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Results for “Lagrangian integration”

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.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Nonlinear simulation of a flexible aircraft in maneuvering flight

A mathematical model integrating nonlinear rigid-body flight mechanics and linear aeroelastic dynamics is examined; the equations of motion for an elastic aircraft in accelerated flight are developed using Lagrangian mechanics. This approach is used to construct a simulation model of an F/A-18 (configured with tip missiles) which includes angular/elastic inertial coupling (IC). In general, the elastic modes significantly affected by IC were aerodynamically decoupled from the rest of the model. The affected modes were those which induced changes in total aircraft mass distribution. The elastic effect is noticeable if deformation-induced mass distribution changes are significant with respect to modal mass and modal frequencies. A modal parameter is presented which characterizes the level of IC between elastic momentum and rigid-body angular momentum.

Buttrill, Carey S.↗
NASA NTRS1992

Full field flow visualization and computer-aided velocity measurements in a bank of cylinders in a wind tunnel

The full field flow tracking (FFFT) method that is presented in this paper uses a laser-generated, mechanically strobed planar sheet of light, a low luminosity TV camera coupled with a long distance microscope, and a computer-controlled video recorder to study nonintrusively and qualitatively the flow structures in a bank of cylinders that are placed in a wind tunnel. This setup simulates an upscale version of the geometry of internal cooling passageways characteristic of small air-cooled radial turbines. The qualitative images supplied by the FFFT system are processed by means of a computer-integrated image quantification (CIIQ) method into quantitative information, trajectories and velocities, that describe the flow upstream of and within the bank of cylinders. The tracking method is Lagrangian in concept, and permits identification and tracking of the same particle, thus facilitating construction of time dependent trajectories and the calculation of true velocities and accelerations. The error analysis evaluates the accuracy with which the seed particles follow the flow and the errors incurred during the quantitative processing of the raw data derived from the FFFT/CIIQ method.

Braun, M. J.↗
NASA NTRS1984

Application of augmented-Lagrangian methods in meteorology: Comparison of different conjugate-gradient codes for large-scale minimization

A Lagrange multiplier method using techniques developed by Bertsekas (1982) was applied to solving the problem of enforcing simultaneous conservation of the nonlinear integral invariants of the shallow water equations on a limited area domain. This application of nonlinear constrained optimization is of the large dimensional type and the conjugate gradient method was found to be the only computationally viable method for the unconstrained minimization. Several conjugate-gradient codes were tested and compared for increasing accuracy requirements. Robustness and computational efficiency were the principal criteria.

Navon, I. M.↗
NASA NTRSDate not supplied

Numerical Simulation of Lean Blowout of Alternative Fuels in 7-element Lean Direct Injector

This research presents the result of numerically simulating 7-element swirl-venturi Lean Direct Injector (SV-LDI) lean blowout (LBO) experiments conducted at NASA Glenn Research Center in May of 2019. After simulating a cold flow case to confirm the pressure drop agrees well with the experiment, additional cases with two different fuels (an average jet fuel and a Gevo alcohol-to-jet fuel) from the National Jet Fuels Combustion Program (NJFCP) were computed to numerically determine the LBO condition. The procedure to approach the LBO follows the method used in the experiment where the air mass flow rate is gradually increased while the fuel supply is maintained. Transient history of global heat release rate as a function of air flow rate is presented, as well as temperature contours at different conditions to give a visual representation of the flame state. The Open National Combustion Code (OpenNCC) used in this research adopted reduced HyChem (Hybrid Chemistry) models along with k-LES turbulence model and a Lagrangian spray model that takes into account droplet internal temperature distribution affected by the shear force on the droplet surface. The transport equations and chemical reaction terms are integrated together to enhance conservation of chemical species that are especially important in the near LBO conditions. After showing the computed range of LBO agrees well with the experimental measurements, time averaged solutions of both fuels at their initial condition and at their limiting condition just before LBO are compared in detail to facilitate the understanding of LBO mechanism.

combustion↗
NASA NTRS1989

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

Ho, Lee-Wing↗
NASA NTRS1985

A panel method study of vortex sheets with special emphasis on sheets of axisymmetric geometry

The self induced evolution of a vortex sheet was simulated by modeling the sheet using an integration of discrete elements of vorticity. Replacing small sections of a vortex sheet by flat panels of constant vorticity is found to reproduce more accurately the initial conditions for the Lagrangian simulation technique than replacement by point vortices. The flat panel method for the vortex sheet was then extended to model axisymmetric vortex sheets. The local and far field velocities induced by the axisymmetric panels were obtained using matched asymptotic analysis, and some of the uncertainties involved in other models of the axisymmetric vortex sheet have been eliminated. One important result of this analysis is the determination of the proper choice of core size for a circular vortex filament which may replace a section of an axisymmetric vortex sheet. Roll-up of both two dimensional and axisymmetric vortex sheets was computed using the panel methods developed in the report.

Sugioka, I.↗
NASA NTRS1997

Modeling of Water Injection into a Vacuum

A loosely coupled two-phase vacuum water plume model has been developed. This model consists of a source flow model to describe the expansion of water vapor, and the Lagrangian equations of motion for particle trajectories. Gas/Particle interaction is modeled through the drag force induced by the relative velocities. Particles are assumed traveling along streamlines. The equations of motion are integrated to obtain particle velocity along the streamline. This model has been used to predict the mass flux in a 5 meter radius hemispherical domain resulting from the burst of a water jet of 1.5 mm in diameter, mass flow rate of 24.2 g/s, and stagnation pressure of 21.0 psia, which is the nominal Orbiter water dump condition. The result is compared with an empirical water plume model deduced from a video image of the STS-29 water dump. To further improve the model, work has begun to numerically simulate the bubble formation and bursting present in a liquid stream injected into a vacuum. The technique of smoothed particle hydrodynamics was used to formulate this simulation. A status and results of the on-going effort are presented and compared to results from the literature.

Alred, John W.↗
NASA NTRS2003

Tensor Fields for Use in Fractional-Order Viscoelasticity

To be able to construct viscoelastic material models from fractional0order differentegral equations that are applicable for 3D finite-strain analysis requires definitions for fractional derivatives and integrals for symmetric tensor fields, like stress and strain. We define these fields in the body manifold. We then map them ito spatial fields expressed in terms of an Eulerian or Lagrangian reference frame where most analysts prefer to solve boundary problems.

Freed, Alan D.↗
NASA NTRS2010

Aerosol Observability and Predictability: From Research to Operations for Chemical Weather Forecasting. Lagrangian Displacement Ensembles for Aerosol Data Assimilation

A challenge common to many constituent data assimilation applications is the fact that one observes a much smaller fraction of the phase space that one wishes to estimate. For example, remotely sensed estimates of the column average concentrations are available, while one is faced with the problem of estimating 3D concentrations for initializing a prognostic model. This problem is exacerbated in the case of aerosols because the observable Aerosol Optical Depth (AOD) is not only a column integrated quantity, but it also sums over a large number of species (dust, sea-salt, carbonaceous and sulfate aerosols. An aerosol transport model when driven by high-resolution, state-of-the-art analysis of meteorological fields and realistic emissions can produce skillful forecasts even when no aerosol data is assimilated. The main task of aerosol data assimilation is to address the bias arising from inaccurate emissions, and Lagrangian misplacement of plumes induced by errors in the driving meteorological fields. As long as one decouples the meteorological and aerosol assimilation as we do here, the classic baroclinic growth of error is no longer the main order of business. We will describe an aerosol data assimilation scheme in which the analysis update step is conducted in observation space, using an adaptive maximum-likelihood scheme for estimating background errors in AOD space. This scheme includes e explicit sequential bias estimation as in Dee and da Silva. Unlikely existing aerosol data assimilation schemes we do not obtain analysis increments of the 3D concentrations by scaling the background profiles. Instead we explore the Lagrangian characteristics of the problem for generating local displacement ensembles. These high-resolution state-dependent ensembles are then used to parameterize the background errors and generate 3D aerosol increments. The algorithm has computational complexity running at a resolution of 1/4 degree, globally. We will present the result of assimilating AOD retrievals from MODIS (on both Aqua and TERRA satellites) from AERONET for validation. The impact on the GEOS-5 Aerosol Forecasting will be fully documented.

da Silva, Arlindo↗
NASA NTRS1981

Quasi-Langrangian models of nascent thermals

The motions in and around an isolated thermal were studied and rising motion in the core, and sinking motion on the outside were found; while the circulation resembled that of a vortex ring. In an entity cloud model, cloudy thermal is tracked, in a Lagrangian fashion, as a discrete entity; the field of motion in and around the thermal is not explicitly simulated. Field of motion cloud models, in which the equations of motion are numerically integrated on an Eulerian grid were developed. It is shown that the great potential of a hybrid cloud model can combine the simplicity of the entity models with the generality and flexibility of the field-of-motion models. A key problem to be overcome in the development of a hybrid model is the formulation of a mathematical framework within which the cloud dynamics can be represented.

Rambaldi, S.↗
NASA NTRS1994

The permeability of the Antarctic vortex edge

Mixing and cross-vortex mass transport along isentropic surfaces in the lower stratosphere are investigated with a 'contour advection' technique and a semi-Lagrangian transport model for the Antarctic winter of 1993 using analyzed winds from the United Kingdom Meteorological Office data assimilation system. Results from the 'contour advection' technique show that at the vortex edge there exists a potential vorticity (PV) contour that has the smallest lengthening rate. This PV contour is referred to as the 'line of separation' because it essentially separates the inner and outer vortex. The average e-folding time for the lengthening of the 'line of separation' increases monotonically with altitude, ranging from about 7 days on the 350 K isentropic surface to about 105 days on the 500 K isentropic surface. The results also suggest the existence of a transition layer around the 400 K isentropic surface, above which the vortex is nearly completely isolated from the midlatitudes and below which the vortex is less isolated. Results from a semi-Lagrangian transport model with an idealized tracer initially inside the inner vortex show that at 425 K and above virtually no tracer is transported out of the vortex during a 40-day integration starting from July 21, 1993. At 400 K and below a small amount of the tracer is transported out of the vortex while the bulk of the tracer remains confined within the inner vortex.

Chen, Ping↗
NASA NTRS1991

Dynamic analysis and control of lightweight manipulators with flexible parallel link mechanisms

The flexible parallel link mechanism is designed for increased rigidity to sustain the buckling when it carries a heavy payload. Compared to a one link flexible manipulator, a two link flexible manipulator, especially the flexible parallel mechanism, has more complicated characteristics in dynamics and control. The objective of this research is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model. The step response of the analytical model and the TREETOPS model match each other well. The nonlinear dynamics is studied using a sinusoidal excitation. The actuator dynamic effect on a flexible robot was investigated. The effects are explained by the root loci and the Bode plot theoretically and experimentally. For the base performance for the advanced control scheme, a simple decoupled feedback scheme is applied.

Lee, Jeh Won↗
NASA NTRSDate not supplied

Simulation of Dust-Laden Flow in the DLR L2K Facility

An integrated CFD-particle trajectory code called US3D-DUST is used to simulate the dusty flow environments performed in the German Aerospace Center (DLR) L2K arcjet facility. The particle trajectory code uses a Lagrangian approach, where the particle trajectories through the shock layer can be computed using a set of coupled ordinary differential equations. The L2K experiments measured mass loss to flat-face shaped samples of the Norcoat-Liège thermal protection system material. The US3D-DUST simulations were able to reproduce particle velocity and stagnation point heating rate data. When applied to the L2K dusty flow conditions, the US3D-DUST predictions of mass loss due to particle impacts and surface recession rates over-predicted the experimental values. It is recommended to perform additional dusty flow tests in the L2Kto provide and improve the surface damage model for Norcoat-Liège.

Thermal protection systems↗
NASA NTRS1985

Translational and extensional energy release rates (the J- and M-integrals) for a crack layer in thermoelasticity

A number of papers have been presented on the evaluation of energy release rate for thermoelasticity and corresponding J integral. Two main approaches were developed to treat energy release rate in elasticity. The first is based on direct calculation of the potential energy rate with respect to crack length. The second makes use of Lagrangian formalism. The translational and expansional energy release rates in thermoelasticity are studied by employing the formalism of irreversible thermodynamics and the Crack Layer Approach.

Chudnovsky, A.↗
NASA NTRS1990

In defense of Ertel's potential vorticity and its general applicability as a meteorological tracer

A potential vorticity theorem and its two summary statements published by Haynes and McIntyre are challenged conceptually by equations, discussions and examples. The apparent simplification proposed by the authors to convert from a mass to volume integral, i.e., by cancelling density against the specific volume in the potential vorticity, changes the physical significance of the integrand. It no longer is the potential vorticity. The resulting mean for either a bulk Eulerian or Lagrangian system is then not analogous to a mixing ratio and therefore not independent of the broad spectrum of internal waves, the independence that makes Ertel's potential vorticity so valuable either as a stratospheric tracer or as a predictive or diagnostic, large scale, meteorological variable.

Danielsen, Edwin F.↗
NASA NTRS1995

Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes

The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfven waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfven waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions for xi(sub r), and P' across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg for xi(sub r), and P' in terms of double integrals of Hankel functions of complex argument of order 1/3 with compact analytical solutions that allow a straight- forward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpen- dicular to the magnetic field lines xi(sub perpendicular) which enables us to determine the dominant dynamics of resonant Alfven waves in dissipative MHD.

Goossens, Marcel↗
NASA NTRS1987

DYCAST: A finite element program for the crash analysis of structures

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.

Pifko, A. B.↗
NASA NTRS2015

Resurrected DSCOVR Propulsion System - Challenges and Lessons Learned

The Deep Space Climate Observatory (DSCOVR), formerly known as Triana, is a unique mission, not because of its objectives but because of how long it was in storage before launch. The Triana spacecraft was built in the late 90s and later renamed as DSCOVR, but the project was canceled before the spacecraft was launched. The nearly-complete spacecraft was put in controlled storage for 10 years, until the National Oceanic and Atmospheric Administration (NOAA) provided funding for the National Aeronautics and Space Administration (NASA) to refurbish the spacecraft. On February 11, 2015, DSCOVR was launched on a Falcon 9 v1.1 from launch complex 40 at Cape Canaveral Air Force Station. This paper describes the DSCOVR propulsion system, which utilizes ten 4.5 N thrusters in blowdown mode to perform Midcourse Correction (MCC) maneuvers, Lissajous Orbit Insertion (LOI) at Lagrangian point L1, momentum unloading maneuvers, and station keeping delta-v maneuvers at L1. This paper also describes the testing that was performed, including susbsystem-level and spacecraft-level tests, to verify the propulsion system's integrity for flight. Finally, this paper concludes with a discussion of the challenges and lessons learned during this unique mission, including replacement of a bent thruster and installation of an auxiliary heater over existing propellant line heaters.

System↗