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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 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

On the flame spreading over a polymer surface

The characteristics of flame propagation along the interface between a solid fuel and a gaseous oxidizer are considered. It is found that difficulties in a study of this problem are related to the eigenvalue character of the relative velocity of the flame with respect to the oxidizer flow. In the proposed model of flame spreading the difficulties are overcome by retaining the ellipticity of the governing equations and by taking the surface pyrolysis into account. The solution procedure makes use of a sink-source approach and the Fourier-transform method. Flame propagation velocity data computed on the basis of the described approach are compared with experimental results.

Ohki, Y.↗
NASA NTRS1976

Ground location of satellite scanner data

This paper presents simple and accurate mathematical formulation for determining the ground location of remote sensor data. The techniques used are based on elementary concepts of differential geometry and lead to the development of a relation that gives location as a function of surface ellipticity, satellite position, velocity, attitude, and scanner orientation. The formula lends itself to simply computer coding and will hopefully lead to a standardization of the various techniques which have been developed to solve this problem.

Puccinelli, E. F.↗
NASA NTRS1987

Aerodynamic interaction between vortical wakes and lifting two-dimensional bodies

Unsteady rotor wake interactions with the empenage, tail boom, and other aerodynamic surfaces of a helicopter have a significant influence on its aerodynamic performance, the ride quality, and amount of vibration. A numerical method for computing the aerodynamic interaction between an interacting vortex wake and the viscous flow about arbitrary two-dimensional bodies has been developed to address this helicopter problem. The method solves for the flow field velocities on a body-fitted computational mesh using finite-difference techniques. The interaction of a rotor wake with the flow about a 4:1 elliptic cylinder at 45-deg incidence was calculated for a Reynolds number of 3000.

Stremel, Paul M.↗
DOE OSTI2020

Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: A Generalized Moving Least-Squares (GMLS) approach

We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime and handle the divergence-free constraints via a generalized vector potential. This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and splitting schemes for the fourth-order governing equations in terms of a system of second-order elliptic operators. Using a Hodge decomposition, we develop methods for manifolds having spherical topology. We show the methods exhibit high-order convergence rates for solving hydrodynamic flows on curved surfaces. The methods also provide general high-order approximations for the metric, curvature, and other geometric quantities of the manifold and associated exterior calculus operators. The approaches also can be utilized to develop high-order solvers for other scalar-valued and vector-valued problems on manifolds.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1926

Inertia Factors of Ellipsoids for Use in Airship Design

This report is based on a study made by the writer as a member of the Special Committee on Design of Army Semirigid Airship RS-1 appointed by the National Advisory Committee for Aeronautics. The increasing interest in airships has made the problem of the potential flow of a fluid about an ellipsoid of considerable practical importance. In 1833 George Green, in discussing the effect of the surrounding medium upon the period of a pendulum, derived three elliptic integrals, in terms of which practically all the characteristics of this type of motion can be expressed. The theory of this type of motion is very fully given by Horace Lamb in his "Hydrodynamics," and applications to the theory of airships by many other writers. Tables of the inertia coefficients derived from these integrals are available for the most important special cases. These tables are adequate for most purposes, but occasionally it is desirable to know the values of these integrals in other cases where tabulated values are not available. For this reason it seems worth while to assemble a collection of formulae which would enable them to be computed directly from standard tables of elliptic integrals, circular and hyperbolic functions and logarithms without the need of intermediate transformations. Some of the formulae for special cases (elliptic cylinder, prolate spheroid, oblate spheroid, etc.) have been published before, but the general forms and some special cases have not been found in previous publications. (author)

Tuckerman, L. B.↗
NASA NTRS1936

Potential flow about elongated bodies of revolution

This report presents a method of solving the problem of axial and transverse potential flows around arbitrary elongated bodies of revolution. The solutions of Laplace's equation for the velocity potentials of the axial and transverse flows, the system of coordinates being an elliptic one in a meridian plane, are given. The theory is applied to a body of revolution obtained from a symmetrical Joukowsky profile, a shape resembling an airship hull. The pressure distribution and the transverse-force distribution are calculated and serve as examples of the procedure to be followed in the case of an actual airship. A section on the determination of inertia coefficients is also included in which the validity of some earlier work is questioned.

Kaplan, Carl↗
NASA NTRS1996

Hyperbolic Methods for Surface and Field Grid Generation

This chapter describes the use of hyperbolic partial differential equation methods for structured surface grid generation and field grid generation. While the surface grid generation equations are inherently three dimensional, the field grid generation equations can be formulated in two or three dimensions. The governing equations are derived from orthogonality relations and cell area/volume constraints; and are solved numerically by marching from an initial curve or surface. The marching step size and marching distance can be prescribedly the user. Exact specifications of the side and outer boundaries are not possible with a one sweep marching scheme but limited control is achievable. Excellent orthogonality and grid clustering characteristics are provided by hyperbolic methods with one to two orders of magnitude savings in time over typical elliptic methods. Since hyperbolic grid generation methods do not require the exact specifications of the side and outer boundaries of a grid, these methods are particularly well suited for the overlapping grid approach for solving problems on complex configurations. Grid generation software based on hyperbolic methods and their applications on several complex configurations will be described.

Chan, William M.↗
DOE OSTI2024

Mixed gauge-global symmetries, elliptic modes, and black hole thermodynamics in Hořava-Lifshitz gravity

In Hořava-Lifshitz gravity, a putative consistent theory of quantum gravity for which there is evidence for both black hole thermodynamics and a holographic construction, spacetime is endowed with a preferred dynamical spacelike foliation. The theory has a leaf reparameterization symmetry that is neither global nor local gauge, hyperbolic and elliptic equations of motion, a lack of splittability, and universal horizon black hole solutions. The reparameterization symmetry is “mixed”: it is a local symmetry in one coordinate yet global on each leaf. More broadly it is an example of both unfree and projectable gauge symmetries. The mixed symmetry and associated charge has not yet been accounted for in calculations of universal horizon thermodynamics in Hořava-Lifshitz gravity. This has led to problems, in particular the failure of the first law in a class of asymptotically AdS solutions where the normal to the leaves of the foliation is not aligned with the time translation Killing vector at infinity. We show how the dynamics of the charge corresponding to this symmetry coupled with the other features above resolves this issue. We then briefly comment how this mixed symmetry, the corresponding charge, and the elliptic equations of motion also conspire to evade recent holographic arguments for only local gauge fields in consistent theories of quantum gravity due to the lack of splittability of the elliptic equation and associated mode.

Global Symmetries↗
DOE OSTI2015

PLANET FORMATION IN BINARIES: DYNAMICS OF PLANETESIMALS PERTURBED BY THE ECCENTRIC PROTOPLANETARY DISK AND THE SECONDARY

Detections of planets in eccentric, close (separations of ∼20 AU) binary systems such as α Cen or γ Cep provide an important test of planet formation theories. Gravitational perturbations from the companion are expected to excite high planetesimal eccentricities, resulting in destruction rather than growth of objects with sizes of up to several hundred kilometers in collisions of similar-sized bodies. It was recently suggested that the gravity of a massive axisymmetric gaseous disk in which planetesimals are embedded drives rapid precession of their orbits, suppressing eccentricity excitation. However, disks in binaries are themselves expected to be eccentric, leading to additional planetesimal excitation. Here we develop a secular theory of eccentricity evolution for planetesimals perturbed by the gravity of an elliptical protoplanetary disk (neglecting gas drag) and the companion. For the first time, we derive an expression for the disturbing function due to an eccentric disk, which can be used for a variety of other astrophysical problems. We obtain explicit analytical solutions for planetesimal eccentricity evolution neglecting gas drag and delineate four different regimes of dynamical excitation. We show that in systems with massive (≳ 10{sup –2} M {sub ☉}) disks, planetesimal eccentricity is usually determined by the gravity of the eccentric disk alone, and is comparable to the disk eccentricity. As a result, the latter imposes a lower limit on collisional velocities of solids, making their growth problematic. In the absence of gas drag, this fragmentation barrier can be alleviated if the gaseous disk rapidly precesses or if its own self-gravity is efficient at lowering disk eccentricity.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

High-speed code validation

The topics are presented in viewgraph form and include the following: NFL body experiment; high-speed validation problems; 3-D Euler/Navier-Stokes inlet code; two-strut inlet configuration; pressure contours in two longitudinal planes; sidewall pressure distribution; pressure distribution on strut inner surface; inlet/forebody tests in 60 inch helium tunnel; pressure distributions on elliptical missile; code validations; small scale test apparatus; CARS nonintrusive measurements; optimized cone-derived waverider study; etc.

Barnwell, Richard W.↗
NASA NTRS1993

Large-scale computation of incompressible viscous flow by least-squares finite element method

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

Jiang, Bo-Nan↗
NASA NTRS1976

Some problems concerned with the geodetic use of high precision altimeter data

The definition of the geoid in view of different height systems is discussed. A definition is suggested which makes it possible to take into account the influence of the unknown corrections to the various height systems on the solution of Stokes' problem. A solution to Stokes' problem with an accuracy of 10 cm is derived which allows the inclusion of the results of satellite geodesy. In addition equations are developed for the determination of spherical harmonies using altimeter measurements. The influence of the ellipticity of the reference surface is considered.

Lelgemann, D.↗
NASA NTRS1977

Volumetric pattern analysis of airborne antennas

By blending together the roll and elevation plane high frequency solutions, a very efficient technique was developed for the volumetric pattern analysis of antennas mounted on the fuselage of a generalized aircraft. The fuselage is simulated by an infinitely long, perfectly conducting, elliptic cylinder in cross-section and a composite elliptic cylinder in profile. The wings, nose section, stabilizers, and landing gear doors may be modeled by finite flat or bent plates. Good agreement with accurate scale model measurements was obtained for a variety of airborne antenna problems.

Yu, C. L.↗
NASA NTRS1987

Prediction of tip vortex self-induced motion parameters in terms of rotor blade loading

The self-induced motion of curved vortex filaments at the tip of a helicopter rotor blade is investigated analytically. The derivation of a method for inviscid roll-up (IRU) is presented in detail, with attention to the cutoff-distance reformulation of the problem, a control-volume analysis of the self-induction properties of the vortex core, the adaptation of the roll-up method of Betz (1932) to IRU in three dimensions, the treatment of linear and elliptic loading, vortices with turbulent central cores, and the effect of cutoff distance on helicopter free-wake computations. Numerical results showing the significant effect of core properties on the geometry of a rotor wake in hover are presented in graphs and briefly characterized.

Bliss, Donald B.↗
NASA NTRS1992

A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting

The present treatment of elliptic regions via hyperbolic flux-splitting and high order methods proposes a flux splitting in which the corresponding Jacobians have real and positive/negative eigenvalues. While resembling the flux splitting used in hyperbolic systems, the present generalization of such splitting to elliptic regions allows the handling of mixed-type systems in a unified and heuristically stable fashion. The van der Waals fluid-dynamics equation is used. Convergence with good resolution to weak solutions for various Riemann problems are observed.

Shu, Chi-Wang↗
NASA NTRS1949

On the Theory of the Laval Nozzle

In the present paper, the motion of a gas in a plane-parallel Laval nozzle in the neighborhood of the transition from subsonic to supersonic velocities is studied. In a recently published paper, F. I. Frankl, applying the holograph method of Chaplygin, undertook a detailed investigation of the character of the flow near the line of transition from subsonic to supersonic velocities. From the results of Tricomi's investigation on the theory of differential equations of the mixed elliptic-hyperbolic type, Frankl introduced as one of the independent variables in place of the modulus of the velocity, a certain specially chosen function of this modulus. He thereby succeeded in explaining the character of the flow at the point of intersection of the transition line and the axis of symmetry (center of the nozzle) and in studying the behavior of the stream function in the neighborhood of this point by separating out the principal term having, together with its derivatives, the maximum value as compared with the corresponding corrections. This principal term is represented in Frankl's paper in the form of a linear combination of two hypergeometric functions. In order to find this linear combination, it is necessary to solve a number of boundary problems, which results in a complex analysis. In the investigation of the flow with which this paper is concerned, a second method is applied. This method is based on the transformation of the equations of motion to a form that may be called canonical for the system of differential equations of the mixed elliptic-hyperbolic type to which the system of equations of the motion of an ideal compressible fluid refers. By studying the behavior of the integrals of this system in the neighborhood of the parabolic line, the principal term of the solution is easily separated out in the form of a polynomial of the third degree. As a result, the computation of the transitional part of the nozzle is considerably simplified.

Falkovich, S. V.↗
NASA NTRS1980

Application of the multigrid method to grid generation

The multigrid method (MGM), used to numerically solve the pair of nonlinear elliptic equations commonly used to generate two dimensional boundary-fitted coordinate systems is discussed. Two different geometries are considered: one involving a coordinate system fitted about a circle and the other selected for an impinging jet flow problem. Two different relaxation schemes are tried: one is successive point overrelaxation and the other is a four-color scheme vectorizeable to take advantage of a parallel processor computer for greater computational speed. Results using MGM are compared with those using SOR (doing successive overrelaxations with the corresponding relaxation scheme on the fine grid only). It is found that MGM becomes significantly more effective than SOR as more accuracy is demanded and as more corrective grids, or more grid points, are used. For the accuracy required, it is found that MGM is two to three times faster than SOR in computing time. With the four-color relaxation scheme as applied to the impinging jet problem, the advantage of MGM over SOR is not as great. This may be due to the effect of a poor initial guess on MGM for this problem.

Ohring, S.↗
NASA NTRS1988

Control of supersonic intersection flowfields through filleting and sweep

The problem of supersonic flow control using fillets and sweep for a wing/body junction has been investigated numerically using a three-dimensional Navier-Stokes code which employs the MacCormack time-split finite-volume technique. An elliptic grid generation technique with direct control over spacing has been incorporated for constructing the grid at a filleted wing/body junction. The computed results for pressure distribution, particle paths, and limiting streamlines on the flat plate and fin surface for a swept fin show a decrease in the peak pressure on the fin leading edge and in the extent of the separated flow region. Moreover, the results for the filleted juncture clearly show that the flow streamline patterns lose much of their vortical character with proper filleting. It is demonstrated that fillets with a radius of 3.5 times the fin leading edge diameter are required to weaken the usual necklace vortex interaction.

Lakshmanan, B.↗