Search NASA⌕ Search

SEARCH · Search NASA

Results for “Model Theory”

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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Buchert, T.↗
NASA NTRS1992

Transition operators in electromagnetic-wave diffraction theory - General theory

A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.

Hahne, G. E.↗
NASA NTRS1992

Further investigations of the aeroelastic behavior of the AFW wind-tunnel model using transonic small disturbance theory

The Computational Aeroelasticity Program-Transonic Small Disturbance (CAP-TSD) code, developed at LaRC, is applied to the active flexible wing wind-tunnel model for prediction of transonic aeroelastic behavior. A semi-span computational model is used for evaluation of symmetric motions, and a full-span model is used for evaluation of antisymmetric motions, and a full-span model is used for evaluation of antisymmetric motions. Static aeroelastic solutions using CAP-TSD are computed. Dynamic deformations are presented as flutter boundaries in terms of Mach number and dynamic pressure. Flutter boundaries that take into account modal refinements, vorticity and entropy corrections, antisymmetric motion, and sensitivity to the modeling of the wing tip ballast stores are also presented with experimental flutter results.

Silva, Walter A.↗
NASA NTRS2020

Convolutional Neural Network for Transition Modeling Based on Linear Stability Theory

Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based empirical formulas based on integral quantities such as the shape factor of the boundary layer. However, in many applications of computational fluid dynamics, the shape factor is not straightforwardly available or not well-defined. We propose using the complete velocity profile along with other quantities (e.g., frequency, Reynolds number) to predict the perturbation amplification factor. While this can be achieved with regression models based on a classical fully connected neural network, such a model can be computationally more demanding. We propose a novel convolutional neural network inspired by the underlying physics as described by the stability equations. Specifically, convolutional layers are first used to extract integral quantities from the velocity profiles, and then fully connected layers are used to map the extracted integral quantities, along with frequency and Reynolds number, to the output (amplification ratio). Numerical tests on classical boundary layers clearly demonstrate the merits of the proposed method. More importantly, we demonstrate that, for Tollmien-Schlichting instabilities in two-dimensional, low-speed boundary layers, the proposed network encodes information in the boundary layer profiles into an integral quantity that is strongly correlated to a well-known, physically defined parameter – the shape factor.

Laminar-turbulent transition↗
NASA NTRS2003

Data and Modeling of Dendrites Subject to A Step Change in Pressure (TDSE)

There is considerable interest in dendritic solidification because of the influence dendrites have in the determination of microstructure, and thereby in the physical properties of cast metals and alloys. Current theories and models of dendritic growth generally couple diffusion effects in the melt with the physics of the interface. Data and subsequent analysis prior of the tip growth speed and radii of thermal succinonitrile dendrites in the near-convection free, on-orbit, free-fall environment demonstrate that these theories yield predictions that are reasonably in agreement with the results of experiment. However, data and analysis for assessing the interfacial physics component of theory are not sufficiently detailed or definitive. To study fundamental aspects of dendritic interface stability, we are measuring and modeling the kinetics and morphology of dendrites as they evolve from one well-defined steady state at a pre-set supercooling, through a transient stage, to a different well-defined steady state. More specifically, we subject succinonitrile dendrites, growing under steady-state conditions, to a rapid change in pressure. This leads to a rapid change in thermal driving force from the corresponding change in both the equilibrium melting temperature due to the Clapeyron effect, and a change in the far-field temperature due to adiabatic temperature changes in the bulk liquid and solid. Subsequently, we observe transformations from a well-characterized initial state into a new steady-state. Initial data reveal that the dendrite tip velocity changes almost as fast as the pressure charges, while the tip radius changes occur more slowly, taking from 10 60 seconds depending on the size of the step change and the final supercooling. Computer modeling of this process shows both agreements and disagreements with the experimental data. In making these observations and measurements, we are gaining new understandings of interfacial dynamics and state-selection physics.

Koss, Matthew B.↗
NASA NTRS1996

Turbulent Inflow Measurements

In the present research, tilt rotor aeroacoustics have been studied experimentally and computationally. Experimental measurements were made on a 1/12.5 scale model. A dimensional analysis showed that the model was a good aeroacoustic approximation to the full-scale aircraft, and scale factors were derived to extrapolate the model measurements to the full-scale XV-15. The experimental measurements included helium bubble flow visualization, silk tuft flow visualization, 2-component hot wire anemometry, 7-hole pressure probe measurements, vorticity measurements, and outdoor far field acoustic measurements. The hot wire measurements were used to estimate the turbulence statistics of the flow field into the rotors, such as length scales, velocity scales, dissipation, and turbulence intermittency. To date, these flow measurements are the only ones in existence for a hovering tilt rotor. Several different configurations of the model were tested: (1) standard configurations (single isolated rotor, two rotors without the aircraft, standard tilt rotor configuration); (2) flow control devices (the 'plate', the 'diagonal fences'); (3) basic configuration changes (increasing the rotor/rotor spacing, reducing the rotor plane/wing clearance, operating the rotors out of phase). Also, an approximation to Sikorsky's Variable Diameter Tilt Rotor (VDTR) configuration was tested, and some flow measurements were made on a semi-span configuration of the model. Acoustic predictions were made using LOWSON.M, a Mathematica code. This hover prediction code, from HOVER.FOR, used blade element theory for the aerodynamics, and Prandtl's Vortex theory to model the wake, along with empirical formulas for the effects of Reynolds number, Mach number, and stall. Aerodynamic models were developed from 7-hole pressure probe measurements of the mean velocity into the model rotors. LOWSON.M modeled a rotor blade as a single force and source/sink combination separated in the chordwise direction, at an effective blade radius. Spanwise, Mach-weighted integrals were used to find the equivalent forces and equivalent source strengths.

George, Albert R.↗
NASA NTRS1992

Design and analysis of low boom concepts at Langley Research Center

The objective of the sonic boom research in the current High Speed Research Program is to ultimately make possible overland supersonic flight by a high speed civil transport. To accomplish this objective, it is felt that results in four areas must demonstrate that such a vehicle would be acceptable by the general public, by the airframers, and by the airlines. It should be demonstrated: (1) that some waveform shape has the possibility of being acceptable to the general public; (2) that the atmosphere would not totally destroy such a waveform during propagation; (3) that a viable airplane could be built which produces such a waveform; and (4) that any performance penalty suffered by a low boom aircraft would be counteracted by the economic benefit of overland supersonic flight. The work being done at LaRC is in support of the third element listed above--the area of configuration design. The initial part of the paper will give a review of the theory being used for configuration designs and discuss two theory validation models which were built and tested within the past two years. Discussion of the wind tunnel and theoretical results (linear theory and higher order methods) and their implications for future designs will be included.

Darden, Christine M.↗
NASA NTRS1992

Further investigations of the aeroelastic behavior of the AFW wind-tunnel model using transonic small disturbance theory

The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code, developed at the NASA Langley Research Center, is applied to the Active Flexible Wing wind-tunnel model for prediction of transonic aeroelastic behavior. A semi-span computational model is used for evaluation of symmetric motions, and a full-span model is used for evaluation of antisymmetric motions. Static aeroelastic solutions using CAP-TSD are computed. Dynamic (flutter) analyses then are performed as perturbations about the static aeroelastic deformations and presented as flutter boundaries in terms of Mach number and dynamic pressure. Flutter boundaries that take into account modal refinements, vorticity and entropy corrections, antisymmetric motions and sensitivity to the modeling of the wing tip ballast stores also are presented and compared with experimental flutter results.

Silva, Walter A.↗
NASA NTRS1979

Investigation of high frequency oscillations in the OV102 elevon actuation subsystems using continuous system modeling program simulation

Two theories emerged as the cause of undesired oscillations at frequencies between 40 and 60 Hz in the Orbiter Vehicle inboard and outboard elevon actuation subsystems during hardware testing. Both the "hardover feedback" and "deadspace" theories were examined using continuous system modeling program simulation. Results did not support the "hardover feedback" theory but showed that deadspace in the torque feedback spring connections to the servospools must be considered to be a possible cause of the oscillations. Further investigation is recommended.

Powell, W. W., Sr.↗
NASA NTRS1995

Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

Melott, A. L.↗
NASA NTRS1989

An entrance region friction factor model applied to annular seal analysis - Theory versus experiment for smooth and honeycomb seals

A friction factor model is developed for the entrance-region of a duct. The model is used in an annular gas seal analysis similar to Nelson's (1984). Predictions of the analysis are compared to experimental results for a smooth-stator/smooth-rotor seal and three honeycomb-stator/smooth-rotor seals. The model predicts a leakage and direct damping well. The model overpredicts the dependence of cross-coupled stiffness on fluid prerotation. The model predicts direct stiffness poorly.

Elrod, D.↗
NASA NTRS1990

Predicting the aeroelastic behavior of a wind-tunnel model using transonic small disturbance theory

The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code, developed at the NASA-Langley Research Center, is applied to the Active Flexible Wing (AFW) wind-tunnel model for prediction of the model's transonic aeroelastic behavior. Static aeroelastic solutions using CAP-TSD are computed. Dynamic (flutter) analyses are then performed as perturbations about the static aeroelastic deformations of the AFW. The accuracy of the static aeroelastic procedure is investigated by comparing analytical results to those from AFW wind-tunnel experiments. Dynamic results are presented in the form of root loci at different Mach numbers for a heavy gas and for air test mediums. The resultant flutter boundaries for both gases, and the effects of viscous damping and angle of attack on the flutter boundary in air, are also presented.

Silva, Walter A.↗
NASA NTRS2003

Gravitational Lenses and the Structure and Evolution of Galaxies

The grant has supported the completion of 16 papers and 4 conference proceedings to date. During the first year of the project we completed five papers, each of which represents a new direction in the theory and interpretation of gravitational lenses. In the first paper, "The Importance of Einstein Rings", we developed the first theory for the formation and structure of the Einstein rings formed by lensing extended sources like the host galaxies of quasar and radio sources. We applied the theory to three lenses with lensed host galaxies. For the time delay lens PG 1115+080 we found that the structure of the Einstein ring ruled out models of the gravitational potential which permitted a large Hubble constant (70 km/s Mpc). In the second paper, :Cusped Mass Models Of Gravitational Lenses", we introduced a new class of lens models where the central density is characterized by a cusp ( rho proportional to tau(sup -gamma), 1 less than gamma less than 2) as in most modern models and theories of galaxies rather than a finite core radius. In the third paper, "Global Probes of the Impact of Baryons on Dark Matter Halos", we made the first globally consistent models for the separation distribution of gravitational lenses including both galaxy and cluster lenses. We show that the key physics for the origin of the sharp separation cutoff in the separation distribution near 3 arc sec is the effect of the cooling baryons in galaxies on the density structure of the system.

Kochanek, Christopher↗
NASA NTRS1990

Stratospheric dynamics and transport studies

A three dimensional General Circulation Model/Transport Model is used to simulate stratospheric circulation and constituent distributions. Model simulations are analyzed to interpret radiative, chemical, and dynamical processes and their mutual interactions. Concurrent complementary studies are conducted using both global satellite data and other appropriate data. Comparisons of model simulations and data analysis studies are used to aid in understanding stratospheric dynamics and transport processes and to assess the validity of current theory and models.

Grose, William L.↗
NASA NTRS1995

One-dimensional hybrid satellite track model for the Dynamics Explorer 2 (DE 2) satellite

A one-dimensional hybrid satellite track model has been developed to calculate the high-latitude thermospheric/ionospheric structure below the satellite altitude using Dynamics Explorer 2 (DE 2) satellite measurements and theory. This model is based on Emery et al. (1985) satellite track code but also includes elements of Roble et al. (1987b) global mean thermosphere/ionosphere model. A number of parameterizations and data handling techniques are used to input satellite data from several DE 2 instruments into this model. Profiles of neutral atmospheric densities are determined from the Mass Spectrometer Incoherent Scatter 1990 (MSIS-90) model and measured neutral temperatures. Measured electron precipitation spectra are used in an auroral model to calculate particle impact ionization rates below the satellite. These rates are combined with a solar ionization rate profile and used to solve the O(+) diffusion equation, with the measured electron density as an upper boundary condition. The calculated O(+) density distribution, as well as the ionization profiles, are then used in a photochemical equilibrium model to calculate the electron and molecular ion densities. The electron temperature is also calculated by solving the electron energy equation with an upper boundary condition determined by the DE 2 measurement. The model enables calculations of altitude profiles of conductivity and Joule heating rate along and below the satellite track. In a first application of the new model, a study is made of thermospheric and ionospheric structure below the DE 2 satellite for a single orbit which occurred on October 25, 1981. The field-aligned Poynting flux, which is independently obtained for this orbit, is compared with the model predictions of the height-integrated energy conversion rate. Good quantitative agreement between these two estimates has been reached. In addition, measurements taken at the incoherent scatter radar site at Chatanika (65.1 deg N, 147.4 deg W) during a DE 2 overflight are compared with the model calculations. A good agreement was found in lower thermospheric conductivities and Joule heating rate.

Deng, Wei↗
NASA NTRS1995

One-Dimensional Hybrid Satellite Track Model for the Dynamics Explorer 2 (DE 2) Satellite

A one-dimensional hybrid satellite track model has been developed to calculate the high-latitude thermospheric/ionospheric structure below the satellite altitude using Dynamics Explorer 2 (DE 2) satellite measurements and theory. This model is based on Emery et al. satellite track code but also includes elements of Roble et al. global mean thermosphere/ionosphere model. A number of parameterizations and data handling techniques are used to input satellite data from several DE 2 instruments into this model. Profiles of neutral atmospheric densities are determined from the MSIS-90 model and measured neutral temperatures. Measured electron precipitation spectra are used in an auroral model to calculate particle impact ionization rates below the satellite. These rates are combined with a solar ionization rate profile and used to solve the O(+) diffusion equation, with the measured electron density as an upper boundary condition. The calculated O(+) density distribution, as well as the ionization profiles, are then used in a photochemical equilibrium model to calculate the electron and molecular ion densities. The electron temperature is also calculated by solving the electron energy equation with an upper boundary condition determined by the DE 2 measurement. The model enables calculations of altitude profiles of conductivity and Joule beating rate along and below the satellite track. In a first application of the new model, a study is made of thermospheric and ionospheric structure below the DE 2 satellite for a single orbit which occurred on October 25, 1981. The field-aligned Poynting flux, which is independently obtained for this orbit, is compared with the model predictions of the height-integrated energy conversion rate. Good quantitative agreement between these two estimates has been reached. In addition, measurements taken at the incoherent scatter radar site at Chatanika (65.1 deg N, 147.4 deg W) during a DE 2 overflight are compared with the model calculations. A good agreement was found in lower thermospheric conductivities and Joule heating rate.

Deng, Wei↗
NASA NTRS1957

Comparison of Experimental and Theoretical Zero-Lift Wave-Drag Results for Various Wing-Body-Tail Combinations at Mach Numbers up to 1.9

Comparisons are made of experimental and theoretical zero-lift wave drag for several nose shapes, wing-body combinations, and models of current airplanes at Mach numbers up to 1.0. The experimental data were obtained from tests in the Ames 6- by6-foot supersonic wind tunnel and at the NACA Wallops Island facility. The theoretical drag was found by use of linear theory utilizing model area distributions. The agreement between theoretical and experimental zero-lift wave-drag coefficients was generally very good, especially for a fuselage or for fuselage-wing combinations that were vertically symmetrical. For other models that had rapid changes in body shape and/or were not vertically symmetrical, the agreement of theory with experiment ranged from fair to poor, depending on the severity of the change in shape.

DRAG COEFFICIENT↗