Search NASA⌕ Search

SEARCH · Search NASA

Results for “Lagrangian 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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Multi-parametric analysis for mixed integer linear programming: An application to transmission upgrade and congestion management

Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be expanded from the perspective of the Independent System Operators (ISOs) to minimize the total system cost. We employ advanced multi-parametric programming and an enhanced branch-and-bound algorithm to address complex mixed-integer linear programming (MILP) problems, considering multi-period time constraints and physical limitations of generators and transmission lines. To characterize the various decisions in transmission expansion, we model the increased capacity of existing lines as parameters within a specified range. This study first relaxes the binary variables to continuous variables and applies the Lagrange method and Karush-Kuhn-Tucker (KKT) conditions to obtain optimal solutions and identify critical regions associated with active and inactive constraints. Moreover, we extend the traditional branch-and-bound (B&B) method by determining the problem’s upper and lower bounds at each node of the B&B decision tree, helping to manage computational challenges in large-scale MILP problems. Here, we compare the difference between the upper and lower bounds to obtain an approximate optimal solution within the decision-makers’ tolerable error range. In addition, the first derivative of the objective function on the parameters of each line is used to inform the selection of lines for easing congestion and maximizing social welfare. Finally, the capacity upgrades are selected by weighing the reductions in system costs against the expense of upgrading line capacities. The findings are supported by numerical simulations and provide transmission-line planners with decision-making guidance.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1981

Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams

Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.

Noor, A. K.↗
NASA NTRS1992

A two-phase restricted equilibrium model for combustion of metalized solid propellants

An Eulerian-Lagrangian two-phase approach was adopted to model the multi-phase reacting internal flow in a solid rocket with a metalized propellant. An Eulerian description was used to analyze the motion of the continuous phase which includes the gas as well as the small (micron-sized) particulates, while a Lagrangian description is used for the analysis of the discrete phase which consists of the larger particulates in the motor chamber. The particulates consist of Al and Al2O3 such that the particulate composition is 100 percent Al at injection from the propellant surface with Al2O3 fraction increasing due to combustion along the particle trajectory. An empirical model is used to compute the combustion rate for agglomerates while the continuous phase chemistry is treated using chemical equilibrium. The computer code was used to simulate the reacting flow in a solid rocket motor with an AP/HTPB/Al propellant. The computed results show the existence of an extended combustion zone in the chamber rather than a thin reaction region. The presence of the extended combustion zone results in the chamber flow field and chemical being far from isothermal (as would be predicted by a surface combustion assumption). The temperature in the chamber increases from about 2600 K at the propellant surface to about 3350 K in the core. Similarly the chemical composition and the density of the propellant gas also show spatially non-uniform distribution in the chamber. The analysis developed under the present effort provides a more sophisticated tool for solid rocket internal flow predictions than is presently available, and can be useful in studying apparent anomalies and improving the simple correlations currently in use. The code can be used in the analysis of combustion efficiency, thermal load in the internal insulation, plume radiation, etc.

Sabnis, J. S.↗
NASA NTRS2018

Improved Rice Residue Burning Emissions Estimates: Accounting for Practice-Specific Emission Factors in Air Pollution Assessments of Vietnam

In Southeast Asia and Vietnam, rice residues are routinely burned after the harvest to prepare fields for the next season. Specific to Vietnam, the two prevalent burning practices include: a). piling the residues after hand harvesting; b). burning the residues without piling, after machine harvesting. In this study, we synthesized field and laboratory studies from the literature on rice residue burning emission factors for Particulate Matter less than 2.5 microns (PM2.5). We found significant differences in the resulting burning-practice specific emission factors, with 16.9 grams per square kilogram (plus or minus 6.9) for pile burning and 8.8 grams per square kilogram (plus or minus 3.5) for non-pile burning. We calculated burning practice specific emissions based on rice area data, region-specific fuel-loading factors, combined emission factors, and estimates of burning from the literature. Our results for year 2015 estimate 180 gigagrams of PM2.5 result from the pile burning method and 130 gigagrams result from non-pile burning method, with the most-likely current emission scenario of 150 gigagrams PM2.5 emissions for Vietnam. For comparison purposes, we calculated emissions using generalized agricultural emission factors employed in global biomass burning studies. These results estimate 80 gigagrams PM2.5, which is only 44 percent of the pile burning-based estimates, suggesting underestimation in previous studies. We compare our emissions to an existing all-combustion sources inventory, results show emissions account for 14-18 percent of Vietnam's total PM2.5 depending on burning practice. Within the highly-urbanized and cloud-covered Hanoi Capital region (HCR), we use rice area from Sentinel-1A to derive spatially-explicit emissions and indirectly estimate residue burning dates. Results from HYSPLIT (Hybrid Single-Particle Lagrangian Integrated Trajectory) back-trajectory analysis stratified by season show autumn has most emission trajectories originating in the North, while spring has most originating in the South, suggesting the latter may have bigger impact on air quality. From these results, we highlight locations where emission mitigation efforts could be focused and suggest measures for pollutant mitigation. Our study demonstrates the need to account for emissions variation due to different burning practices.

Air Pollution↗
NASA NTRS2012

Ice Accretion Modeling using an Eulerian Approach for Droplet Impingement

A three-dimensional Eulerian analysis has been developed for modeling droplet impingement on lifting bodes. The Eulerian model solves the conservation equations of mass and momentum to obtain the droplet flow field properties on the same mesh used in CFD simulations. For complex configurations such as a full rotorcraft, the Eulerian approach is more efficient because the Lagrangian approach would require a significant amount of seeding for accurate estimates of collection efficiency. Simulations are done for various benchmark cases such as NACA0012 airfoil, MS317 airfoil and oscillating SC2110 airfoil to illustrate its use. The present results are compared with results from the Lagrangian approach used in an industry standard analysis called LEWICE.

Kim, Joe Woong↗
NASA NTRS1975

Analysis of liquid rocket combustion chamber turbulence levels from diffusion data

The intensity of turbulence and the Lagrangian correlation coefficient in a liquid-rocket combustion chamber have been analytically determined from an analysis of experimental diffusion data obtained in a small rocket engine which operated at 300-psia chamber pressure and produced approximately 250 pounds thrust. Results of gas-sample measurements obtained by Orsat and gas-chromatograph techniques to determine helium-concentration profiles were analyzed on the basis of Taylor's (1921) turbulent diffusion theory to obtain turbulence flow-field parameters. The results of the analysis indicate that turbulent diffusion in a combustion chamber can be adequately modeled by the one-dimensional Taylor theory, which assumes that the intensity of turbulence is a function only of axial distance in the chamber and that the Lagrangian correlation coefficient is expressed by a power law. The results indicate a higher intensity of turbulence and lower correlation than previously expected.

Smith, L. O., Jr.↗
DOE OSTI2025

Analysis of Σ* via isospin selective reaction 𝐾 𝐿 ⁢𝑝 →𝜋 + ⁢Σ 0

The isospin-selective reaction 𝐾 𝐿 ⁢𝑝 →𝜋 + ⁢Σ 0 provides a clean probe for investigating 𝐼 =1 Σ* resonances. In this work, we perform an analysis of this reaction using an effective Lagrangian approach for the first time, incorporating the well-established Σ⁡(1189)⁢1/2 + , Σ⁡(1385)⁢3/2 + , Σ⁡(1670)⁢3/2 − , and Σ⁡(1775)⁢5/2 − states, while also exploring contributions from other unestablished states. By fitting the available differential cross-section and recoil polarization data, adhering to partial-wave phase conventions same as the Particle Data Group, we find that besides the established resonances, contributions from Σ⁡(1660)⁢1/2 + , Σ⁡(1580)⁢3/2 − , and a Σ*⁢(1/2 − ) improve the description. Notably, a Σ*⁢(1/2 − ) resonance with mass around 1.54 GeV, consistent with Σ⁡(1620)⁢1/2 − , is found to be essential for describing the data in this channel, a stronger indication than found in previous analyses focusing on 𝜋⁢Λ final states. While providing complementary support for Σ⁡(1660)⁢1/2 + and Σ⁡(1580)⁢3/2 − , our results highlight the importance of the Σ⁡(1620)⁢1/2 − region in 𝐾 𝐿 ⁢𝑝 →𝜋 + ⁢Σ 0 . Future high-precision measurements are needed to solidify these findings and further constrain the Σ* spectrum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1978

CELFE: Coupled Eulerian-Lagrangian Finite Element program for high velocity impact. Part 1: Theory and formulation

A 3-D finite element program capable of simulating the dynamic behavior in the vicinity of the impact point, together with predicting the dynamic response in the remaining part of the structural component subjected to high velocity impact is discussed. The finite algorithm is formulated in a general moving coordinate system. In the vicinity of the impact point contained by a moving failure front, the relative velocity of the coordinate system will approach the material particle velocity. The dynamic behavior inside the region is described by Eulerian formulation based on a hydroelasto-viscoplastic model. The failure front which can be regarded as the boundary of the impact zone is described by a transition layer. The layer changes the representation from the Eulerian mode to the Lagrangian mode outside the failure front by varying the relative velocity of the coordinate system to zero. The dynamic response in the remaining part of the structure described by the Lagrangian formulation is treated using advanced structural analysis. An interfacing algorithm for coupling CELFE with NASTRAN is constructed to provide computational capabilities for large structures.

Lee, C. H.↗
NASA NTRS1980

The narrow rings of Jupiter, Saturn and Uranus

The origin of the newly discovered narrow ring systems around Jupiter, Saturn and Uranus is considered. It is pointed out that both the Uranian and Jovian ring systems have mean orbital radii of 1.8 planetary radii and lie within the Roche zones of their respective planets, and it is suggested that the Jovian ring is the product of the disintegration of a satellite that entered the Roche zone, and that large numbers of small particles are now in horseshoe orbits about the Lagrangian equilibrium points of the remnant chunks. Analysis of the path of a ring particle in a horseshoe orbit is shown to result in ring structures in agreement with those observed for the circular rings of Jupiter and the highly eccentric ring of Uranus. The stability of these ring systems is then considered, and it is suggested that the F ring of Saturn, which lies outside the Roche zone, represents primordial matter not yet accreted by small satellites just inside the Mimas first-order resonances.

Dermott, S. F.↗
NASA NTRS2004

Non-Deterministic Dynamic Instability of Composite Shells

A computationally effective method is described to evaluate the non-deterministic dynamic instability (probabilistic dynamic buckling) of thin composite shells. The method is a judicious combination of available computer codes for finite element, composite mechanics, and probabilistic structural analysis. The solution method is incrementally updated Lagrangian. It is illustrated by applying it to thin composite cylindrical shell subjected to dynamic loads. Both deterministic and probabilistic buckling loads are evaluated to demonstrate the effectiveness of the method. A universal plot is obtained for the specific shell that can be used to approximate buckling loads for different load rates and different probability levels. Results from this plot show that the faster the rate, the higher the buckling load and the shorter the time. The lower the probability, the lower is the buckling load for a specific time. Probabilistic sensitivity results show that the ply thickness, the fiber volume ratio and the fiber longitudinal modulus, dynamic load and loading rate are the dominant uncertainties, in that order.

Chamis, Christos C.↗
NASA NTRS2009

Dynamic Probabilistic Instability of Composite Structures

A computationally effective method is described to evaluate the non-deterministic dynamic instability (probabilistic dynamic buckling) of thin composite shells. The method is a judicious combination of available computer codes for finite element, composite mechanics and probabilistic structural analysis. The solution method is incrementally updated Lagrangian. It is illustrated by applying it to thin composite cylindrical shell subjected to dynamic loads. Both deterministic and probabilistic buckling loads are evaluated to demonstrate the effectiveness of the method. A universal plot is obtained for the specific shell that can be used to approximate buckling loads for different load rates and different probability levels. Results from this plot show that the faster the rate, the higher the buckling load and the shorter the time. The lower the probability, the lower is the buckling load for a specific time. Probabilistic sensitivity results show that the ply thickness, the fiber volume ratio and the fiber longitudinal modulus, dynamic load and loading rate are the dominant uncertainties in that order.

Chamis, Christos C.↗
NASA NTRS1982

Geometrically nonlinear analysis of layered composite shells

Two kinds of finite-element analyses are developed for the geometrically nonlinear study of the large deformations in laminated composite structures, especially shells. The first kind of finite-element analysis utilizes the general incremental variational formulation as well as the total Lagrangian description of motion, and a three-dimensional degenerate element is adopted. The second kind of analysis employs a formulation based on deformable shell theory, and the plate-bending element is used. Numerical results for bending are presented for five plate and shell structures of isotropic as well as orthotropic composition, including an isotropic cylindrical panel with uniform loading and a laminated cylindrical panel with uniform loading. The results obtained using these analyses are found to be in good agreement with those available in the literature.

Chao, W. C.↗
NASA NTRS1978

CELFE/NASTRAN Code for the Analysis of Structures Subjected to High Velocity Impact

CELFE (Coupled Eulerian Lagrangian Finite Element)/NASTRAN Code three-dimensional finite element code has the capability for analyzing of structures subjected to high velocity impact. The local response is predicted by CELFE and, for large problems, the far-field impact response is predicted by NASTRAN. The coupling of the CELFE code with NASTRAN (CELFE/NASTRAN code) and the application of the code to selected three-dimensional high velocity impact problems are described.

Chamis, C. C.↗
NASA NTRS1982

Analysis of the decay of temperature fluctuations in isotropic turbulence

The Lagrangian dispersion theory of Durbin (1980) is used to analyze experiments by Warhaft and Lumley (1978) and by Sreenivasan et al. (1980) on temperature fluctuations in grid-generated turbulence. Both theory and experiment show that the decay exponent m depends on the ratio of the initial length scales of velocity and temperature, although when this ratio is greater than 2.5 such dependence is negligible. The theory shows that m is not truly constant, but within the range covered by the experiments it is nearly so. The agreement between theory and experiment lends credence to the idea that the decay of fluctuations is controlled largely by turbulent relative dispersion.

Durbin, P. A.↗
NASA NTRS1984

Finite element analysis of steadily moving contact fields

By introducing a moving updated Lagrangian observer, this paper develops traveling finite elements with the capacity to handle the global response resulting from steadily moving contact fields. The generality of the results is such that large deformation kinematics and kinetics as well as the full compliment of inertial fields can be handled. To streamline the handling of nonlinear behavior, an elliptically constrained solution algorithm is also developed. Employing this algorithm, the results of several numerical benchmarking studies are presented which illustrate the capacity of the moving updated Lagrangian formulation as well as the potential effects of nonlinearity.

Padovan, J.↗
NASA NTRS1983

Geometrically nonlinear analysis of layered composite plates and shells

A degenerated three dimensional finite element, based on the incremental total Lagrangian formulation of a three dimensional layered anisotropic medium was developed. Its use in the geometrically nonlinear, static and dynamic, analysis of layered composite plates and shells is demonstrated. A two dimenisonal finite element based on the Sanders shell theory with the von Karman (nonlinear) strains was developed. It is shown that the deflections obtained by the 2D shell element deviate from those obtained by the more accurate 3D element for deep shells. The 3D degenerated element can be used to model general shells that are not necessarily doubly curved. The 3D degenerated element is computationally more demanding than the 2D shell theory element for a given problem. It is found that the 3D element is an efficient element for the analysis of layered composite plates and shells undergoing large displacements and transient motion.

Chao, W. C.↗
NASA NTRSDate not supplied

Calculating the Height of Volcanic Cloud SO2 With a Lagrangian Trajectory Tool: Raikoke (2019) and Pinatubo (1991) Cases

We have developed a new data analysis tool to reconstruct the altitude of SO2 clouds ejected by avolcanic eruption. Starting with 2D fields of satellite observed SO2 column density, known volcanolocation, and reanalysis wind fields, the Goddard Lagrangian trajectory tool allows us to estimatethe altitude and local concentration of SO2 at the time of observation. We demonstrate this tool forthe June 21, 2019 Mt. Raikoke eruption (8h, 30h and 78 hours after eruption). We use SO2 data fromthe Ozone Mapping and Profiler Suite/Nadir Mapper (OMPS/NM) onboard the NASA-NOAASuomi National Polar Partnership satellite and the Tropospheric Monitoring Instrument(TROPOMI) onboard the European Copernicus Sentinel 5 precursor satellite and wind fields fromthe NASA Goddard Earth Observing System (GEOS) model. We obtained a wide distribution ofSO2 altitudes between 1 and 19 kilometers in different parts of the Raikoke SO2 clouds, with thehighest SO2 concentration between 11 and 16 km, in good agreement with data from independentSO2 layer height retrievals from TROPOMI and Infrared Atmospheric Sounding Interferometer(IASI). We then applied this method to the June 15, 1991 Mt. Pinatubo eruption using SO2 columnmeasurements from the NASA Total Ozone Mapping Spectrometer (TOMS) on June 16, 17, 18 andusing wind fields from the National Centers for Environmental Prediction Reanalysis version 2. Weobtained a wide distribution of SO2 heights from 6 km up to 30 km in the northern part of the cloud.We use our new trajectory tool to reconstruct volcanic SO2/aerosol emission sources as functions oftime and altitude, providing inputs to the GEOS model aerosol and chemistry schemes in order tosimulate the dispersion of volcanic SO2 and aerosol clouds from these events.

SO2↗