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NASA NTRS2012

Project 5S: A Safe Stepping Stone into the Solar System

The human exploration program, at least in NASA, has been directed to move beyond the Moon and travel on a flexible path into the solar system. Reaching a Near-Earth Asteroid (NEA) is a major human space flight goal but such missions have tight times and life-support requirements that require huge steps from current capabilities. An objective between the Moon and a NEA is needed. Example interim objectives are the Lagrangian points in either the Sun-Earth or Earth-Moon (EM) system. The nearest of these points beyond the Moon is E-M L2. The Lagrangian points are empty (as far as we know). As objectives for human flight,it has been argued that they suffer from a lack of public interest and of meaningful objectives for astronaut operations. To provide a physical target, a robotic spacecraft could retrieve a small NEA and bring it to a Lagrangian or other nearer-Earth point to be accessed and utilized for human-mission objectives. This paper reports on the results of a recently completed study of an asteroid retrieval mission sponsored by the Keck Institute for Space Studies (KISS) at the California Institute of Technology. The study included an evaluation of potential targets, mission objectives, mission and system design, and potential capture mechanisms. The study concluded that, while challenging, there are no fundamental show stoppers and that such a mission would be possible with technology expected to be available in this decade. The final destination selected (for safety and mission operations) was high lunar orbit. Two options for target selection are considered: (i) retrieving a small (7 meter) NEA with a mass of order 500,000 kg, and (ii) taking a similar size boulder of a large known carbonaceous NEA. Several areas of technology and program requirements were identified, but the most important conclusion was that this approach enables meeting a goal of humans going to a NEA by the mid-2020s. The advantages and benefits for human exploration are considerable as are the advances that would be made in space-resource utilization and science for further exploration and development of the solar system. The combination of the robotic mission to move the asteroid and the human mission to go to its new destination and conduct astronaut operations there would provide a boost and purpose to human space flight.

asteroid retrieval↗

NASA NTRSDate not supplied

An Automated Refinement Process for Particle Trajectory Methods in GlennICE

Computational methods for ice accretion can simulate the impact of water drops and ice crystals on an aircraft surface in a Lagrangian reference frame or in the Eulerian reference frame. In the Eulerian reference frame, particles are considered a continuous fluid while in the Lagrangian frame individual particle trajectories are calculated. Methods that use the Eulerian reference frame are typically easier to develop as established modules used for continuum mechanics can be leveraged. The Eulerian systems can also be faster since the user does not have to simulate millions of particles in order to achieve good results. It is imperative therefore that a Lagrangian method optimize the release points of trajectories such that accurate solutions can be obtained while minimizing as much as possible the number of trajectories computed. This paper will present a methodology for this refinement process and demonstrate its effectiveness on sample three dimensional test cases.

William B Wright↗

NASA NTRSDate not supplied

An Automated Refinement Process for Particle Trajectory Methods in GlennICE

William Wright↗

NASA NTRS2023

Assessment of Oceanographic Conditions during the North Atlantic EXport Processes in the Ocean from RemoTe Sensing (EXPORTS) Field Campaign

This manuscript presents an overview of NASA’s EXport Processes in the Ocean from Remote Sensing 2021 Field Campaign in the North Atlantic (EXPORTS NA) and provides quantitative and dynamical descriptions of the physical processes modulating water transformations during the study. A major programmatic goal was to conduct the sampling in a Lagrangian mode so that ocean ecological and biogeochemical changes can be observed independent from physical advective processes. To accomplish this goal, EXPORTS NA conducted a multi-ship, multi-asset field sampling program within a retentive, anticyclonic mode water eddy. Beneath depths of ∼100 m, Lagrangian sampling assets remained within the eddy core waters (ECWs) throughout the experiment, demonstrating that the ECWs within the mode water eddy were retentive. However, strong westerly winds from four storm events deepened the mixed layer (ML) of the surface core waters (SCWs) above the eddy’s mode water core by 25-40 m and exchanged some of the SCWs with surface waters outside of the eddy via Ekman transport. Estimates of flushing times ranged from 5-8 days, with surface exchange fractions ranging from 20-75% and were consistent with particle tracking advected by combined geostrophic and Ekman velocities. The relative contributions of horizontal and vertical advection on changes in ECW tracers depended on the horizontal and vertical gradients of that tracer. For example, horizontal advection played a large role in ECW salinity fluxes, while vertical entrainment played a larger role in the fluxes of nutrients into SCW ML. Each storm injected nutrients and low oxygen waters into the ML, after which the surface ocean ecosystem responded by reducing nutrient concentrations and increasing %O2 saturation levels. Overall, ECW values of chlorophyll and POC were the largest at the onset of the field program and decreased throughout the campaign. The analysis presented provides a physical oceanographic context for the many measurements made during the EXPORTS NA field campaign while illustrating the many challenges of conducting a production-flux experiment, even in a Lagrangian frame, and the inherent uncertainties of interpreting biological carbon pump observations that were collected in a Eulerian frame of reference.

oceanography↗

NASA NTRSDate not supplied

Gigatraj: An Atmospheric Trajectory Model

Atmospheric trajectory models have a long history of success in tracking air motions in the lower stratosphere and upper troposphere over periods of up to a few days. Parcels have been traced backwards from observations to identify whatever phenomena (strong convection, volcanic eruptions, rocket launches, etc.) put their signature on them. Parcels have also been initialized at a known event and traced forward to examine their subsequent physical and chemical evolution. We describe a new trajectory model, "gigatraj," that aims to increase exibility by (a) making it straightforward to use new meteorological data sources, including those not based on regular latitude-longitude grids; (b) enabling a run-time choice of vertical coordinate system for kinematic and/or quasi-isentropic calculations; (c) allowing for the output of arbitrary meteorological products, selectable by the user and interpolated to the parcels' locations and times. The model can be run in a serial or parallel processing environment, so that large numbers of parcels can be traced in a reasonable time. Information is presented on model accuracy and performance. The former is demonstrated by runs using both test-pattern winds (comparing expected paths with actual output) and real-world winds (comparing forward and backward runs to characterize how well parcels retrace their paths). Sample cases are also shown, including a reverse domain lling (RDF) calculation illustrating a tropopause fold event. Model output can be displayed using the new Visualization And Lagrangian dynamics Immersive eXtended Reality (VALIXR) system, and an example will be shown. In addition, we describe work to incorporate a version of gigatraj into the Goddard Earth Observing System (GEOS) of NASA's Global Modeling and Assimilation O ce (GMAO) at Goddard Space Flight Center. This enables trajectory calculations to be performed within the running GEOS model at the latter's native time resolution, instead of using the winds from every few hours. It also provides access to all of GEOS's internal variables as they are calculated. This module may be useful, for example, for tracking rapid chemical changes in a Lagrangian framework.

dynamics↗

NASA NTRS1972

Experimental determination of the turbulence in a liquid rocket combustion chamber

The intensity of turbulence and the Lagrangian correlation coefficient for a liquid rocket combustion chamber were determined experimentally using the tracer gas diffusion method. The results indicate that the turbulent diffusion process can be adequately modeled by the one-dimensional Taylor theory; however, the numerical values show significant disagreement with previously accepted values. The intensity of turbulence is higher by a factor of about two, while the Lagrangian correlation coefficient which was assumed to be unity in the past is much less than unity.

Hara, J.↗

NASA NTRS1972

Stability of orthotropic stiffened composite plates.

It is pointed out that the buckling problem of a plate with restrictions resulting from boundary conditions is suited for an application of Lagrangian multipliers. An approach used by Budiansky and Hu (1946) is extended to the study of orthotropic stiffened plates. The variations of the total energy with respect to the three deformation components are considered. The equilibrium equations and the boundary conditions are obtained. It is shown that the deflection functions must satisfy the equilibrium equations. The Lagrangian multipliers are then used to solve stability problems on the basis of the total energy involved, the equilibrium equations, and the boundary conditions. The theoretical analysis is supplemented by an experimental investigation.

Chiu, K. D.↗

NASA NTRS1972

Foundations for a theory of gravitation theories

A foundation is laid for future analyses of gravitation theories. This foundation is applicable to any theory formulated in terms of geometric objects defined on a 4-dimensional spacetime manifold. The foundation consists of (1) a glossary of fundamental concepts; (2) a theorem that delineates the overlap between Lagrangian-based theories and metric theories; (3) a conjecture (due to Schiff) that the Weak Equivalence Principle implies the Einstein Equivalence Principle; and (4) a plausibility argument supporting this conjecture for the special case of relativistic, Lagrangian-based theories.

Thorne, K. S.↗

NASA NTRS1973

Subgrid resolution of flow and force fields.

By means of spline fitting, both while converting a Lagrangian distribution of field sources onto an Eulerian grid, and while interpolating the field from its Eulerian grid to the Lagrangian positions of the responding elements, one achieves effective resolution down to about one-eight of a grid mesh unit. One also avoids discontinuities and noise due to cell boundary crossings.

Buneman, O.↗

NASA NTRS1975

A feasibility study for measuring stratospheric turbulence using metrac positioning system

The feasibility of obtaining measurements of Lagrangian turbulence at stratospheric altitudes is demonstrated by using the METRAC System to track constant-level balloons. The basis for current estimates of diffusion coefficients are reviewed and it is pointed out that insufficient data is available upon which to base reliable estimates of vertical diffusion coefficients. It is concluded that diffusion coefficients could be directly obtained from Lagrangian turbulence measurements. The METRAC balloon tracking system is shown to possess the necessary precision in order to resolve the response of constant-level balloons to turbulence at stratospheric altitudes. A small sample of data recorded from a tropospheric tetroon flight tracked by the METRAC System is analyzed to obtain estimates of small-scale three-dimensional diffusion coefficients. It is recommended that this technique be employed to establish a climatology of diffusion coefficients and to ascertain the variation of these coefficients with altitude, season, and latitude.

Gage, K. S.↗

NASA NTRS1974

Microscopic plasma Hamiltonian

A Hamiltonian for the microscopic plasma model is derived from the Low Lagrangian after the dual roles of the generalized variables are taken into account. The resulting Hamilton equations are shown to agree with the Euler-Lagrange equations of the Low Lagrangian.

Peng, Y.-K. M.↗

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.↗

NASA NTRS1976

Repeated-cascade theory of strong turbulence in a magnetized plasma

A two-dimensional Navier-Stokes equation of vorticity in fluid turbulence is used to model drift turbulence in a plasma with a strong constant magnetic field and a constant mean density gradient. The nonlinear eddy diffusivity is described by a time-integrated Lagrangian correlation of velocities, and the repeated-cascade method is employed to choose the rank accounting for nearest-neighbor interactions, to calculate the Lagrangian correlation, and to close the correlation hierarchy. As a result, the diffusivity becomes dependent on the plasma's induced diffusion and is represented by a memory chain that is cut off by similarity and inertial randomization. Spectral laws relating the kinetic-energy spectrum to the -5, -5/2, -3, and -11 powers of wavenumber are derived for the velocity subranges of production, approach to inertia, inertia, and dissipation, respectively. It is found that the diffusivity is proportional to some inverse power of the magnetic field, that power being 1, 2/3, 5/6, and 2, respectively, for the four velocity subranges.

Tchen, C. M.↗

NASA NTRS1976

A note on the solution of the variational equations of a class of dynamical systems

Some properties are derived for the solutions of the variational equations of a class of dynamical systems. It is shown that under rather general conditions, the matrix of the linearized Lagrangian equations of motion have an important property for which the word 'skew-symplectic' has been introduced. It is also shown that the fundamental matrix of solutions is 'symplectic', the word symplectic being used here in a more general sense than in the classical literature. Two consequences of the symplectic property are that the fundamental matrix is easily invertible and that the eigenvalues appear in reciprocal pairs. The effect of coordinate transformations is also analyzed; in particular, the change from Lagrangian to canonical systems.

Broucke, R.↗

NASA NTRS1978

Investigation of turbulent diffusion in the extreme lower atmosphere

Turbulent diffusion in the extreme lower layer of the atmosphere (up to 5 m) has been investigated. Turbulent flow was simulated under dry, stable and calm conditions by means of a 3.04 m diameter fan installed at a field site situated on flat grassland. The ambient wind was continuously monitored by means of a cup anemometer placed outside the wake, and the temperature distribution was measured by four thermometers placed on an 18 m tower, also outside the wake. Balloons and red smoke were used to visualize the wake flow and investigate the predominant sizes of turbulent eddies and their streamwise behavior. The mean and turbulent velocities along the turbulence line were measured using an array of hot-wire anomometers. Results provide substantial verification of a recently proposed model (Koper and Sadeh, 1975; Koper et al., 1978) relating the Lagrangian to the Eulerian turbulent velocity autocorrelation. In this model the Lagrangian autocorrelation is given by a domain integral over a set of ordinary Eulerian autocorrelations acquired simultaneously at all points within the flow field in question, which is viewed as a turbulence 'box'.

Koper, C. A., Jr.↗

NASA NTRS1980

The finite element duct eigenvalue problem - An improved formulation with Hermitian elements and no-flow condensation

Hermitian elements are used in a finite element solution for the eigenvalue problem in lined ducts with flow. These elements give significantly greater accuracy for reduced dimensionality when compared with Lagrangian elements. Spurious mode generation associated with the Lagrangian formulation is eliminated. A dramatic improvement in the ratio of the number of reliable eigenvalues to the total number of computed eigenvalues is effected by the use of a condensation scheme based on the no-flow eigenvectors. Results are presented for two dimensional and axisymmetric ducts. In the axisymmetric case good resolution is obtained even for high order, high frequency modes by the use of continuously graded meshes.

Astley, R. J.↗

NASA NTRS1981

The secondary flow near a baroclinic planetary wave critical line

A critical line (CL) is the surface where the phase speed of a wave in a fluid is equal to the speed of the background flow. The considered investigation is concerned with one aspect of the simplest model of a CL in which the CL is assumed to totally absorb energy from steady, stationary, planetary waves. The aspect of interest is the secondary mean circulation near a CL in a baroclinic atmosphere. The motivation for this study is the observation of the nearly vertical CL by O'Neill and Taylor (1979) which appeared during the sudden warming of 1976/77. Even though the treatment of the CL is highly idealized in the investigation, there is evidence which indicates a very large rate of change in the zonally averaged temperature along a CL may occur. The Lagrangian-mean properties of an idealized baroclinic CL are also examined. It is found that the Lagrangian jets may provide an important transport process for exchange of stratospheric and tropospheric air.

Schoeberl, M. R.↗

NASA NTRS1981

Accuracy and stability of finite element schemes for the duct transmission problem

An investigation is conducted regarding the feasibility of approaches for improving the efficiency and stability of existing finite element method (FEM) schemes, taking into account both analytical and numerical studies. Of the four schemes considered for the 'steady' problem, the Hermitian Galerkin formulation appears to be the most efficient and therefore the most suitable scheme for futher full scale implementation. The Hermitian residual least squares (RLS) scheme although comparable in accuracy for the cases considered exhibits a slight tendency to cumulative errors. The performance of both the Lagrangian element schemes considered compares poorly with that of their Hermitian element counterparts. This is particularly true of the Lagrangian RLS scheme. The presence of internal oscillatory components is an inevitable consequence of all Galerkin schemes irrespective of element type.

Astley, R. J.↗