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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 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Limits to Open Class Performance?

This presentation discusses open or unlimited class aircraft performance limitations and design solutions. Limitations in this class of aircraft include slow climbing flight which requires low wing loading, high cruise speed which requires high wing loading, gains in induced or viscous drag alone which result in only half the gain overall and other structural problems (yaw inertia and spins, flutter and static loads integrity). Design solutions include introducing minimum induced drag for a given span (elliptical span load or winglets) and introducing minimum induced drag for a bell shaped span load. It is concluded that open class performance limits (under current rules and technologies) is very close to absolute limits, though some gains remain to be made from unexplored areas and new technologies.

Bowers, Albion H.↗
DOE OSTI2018

On the Theory of Anisotropic Flat Elasticity

For the Lamé system from the flat anisotropic theory of elasticity, we introduce generalized double-layer potentials in connection with the function-theory approach. These potentials are built both for the translation vector (the solution of the Lamé system) and for the adjoint vector functions describing the stress tensor. The integral representation of these solutions is obtained using the potentials. As a corollary, the first and the second boundary-value problems in various spaces (Hölder, Hardy, and the class of functions just continuous in a closed domain) are reduced to the equivalent system of the Fredholm boundary equations in corresponding spaces. Note that such an approach was developed in [19, 20] for common second-order elliptic systems with constant (higher-order only) coefficients. However, due to important applications, it makes sense to consider this approach in detail directly for the Lamé system. To illustrate these results, in the last two sections we consider the Dirichlet problem with piecewise-constant Lamé coefficients when contact conditions are given on the boundary between two media. This problem is reduced to the equivalent system of the Fredholm boundary equations. The smoothness of kernels of the obtained integral operators is investigated in detail depending on the smoothness of the boundary contours.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Motions of Kepler circumbinary planets in restricted three-body problem under radiating primaries

By observing continuously a single field of view in the sky, Kepler mission reveals outstanding results on discoveries of exoplanets. One of its recent progress is the discoveries of circumbinary planets. A circumbinary planet is an exoplanet that moves around a binary system. In this study we investigate motions of Kepler circumbinary planets belong to six binary systems, namely Kepler-16, -34, -35, -38, -47, and -413. The motions are considered to follow the Restricted Three-Body Problem (RTBP). Because the primaries (central massive objects) are stars, they are both radiatives, while the planet is an infinitesimal object. The primaries move in nearly circular and elliptic orbits with respect to their center of masses. We describe, in general, motions of the circumbinary planets in RTBP under radiating primaries. With respect to the averaged zero velocity curves, we show that motions of the exoplanets are stable, in accordance with their Hill stabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Resonant coupling applied to superconducting accelerator structures

The concept of resonant coupling and the benefits that accrue from its application is well known in the world of room temperature coupled cavity linacs. Design studies show that it can be applied successfully between sections of conventional elliptical superconducting coupled cavity accelerator structures and internally to structures with spoked cavity resonators. The coupling mechanisms can be designed without creating problems with high field regions or multipactoring. The application of resonant coupling to superconducting accelerators eliminates the need for complex cryogenic mechanical tuners and reduces the time needed to bring a superconducting accelerator into operation.

43 PARTICLE ACCELERATORS↗
NASA NTRS1980

Predicted vortex shedding from noncircular bodies in supersonic flow

A method to predict nose vortex shedding from circular and noncircular bodies in supersonic flow at angles of attack and roll is presented. The body is represented by a supersonic panel method, and the lee side vortex wake is modeled by discrete vortices in crossflow planes. The three-dimensional steady flow problem is reduced to a two-dimensional, unsteady, separated flow problem for solution. Comparison of measured and predicted surface pressure distributions, flow field surveys, and aerodynamic characteristics are presented for circular and elliptic bodies.

Mendenhall, M. R.↗
NASA NTRS1995

On the consistency of Reynolds stress turbulence closures with hydrodynamic stability theory

The consistency of second-order closure models with results from hydrodynamic stability theory is analyzed for the simplified case of homogeneous turbulence. In a recent study, Speziale, Gatski, and MacGiolla Mhuiris showed that second-order closures are capable of yielding results that are consistent with hydrodynamic stability theory for the case of homogeneous shear flow in a rotating frame. It is demonstrated in this paper that this success is due to the fact that the stability boundaries for rotating homogeneous shear flow are not dependent on the details of the spatial structure of the disturbances. For those instances where they are -- such as in the case of elliptical flows where the instability mechanism is more subtle -- the results are not so favorable. The origins and extent of this modeling problem are examined in detail along with a possible resolution based on rapid distortion theory (RDT) and its implications for turbulence modeling.

Speziale, Charles G.↗
NASA NTRS1996

The Effects of Dissipation and Coarse Grid Resolution for Multigrid in Flow Problems

The objective of this paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For two-dimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density.

Eliasson, Peter↗
DOE OSTI2025

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2001

A Curved, Elastostatic Boundary Element for Plane Anisotropic Structures

The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.

Smeltzer, Stanley S.↗
DOE OSTI2015

A transmission line model for propagation in elliptical core optical fibers

The calculation of mode propagation constants of elliptical core fibers has been the purpose of extended research leading to many notable methods, with the classic step index solution based on Mathieu functions. This paper seeks to derive a new innovative method for the determination of mode propagation constants in single mode fibers with elliptic core by modeling the elliptical fiber as a series of connected coupled transmission line elements. We develop a matrix formulation of the transmission line and the resonance of the circuits is used to calculate the mode propagation constants. The technique, used with success in the case of cylindrical fibers, is now being extended for the case of fibers with elliptical cross section. The advantage of this approach is that it is very well suited to be able to calculate the mode dispersion of arbitrary refractive index profile elliptical waveguides. The analysis begins with the deployment Maxwell’s equations adjusted for elliptical coordinates. Further algebraic analysis leads to a set of equations where we are faced with the appearance of harmonics. Taking into consideration predefined fixed number of harmonics simplifies the problem and enables the use of the resonant circuits approach. According to each case, programs have been created in Matlab, providing with a series of results (mode propagation constants) that are further compared with corresponding results from the ready known Mathieu functions method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Reweighted ℓ{sub 1} minimization method for stochastic elliptic differential equations

We consider elliptic stochastic partial differential equations (SPDEs) with random coefficients and solve them by expanding the solution using generalized polynomial chaos (gPC). Under some mild conditions on the coefficients, the solution is “sparse” in the random space, i.e., only a small number of gPC basis makes considerable contribution to the solution. To exploit this sparsity, we employ reweighted l{sub 1} minimization to recover the coefficients of the gPC expansion. We also combine this method with random sampling points based on the Chebyshev probability measure to further increase the accuracy of the recovery of the gPC coefficients. We first present a one-dimensional test to demonstrate the main idea, and then we consider 14 and 40 dimensional elliptic SPDEs to demonstrate the significant improvement of this method over the standard l{sub 1} minimization method. For moderately high dimensional (∼10) problems, the combination of Chebyshev measure with reweighted l{sub 1} minimization performs well while for higher dimensional problems, reweighted l{sub 1} only is sufficient. The proposed approach is especially suitable for problems for which the deterministic solver is very expensive since it reuses the sampling results and exploits all the information available from limited sources.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Transonic conical flow

The problem of inviscid, steady transonic conical flow, formulated in terms of the small disturbance theory, is studied. The small disturbance equation and similarity rules are presented, and a boundary value problem is formulated for the case of a supersonic freestream Mach number. The equation for the perturbation potential is solved numerically using an elliptic finite difference system. The difference equations are solved with a point relaxation algorithm that is also capable of capturing the shock wave during the iteration procedure by using the boundary conditions at the shock. Numerical calculations, for shock location, pressure distribution and drag coefficient, are presented for a family of nonlifting conical wings. The theory of slender wings is also presented and analytical results for pressure and drag coefficients are obtained.

Agopian, K. G.↗
NASA NTRS1974

Finite element solution theory for three-dimensional boundary flows

A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.

Baker, A. J.↗
NASA NTRS1986

Bodies with noncircular cross sections and bank-to-turn missiles

An evaluation is made of prospective missile applications for noncircular cross section bodies, and of recent developments in bank-to-turn missile configuration aerodynamics. The discussion encompasses cross-flow analysis techniques, as well as study results obtained for bodies with elliptical and square cross sections and with variable cross sections. Attention is given to both the performance advantages and the stability and control problems of bank-to-turn missile configurations; the aerodynamic data presented for monoplanar configurations extend to those incorporating airbreathing propulsion systems.

Jackson, C. M., Jr.↗
DOE OSTI2014

Acoustic scattering by elastic cylinders of elliptical cross-section and splitting up of resonances

The scattering of a plane acoustic wave by an infinite elastic cylinder of elliptical cross section is studied from a modal formalism by emphasizing the role of the symmetries. More precisely, as the symmetry is broken in the transition from the infinite circular cylinder to the elliptical one, the splitting up of resonances is observed both theoretically and experimentally. This phenomenon can be interpreted using group theory. The main difficulty stands in the application of this theory within the framework of the vectorial formalism in elastodynamics. This method significantly simplifies the numerical treatment of the problem, provides a full classification of the resonances, and gives a physical interpretation of the splitting up in terms of symmetry breaking. An experimental part based on ultrasonic spectroscopy complements the theoretical study. A series of tank experiments is carried out in the case of aluminium elliptical cylinders immersed in water, in the frequency range 0 ≤ kr ≤ 50, where kr is the reduced wave number in the fluid. The symmetry is broken by selecting various cylinders of increasing eccentricity. More precisely, the greater the eccentricity, the higher the splitting up of resonances is accentuated. The experimental results provide a very good agreement with the theoretical ones, the splitting up is observed on experimental form functions, and the split resonant modes are identified on angular diagrams.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Plasmoid solutions of the Hahm–Kulsrud–Taylor equilibrium model

The Hahm–Kulsrud (HK) [T. S. Hahm and R. M. Kulsrud, Phys. Fluids 28, 2412 (1985)] solutions for a magnetically sheared plasma slab driven by a resonant periodic boundary perturbation illustrate fully shielded (current sheet) and fully reconnected (magnetic island) responses. On the global scale, reconnection involves solving a magnetohydrodynamic (MHD) equilibrium problem. In systems with a continuous symmetry, such MHD equilibria are typically found by solving the Grad–Shafranov equation, and in slab geometry the elliptic operator in this equation is the 2-D Laplacian. Thus, assuming appropriate pressure and poloidal current profiles, a conformal mapping method can be used to transform one solution into another with different boundary conditions, giving a continuous sequence of solutions in the form of partially reconnected magnetic islands (plasmoids) separated by Syrovatsky current sheets. The two HK solutions appear as special cases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2002

Analytical Modal Analysis for Thin-Film Flat Lenses

Due to strong potential applications and more demanding requirements imposed upon thin-film structures for space deployable, there has been increasing research and development activities during recent years in the field of vibration analysis of these types of structures. Moreover, interests in employing these structural components have received renewed emphasis in recent years within NASA and the Air Force. This is due to their inherent lightweight, low packaging and launch volume, and relative simplicity of deployment. Among the potential mission concepts for which these structural elements are included, one can mention solar sails, space solar power generation systems, solar thermal propulsion vehicles, large space telescopes, and inflatable communication antennas. This paper presents analytical procedures to determine vibration and physical characteristics of thin film lenses with circular and elliptical shapes membranes considered in design of a solar concentrator. In general, three methods are used to obtain approximate solutions of Helmholtz boundary value problems. One method requires that solution satisfy the differential equation exactly and the boundary condition approximately. Another method demands a solution that satisfies the boundary conditions exactly and the governing equations approximately. The third method sees a solution that satisfies both the governing equation and boundary conditions approximately. Extensive reviews of vibrations of membrane and plates are provided by Leissa and Mazumdar.

Hamid R. Hamidzadeh↗