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At least 721 records · Page 40

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NASA NTRS1978

An extension of A-stability to alternating direction implicit methods

An alternating direction implicit (ADI) scheme was constructed by the method of approximate factorization. An A-stable linear multistep method (LMM) was used to integrate a model two-dimensional hyperbolic-parabolic partial differential equation. Sufficient conditions for the A-stability of the LMM were determined by applying the theory of positive real functions to reduce the stability analysis of the partial differential equations to a simple algebraic test. A linear test equation for partial differential equations is defined and then used to analyze the stability of approximate factorization schemes. An ADI method for the three-dimensional heat equation is also presented.

Warming, R. F.↗

NASA NTRS1978

Anastigmatic three-mirror telescope

A three-mirror telescope for extraterrestrial observations is described. An ellipsoidal primary mirror, a hyperbolic secondary mirror, and an ellipsoidal tertiary mirror, produce an image in a conveniently located finite plane for viewing.

Korsch, D. G.↗

NASA NTRS1979

A theoretical investigation of forebody shapes designed for natural laminar boundary-layer flow

The design of forebody shapes for natural laminar flow is discussed. For subsonic flow, computed results for three shapes of different fineness ratios indicate that laminar flow can be attained under conditions that approximate those on the forebody of a cruise missile flying at a low altitude at a high subsonic Mach number. For supersonic (Mach 2.00) design, a one-parameter family of hyperbolic arcs was used to generate forebody shapes having a favorable pressure gradient over the forebody length. Computed results for these shapes indicated laminar and transitional flow over the range of Reynolds numbers considered.

Barger, R. L.↗

NASA NTRS1979

Recent developments in finite element analysis for transonic airfoils

The prediction of aerodynamic forces in the transonic regime generally requires a flow field calculation to solve the governing non-linear mixed elliptic-hyperbolic partial differential equations. Finite difference techniques were developed to the point that design and analysis application are routine, and continual improvements are being made by various research groups. The principal limitation in extending finite difference methods to complex three-dimensional geometries is the construction of a suitable mesh system. Finite element techniques are attractive since their application to other problems have permitted irregular mesh elements to be employed. The purpose of this paper is to review the recent developments in the application of finite element methods to transonic flow problems and to report some recent results.

Hafez, M. M.↗

NASA NTRS1977

An accuracy analysis of the LDAR system

An accuracy report of the Lightning Detection and Ranging System is presented. The effect of quantizing errors are modelled by use of a computer. The errors in the four configurations of the LDAR System are compared to the limiting errors in an ideal hyperbolic system. Performance data from the track of a jet plane and for the indicated position of a fixed lightning simulator are analyzed for dispersions in the data. Error models show the quality and the areas of highly accurate data, and show how the data deteriorates outside the primary measuring range.

Poehler, H. A.↗

NASA NTRS1979

Flux vector splitting of the inviscid equations with application to finite difference methods

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Steger, J. L.↗

NASA NTRS1978

Finite elements and finite differences for transonic flow calculations

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Hafez, M. M.↗

NASA NTRS1978

A three-dimensional model of corotating streams in the solar wind. I - Theoretical foundations

The paper is concerned with the development of the theoretical and mathematical background pertinent to the study of steady, corotating solar wind structure in all three spatial dimensions. The dynamical evolution of the plasma in interplanetary space (defined as the region beyond roughly 35 Rs where the flow is supersonic) is approximately described by the nonlinear, single-fluid, polytropic magnetohydrodynamic or hydrodynamic equations. Efficient numerical techniques are outlined for solving this complex system of coupled, hyperbolic partial differential equations. The present formulation is inviscid and nonmagnetic, but the methods used allow for the potential inclusion of both features with only modest modifications. A simple, highly idealized hydrodynamic model stream is examined to illustrate the fundamental processes involved in the three-dimensional dynamics of stream evolution. It is found that spatial variations in the rotational stream interaction mechanism produce small nonradial flows on a global scale that lead to the transport of mass, energy, and momentum away from regions of relative compression and into regions of relative rarefaction. Comparison with simpler models demonstrates the essential nonlinear, multidimensional nature of the interplanetary dynamics.

Pizzo, V.↗

NASA NTRS1979

On the optimality of the MAP estimation loop for carrier phase tracking BPSK and QPSK signals

Starting with MAP estimation theory as a basis for optimally estimating carrier phase of BPSK and QPSK modulations, it is shown in this paper that the closed loop phase trackers, which are motivated by this approach, are indeed closed loop optimum in the minimum mean-square phase tracking jitter sense. The corresponding squaring loss performance of these so-called MAP estimation loops is compared with that of more practical implementations wherein the hyperbolic tangent nonlinearity is approximated by simpler functions.

Simon, M. K.↗

NASA NTRS1978

Effects of moisture profiles and laminate configuration on the hygro stress in advanced composites

A theoretical investigation was performed using a recently developed integrated theory for predicting the hygrothermomechanical response to investigate the effects of three different moisture profiles on the ply hygro stresses in angleplied laminates. The moisture profiles were linear, parabolic and hyperbolic varying from 1 percent at the exposed ply to '0' percent in the protected ply. The angleplied laminates were of two generic configurations. The results obtained are summarized graphically to illustrate the effects of both moisture profile and laminate configuration.

Chamis, C. C.↗

NASA NTRS1979

Sound radiation from hyperboloidal inlet ducts

This paper presents rigorous solutions for the problem of sound radiation from various inlet ducts including hyperboloidal (or hyperbolic) inlet ducts and circular ducts with wide flange. The numerical results include the complex conversion (or reflection) coefficients and the radiation directivity for the various incident wave modes - spinning modes as well as axisymmetric modes. The analysis utilizes hyperboloidal wave functions which are defined here as a class of eigensolutions of the wave equation for oblate spheroidal coordinates, and is valid for the whole frequency range including frequencies above and below the cutoff frequencies of duct modes involved.

Cho, Y. C.↗

NASA NTRS1979

Physical and dynamical evolution of long-period comets

The source of long-period comets was investigated using a Monte Carlo simulation of comet evolution under the influence of a combination of physical and dynamical processes. The perturbation of cometary orbits by major planets and by non-gravitational forces was modeled, as was physical loss of comets due to random disruption (splitting) and planetary collision; a model was also derived for loss of all volatiles. The importance of each of these processes was examined. The primary end states found for long-period comets were: ejection on hyperbolic orbit, 65.2%; random disruption, 27.6%; and formation of silicate crusts, 7.1%. The basic correctness of the Ort hypothesis was confirmed.

Weissman, P. R.↗

NASA NTRS1979

Two-dimensional ultraviolet imagery with a microchannel-plate/resistive-anode detector

An imaging ultraviolet detector has been designed for use with a precision pointed telescope flown on a sounding rocket. Resolution of better than 80 microns over a field of 5 mm has been achieved. The ultraviolet image is converted to electrons at the front surface of a CsI coated chevron microchannel-plate electron multiplier. For each photoelectron, the multiplier produces a burst of about 3,000,000 electrons, which impinges on a tellurium-coated resistive anode with four evaporated hyperbolic readout electrodes. The sizes of the four resulting output pulses are digitized to 10 bit accuracy and telemetered to the ground, where they are divided in pairs to give the x and y coordinates of the photoelectron event. The coordinates are used to generate a picture in real time, and are recorded for computer processing later. The detector was successfully flown in December 1978. Good images of Jupiter and Capella in hydrogen Lyman alpha emission were obtained.

Opal, C. B.↗

NASA NTRS1978

On the accuracy and convergence of implicit numerical integration of finite element generated ordinary differential equations

A study of accuracy and convergence of linear functional finite element solution to linear parabolic and hyperbolic partial differential equations is presented. A variable-implicit integration procedure is employed for the resultant system of ordinary differential equations. Accuracy and convergence is compared for the consistent and two lumped assembly procedures for the identified initial-value matrix structure. Truncation error estimation is accomplished using Richardson extrapolation.

Baker, A. J.↗

NASA NTRS1979

The lambda-scheme

A method for integrating the Euler equations of gas dynamics for compressible flows in any hyperbolic case is presented. This method is applied to the Mach number distribution over a stretch of an infinite duct having a variable cross section, and to the distribution in a channel opening into a vacuum with the Mach number equalling 1.04. An example of the ability of this method to handle two-dimensional unsteady flows is shown using the steady shock-and-isobars pattern reached asymptotically about an ablated blunt body with a free stream Mach number equalling 12. A final example is presented where the technique is applied to a three-dimensional steady supersonic flow, with a Mach number of 2 and an angle of attack of 5 deg.

Moretti, G.↗

NASA NTRS1979

Science aspects of a mission beyond the planets

A mission out of the planetary system, launched about the year 2000, could provide valuable data concerning characteristics of the heliopause, the interstellar medium, stellar distances (by parallax measurements), low-energy cosmic rays, interplanetary gas distribution, and mass of the solar system. Secondary objectives include investigation of Pluto. Candidate science measurements, instruments, and instrument development needs are discussed. The mission should extend from 400 to 1000 AU from the sun. A heliocentric hyperbolic escape velocity of 50-100 km/sec or more is needed to attain this distance within a reasonable mission duration (20-50 years). The trajectory should be toward the incoming interstellar gas. For a year 2000 launch, a Pluto encounter and orbiter can be included. A second mission targeted parallel to the solar axis would also be worthwhile.

Jaffe, L. D.↗

NASA NTRS1979

Aerocapture - A system design for planetary exploration

The paper presents the results of a study that developed conceptual designs of an atmospheric entry system with moderate to high L/D ratios to establish the concepts of aerocapture into low circular Mars orbits from hyperbolic flyby trajectories. The payloads considered in this study were those currently conceived for the Mars Sample Return (MSR) mission including single mission (SM) and multi-mission (MM) modes. The design concepts developed are also applicable (with small modification) for establishment of closed orbits about Venus and Saturn. The MSR mission payload requires an orbiter, lander, ascent vehicle, and rover, with a total mass of approximately 4000 kg. The emphasis during the study was placed on development of concepts for aerodynamic configuration, the aeroshell design, and a guidance, navigation, and control subsystem.

Cruz, M. I.↗

NASA NTRS1980

An analysis of turbulent diffusion flame in axisymmetric jet

The kinetic theory of turbulent flow was employed to study the mixing limited combustion of hydrogen in axisymmetric jets. The integro-differential equations in two spatial and three velocity coordinates describing the combustion were reduced to a set of hyperbolic partial differential equations in the two spatial coordinates by a binodal approximation. The MacCormick's finite difference method was then employed for solution. The flame length was longer than that predicted by the flame-sheet analysis, and was found to be in general agreement with a recent experimental result. Increase of the turbulence energy and scale resulted in an enhancement of the combustion rate and, hence, in a shorter flame length. Details of the numerical method as well as of the physical findings are discussed.

Chung, P. M.↗