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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Exact wave solver for nonparaxial laser beam propagation

Simulations of inertial confinement fusion (ICF) experiments require high-fidelity models for laser beam propagation in a nonuniform plasma with varying index of refraction. We describe a new numerical wave solver that is applicable to centimeter-scale length plasmas encountered in indirect drive ICF applications. The one-way Helmholtz equation (OHE) generalizes the time-harmonic paraxial wave equation to large angles. Here, we present a methodology to numerically evaluate the exact solution to the OHE. This solution is computed by analytically advancing eigenfunctions of the one-way Helmholtz operator along a propagation direction and is applicable to any given index of a refraction profile. We compare our exact method with a commonly used approximate split-step technique for solving the OHE. As a test problem, we consider nonparaxial propagation of Gaussian and speckled beams in a plasma density channel with internal reflection. We find that the split-step approach incurs significant errors compared to the exact solution computed using the novel algorithm.

Belyaev, Mikhail A. (ORCID:0000000224908887)↗
NASA NTRS1977

Features of sound propagation through and stability of a finite shear layer

The plane wave propagation, the stability, and the rectangular duct mode problems of a compressible, inviscid, linearly sheared, parallel, homogeneous flow are shown to be governed by Whittaker's equation. The exact solutions for the perturbation quantities are essentially the Whittaker M-functions where the nondimensional quantities have precise physical meanings. A number of known results are obtained as limiting cases of the exact solutions. For the compressible finite thickness shear layer it is shown that no resonances and no critical angles exist for all Mach numbers, frequencies, and shear layer velocity profile slopes except in the singular case of the vortex sheet.

Koutsoyannis, S. P.↗
NASA NTRS1949

General Theory of Aerodynamic Instability and the Mechanism of Flutter

The aerodynamic forces on an oscillating airfoil or airfoil-aileron combination of three independent degrees of freedom have been determined. The problem resolves itself into the solution of certain definite integrals, which have been identified as Bessel functions of the first and second kind and of zero and first order. The theory, being based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing-section theory relating to the steady case. The air forces being known, the mechanism of aerodynamic instability has been analyzed in detail. An exact solution, involving potential flow and the adoption of the Kutta condition, has been analyzed in detail. An exact solution, involving potential flow and the adoption of the Kutta condition, has been arrived at. The solution is of a simple form and is expressed by means of an auxiliary parameter K.

Theodorsen, Theodore↗
DOE OSTI2026

Spatial Correlations of the Poisson Model for Radiation Transport

Characterizing the relationship between bulk physical properties and mixing in randomly heterogeneous media is a central challenge across many areas of science and engineering. A benchmark model for such studies is the Poisson model, a random tessellation of space by a Poisson process of hyperplanes. In radiation transport studies, the lack of exact expressions for the Poisson model’s spatial multipoint functions has led to approximate methods being used, introducing unquantified sources of error. Here, we recently introduced an exact solution for the Poisson model’s multipoint functions and closely related conditional probability functions (CPFs), providing a new opportunity to understand and reduce these sources of error. In this paper, we enable a more rigorous investigation of radiation transport in stochastic media by applying the recently introduced exact solution for the Poisson model’s CPFs. This paper consists of three main contributions. First, we introduce a unified framework for CPFs of the Poisson model, encompassing the recently introduced exact CPFs as well as the previously introduced atomic mix, nearest-neighbor, and combination CPFs. This framework also includes existing pruning techniques for the approximate CPFs, such as angular exclusion, as well as a novel form of angular exclusion suitable for the exact CPFs. Second, we use the exact CPFs to characterize the spatial regions where each approximate three-point CPF is most accurate, thereby explaining the observed hierarchy of accuracy among the approximate models. Finally, we evaluate material transmittance, reflectance, and flux in a three-dimensional test problem using conditional point sampling, demonstrating the relationship between CPF accuracy and transport simulation accuracy.

Poisson model↗
DOE OSTI2023

GnarlyX: Eulerian multi-material hydrodynamics coupled to equation of state and hyperelastic, plastic constitutive models

GnarlyX is a new hydrocode for direct numerical simulations of the microstructural behavior of high explosives at the mesoscale. We summarize the computational framework for multidimensional, Eulerian multi-material hydrodynamics coupled to EOS and hyperelastic, plastic constitutive models. We present 1D verification tests of multi-material only and combined multimaterial and strength capabilities with comparisons to exact solutions of shock states resulting from an incident shock impacting the material interface of PBX9502 and aluminum. We show that GnarlyX performs well in capturing the resulting shock waves in examining numerical convergence with exact solutions. In later work, we will summarize the thermomechanics and multi-dimensional, parallel computing capabilities in GnarlyX with multi-dimensional verification tests.

42 ENGINEERING↗
NASA NTRS1994

On current sheet approximations in models of eruptive flares

We consider an approximation sometimes used for current sheets in flux-rope models of eruptive flares. This approximation is based on a linear expansion of the background field in the vicinity of the current sheet, and it is valid when the length of the current sheet is small compared to the scale length of the coronal magnetic field. However, we find that flux-rope models which use this approximation predict the occurrence of an eruption due to a loss of ideal-MHD equilibrium even when the corresponding exact solution shows that no such eruption occurs. Determination of whether a loss of equilibrium exists can only be obtained by including higher order terms in the expansion of the field or by using the exact solution.

Bungey, T. N.↗
NASA NTRS1993

An improved calibration technique for wind tunnel model attitude sensors

Aerodynamic wind tunnel tests at NASA Langley Research Center (LaRC) require accurate measurement of model attitude. Inertial accelerometer packages have been the primary sensor used to measure model attitude to an accuracy of +/- 0.01 deg as required for aerodynamic research. The calibration parameters of the accelerometer package are currently obtained from a seven-point tumble test using a simplified empirical approximation. The inaccuracy due to the approximation exceeds the accuracy requirement as the misalignment angle between the package axis and the model body axis increases beyond 1.4 deg. This paper presents the exact solution derived from the coordinate transformation to eliminate inaccuracy caused by the approximation. In addition, a new calibration procedure is developed in which the data taken from the seven-point tumble test is fit to the exact solution by means of a least-squares estimation procedure. Validation tests indicate that the new calibration procedure provides +/- 0.005-deg accuracy over large package misalignments, which is not possible with the current procedure.

Tripp, John S.↗
NASA NTRS1989

Application of the p-version of the finite-element method to global-local problems

A brief survey is given of some recent developments in finite-element analysis technology which bear upon the three main research areas under consideration in this workshop: (1) analysis methods; (2) software testing and quality assurance; and (3) parallel processing. The variational principle incorporated in a finite-element computer program, together with a particular set of input data, determines the exact solution corresponding to that input data. Most finite-element analysis computer programs are based on the principle of virtual work. In the following, researchers consider only programs based on the principle of virtual work and denote the exact displacement vector field corresponding to some specific set of input data by vector u(EX). The exact solution vector u(EX) is independent of the design of the mesh or the choice of elements. Except for very simple problems, or specially constructed test problems, vector u(EX) is not known. Researchers perform a finite-element analysis (or any other numerical analysis) because they wish to make conclusions concerning the response of a physical system to certain imposed conditions, as if vector u(EX) were known.

Szabo, Barna A.↗
NASA NTRS2006

Development of a Nonlinear Probability of Collision Tool for the Earth Observing System

The Earth Observing System (EOS) spacecraft Terra, Aqua, and Aura fly in constellation with several other spacecraft in 705-kilometer mean altitude sun-synchronous orbits. All three spacecraft are operated by the Earth Science Mission Operations (ESMO) Project at Goddard Space Flight Center (GSFC). In 2004, the ESMO project began assessing the probability of collision of the EOS spacecraft with other space objects. In addition to conjunctions with high relative velocities, the collision assessment method for the EOS spacecraft must address conjunctions with low relative velocities during potential collisions between constellation members. Probability of Collision algorithms that are based on assumptions of high relative velocities and linear relative trajectories are not suitable for these situations; therefore an algorithm for handling the nonlinear relative trajectories was developed. This paper describes this algorithm and presents results from its validation for operational use. The probability of collision is typically calculated by integrating a Gaussian probability distribution over the volume swept out by a sphere representing the size of the space objects involved in the conjunction. This sphere is defined as the Hard Body Radius. With the assumption of linear relative trajectories, this volume is a cylinder, which translates into simple limits of integration for the probability calculation. For the case of nonlinear relative trajectories, the volume becomes a complex geometry. However, with an appropriate choice of coordinate systems, the new algorithm breaks down the complex geometry into a series of simple cylinders that have simple limits of integration. This nonlinear algorithm will be discussed in detail in the paper. The nonlinear Probability of Collision algorithm was first verified by showing that, when used in high relative velocity cases, it yields similar answers to existing high relative velocity linear relative trajectory algorithms. The comparison with the existing high velocity/linear theory will also be used to determine at what relative velocity the analysis should use the new nonlinear theory in place of the existing linear theory. The nonlinear algorithm was also compared to a known exact solution for the probability of collision between two objects when the relative motion is strictly circular and the error covariance is spherically symmetric. Figure I shows preliminary results from this comparison by plotting the probabilities calculated from the new algorithm and those from the exact solution versus the Hard Body Radius to Covariance ratio. These results show about 5% error when the Hard Body Radius is equal to one half the spherical covariance magnitude. The algorithm was then combined with a high fidelity orbit state and error covariance propagator into a useful tool for analyzing low relative velocity nonlinear relative trajectories. The high fidelity propagator is capable of using atmospheric drag, central body gravitational, solar radiation, and third body forces to provide accurate prediction of the relative trajectories and covariance evolution. The covariance propagator also includes a process noise model to ensure realistic evolutions of the error covariance. This paper will describe the integration of the nonlinear probability algorithm and the propagators into a useful collision assessment tool. Finally, a hypothetical case study involving a low relative velocity conjunction between members of the Earth Observation System constellation will be presented.

McKinley, David P.↗
NASA NTRS1988

Accuracy of analytic energy level formulas applied to hadronic spectroscopy of heavy mesons

Linear and harmonic potential models are used in the nonrelativistic Schroedinger equation to obtain article mass spectra for mesons as bound states of quarks. The main emphasis is on the linear potential where exact solutions of the S-state eigenvalues and eigenfunctions and the asymptotic solution for the higher order partial wave are obtained. A study of the accuracy of two analytical energy level formulas as applied to heavy mesons is also included. Cornwall's formula is found to be particularly accurate and useful as a predictor of heavy quarkonium states. Exact solution for all partial waves of eigenvalues and eigenfunctions for a harmonic potential is also obtained and compared with the calculated discrete spectra of the linear potential. Detailed derivations of the eigenvalues and eigenfunctions of the linear and harmonic potentials are presented in appendixes.

Badavi, Forooz F.↗
NASA NTRS1997

Modeling of Structural-Acoustic Interaction Using Coupled FE/BE Method and Control of Interior Acoustic Pressure Using Piezoelectric Actuators

A coupled finite element (FE) and boundary element (BE) approach is presented to model full coupled structural/acoustic/piezoelectric systems. The dual reciprocity boundary element method is used so that the natural frequencies and mode shapes of the coupled system can be obtained, and to extend this approach to time dependent problems. The boundary element method is applied to interior acoustic domains, and the results are very accurate when compared with limited exact solutions. Structural-acoustic problems are then analyzed with the coupled finite element/boundary element method, where the finite element method models the structural domain and the boundary element method models the acoustic domain. Results for a system consisting of an isotropic panel and a cubic cavity are in good agreement with exact solutions and experiment data. The response of a composite panel backed cavity is then obtained. The results show that the mass and stiffness of piezoelectric layers have to be considered. The coupled finite element and boundary element equations are transformed into modal coordinates, which is more convenient for transient excitation. Several transient problems are solved based on this formulation. Two control designs, a linear quadratic regulator (LQR) and a feedforward controller, are applied to reduce the acoustic pressure inside the cavity based on the equations in modal coordinates. The results indicate that both controllers can reduce the interior acoustic pressure and the plate deflection.

Mei, Chuh↗
NASA NTRS2003

Fully Nonlinear Modeling and Analysis of Precision Membranes

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Pai, P. Frank↗
NASA NTRS1999

Phenomenological Theory of the Translational Relaxation Times in Gases

The exact solution to the classical equations governing the translational dispersion and absorption of sound in a gas obscures its relaxational character because of its mathematical complexity. The approach taken here is to solve the secular equation by the method of Pade approximants, which even to the relatively low order R(sub 11) yields a remarkably close approximation to the exact solution over a wide range of frequency/pressure (f/P) ratios. As a result, translational relaxation can be formulated in terms of a conventional relaxation process with well-defined relaxation times, relaxation strength, collision numbers, additivity relations, etc. To extend the theory to high values of f/P ratio, a model is proposed to account for the noncontinuum behavior of the transport coefficients (viscosity and thermal conductivity) as the molecular mean free path approaches the acoustical enclosure dimensions. The theoretical dispersion and absorption show good agreement with measurements in argon over the classical and transition regions of f/P, but a discrepancy appears at higher values of f/P, where collective propagating modes, assumed in the theory, give way to single-particle modes, prevailing in the experiments.

Zuckerwar, Allan J.↗
NASA NTRS1994

Time-evolving bubbles in two-dimensional stokes flow

A general class of exact solutions is presented for a time evolving bubble in a two-dimensional slow viscous flow in the presence of surface tension. These solutions can describe a bubble in a linear shear flow as well as an expanding or contracting bubble in an otherwise quiescent flow. In the case of expanding bubbles, the solutions have a simple behavior in the sense that for essentially arbitrary initial shapes the bubble will asymptote an expanding circle. Contracting bubbles, on the other hand, can develop narrow structures ('near-cusps') on the interface and may undergo 'break up' before all the bubble-fluid is completely removed. The mathematical structure underlying the existence of these exact solutions is also investigated.

Tanveer, Saleh↗
DOE OSTI2022

Geometrical picture of the electron–electron correlation at the large- D limit

In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrödinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation. Both, the mean field, and the exact solutions at the large-D limit have distinct geometries. Thus, the difference might be used to describe the correlation effect. Moreover, correlations can be also described and quantified by the entanglement between the electrons, which is a strong correlation without a classical analog. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics and bounded by the area law for local gapped Hamiltonians of interacting many-body systems. This study opens up the possibility of presenting a geometrical picture of the electron–electron correlations and might give a bound on the correlation energy. Furthermore, the results at the large-D limit and at D = 3 indicate the feasibility of using the geometrical picture to get a bound on the electron–electron correlations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1972

Stability criteria for accelerating and decelerating aircraft.

Derivation of the linearized differential equation for the longitudinal oscillations of an aircraft for the general case when the atmospheric density, thrust force, and velocity are varying. Exact solutions and stability criteria are presented for several different conditions. For the zero thrust coasting aircraft that is being decelerated by its drag force, new stability criteria are derived for both ascending and descending flight. A critical altitude is found for ascending aircraft that are attempting to coast out of the atmosphere. Above this critical altitude the oscillations cease, and there is a monotonic increase in the angle of attack. Exact solutions for the oscillations of coasting aircraft are presented in terms of the confluent hypergeometric functions. It is shown that previous attempts to predict a critical altitude for ascending vehicles were in error because they did not include the second type, or logarithmic solution, of the confluent hypergeometric function.

Laitone, E. V.↗
DOE OSTI2025

The Implications of Collisions on the Spatial Profile of Electric Potential and the Space-Charge-Limited Current

The space-charge-limited current (SCLC) in a vacuum diode is given by the Child-Langmuir law (CLL), whose electric potential ϕ(x) ∝ (x/D) 4/3 , where x is the spatial coordinate across the gap and D is the gap separation distance. For a collisional diode, SCLC is given by the Mott-Gurney law (MGL) and ϕ(x) ∝ (x/D) 3/2 . Here, we apply a capacitance argument for SCLC and use the transit time from a recent exact solution for collisional SCLC to show that ϕ(x) ∝ (x/D)ξ for a general collisional gap, where 4/3 ≤ ξ ≤ 3/2 . Furthermore, ξ is strictly a function of νT, where ν is the collision frequency and T is the electron transit time. Using this definition of ξ, we estimate the spatial dependence of the electron velocity and use the gap capacitance to derive an analytic equation for collisional SCLC that agrees within ~4.5% of the exact solution that requires solving parametrically through T. This analytic equation for general ξ asymptotically recovers the CLL as ν → 0 and the MGL as ν → ∞. As a result, matching these limits shows that ξ ≈ 1.40 and V ∝ D 2 ν 2 at the transition from a vacuum to a collisional diode for any device condition.

Anodes↗
NASA NTRS1986

Theoretical and material studies on thin-film electroluminescent devices

A theoretical study of resonant tunneling in multilayered heterostructures is presented based on an exact solution of the Schroedinger equation under the application of a constant electric field. By use of the transfer matrix approach, the transmissivity of the structure is determined as a function of the incident electron energy. The approach presented is easily extended to many layer structures where it is more accurate than other existing transfer matrix or WKB models. The transmission resonances are compared to the bound state energies calculated for a finite square well under bias using either an asymmetric square well model or the exact solution of an infinite square well under the application of an electric field. The results show good agreement with other existing models as well as with the bound state energies. The calculations were then applied to a new superlattice structure, the variablly spaced superlattice energy filter, (VSSEP) which is designed such that under bias the spatial quantization levels fully align. Based on these calculations, a new class of resonant tunneling superlattice devices can be designed.

Summers, C. J.↗