Search NASA⌕ Search

SEARCH · Search NASA

Results for “Lagrangian function”

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 127 records · Page 7

Towards understanding turbulent scalar mixing

In an effort towards understanding turbulent scalar mixing, we study the effect of molecular mixing, first in isolation and then by accounting for the effects of the velocity field. The chief motivation for this approach stems from the strong resemblance of the scalar probability density function (PDF) obtained from the scalar field evolving from the heat conduction equation that arises in a turbulent velocity field. However, the evolution of the scalar dissipation is different for the two cases. We attempt to account for these differences, which are due to the velocity field, using a Lagrangian frame analysis. After establishing the usefulness of this approach, we use the heat-conduction simulations (HCS), in lieu of the more expensive direct numerical simulations (DNS), to study many of the less understood aspects of turbulent mixing. Comparison between the HCS data and available models are made whenever possible. It is established that the beta PDF characterizes the evolution of the scalar PDF during mixing from all types of non-premixed initial conditions.

Girimaji, Sharath S.↗

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↗

Current Status on the use of Parallel Computing in Turbulent Reacting Flow Computations Involving Sprays, Monte Carlo PDF and Unstructured Grids

The state of the art in multidimensional combustor modeling as evidenced by the level of sophistication employed in terms of modeling and numerical accuracy considerations, is also dictated by the available computer memory and turnaround times afforded by present-day computers. With the aim of advancing the current multi-dimensional computational tools used in the design of advanced technology combustors, a solution procedure is developed that combines the novelty of the coupled CFD/spray/scalar Monte Carlo PDF (Probability Density Function) computations on unstructured grids with the ability to run on parallel architectures. In this approach, the mean gas-phase velocity and turbulence fields are determined from a standard turbulence model, the joint composition of species and enthalpy from the solution of a modeled PDF transport equation, and a Lagrangian-based dilute spray model is used for the liquid-phase representation. The gas-turbine combustor flows are often characterized by a complex interaction between various physical processes associated with the interaction between the liquid and gas phases, droplet vaporization, turbulent mixing, heat release associated with chemical kinetics, radiative heat transfer associated with highly absorbing and radiating species, among others. The rate controlling processes often interact with each other at various disparate time 1 and length scales. In particular, turbulence plays an important role in determining the rates of mass and heat transfer, chemical reactions, and liquid phase evaporation in many practical combustion devices.

Raju, M. S.↗

Stratospheric aircraft exhaust plume and wake chemistry

Progress to date in an ongoing study to analyze and model emissions leaving a proposed High Speed Civil Transport (HSCT) from when the exhaust gases leave the engine until they are deposited at atmospheric scales in the stratosphere is documented. A kinetic condensation model was implemented to predict heterogeneous condensation in the plume regime behind an HSCT flying in the lower stratosphere. Simulations were performed to illustrate the parametric dependence of contrail droplet growth on the exhaust condensation nuclei number density and size distribution. Model results indicate that the condensation of water vapor is strongly dependent on the number density of activated CN. Incorporation of estimates for dilution factors into a Lagrangian box model of the far-wake regime with scale-dependent diffusion indicates negligible decrease in ozone and enhancement of water concentrations of 6-13 times background, which decrease rapidly over 1-3 days. Radiative calculations indicate a net differential cooling rate of the plume about 3K/day at the beginning of the wake regime, with a total subsidence ranging between 0.4 and 1 km. Results from the Lagrangian plume model were used to estimate the effect of repeated superposition of aircraft plumes on the concentrations of water and NO(y) along a flight corridor. Results of laboratory studies of heterogeneous chemistry are also described. Kinetics of HCl, N2O5 and ClONO2 uptake on liquid sulfuric acid were measured as a function of composition and temperature. Refined measurements of the thermodynamics of nitric acid hydrates indicate that metastable dihydrate may play a role in the nucleation of more stable trihydrates PSC's.

Miake-Lye, R. C.↗

Are You In or Out: the Influence of Sea Ice Drift on Sea Ice Survivability

The state of Arctic sea ice influences aspects of many global systems including ecosystems, economies, geopolitics, and climate. And, it is in severe decline. Numerous studies have considered the factors that influence Arctic sea ice decline using monthly mean or gridded data. However, these methods struggle to cleanly separate the influences on sea ice melt because the sea ice cover is always moving; thus, different sea ice floes and sea ice regimes constitute the monthly average sea ice state within the Eulerian frame. This study uses a LaGrangian sea ice parcel tracking satellite database to investigate the factors that influence sea ice parcel survivability. The concept of sea ice survivability is defined as the likelihood that a sea ice parcel will last through the summer melt season. Survivability can be stratified in many ways to analyze how it changes as a function of sea ice regime, region, and sea ice characteristics. How is the survivability of first year (FY) and multi-year (MY) ice classes influenced by sea ice motion? This is the central question addressed in this presentation. Specifically, this analysis determines sea ice survivability as a function of distance traveled by sea ice parcels and compares the survivability statistics for sea ice parcels that stay in their starting region versus those that leave their starting region. The preliminary results indicate that the influence of sea ice movement on survivability depends strongly on which region the sea ice resides in at the beginning of the growth season. Lastly, we find substantial inter-annual variability in the regional distribution of sea ice survivability that seems to be strongly linked to sea ice parcel drift between regions of the Arctic Ocean. Moreover, we use these results to discuss the potential contribution of changes in sea ice motion on the observed slowdown in Arctic sea ice extent loss.

Patrick C Taylor↗

An objective method for determining the generalized transport tensor for two-dimensional Eulerian models

An objective method for deriving the components of a generalized transport tensor for a two-dimensional model is presented. Representative meridional and vertical velocities and thermodynamic scalars at a uniform grid are used to reduce the problem to the solution of two flux equations for two unknowns. One unknown is the stream-function, coefficient of an antisymmetric tensor, which corrects the Eulerian mean motions for Stokes drift; the other is a time constant, which converts the deviatory velocity tensor to a symmetric transport tensor. The complete asymmetric tensor, called a transport tensor, has a divergence which yields both advection and diffusion by the deviatory velocities. Advantages and disadvantages of Lagrangian and Eulerian averages are discussed, and meridional-vertical velocity correlations are provided.

Danielsen, E. F.↗

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↗

Computational Methods for Frictional Contact With Applications to the Space Shuttle Orbiter Nose-Gear Tire

A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.

Tanner, John A.↗

Computational methods for frictional contact with applications to the Space Shuttle orbiter nose-gear tire: Comparisons of experimental measurements and analytical predictions

A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical-loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.

Tanner, John A.↗

LSPRAY-V: A Lagrangian Spray Module

LSPRAY-V is a Lagrangian spray solver developed for application with unstructured grids and massively parallel computers. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray encountered over a wide range of operating conditions in modern aircraft engine development. It could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-V, we have advanced the state-of-the-art in spray computations in several important ways.

CFD↗

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.↗

Generalized Roche potential for misaligned binary systems - Properties of the critical lobe

The paper considers the Roche potential for binary systems where the stellar rotation axis is not aligned with the orbital revolution axis. It is shown that, as the degree of misalignment varies, internal Lagrangian points and external Lagrangian points may switch their roles. A systematic method to identify the internal Lagrangian point and to calculate the volume of the critical lobe is developed, and numerical results for a wide range of parameters of binary systems with circular orbits are presented. For binary systems with large enough misalignment, discrete changes occur in the topological structure of the equipotential surfaces as the orbital phase varies. The volume of the critical lobe has minima, as a function of orbital phase, at the two instances when the secondary crosses the equatorial plane of the primary. In semidetached systems, mass transfer may be confined to the vicinity of these two instances.

Avni, Y.↗

An investigation of using an RQP based method to calculate parameter sensitivity derivatives

Estimation of the sensitivity of problem functions with respect to problem variables forms the basis for many of our modern day algorithms for engineering optimization. The most common application of problem sensitivities has been in the calculation of objective function and constraint partial derivatives for determining search directions and optimality conditions. A second form of sensitivity analysis, parameter sensitivity, has also become an important topic in recent years. By parameter sensitivity, researchers refer to the estimation of changes in the modeling functions and current design point due to small changes in the fixed parameters of the formulation. Methods for calculating these derivatives have been proposed by several authors (Armacost and Fiacco 1974, Sobieski et al 1981, Schmit and Chang 1984, and Vanderplaats and Yoshida 1985). Two drawbacks to estimating parameter sensitivities by current methods have been: (1) the need for second order information about the Lagrangian at the current point, and (2) the estimates assume no change in the active set of constraints. The first of these two problems is addressed here and a new algorithm is proposed that does not require explicit calculation of second order information.

Beltracchi, Todd J.↗

Theory of local thermal instability in spherical systems

The gasdynamical properties of local thermal instability in optically thin astrophysical plasmas as it occurs in spherical accretion and winds is investigated. In a medium characterized by both thermal and hydrostatic equilibrium, if the cooling function is not an explicit function of position and does not display isentropic thermal instability, then isobaric thermal instability by the Field criterion is present if and only if convective instability is present by the Schwarzschild criterion. In this case, thermal overstability cannot occur. Convective instability by the Schwarzschild criterion will also occur in accretion flows locally dominated by external heating or in marginally unbound, radiatively cooling outflows. A very general Lagrangian equation for the development of nonradial thermal instability in flows with spherical symmetry is derived and is solved analytically in certain regimes. The results are applied to cluster X-ray cooling flows.

Balbus, Steven A.↗

Quadrature Moments Method for the Simulation of Turbulent Reactive Flows

A sub-filter model for reactive flows, namely the DQMOM model, was formulated for Large Eddy Simulation (LES) using the filtered mass density function. Transport equations required to determine the location and size of the delta-peaks were then formulated for a 2-peak decomposition of the FDF. The DQMOM scheme was implemented in an existing structured-grid LES solver. Simulations of scalar shear layer using an experimental configuration showed that the first and second moments of both reactive and inert scalars are in good agreement with a conventional Lagrangian scheme that evolves the same FDF. Comparisons with LES simulations performed using laminar chemistry assumption for the reactive scalar show that the new method provides vast improvements at minimal computational cost. Currently, the DQMOM model is being implemented for use with the progress variable/mixture fraction model of Pierce. Comparisons with experimental results and LES simulations using a single-environment for the progress-variable are planned. Future studies will aim at understanding the effect of increase in environments on predictions.

Raman, Venkatramanan↗

Survey and development of finite elements for nonlinear structural analysis. Volume 2: Nonlinear shell finite elements

The development of two new shell finite elements for applications to large deflection problems is considered. The elements in question are doubly curved and of triangular and quadrilateral planform. They are restricted to small strains of elastic materials, and can accommodate large rotations. The elements described, which are based on relatively simple linear elements, make use of a new displacement function approach specifically designed for strongly nonlinear problems. The displacement function development for nonlinear applications is based on certain beam element formulations, and the strain-displacement equations are of a shallow shell type. Additional terms were included in these equations in an attempt to avoid the large errors characteristic of shallow shell elements in certain types of problems. An incremental nonlinear solution procedure specifically adopted to the element formulation was developed. The solution procedure is of combined incremental and total Lagrangian type, and uses a new updating scheme. A computer program was written to evaluate the developed formulations. This program can accommodate small element groups in arbitrary arrangements. Two simple programs were successfully solved. The results indicate that this new type of element has definite promise and should be a fruitful area for further research.

Source record↗

Nonlinear program based optimization of boost and buck-boost converter designs

The facility of an Augmented Lagrangian (ALAG) multiplier based nonlinear programming technique is demonstrated for minimum-weight design optimizations of boost and buck-boost power converters. Certain important features of ALAG are presented in the framework of a comprehensive design example for buck-boost power converter design optimization. The study provides refreshing design insight of power converters and presents such information as weight and loss profiles of various semiconductor components and magnetics as a function of the switching frequency.

Rahman, S.↗

PHILLS Vicarious Calibration: A WFS Experiment and Guidance for LEO-15 Calibration Efforts

On April 24, 2001, Florida Shelf Lagrangian Experiment (FSLE) cruises were accompanied by PHILLS hyperspectral overflights at 30,000 ft altitude. Robert Steward, and Jim Ivey collected remote sensing reflectance and water samples for absorption during two FSLE experiments. The PHILLS was flown on several transects over the area with vicarious calibration measurements conducted by USF from the R/V LINK. The USF slow-drop package was also deployed to collect inherent and apparent optical properties as a function of depth for an evaluation of effects of vertical structure on remote sensing spectra. The PHILLS imagery has been successfully calibrated. We show the procedures, results, derived bathymetry, and some noise effects with a 3 s period.

Carder, Kendall L.↗