Search NASA⌕ Search

SEARCH · Search NASA

Results for “Variational formulation”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

A generalized procedure for constructing an upwind-based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some nonlinear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to a scalar nonlinear equation and constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance to numerical experiments. Then the formulation is formally extended to the nonlinear system of equations. It is demonstrated that use of the present procedure allows easy conversion of existing central or upwind, and second- or higher-order differencing schemes so as to preserve monotonicity and to yield physically admissible solutions. The formulation is simple mathematically as well as numerically; neither matrix-vector multiplication nor Riemann solver is required. Roughly twice as much computational effort is needed as compared to conventional scheme. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made. Numerical examples including various ranges of problems show both time- and spatial-accuracy in comparison with exact solutions.

Liou, Meng-Sing↗
DOE OSTI2023

Effect of hydrogen on plasticity of $α$-Fe: A multi-scale assessment

A multi-scale study was carried out to quantify the effect of interstitial hydrogen concentration on plasticity in $α$-Fe. Here, in this work, the influence of hydrogen on the screw dislocation glide behavior was examined across several length-scales. The insights obtained were integrated to provide an accurate continuum description for the effect of hydrogen on the dislocation based plasticity in polycrystalline $α$-Fe. At the outset of this work, a new Fe—H interatomic potential was formulated that enhanced the atomistic estimation of the variation in dislocation glide behavior in presence of hydrogen. Next, the dislocation core reconstruction observed due to the addition of hydrogen using atomistic simulations was validated with the help of large-scale DFT calculations based on the DFT-FE framework. Several atomistic simulations were carried out to comprehensively quantify the effect of hydrogen on the non-Schmid behavior exhibited during the dislocation glide in $α$-Fe. Finally, crystal plasticity simulations were carried out to understand the effect of hydrogen on the meso-scale deformation behavior of polycrystalline $α$-Fe.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A Bayesian Deep Learning Approach to Near-Term Climate Prediction

Since model bias and associated initialization shock are serious shortcomings that reduce prediction skills in state-of-the-art decadal climate prediction efforts, we pursue a complementary machine-learning-based approach to climate prediction. The example problem setting we consider consists of predicting natural variability of the North Atlantic sea surface temperature on the interannual timescale in the pre-industrial control simulation of the Community Earth System Model. While previous works have considered the use of recurrent networks such as convolutional LSTMs and reservoir computing networks in this and other similar problem settings, we currently focus on the use of feedforward convolutional networks. In particular, we find that a feedforward convolutional network with a Densenet architecture is able to outperform a convolutional LSTM in terms of predictive skill. Next, we go on to consider a probabilistic formulation of the same network based on Stein variational gradient descent and find that in addition to providing useful measures of predictive uncertainty, the probabilistic (Bayesian) version improves on its deterministic counterpart in terms of predictive skill. Finally, we characterize the reliability of the ensemble of machine learning models obtained in the probabilistic setting by using analysis tools developed in the context of ensemble numerical weather prediction.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Exposing and Reducing Biases of Simulating Mixed-Phase Clouds in the Convection-Permitting E3SM Atmosphere Model: Lessons From an Arctic Cold-Air Outbreak

Mixed-phase clouds modulate the water and energy cycles of high-latitude regions, yet their liquid-ice phase partitioning has long been poorly simulated in climate models. Here, simulations of Arctic mixed-phase clouds by the Simple Cloud-Resolving E3SM Atmosphere Model (SCREAM) are assessed against large-eddy simulations, satellite data, and ground-based observations during the Cold-Air Outbreaks in the Marine Boundary Layer Experiment field campaign. SCREAM simulates nearly completely frozen clouds, which is attributed largely to the unreasonably strong Wegener–Bergeron–Findeisen (WBF) process that converts liquid to ice excessively and partly to the early over-abundant ice production at cold temperatures from a temperature-deterministic deposition ice nucleation scheme. Assuming no subgrid variation for the WBF process in the original formulation particularly conflicts with the instantaneous saturation adjustment assumption in the condensation scheme that assumes subgrid variability, leading to exaggerated WBF process rates. A proposed simple physically-based improvement on the treatment of subgrid cloud overlap substantially increases supercooled liquid water content and notably improves cloud-top phase partitioning, aligning better with observations. Improvement of supercooled liquid water content also converges with increasing horizontal resolution. The deposition ice nucleation scheme is found responsible for a falsely-produced ice cloud aloft that is not observed, biasing the simulated cloud radiative effects and top-of-atmosphere radiative fluxes. This study identifies key deficiencies in cloud parameterizations that continue to challenge convection-permitting models.

Geosciences↗
NASA NTRS1987

Prediction of added noise due to the effect of unsteady flow on pusher propellers

An analytical/computational study has been conducted to predict the effect of an upstream wing or pylon on the noise of an operating propeller. The wing trailing edge was placed at variable distances (0.1 and 0.3 chord) upstream of a scaled model propeller (SR-2). The wake was modeled using a similarity formulation. The instantaneous pressure distribution on the propeller blades during the passage through the wake was formulated in terms of a time-dependent variation of each blade section's angle of attack and in terms of the shed vortices from the blade trailing edge. It was found that the final expressions for the unsteady loads considerably altered the radiated noise pattern. Predicted noise for various observer positions, rotational speeds and propeller/pylon distances were computed and are presented in terms of the pressure time history. It has been shown that the positioning of a pylon upstream of a propeller indeed increases the noise. Some comparisons with experimental results are also given.

Takallu, M. A.↗
NASA NTRS1987

Added noise due to the effect of an upstream wake on a propeller

An analytical/computational study has been conducted to predict the effect of an upstream wing or pylon on the noise of an operating propeller. The wing trailing edge was placed at variable distances (0.1 and 0.3 chord) upstream of a scaled model propeller (SR-2). The wake was modeled using a similarity formulation. The instantaneous pressure distribution on the propeller blades during the passage through the wake was formulated in terms of a time-dependent variation of each blade section's angle of attack and in terms of the shed vortices from the blade trailing edge. It was found that the final expressions for the unsteady loads considerably altered the radiated noise pattern. Predicted noise for various observer positions, rotational speeds, and propeller/pylon distances were computed and are presented in terms of the pressure time history, harmonics of the Fourier analysis, and overall sound pressure levels (OASPL). The addition of the tangential stress due to skin friction was found to have a damping effect on the acoustic pressure time history and the resulting spectrum of the generated noise. It is shown that the positioning of a pylon upstream of a propeller indeed increases the overall noise.

Takallu, M. A.↗
NASA NTRS1989

Synthesis of organic salts with large second-order optical nonlinearities

The variation of the anion counterion in the presently formulated organic salts, whose cation possesses large molecular hyperpolarizability, will in many cases yield materials with large powder second-harmonic generation efficiencies. The highest such efficiency is three orders of magnitude greater than that of the urea used as a reference compound. It is demonstrated that such nonconventional donors as Br(-) and the pyrenyl moiety can be incorporated into molecules which, in the requisite crystallographic environment, will exhibit substantial bulk susceptibilities.

Marder, Seth R.↗
NASA NTRS1991

Linear and nonlinear dynamic analysis by boundary element method

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Ahmad, Shahid↗
DOE OSTI2025

In‐situ Analysis of Paste Properties in Resonant Acoustic Mixers for Quality Monitoring

Formulation control is key to achieving consistent target properties of energetic materials, as feedstock variations and slight deviations in the ratios of different ingredients can have major effects on final product properties, particularly in dense pastes with high particle loading >65 vol.%. In large‐scale operations, it is imperative to either correct or remove batches of material that perform outside baseline property specifications as early as possible to avoid unnecessary processing of suboptimal material. Quality monitoring is the practice of measuring material properties during processing using process analytical technologies as opposed to only testing the properties of the final product; it is a key principle in the quality‐by‐design frameworks used for designing formulations and manufacturing processes. Herein, a process analytical technology method for correlating material properties of dense pastes directly after mixing in a Resonant Acoustic Mixer to motor data is developed and used to detect differences in the particle content of dense paste formulations. This method was also capable of detecting variations in powder feedstock properties, such as particle packing efficiency, and is sensitive enough to detect changes of 2 wt.% in the total solids content of the formulation. The techniques presented herein show excellent promise for use as a process analytical technology capable of quantifying formulation effects on material movement modes during resonant acoustic mixing.

Materials science↗
DOE OSTI2020

Laminar-to-turbulent flame transition and cycle-to-cycle variations in large eddy simulation of spark-ignition engines

This paper investigates the effect of laminar-to-turbulent flame transition modeling on the prediction of cycle-to-cycle variations (CCVs) in large eddy simulation (LES) of spark-ignition (SI) engines. A laminar-to-turbulent flame transition model that describes the non-equilibrium sub-filter flame speed evolution during an early stage of flame kernel growth is developed. In the present model, the flame transition is characterized by the flame kernel size at which the flame transition ends, defined here as the flame transition scale. The proposed model captures the effects that variations in a turbulent flow field have on the evolution of early-stage burning rates, through variations in the flame transition scale. The proposed flame transition model is combined with the front propagation formulation (FPF) method and a spark-ignition model to predict CCVs in a gasoline direct injection SI engine. It is found that multi-cycle LES with the proposed flame transition model reproduces experimentally-observed CCVs satisfactorily. When the transition model is not considered or when variations in the transition process are neglected, CCVs are significantly under-predicted for the case considered here. These results indicate the importance of modeling the laminar-to-turbulent flame transition and the effect of turbulence on the transition process, when predicting CCVs, under certain engine conditions. The LES results are also used to analyze sources for variations in the flame transition. It is found, for the present engine case, that the most important source is the cycle-to-cycle variation in the turbulence dissipation rate, which is used to measure the strength of turbulence in the proposed model, near a spark plug. The large-scale velocity field and the variations of the laminar flame speed due to the mixture composition and thermal stratification are also found to be important factors to contribute to the variations in the flame transition.

42 ENGINEERING↗
NASA NTRS1993

Dynamical response of the tropical total ozone to sea surface temperature changes

Interannual variations of total ozone in the equatorial region are discussed in terms of the lower-stratospheric dynamical processes associated with sea surface temperature (SST) changes on an El Nino-Southern Oscillation time scale. Tropospheric diabatic heating by the latent heat release in convective systems drives the interannual variations of tropopause height and atmospheric vertical motions. The adiabatic cooling associated with the dynamically forced ascending motion is subject to radiative heating, which further extends the upwelling motion into the stratosphere. SST variations can thus influence total ozone amounts by changing the tropopause height and vertical advection through modulation of tropospheric diabatic heating. Mechanistic relationships that describe total ozone fluctuations through the advection effect and the tropopause effect of SST variations are derived using the equivalent potential temperature. Total ozone fluctuations are estimated using a quantitative formulation of these mechanistic equations together with the observed SST data. These results indicate that the interannual variations of the zonal wave component of equatorial total ozone are governed by the tropopause effect of SST variations. Preliminary investigation suggests that the annual cycle of tropical total ozone is coupled to the tropopause height changes under the influence of the planetary wave-induced lower-stratospheric temperature rather than local SST.

Hasebe, Fumio↗
NASA NTRS1976

A numerically efficient finite element hydroelastic analysis

A finite element hydroelastic analysis formulation is developed on the basis of Toupin's complementary variational principle. Emphasis is placed on the special case of an incompressible fluid model which is applicable to propellant tank hydroelastic analysis. A concise fluid inertia representation results from the assumption of incompressibility and the hydroelastic equations reduce to a simplified form associated with the structure alone. The efficiency of the incompressible hydroelastic formulation is enhanced for both fluid and structure by introduction of harmonic reduction as an alternative to Guyan reduction. The theoretical developments are implemented in the NASTRAN Program and the technique is verified and demonstrated as an efficient and accurate approach with a series of illustrative problems including the 1/8-scale Space Shuttle external tank.

Coppolino, R.↗
NASA NTRS1976

A numerically efficient finite element hydroelastic analysis

A finite element hydroelastic analysis formulation is developed on the basis of Toupin's complementary variational principle. Emphasis is placed on the special case of an incompressible fluid model which is applicable to propellant tank hydroelastic analysis. A concise fluid inertia representation results from the assumption of incompressibility and the hydroelastic equations reduce to a simplified form associated with the structure alone. The efficiency of the incompressible hydroelastic formulation in unhanced for both fluid and structure by introduction of harmonic reduction as an alternative to Guyan reduction. The theoretical developments are implemented in the NASTRAN Program and the technique is verified and demonstrated as an efficient and accurate approach with a series of illustrative problems including the 1/8 scale space shuttle external tank.

Coppolino, R. N.↗
DOE OSTI2023

On formulations for modeling pressurized cracks within phase-field methods for fracture

Over the past few decades, the phase-field method for fracture has seen widespread appeal due to the many benefits associated with its ability to regularize a sharp crack geometry. Along the way, several different models for including the effects of pressure loads on the crack faces have been developed. Further, this work investigates the performance of these models and compares them to a relatively new formulation for incorporating crack-face pressure loads. It is shown how the new formulation can be obtained either by modifying the trial space in the traditional variational principle or by postulating a new functional that is dependent on the rates of the primary variables. The key differences between the new formulation and existing models for pressurized cracks in a phase-field setting are highlighted. Model-based simulations developed with discretized versions of the new formulation and existing models are then used to illustrate the advantages and differences. In order to analyze the results, a domain form of the J-integral is developed for diffuse cracks subjected to pressure loads. Results are presented for a one-dimensional cohesive crack, steady crack growth, and crack nucleation from a pressurized enclosure.

42 ENGINEERING↗
NASA NTRS1974

Finite element formulations for problems of large elastic-plastic deformation

An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is suited to isotropically hardening Prandtl-Reuss materials. The formulation is given in a manner which allows any conventional finite element program, for "small strain" elasticplastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. A unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures, and a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain.

Mcmeeking, R. M.↗
NASA NTRS2015

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

Olson, Erik D.↗
NASA NTRS1992

Membrane triangles with corner drilling freedoms. I - The EFF element

The formulation of 3-node 9-DOF membrane elements with normal-to-element-plane rotations (drilling freedoms) is examined in the context of parametrized variational principles. In particular, attention is given to the application of the extended free formulation (EFF) to the construction of a triangular membrane element with drilling freedoms that initially has complete quadratic polynomial expansions in each displacement component. The main advantage of the EFF over the free formulation triangle is that an explicit form is obtained for the higher-order stiffness.

Alvin, Ken↗
DOE OSTI2021

The quest for efficient oxygenated fuels: Examining interactions between lubricant components and oxygenates

This work empirically evaluated oxygenated blendstock-lubricant compatibility using a novel but simple method. The reactivity or compatibility was evaluated via gas chromatograph equipped with a flame ionization detector (GC-FID) before and after heating for 2h at 150 °C, which would roughly mimic conditions encountered in the combustion chamber of an Spark Ignition (SI) or Compression-Ignition (CI) engine. Five oxygenate blendstocks spanning several functional groups and chain lengths (prenol, isoprenol, butyl acetate, isohexanol, polyoxymethylene dimethyl ethers) were evaluated in a base fuel with nine variations of lubricant components of controlled concentrations, including fully formulated commercial lubricants. Baseline comparative examples were also generated, to decouple the effect of the oxygenate on the mixture, by heating only the base fuel with the lubricant component. Results demonstrate the relative compatibility between noted lubricants and oxygenates in base fuel upon heating. This was illustrated by minimal to no changes in the GC-FID traces. However, reactions of several of the chosen lubricants, especially Molybdenum di (2-ethylhexyl) phosphorodithioate (Molyvan L) and zinc dialkyldithiophosphate (ZDDP), with prenol and polyoxymethylene dimethyl ethers blendstocks showed substantial side reactions compared to corresponding baseline examples. Control experiments without oxygenates but comprising the same lubricant components showed no change in the mixture with heating. We concluded the incompatibility is due to the oxygenate and not the components of the base fuel. This preliminary work is valuable in establishing trends as well as provide useful information when a new component is introduced in the fuel.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗