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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Development of an Efficient Binaural Simulation for the Analysis of Structural Acoustic Data

Applying binaural simulation techniques to structural acoustic data can be very computationally intensive as the number of discrete noise sources can be very large. Typically, Head Related Transfer Functions (HRTFs) are used to individually filter the signals from each of the sources in the acoustic field. Therefore, creating a binaural simulation implies the use of potentially hundreds of real time filters. This paper details two methods of reducing the number of real-time computations required by: (i) using the singular value decomposition (SVD) to reduce the complexity of the HRTFs by breaking them into dominant singular values and vectors and (ii) by using equivalent source reduction (ESR) to reduce the number of sources to be analyzed in real-time by replacing sources on the scale of a structural wavelength with sources on the scale of an acoustic wavelength. The ESR and SVD reduction methods can be combined to provide an estimated computation time reduction of 99.4% for the structural acoustic data tested. In addition, preliminary tests have shown that there is a 97% correlation between the results of the combined reduction methods and the results found with the current binaural simulation techniques

Johnson, Marty E.↗
NASA NTRS2003

Predictive models for moving contact line flows

Modeling flows with moving contact lines poses the formidable challenge that the usual assumptions of Newtonian fluid and no-slip condition give rise to a well-known singularity. This singularity prevents one from satisfying the contact angle condition to compute the shape of the fluid-fluid interface, a crucial calculation without which design parameters such as the pressure drop needed to move an immiscible 2-fluid system through a solid matrix cannot be evaluated. Some progress has been made for low Capillary number spreading flows. Combining experimental measurements of fluid-fluid interfaces very near the moving contact line with an analytical expression for the interface shape, we can determine a parameter that forms a boundary condition for the macroscopic interface shape when Ca much les than l. This parameter, which plays the role of an "apparent" or macroscopic dynamic contact angle, is shown by the theory to depend on the system geometry through the macroscopic length scale. This theoretically established dependence on geometry allows this parameter to be "transferable" from the geometry of the measurement to any other geometry involving the same material system. Unfortunately this prediction of the theory cannot be tested on Earth.

Rame, Enrique↗
NASA NTRS2005

ATTITUDE FILTERING ON SO(3)

A new method is presented for the simultaneous estimation of the attitude of a spacecraft and an N-vector of bias parameters. This method uses a probability distribution function defined on the Cartesian product of SO(3), the group of rotation matrices, and the Euclidean space W N .The Fokker-Planck equation propagates the probability distribution function between measurements, and Bayes s formula incorporates measurement update information. This approach avoids all the issues of singular attitude representations or singular covariance matrices encountered in extended Kalman filters. In addition, the filter has a consistent initialization for a completely unknown initial attitude, owing to the fact that SO(3) is a compact space.

Markley, F. Landis↗
NASA NTRS2002

Geostrophic balance with a full Coriolis Force: implications for low latitutde studies

In its standard form, geostrophic balance uses a partial representation of the Coriolis force. The resulting formation has a singularity at the equator, and violates mass and momentum conservation. When the horizontal projection of the planetary rotation vector is considered, the singularity at the equator disappears, continuity can be preserved, and quasigeostrophy can be formulated at planetary scale.

balance atmosphere geostrophy remote sensing wind↗
NASA NTRS2008

The Aeroacoustics of Slowly Diverging Supersonic Jets

This paper is concerned with utilizing the acoustic analogy approach to predict the sound from unheated supersonic jets. Previous attempts have been unsuccessful at making such predictions over the Mach number range of practical interest. The present paper, therefore, focuses on implementing the necessary refinements needed to accomplish this objective. The important effects influencing peak supersonic noise turn out to be source convection, mean flow refraction, mean flow amplification, and source non-compactness. It appears that the last two effects have not been adequately dealt with in the literature. The first of these because the usual parallel flow models produce most of the amplification in the so called critical layer where the solution becomes singular and, therefore, causes the predicted sound field to become infinite as well. We deal with this by introducing a new weakly non parallel flow analysis that eliminates the critical layer singularity. This has a strong effect on the shape of the peak noise spectrum. The last effect places severe demands on the source models at the higher Mach numbers because the retarded time variations significantly increase the sensitivity of the radiated sound to the source structure in this case. A highly refined (non-separable) source model is, therefore, introduced in this paper.

Goldstein, M. E.↗
NASA NTRS2005

Computation of Sound Propagation by Boundary Element Method

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Guo, Yueping↗
NASA NTRS2008

Robustness Analysis and Reliable Flight Regime Estimation of an Integrated Resilent Control System for a Transport Aircraft

Formal robustness analysis of aircraft control upset prevention and recovery systems could play an important role in their validation and ultimate certification. As a part of the validation process, this paper describes an analysis method for determining a reliable flight regime in the flight envelope within which an integrated resilent control system can achieve the desired performance of tracking command signals and detecting additive faults in the presence of parameter uncertainty and unmodeled dynamics. To calculate a reliable flight regime, a structured singular value analysis method is applied to analyze the closed-loop system over the entire flight envelope. To use the structured singular value analysis method, a linear fractional transform (LFT) model of a transport aircraft longitudinal dynamics is developed over the flight envelope by using a preliminary LFT modeling software tool developed at the NASA Langley Research Center, which utilizes a matrix-based computational approach. The developed LFT model can capture original nonlinear dynamics over the flight envelope with the ! block which contains key varying parameters: angle of attack and velocity, and real parameter uncertainty: aerodynamic coefficient uncertainty and moment of inertia uncertainty. Using the developed LFT model and a formal robustness analysis method, a reliable flight regime is calculated for a transport aircraft closed-loop system.

Shin, Jong-Yeob↗
NASA NTRS2009

Regression Model Optimization for the Analysis of Experimental Data

A candidate math model search algorithm was developed at Ames Research Center that determines a recommended math model for the multivariate regression analysis of experimental data. The search algorithm is applicable to classical regression analysis problems as well as wind tunnel strain gage balance calibration analysis applications. The algorithm compares the predictive capability of different regression models using the standard deviation of the PRESS residuals of the responses as a search metric. This search metric is minimized during the search. Singular value decomposition is used during the search to reject math models that lead to a singular solution of the regression analysis problem. Two threshold dependent constraints are also applied. The first constraint rejects math models with insignificant terms. The second constraint rejects math models with near-linear dependencies between terms. The math term hierarchy rule may also be applied as an optional constraint during or after the candidate math model search. The final term selection of the recommended math model depends on the regressor and response values of the data set, the user s function class combination choice, the user s constraint selections, and the result of the search metric minimization. A frequently used regression analysis example from the literature is used to illustrate the application of the search algorithm to experimental data.

Ulbrich, N.↗
NASA NTRS2010

A General Closed-Form Solution for the Lunar Reconnaissance Orbiter (LRO) Antenna Pointing System

The National Aeronautics and Space Administration s (NASA) Lunar Reconnaissance Orbiter (LRO) launched on June 18, 2009 from the Cape Canaveral Air Force Station aboard an Atlas V launch vehicle into a direct insertion trajectory to the Moon LRO, designed, built, and operated by the NASA Goddard Space Flight Center in Greenbelt, MD, is gathering crucial data on the lunar environment that will help astronauts prepare for long-duration lunar expeditions. During the mission s nominal life of one year its six instruments and one technology demonstrator will find safe landing site, locate potential resources, characterize the radiation environment and test new technology. To date, LRO has been operating well within the bounds of its requirements and has been collecting excellent science data images taken from the LRO Camera Narrow Angle Camera (LROC NAC) of the Apollo landing sites have appeared on cable news networks. A significant amount of information on LRO s science instruments is provided at the LRO mission webpage. LRO s Attitude Control System (ACS), in addition to controlling the orientation of the spacecraft is also responsible for pointing the High Gain Antenna (HGA). A dual-axis (or double-gimbaled) antenna, deployed on a meter-long boom, is required to point at a selected Earth ground station. Due to signal loss over the distance from the Moon to Earth, pointing precision for the antenna system is very tight. Since the HGA has to be deployed in spaceflight, its exact geometry relative to the spacecraft body is uncertain. In addition, thermal distortions and mechanical errors/tolerances must be characterized and removed to realize the greatest gain from the antenna system. These reasons necessitate the need for an in-flight calibration. Once in orbit around the moon, a series of attitude maneuvers was conducted to provide data needed to determine optimal parameters to load onboard, which would account for the environmental and mechanical errors at any antenna orientation. The nominal geometry for the HGA involves an outer gimbal axis that is exactly perpendicular to the inner gimbal axis, and a target direction that is exactly perpendicular to the outer gimbal axis. For this nominal geometry, closed-form solutions of the desired gimbal angles are simple to get for a desired target direction specified in the spacecraft body fame. If the gimbal axes and the antenna boresight are slightly misaligned, the nominal closed-form solution is not sufficiently accurate for computing the gimbal angles needed to point at a target. In this situation, either a general closed-form solution has to be developed for a mechanism with general geometries, or a correction scheme has to be applied to the nominal closed-form solutions. The latter has been adopted for Solar Dynamics Observatory (SDO) as can be seen in Reference 1, and the former has been used for LRO. The advantage of the general closed-form solution is the use of a small number of parameters for the correction of nominal solutions, especially in the regions near singularities. Singularities here refer to cases when the nominal closed-form solutions have two or more solutions. Algorithm complexity, however, is the disadvantage of the general closed-form solution.

Shah, Neerav↗
NASA NTRS2010

Topological Aspects of the FAITH Experiment

This slide presentation reviews the following issues (1) What is relationship between surface pressure extrema and singular points? (2) Does every singular point in a pattern of skin friction lines occur at a surface pressure extremum? (and/or vice versa?) (3) Can this relationship be generalized to all geometries? (4) FAITH Project (5) Ongoing effort at NASA Ames Experimental AeroPhysics Branch (6) Multi-parameter wind tunnel investigation of flow around obstacle (7) Acquire data for CFD validation, optimization and (8) Relationship between FAITH and topology projects

Tobak, Murray↗
NASA NTRS2002

Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling

In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving ~he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required to obtain usable convergence from an iterative solver. The authors have examined the use of an Incomplete LU Threshold (ILUT) preconditioner . to solver linear systems stemming from higher order BEM/FEM formulations in 2D scattering problems. Although the resulting preconditioner provided aD excellent approximation to the system inverse, its size in terms of non-zero entries represented only a modest improvement when compared with the fill-in associated with a sparse direct solver. Furthermore, the fill-in of the preconditioner could not be substantially reduced without the occurrence of instabilities. In addition to the results for these 2D problems, the authors will present iterative solution data from the application of the ILUT preconditioner to 3D problems.

Fink, P. W.↗
NASA NTRS2012

On the Ice Nucleation Spectrum

This work presents a novel formulation of the ice nucleation spectrum, i.e. the function relating the ice crystal concentration to cloud formation conditions and aerosol properties. The new formulation is physically-based and explicitly accounts for the dependency of the ice crystal concentration on temperature, supersaturation, cooling rate, and particle size, surface area and composition. This is achieved by introducing the concepts of ice nucleation coefficient (the number of ice germs present in a particle) and nucleation probability dispersion function (the distribution of ice nucleation coefficients within the aerosol population). The new formulation is used to generate ice nucleation parameterizations for the homogeneous freezing of cloud droplets and the heterogeneous deposition ice nucleation on dust and soot ice nuclei. For homogeneous freezing, it was found that by increasing the dispersion in the droplet volume distribution the fraction of supercooled droplets in the population increases. For heterogeneous ice nucleation the new formulation consistently describes singular and stochastic behavior within a single framework. Using a fundamentally stochastic approach, both cooling rate independence and constancy of the ice nucleation fraction over time, features typically associated with singular behavior, were reproduced. Analysis of the temporal dependency of the ice nucleation spectrum suggested that experimental methods that measure the ice nucleation fraction over few seconds would tend to underestimate the ice nuclei concentration. It is shown that inferring the aerosol heterogeneous ice nucleation properties from measurements of the onset supersaturation and temperature may carry significant error as the variability in ice nucleation properties within the aerosol population is not accounted for. This work provides a simple and rigorous ice nucleation framework where theoretical predictions, laboratory measurements and field campaign data can be reconciled, and that is suitable for application in atmospheric modeling studies.

Barahona, D.↗
NASA NTRS2013

Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

Chebyshev Polynomial↗
NASA NTRS2014

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the ordinary photons, under the approximation of large angle and large optical depth. These assumptions allow the equation to be treated using a diffusion-like approximation.

acceleration of particles↗
NASA NTRS2008

An Improved Wavefront Control Algorithm for Large Space Telescopes

Wavefront sensing and control is required throughout the mission lifecycle of large space telescopes such as James Webb Space Telescope (JWST). When an optic of such a telescope is controlled with both surface-deforming and rigid-body actuators, the sensitivity-matrix obtained from the exit pupil wavefront vector divided by the corresponding actuator command value can sometimes become singular due to difference in actuator types and in actuator command values. In this paper, we propose a simple approach for preventing a sensitivity-matrix from singularity. We also introduce a new "minimum-wavefront and optimal control compensator". It uses an optimal control gain matrix obtained by feeding back the actuator commands along with the measured or estimated wavefront phase information to the estimator, thus eliminating the actuator modes that are not observable in the wavefront sensing process.

adaptive optics↗
NASA NTRS2019

Comparing Flood-Producing Catastrophic Hurricanes in GEOS: A Study of Juan 1985 and Harvey 2017

Hurricanes Juan (1985) and Harvey (2017) bear remarkable similarities because of the exceptional amount of accumulated precipitation over coastal regions in the Gulf, consequent to the peculiar and rare situation in which a hurricane stalls for several days on a coastal area, displaying minimal progress. This is particularly dangerous because: a) terrestrial drag affect only part of the circulation so that weakening is not as fast as when there is rapid motion inland; b) a part of the circulation remains over water and as such low-level moisture flux convergence is maintained; c) precipitation lasts for a very long time over the same area; d) moisture recycling from flooded areas further contributes to maintaining flood conditions. From the forecast perspective, hurricanes with track singularities such as stalling points, loops, or multiple landfalls over the same region are exceptionally difficult to predict because they result from small variations of opposing mechanisms and are therefore intrinsically unstable. Intensity fluctuations and track singularities are strongly coupled. The representation of fluxes undergoing differential drag (ocean vs. land) inside the same circulation is critically dependent upon resolution. Recent modeling development efforts within the NASA Global Modeling and Assimilation Office (GMAO) have brought the horizontal resolution of the global cubed-sphere Goddard Earth Observing System (GEOS) atmospheric model down to 12 km. This has led to innovative findings in the field of tropical cyclone (TC) modeling within a global framework. The GEOS atmospheric model and data assimilation system (DAS), used to produce the MERRA-2 (Modern Era Retrospective analysis for Research and Applications) reanalysis, has a "Replay" capability that adds a forcing term to the model equations to constrain it to follow a specified trajectory. This capability is used to produce global, downscaled versions of the 50 km MERRA-2 reanalysis at a 12.5 km resolution. The full DAS and replay modes both use the Incremental Analysis Update or IAU for applying an analysis increment to the model's background state four times each day at 00Z, 06Z, 12Z and 18Z. In a full DAS mode, a six-hour free run of the model is made (Predictor Step), writing states that will be used as backgrounds or first-guesses for the analysis centered on 00Z. The Analysis system then produces its best estimate of the 00Z state by blending backgrounds with observations. The difference between this best estimate and the model's original first guess at 00Z is treated as an analysis increment and added uniformly as a forcing term to the model during a second, now forced, run of the 12Z to 03Z window, which produces the assimilated results. Replay mode is very similar, except only the 00Z background is needed from the predictor segment, which is thus half as long, and instead of doing an analysis, a previously analyzed state at 00Z is read in. The increment is then computed and applied to the corrector step in the same way as in the original DAS. When downscaling horizontal spatial filters can be applied to the "analysis" increment used to force the Corrector step, so as to reproduce the full meteorological state or selectively choose or discard certain forcings. In this presentation, full global hindcast simulations of Juan and operational forecasts of Harvey are compared.

Flooding↗
NASA NTRSDate not supplied

Realistic gravitational focusing of meteoroid streams

A meteor shower can be modeled, to first order, as a parallel stream of particles encountering the Earth. Gravity bends the trajectories of these particles inward, producing an increase in flux both near the planet and along the anti-radiant line. This effect is known as gravitational focusing, and the interception of a portion of meteoroid trajectories by the Earth or another massive body is known as planetary shielding. For a perfectly parallel meteoroid stream, gravitational focusing produces a flux singularity along the anti-radiant line, near which intense enhancements in flux occur. In reality, meteoroids will exhibit some dispersion in their motion that removes this singularity. We present a modified analytic treatment of gravitational focusing and planetary shielding that takes this dispersion into account and discuss its ramifications for several problems in meteor astronomy.

Althea Valkyrie Moorhead↗
NASA NTRS2023

A 1D Model for Nucleation of Ice From Aerosol Particles: An Application to a Mixed-Phase Arctic Stratus Cloud Layer

Mixed-phase clouds (MPCs) have been identified as significant contributors to uncertainties in climate projections, attributable to model representation of processes controlling the formation and loss of supercooled water droplets and ice particles from the atmosphere. Arctic MPCs are commonly widespread and long-lived, with sustained ice crystal formation processes that challenge current understanding. This study examines the ice-nucleating particle (INP) reservoir dynamics governing immersion-mode heterogeneous freezing in an observed case of Arctic MPCs using a simplified 1D aerosol-cloud model. The model setup includes prescribed dynamical forcings and thermodynamic profiles, and represents INPs as multicomponent and polydisperse particle size distributions. Diagnostic and prognostic approaches to immersion freezing parameterization are compared, including time-independent (singular) number- and surface area-based descriptions and a time-dependent description following classical nucleation theory (CNT). The choice of freezing parameterization defines the size of the INP reservoir. The CNT-based description yields an orders of magnitude larger INP reservoir than the singular parameterizations, which is the dominant factor for sustained ice crystal formation. The efficiency of the freezing process and cloud cooling are of secondary importance. A diagnostic treatment neglecting INP loss is only accurate when the INP reservoir size is large and INP depletion weak. Since a larger INP reservoir sustains ice crystal formation substantially longer, and ice water path scales with ice crystal concentrations for the conditions considered, resolving the source of differences in INP reservoir dynamics due to model implementation is a high priority for advancing climate model physics.

aerosol↗