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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Investigation of radiative interaction in laminar flows using Monte Carlo simulation

The Monte Carlo method (MCM) is employed to study the radiative interactions in fully developed laminar flow between two parallel plates. Taking advantage of the characteristics of easy mathematical treatment of the MCM, a general numerical procedure is developed for nongray radiative interaction. The nongray model is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. To validate the Monte Carlo simulation for nongray radiation problems, the results of radiative dissipation from the MCM are compared with two available solutions for a given temperature profile between two plates. After this validation, the MCM is employed to solve the present physical problem and results for the bulk temperature are compared with available solutions. In general, good agreement is noted and reasons for some discrepancies in certain ranges of parameters are explained.

Liu, Jiwen↗
NASA NTRS1982

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Thompson, J. F.↗
NASA NTRS1997

Computation of Transonic Flows Using Potential Methods

The proposed paper will describe the state of the art associated with numerical solution of the full or exact velocity potential equation for solving transonic, external-aerodynamic flows. The presentation will begin with a review of the literature emphasizing research activities of the past decade. Next, the various forms of the full or exact velocity potential equation, the equation's corresponding mathematical characteristics, and the derivation assumptions will be presented and described in detail. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, will be presented and discussed relative to the more complete Euler or Navier-Stokes formulations. The technical presentation will continue with a description of recently developed full potential numerical approach characteristics. This description will include governing equation nondimensionalization, physical-to-computational-domain mapping procedures, a limited description of grid generation requirements, the spatial discretization scheme, numerical implementation of boundary conditions, and the iteration scheme. The next portion of the presentation will present and discuss numerical results for several two- and three-dimensional aerodynamic applications. Included in the results section will be a discussion and demonstration of a typical grid refinement analysis for determining spatial convergence of the numerical solution and level of solution accuracy. Computer timings for a variety of full potential applications will be compared and contrasted with similar results for the Euler equation formulation. Finally. the presentation will end with concluding remarks and recommendations for future work.

Hoist, Terry L.↗
NASA NTRS1961

Design and Flight Tests of an Adaptive Control System Employing Normal-Acceleration Command

An adaptive control system employing normal-acceleration command has been designed with the aid of an analog computer and has been flight tested. The design of the system was based on the concept of using a mathematical model in combination with a high gain and a limiter. The study was undertaken to investigate the application of a system of this type to the task of maintaining nearly constant dynamic longitudinal response of a piloted airplane over the flight envelope without relying on air data measurements for gain adjustment. The range of flight conditions investigated was between Mach numbers of 0.36 and 1.15 and altitudes of 10,000 and 40,000 feet. The final adaptive system configuration was derived from analog computer tests, in which the physical airplane control system and much of the control circuitry were included in the loop. The method employed to generate the feedback signals resulted in a model whose characteristics varied somewhat with changes in flight condition. Flight results showed that the system limited the variation in longitudinal natural frequency of the adaptive airplane to about half that of the basic airplane and that, for the subsonic cases, the damping ratio was maintained between 0.56 and 0.69. The system also automatically compensated for the transonic trim change. Objectionable features of the system were an exaggerated sensitivity of pitch attitude to gust disturbances, abnormally large pitch attitude response for a given pilot input at low speeds, and an initial delay in normal-acceleration response to pilot control at all flight conditions. The adaptive system chatter of +/-0.05 to +/-0.10 of elevon at about 9 cycles per second (resulting in a maximum airplane normal-acceleration response of from +/-0.025 g to +/- 0.035 g) was considered by the pilots to be mildly objectionable but tolerable.

McNeill, Water E.↗
NASA NTRS1989

Control of the errors of discretization and idealization in finite element analysis

Understanding of the basic principles which control errors of discretization in finite element analysis has increased very substantially since 1980. The main milestones were: (1) development of the theoretical basis of p-extensions (1981); (2) understanding of the proper interplay between mesh design and assignment of polynomial degree to elements. Practical realization of exponential convergence rates, independently of the smoothness of the exact solution (1984); and (3) industrial experience with the new finite element technology known as the p- or hp-version of the finite element method: General Dynamics reported thirty- to forty-fold savings in terms of human time and large savings in computer time (1986). Lockheed reported favorably on their evaluation of error estimation and quality control capabilities of the p-version in industrial settings (1987). The gains in our understanding of how to control the errors of discretization represent only half of the control necessary to ensure that a numerical model is in fact an accurate representation of the corresponding physical system. Control of the errors of idealization is equally important. A brief overview of the main ideas of how to ensure the quality and reliability of mathematical models of structural systems is presented.

Szabo, Barna A.↗
NASA NTRS2007

Validation of Blockage Interference Corrections in the National Transonic Facility

A validation test has recently been constructed for wall interference methods as applied to the National Transonic Facility (NTF). The goal of this study was to begin to address the uncertainty of wall-induced-blockage interference corrections, which will make it possible to address the overall quality of data generated by the facility. The validation test itself is not specific to any particular modeling. For this present effort, the Transonic Wall Interference Correction System (TWICS) as implemented at the NTF is the mathematical model being tested. TWICS uses linear, potential boundary conditions that must first be calibrated. These boundary conditions include three different classical, linear. homogeneous forms that have been historically used to approximate the physical behavior of longitudinally slotted test section walls. Results of the application of the calibrated wall boundary conditions are discussed in the context of the validation test.

Walker, Eric L.↗
NASA NTRS1984

Use of shape-preserving interpolation methods in surface modeling

In many large-scale scientific computations, it is necessary to use surface models based on information provided at only a finite number of points (rather than determined everywhere via an analytic formula). As an example, an equation of state (EOS) table may provide values of pressure as a function of temperature and density for a particular material. These values, while known quite accurately, are typically known only on a rectangular (but generally quite nonuniform) mesh in (T,d)-space. Thus interpolation methods are necessary to completely determine the EOS surface. The most primitive EOS interpolation scheme is bilinear interpolation. This has the advantages of depending only on local information, so that changes in data remote from a mesh element have no effect on the surface over the element, and of preserving shape information, such as monotonicity. Most scientific calculations, however, require greater smoothness. Standard higher-order interpolation schemes, such as Coons patches or bicubic splines, while providing the requisite smoothness, tend to produce surfaces that are not physically reasonable. This means that the interpolant may have bumps or wiggles that are not supported by the data. The mathematical quantification of ideas such as physically reasonable and visually pleasing is examined.

Ftitsch, F. N.↗
NASA NTRS1989

Advances in fluid dynamics

Various papers on advances in fluid dynamics are presented. Individual topics addressed include: nonunique solutions of the Euler equations; numerical solution of the biharmonic equation using a spectral multigrid method; finite-volume shape and placement for efficiency, accuracy, and physics; NND schemes and their application to numerical simulation of complex plume flow problems; symbolic analysis and computational algorithm construction; and velocity and mass flux distribution measurements of spherical glass beads in air flow in a 90-deg vertical-to-horizontal bend. Also discussed are: hyperbolic solution adaptive mesh generation; progress and future directions in CFD; numerical simulation of shock focusing; microbubble formation and splitting in a turbulent boundary layer for turbulence reduction; numerical study of spherical Taylor-Couette flow, trajectories of vortex lines beneath a free surface or above a plane; and a mathematical model for response of the coronary circulation to high sustained gravitational force fields.

Ballhaus, W. F., Jr.↗
NASA NTRS1994

Space proton transport in one dimension

An approximate evaluation procedure is derived for a second-order theory of coupled nucleon transport in one dimension. An analytical solution with a simplified interaction model is used to determine quadrature parameters to minimize truncation error. Effects of the improved method on transport solutions with the BRYNTRN data base are evaluated. Comparisons with Monte Carlo benchmarks are given. Using different shield materials, the computational procedure is used to study the physics of space protons. A transition effect occurs in tissue near the shield interface and is most important in shields of high atomic number.

NASA Discipline Number 45-10↗
NASA NTRS1989

Correlations in alpha-alpha scattering and semi-classical optical models

We show the equivalence of semi-classical solutions to optical model coupled-channel equations derived from Watson's form of the nucleus-nucleus multiple-scattering series to the Glauber multiple-scattering series. A second-order solution to the semi-classical coupled-channel elastic amplitude is shown to be nearly equivalent to a second-order optical-phase-shift approximation to the Glauber amplitude if the densities of all nuclear excited states are approximated by the ground-state density. Using the Jastrow method to model the two-body density we find an average excited-state density to be of negligible importance in the double-scattering region of alpha-alpha scattering.

NASA Discipline Number 04-10↗
NASA NTRS1975

High zonal harmonics of rapidly rotating planets

A new perturbation expansion is derived for the structure of rotating bodies in hydrostatic equilibrium. The method uses an expansion of the density on Legendre polynomial functions of angle, and can be developed analytically in a manner analogous to the standard level-surface perturbation theory. The new theory proceeds from a prescribed pressure-density relation rather than from a prescribed density distribution, and is both simpler and more physically transparent than the level-surface approach. High zonal harmonics are shown to arise via a transfer function involving derivatives of the interior sound velocity, and via mixing of multipole density components in the outer shell of the planet. Sample calculations for polytropic sequences are presented, as well as standard gravity models for Jupiter and Saturn. Mathematical subleties of the theory are discussed in an appendix.

Hubbard, W. B.↗
NASA NTRS2009

System and method for deriving a process-based specification

A system and method for deriving a process-based specification for a system is disclosed. The process-based specification is mathematically inferred from a trace-based specification. The trace-based specification is derived from a non-empty set of traces or natural language scenarios. The process-based specification is mathematically equivalent to the trace-based specification. Code is generated, if applicable, from the process-based specification. A process, or phases of a process, using the features disclosed can be reversed and repeated to allow for an interactive development and modification of legacy systems. The process is applicable to any class of system, including, but not limited to, biological and physical systems, electrical and electro-mechanical systems in addition to software, hardware and hybrid hardware-software systems.

Hinchey, Michael Gerard↗
NASA NTRS1972

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

Scott, R. K.↗
NASA NTRS1999

Uncertainty Analysis of Instrument Calibration and Application

Experimental aerodynamic researchers require estimated precision and bias uncertainties of measured physical quantities, typically at 95 percent confidence levels. Uncertainties of final computed aerodynamic parameters are obtained by propagation of individual measurement uncertainties through the defining functional expressions. In this paper, rigorous mathematical techniques are extended to determine precision and bias uncertainties of any instrument-sensor system. Through this analysis, instrument uncertainties determined through calibration are now expressed as functions of the corresponding measurement for linear and nonlinear univariate and multivariate processes. Treatment of correlated measurement precision error is developed. During laboratory calibration, calibration standard uncertainties are assumed to be an order of magnitude less than those of the instrument being calibrated. Often calibration standards do not satisfy this assumption. This paper applies rigorous statistical methods for inclusion of calibration standard uncertainty and covariance due to the order of their application. The effects of mathematical modeling error on calibration bias uncertainty are quantified. The effects of experimental design on uncertainty are analyzed. The importance of replication is emphasized, techniques for estimation of both bias and precision uncertainties using replication are developed. Statistical tests for stationarity of calibration parameters over time are obtained.

Tripp, John S.↗
NASA NTRS1976

Calculation of the motion of an airplane under the influence of irregular disturbances

The application of mathematical advances made in electricity and other branches to problems of airplane dynamics is demonstrated. The Heaviside-Bromwich methods of solution of linear differential equations are described and it is shown how these methods avoid the consideration of boundary conditions and of particular or complementary integrals. It is pointed out that if the solution of the differential equation is obtained for the case of a unit disturbance, the effect of varying disturbances may be found therefrom by Carson's theorem. A graphical solution of Carson's integral for irregular disturbances is given. The procedure of obtaining unit solutions of the equations is then taken up and the analogy between Heaviside's symbolic series solution and a physical procedure of approximation is shown. It is suggested that a fictitious impulsive disturbance be used in the treatment of initial motions.

Jones, R. T.↗
NASA NTRS2014

Elastic Model Transitions: A Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes a hybrid approach for determining physical displacements by augmenting the original quadratically constrained least squares (LSQI) algorithm with Direct Shape Mapping (DSM) and modifying the energy constraints. The approach presented is applicable to simulation of the elastic behavior of launch vehicles and other structures that utilize discrete LTI finite element model (FEM) derived mode sets (eigenvalues and eigenvectors) that are propagated throughout time. The time invariant nature of the elastic data presents a problem of how to properly transition elastic states from the prior to the new model while preserving motion across the transition and ensuring there is no truncation or excitation of the system. A previous approach utilizes a LSQI algorithm with an energy constraint to effect smooth transitions between eigenvector sets with no requirement that the models be of similar dimension or have any correlation. This approach assumes energy is conserved across the transition, which results in significant non-physical transients due to changing quasi-steady state energy between mode sets, a phenomenon seen when utilizing a truncated mode set. The computational burden of simulating a full mode set is significant so a subset of modes is often selected to reduce run time. As a result of this truncation, energy between mode sets may not be constant and solutions across transitions could produce non-physical transients. In an effort to abate these transients an improved methodology was developed based on the aforementioned approach, but this new approach can handle significant changes in energy across mode set transitions. It is proposed that physical velocities due to elastic behavior be solved for using the LSQI algorithm, but solve for displacements using a two-step process that independently addresses the quasi-steady-state and non-steady-state contributions to the elastic displacement. For structures subject to large external forces, such as thrust or atmospheric drag, it is imperative to capture these forces when solving for elastic displacement. To simplify the mathematical formulation, assumptions are made regarding mass matrix normalization, constant external forcing, and constant viscous damping. These simplifications allow for direct solutions to the quasi-steady-state displacements through a process titled Direct Shape Mapping. DSM solves for the displacements using the eigenvalues of the elastic modes and the external forcing and returns a set of elastic displacements dictated by the eigenvectors of the post-transition mode set. For the non-steady-state contributions to displacement we formulate a LSQI problem that is constrained by energy of the non-steady state terms. The contributions from the quasi-steady-state and non-steady state solutions are then combined to obtain the physical displacements associated with the new set of eigenvectors. Results for the LSQI-DSM approach show significant reduction/complete removal of transients across mode set transitions while maintaining elastic motion from the prior state. For time propagation applications employing discrete elastic models that need to be transitioned in time and where running with full a full mode set is not feasible, the method developed offers a practical solution to simulating vehicle elasticity.

Hannan, Mike R.↗
NASA NTRS2016

Predictive Simulation of Gas Adsorption in Fixed-Beds and Limitations due to the Ill-Posed Danckwerts Boundary Condition

The 1-D axially dispersed plug flow model is a mathematical model widely used for the simulation of adsorption processes. Lumped mass transfer coefficients such as the Glueckauf linear driving force (LDF) term and the axial dispersion coefficient are generally obtained by fitting simulation results to the experimental breakthrough test data. An approach is introduced where these parameters, along with the only free parameter in the energy balance equations, are individually fit to specific test data that isolates the appropriate physics. It is shown that with this approach this model provides excellent simulation results for the C02 on zeolite SA sorbent/sorbate system; however, for the H20 on zeolite SA system, non-physical deviations from constant pattern behavior occur when fitting dispersive experimental results with a large axial dispersion coefficient. A method has also been developed that determines a priori what values of the LDF and axial dispersion terms will result in non-physical simulation results for a specific sorbent/sorbate system when using the one-dimensional axially dispersed plug flow model. A relationship between the steepness of the adsorption equilibrium isotherm as indicated by the distribution factor, the magnitude of the axial dispersion and mass transfer coefficient, and the resulting non-physical behavior is derived. This relationship is intended to provide a guide for avoiding non-physical behavior by limiting the magnitude of the axial dispersion term on the basis of the mass transfer coefficient and distribution factor.

Knox, James Clinton↗
NASA NTRS1995

SAVS: A Space and Atmospheric Visualization Science system

The research environment faced by space and atmospheric scientists in the 1990s is characterized by unprecedented volumes of new data, by ever-increasing repositories of unexploited mission files, and by the widespread use of empirical and large-scale computational models needed for the synthesis of understanding across data sets and discipline boundaries. The effective analysis and interpretation of such massive amounts of information have become the subjects of legitimate concern. With SAVS (a Space and Atmospheric Visualization Science System), we address these issues by creating a 'push-button' software environment that mimics the logical scientific processes in data acquisition, reduction, and analysis without requiring a detailed understanding of the methods, networks, and modules that link the tools and effectively execute the functions. SAVS provides (1) a customizable framework for accessing a powerful set of visualization tools based on the popular AVS visualization software with hooks to PV-Wave and access to Khoros modules, (2) a set of mathematical and statistical tools, (3) an extensible library of discipline-specific functions and models (e.g., MSIS, IRI, Feldstein Oval, IGRF, satellite tracking with CADRE-3, etc.), and (4) capabilities for local and remote data base access. The system treats scalar, vector, and image data, and runs on most common Unix workstations. We present a description of SAVS and its components, followed by several applications based on generic research interests in interplanetary and magnetospheric physics (IMP/ISTP), active experiments in space (CRRES), and mission planning focused on the Earth's thermospheric, ionospheric, and mesospheric domains (TIMED).

Szuszczewicz, E. P.↗