scale CMB temperature we observe on the sky is modulated by perturbations that were super-horizon at recombination, giving differential focussing and lensing that generate a non-zero bispectrum even for single-field inflation where local physics is identical. Understanding this signal is important for primordial non-Gaussianity studies and also parameter constraints from the CMB lensing bispectrum signal. Because of cancellations individual effects can appear larger or smaller than they are in total, so a full analysis may be required to avoid biases. I relate angular scales on the sky to physical scales at recombination using the optical equations, and give full-sky results for the large-scale adiabatic temperature bispectrum from Ricci focussing (expansion of the ray bundle), Weyl lensing (convergence and shear), and temperature redshift modulations of small-scale power. The δN expansion of the beam is described by the constant temperature 3-curvature, and gives a nearly-observable version of the consistency relation prediction from single-field inflation. I give approximate arguments to quantify the likely importance of dynamical effects, and argue that they can be neglected for modulation scales l∼<100, which is sufficient for lensing studies and also allows robust tests of local primordial non-Gaussianity using only the large-scale modulation modes. For accurate numerical results early and late-time ISW effects must be accounted for, though I confirm that the late-time non-linear Rees-Sciama contribution is negligible compared to other more important complications. The total corresponds to f{sub NL} ∼ 7 for Planck-like temperature constraints and f{sub NL} ∼ 11 for cosmic-variance limited data to l{sub max} = 2000. Temperature lensing bispectrum estimates are affected at the 0.2σ level by Ricci focussing, and up to 0.5σ with polarization.

79 ASTRONOMY AND ASTROPHYSICS↗

Experimental Verification of Pulse Shaping in Elastic Metamaterials Under Impact Excitation

Here, we present experimental verification of pulse shaping in elastic metamaterials together with a procedure to design, fabricate, and verify metamaterial pulse shapers under impact excitation. The split Hopkinson pressure bar (SHPB) test, a fundamental dynamic test introduced more than 70 years ago, often incorporates pulse shaping as a means to alter a stress wave, providing the primary motivation for the presented study. Elastic metamaterials hold promise for enhancing conventional pulse shaping abilities and improving capabilities of the SHPB test. We first design the pulse shaper by numerically optimizing its response using finite element analysis. The pulse shaper consists of repeated unit cells based on a combination of a phononic crystal and a local resonator. Then, we fabricate and test pulse shaper candidates to validate the procedural efficacy. An iterative element corrects inaccuracies in input force and material properties and allows convergence on an appropriate pulse shaper. We carry out this procedure by designing pulse shapers fabricated from 3D-printed polylactic acid (PLA) to achieve an extended dwell acceleration pulse shape. In experimental impact tests, the procedure results in rise, dwell, and fall behaviors comparable to that predicted, effectively confirming the efficacy of the presented procedure and verifying the performance of metamaterial-based pulse shapers.

36 MATERIALS SCIENCE↗

Equation solving program for aerodynamic lifting surface theory

A description of and user's manual are presented for one of a group of FORTRAN programs which, together, can be used for the analysis and design of wings in steady, subsonic flow according to a kernel function method lifting surface theory. This particular program is the one which solves the sets of simultaneous, linear, algebraic equations arising from the thin wing analysis. This program has the capability of striking out rows and columns of the aerodynamic influence matrix and rows of the associated boundary condition vectors (right hand sides). This capability significantly enhances the effectiveness of the kernel function method of lifting surface theory because studies of the convergence of solutions with the number of control points can be done with the calculation of only a single influence matrix.

Medan, R. T.↗

Diurnal variation of the Outgoing Long-Wave Radiation - As revealed by the E.R.B.E

The diurnal variation of the Outgoing Longwave Radiation (OLR) and its annual variation were studied using scanner products from the Earth Radiation Budget Experiment (ERBE). Data from the combination of sun synchronous polar orbiter NOAA-9 and mid-inclined precessing orbit Earth Radiation Budget Satellite (ERBS), which provide the best diurnal global coverage, were used for the period of March 1985 to February 1986. Harmonic analysis was performed on monthly mean hourly OLR for both average sky and clear sky conditions in order to obtain the amplitude and phase of the OLR diurnal cycle. Large diurnal amplitudes are noticed mostly over desert regions. Over oceans, convectively active regions like the Inter Tropical Convergence Zone (ITCZ) and the South Pacific Convergence Zone (SPCZ) show noticeable diurnal variation compared to the rest of the regions. Annual variation of the OLR diurnal amplitude was compared with annual variation of the various earth radiation budget parameters. A good relationship was found between the OLR diurnal amplitude and the monthly mean net radiation and incoming solar radiation.

Kondragunta, Chandrasekhara R.↗

Numerical simulation of steady and unsteady viscous flow in turbomachinery using pressure based algorithm

The objective of this research is to simulate steady and unsteady viscous flows, including rotor/stator interaction and tip clearance effects in turbomachinery. The numerical formulation for steady flow developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, and is applicable to both viscous and inviscid flows. The values of these artificial dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and artificial dissipation, that the tip clearance flow field can be captured accurately. The above numerical formulation was modified to incorporate time accurate solutions. An inner loop iteration scheme is used at each time step to account for the non-linear effects. The computation of unsteady flow through a flat plate cascade subjected to a transverse gust reveals that the choice of grid spacing and the amount of artificial dissipation is critical for accurate prediction of unsteady phenomena. The rotor-stator interaction problem is simulated by starting the computation upstream of the stator, and the upstream rotor wake is specified from the experimental data. The results show that the stator potential effects have appreciable influence on the upstream rotor wake. The predicted unsteady wake profiles are compared with the available experimental data and the agreement is good. The numerical results are interpreted to draw conclusions on the unsteady wake transport mechanism in the blade passage.

Lakshminarayana, B.↗