Search NASA⌕ Search

SEARCH · Search NASA

Results for “equation solving”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11

Molecular rotational line profiles from oxygen-rich red giant winds

We have developed a radiative transfer model of the dust and gas envelopes around late-type stars. The gas kinetic temperature for each star is calculated by solving equations of motion and the energy balance simultaneously. The main processes include viscous heating and adiabatic and radiative cooling. Heating is dominated by viscosity as the grains stream outward through the gas, with some contribution in oxygen-rich stars by near-IR pumping of H2O followed by collisional de-excitation in the inner envelope. For O-rich stars, rotational H2O cooling is a dominant mechanism in the middle part of the envelope, with CO cooling being less significant. We have applied our model to three well-studied oxygen-rich red giant stars. The three stars cover a wide range of mass-loss rates, and hence they have different temperature structures. The derived temperature structures are used in calculating CO line profiles for these objects. Comparison of the dust and gas mass-loss rates suggests that mass-loss rates are not constant during the asymptotic giant branch phase. In particular, the results show that the low CO 1-0 antenna temperatures of OH/IR stars reflect an earlier phase of much lower mass-loss rate.

Justtanont, K.↗

Time-Domain Computation Of Electromagnetic Fields In MMICs

Maxwell's equations solved on three-dimensional, conformed orthogonal grids by finite-difference techniques. Method of computing frequency-dependent electrical parameters of monolithic microwave integrated circuit (MMIC) involves time-domain computation of propagation of electromagnetic field in response to excitation by single pulse at input terminal, followed by computation of Fourier transforms to obtain frequency-domain response from time-domain response. Parameters computed include electric and magnetic fields, voltages, currents, impedances, scattering parameters, and effective dielectric constants. Powerful and efficient means for analyzing performance of even complicated MMIC.

Lansing, Faiza S.↗

Alfven wave resonances and flow induced by non-linear Alfven waves in a stratified atmosphere

A nonlinear, time-dependent, ideal MHD code has been developed and used to compute the flow induced by nonlinear Alfven waves propagating in an isothermal, stratified, plane-parallel atmosphere. The code is based on characteristic equations solved in a Lagrangian frame and is highly accurate. Results show that resonance behavior of Alfven waves exists in the presence of a continuous density gradient and that the waves with periods corresponding to resonant peaks exert considerably more force on the medium than off-resonance periods; this leads to enhanced flow. If only off-peak periods are considered, the relationship between the wave period and induced longitudinal velocity shows that short period WKB waves push more on the background medium than longer period, non-WKB, waves. The results also show the development of the longitudinal waves produced by the finite amplitude of the Alfven waves. The longitudinal wave becomes strong as the Alfven wave relative amplitude grows above 10 percent and will lead to strong damping of the Alfven waves.

Stark, B. A.↗

Multicolor Holography With Phase Shifting

Prototype apparatus constructed to test feasibility of two-color holographic interferometric scheme in which data for reconstructing holographic wavefront obtained with help of phase-shifting technique. Provides two sets of data needed to solve equations for effects of temperature and concentration. Concept extended to holography at three or more wavelengths to measure three or more phenomena associated with significant variations in index of refraction

Vikram, Chandra S.↗

Fast Multigrid Techniques in Total Variation-Based Image Reconstruction

Existing multigrid techniques are used to effect an efficient method for reconstructing an image from noisy, blurred data. Total Variation minimization yields a nonlinear integro-differential equation which, when discretized using cell-centered finite differences, yields a full matrix equation. A fixed point iteration is applied with the intermediate matrix equations solved via a preconditioned conjugate gradient method which utilizes multi-level quadrature (due to Brandt and Lubrecht) to apply the integral operator and a multigrid scheme (due to Ewing and Shen) to invert the differential operator. With effective preconditioning, the method presented seems to require Omicron(n) operations. Numerical results are given for a two-dimensional example.

Oman, Mary Ellen↗

Self-Consistent Models of Accretion Disks

The investigations of advection-dominated accretion flows (ADAFs), with emphasis on applications to X-ray binaries containing black holes and neutron stars is presented. This work is now being recognized as the standard paradigm for understanding the various spectral states of black hole X-ray Binaries (BHXBs). Topics discussed include: (1) Problem in BHXBS, namely that several of these binaries have unusually large concentrations of lithium in their companion stars; (2) A novel test to show that black holes have event horizons; (3) Application of the ADAF model to the puzzling X-ray delay in the recent outburst of the BHXB, GRO J1655-40; (4) Description of the various spectral states in BHXBS; (5) Application of the ADAF model to the famous supermassive black hole at the center of our Galaxy, Sgr A(*); (6) Writing down and solving equations describing steady-state, optically thin, advection-dominated accretion onto a Kerr black hole; (7) The effect of "photon bubble" instability on radiation dominated accretion disks; and (8) Dwarf nova disks in quiescence that have rather low magnetic Reynolds number, of order 10(exp 3).

Narayan, Ramesh↗

Numerical Simulation of Three-Dimensional Boattail Afterbody Flowfields

The thin shear-layer approximations of the three-dimensional, compressible Navier-Stokes equations are solved for subsonic, transonic, and supersonic now over axisymmetric boattail bodies at moderate angles of attack. The plume is simulated by a solid body configuration identical to those used In experimental tests. An implicit algorithm of second-order accuracy is used to solve the equations on the ILLIAC 4 computer. The turbulence is expressed by an algebraic model applicable to three-dimensional flowfields with moderate separation. The formulation used is attractive in its independence of boundary-layer parameters. Such a simple model, however, is incapable of supporting detailed quantitative descriptions of complex shear flows. Never-the-less, good qualitative comparisons are found with three different sets of experimental date. Quantitative improvement will depend on improved turbulence transport descriptions.

Deiwert, G. S.↗

Object Locating System

A portable system is provided that is operational for determining, with three dimensional resolution, the position of a buried object or approximately positioned object that may move in space or air or gas. The system has a plurality of receivers for detecting the signal front a target antenna and measuring the phase thereof with respect to a reference signal. The relative permittivity and conductivity of the medium in which the object is located is used along with the measured phase signal to determine a distance between the object and each of the plurality of receivers. Knowing these distances. an iteration technique is provided for solving equations simultaneously to provide position coordinates. The system may also be used for tracking movement of an object within close range of the system by sampling and recording subsequent position of the object. A dipole target antenna. when positioned adjacent to a buried object, may be energized using a separate transmitter which couples energy to the target antenna through the medium. The target antenna then preferably resonates at a different frequency, such as a second harmonic of the transmitter frequency.

Arndt, G. Dickey↗

Nonlinear Refractive Properties

Using nonlinear refractive properties of a salt-water solution at two wavelengths, numerical analysis has been performed to extract temperature and concentration from interferometric fringe data. The theoretical study, using a commercially available equation solving software, starts with critical fringe counting needs and the role of nonlinear refractive properties in such measurements. Finally, methodology of the analysis, codes, fringe counting accuracy needs, etc. is described in detail.

Vikram, Chandra S.↗

Drug Research

NBOD2, a program developed at Goddard Space Flight Center to solve equations of motion coupled N-body systems is used by E.I. DuPont de Nemours & Co. to model potential drugs as a series of elements. The program analyses the vibrational and static motions of independent components in drugs. Information generated from this process is used to design specific drugs to interact with enzymes in designated ways.

Source record↗

Two Color Interferometry with Nonlinear Refractive Properties

Using nonlinear refractive properties of salt-water solution at two wavelengths, numerical analysis has been performed to extract temperature and concentration from virtual interferometric fringe data. The theoretical study, using a commercially available equation solving tool, starts with critical fringe counting needs and the role of nonlinear refractive properties in such measurements. Finally, methodology of the analysis, developed codes, and fringe counting accuracy needs are described in detail.

Vikram, Chandra S.↗

Single Airfoil Gust Response Problem: Category 3, Problem 1

An unsteady aerodynamic code, called GUST3D (ref. 3), has been developed to solve equation (8) for flows with periodic vortical disturbances. The code uses a frequency-domain approach with second-order central differences and a pressure radiation condition in the far field. GUST3D requires as input certain mean flow quantities which are calculated separately by a potential flow solver. The solver calculates the mean ow using a Gothert's Rule approximation (ref. 3). On the airfoil surface, it uses the solution calculated by the potential code FLO36 (ref. 4). Figures 1-2 show the mean pressure along the airfoil surface for the two airfoil geometries. In Figures 3 - 8, we present the RMS pressure on the airfoil surface. Each figure shows three GUST3D solutions (calculated on grids with different far-field boundary locations). Three solutions are shown to provide some indication of the numerical uncertainty in the results. Figures 9 - 13 present the acoustic intensity. We again show three solutions per case. Note that no results are presented for the k1 = k2 = 2.0 loaded airfoil case, as an acceptable solution could not be obtained. A few comments need to be made about the results shown. First, since the last Workshop, the GUST3D code has been substantially upgraded. This includes implementing a more accurate far-field boundary condition (ref. 5) and developing improved gridding capabilities. This is the reason for any differences that may exist between the present results and results from the last Workshop. Second, the intensity results on the circle R = 4C were obtained using a Kirchoff method (ref. 6). The Kirchoff surface was the circle R = 2C. Finally, the GUST3D code is most accurate for low reduced frequencies. A new domain decomposition approach (ref. 7) has been developed to improve accuracy. Both the single domain and domain decomposition approaches were used in generating the present results.

Scott, James R.↗

Computer Simulation of Microwave Devices

The accurate simulation of cold-test results including dispersion, on-axis beam interaction impedance, and attenuation of a helix traveling-wave tube (TWT) slow-wave circuit using the three-dimensional code MAFIA (Maxwell's Equations Solved by the Finite Integration Algorithm) was demonstrated for the first time. Obtaining these results is a critical step in the design of TWT's. A well-established procedure to acquire these parameters is to actually build and test a model or a scale model of the circuit. However, this procedure is time-consuming and expensive, and it limits freedom to examine new variations to the basic circuit. These limitations make the need for computational methods crucial since they can lower costs, reduce tube development time, and lessen limitations on novel designs. Computer simulation has been used to accurately obtain cold-test parameters for several slow-wave circuits. Although the helix slow-wave circuit remains the mainstay of the TWT industry because of its exceptionally wide bandwidth, until recently it has been impossible to accurately analyze a helical TWT using its exact dimensions because of the complexity of its geometrical structure. A new computer modeling technique developed at the NASA Lewis Research Center overcomes these difficulties. The MAFIA three-dimensional mesh for a C-band helix slow-wave circuit is shown.

Kory, Carol L.↗

Three-Dimensional Electron Optics Model Developed for Traveling-Wave Tubes

A three-dimensional traveling-wave tube (TWT) electron beam optics model including periodic permanent magnet (PPM) focusing has been developed at the NASA Glenn Research Center at Lewis Field. This accurate model allows a TWT designer to develop a focusing structure while reducing the expensive and time-consuming task of building the TWT and hot-testing it (with the electron beam). In addition, the model allows, for the first time, an investigation of the effect on TWT operation of the important azimuthally asymmetric features of the focusing stack. The TWT is a vacuum device that amplifies signals by transferring energy from an electron beam to a radiofrequency (RF) signal. A critically important component is the focusing structure, which keeps the electron beam from diverging and intercepting the RF slow wave circuit. Such an interception can result in excessive circuit heating and decreased efficiency, whereas excessive growth in the beam diameter can lead to backward wave oscillations and premature saturation, indicating a serious reduction in tube performance. The most commonly used focusing structure is the PPM stack, which consists of a sequence of cylindrical iron pole pieces and opposite-polarity magnets. Typically, two-dimensional electron optics codes are used in the design of magnetic focusing devices. In general, these codes track the beam from the gun downstream by solving equations of motion for the electron beam in static-electric and magnetic fields in an azimuthally symmetric structure. Because these two-dimensional codes cannot adequately simulate a number of important effects, the simulation code MAFIA (solution of Maxwell's equations by the Finite-Integration-Algorithm) was used at Glenn to develop a three-dimensional electron optics model. First, a PPM stack was modeled in three dimensions. Then, the fields obtained using the magnetostatic solver were loaded into a particle-in-cell solver where the fully three-dimensional behavior of the beam was simulated in the magnetic focusing field. For the first time, the effects of azimuthally asymmetric designs and critical azimuthally asymmetric characteristics of the focusing stack (such as shunts, C-magnets, or magnet misalignment) on electron beam behavior have been investigated. A cutaway portion of a simulated electron beam focused by a PPM stack is illustrated.

Kory, Carol L.↗

Modeling Variability of Plasma Conditions in the Io Torus

Telescopic observations an in situ measurements of the Io plasma torus show the density, temperature and composition to vary over time, sometimes up to a factor of 2. While previous models of the physical and chemical processes in the Io plasma torus have reasonably modeled the conditions of the Voyager 1 era, their authors have not addressed the observed variability nor explored the sensitivity of torus conditions to input parameters. In this paper we present a homogeneous torus model parameterized by five variables (transport timescale, neutral source strength, ratio of oxygen sulfur to atoms in the source, fraction of superthermal electrons, temperature of these hot electrons). The model incorporates the most recent data for ionization, recombination, charge exchange and radiative energy losses for the major torus species (S, S(sup +), S(sup ++), S(sup +++), O, O(sup +), O(sup ++). We solve equations of conservation of mass and energy to find equilibrium conditions for a set of input parameters. We compare model plasma conditions with those observed by Voyager 1 Voyager 2, and Cassini. Furthermore, we explore the sensitivity of torus conditions to each parameter. We find that (1) torus conditions are distinctly different for the Voyager 1, Voyager 2 and Cassini eras, (2) unique torus input parameters for any given era are poorly constrained given the wide range of solution space that is consistent with the range of observed torus conditions, (3) ion composition is highly sensitive to the specification of a non-thermal electron distribution, (4) neutral O/S source ratio is highly variable with model values ranging between 1.7 for Cassini to 4.0 for Voyager 1 conditions, (5) transport times range between 23 days for Voyager 2 to 50 days for Voyager 1 and Cassini, (6) neutral source strengths range between 7 to 30 x 10(sup -4) cm (sup -3) s(sup -1) which corresponds to a net production of 0.4 to 1.3 tons/s for a torus volume of 1.4 x 10(sup 31) cm(sup 3), or 38 R(sub j)(sup 3).

Delamere, P. A.↗

Integrated CFD and Controls Analysis Interface for High Accuracy Liquid Propellant Slosh Predictions

Coupling computational fluid dynamics (CFD) with a controls analysis tool elegantly allows for high accuracy predictions of the interaction between sloshing liquid propellants and the control system of a launch vehicle. Instead of relying on mechanical analogs which are n0t va lid during all stages of flight, this method allows for a direct link between the vehicle dynamic environments calculated by the solver in the controls analysis tool to the fluid now equations solved by the CFD code. This paper describes such a coupling methodology, presents the results of a series of test cases, and compares said results against equivalent results from extensively validated tools. The coupling methodology, described herein, has proven to be highly accurate in a variety of different cases.

Marsell, Brandon↗

Chimera Grid Tools

Chimera Grid Tools (CGT) is a software package for performing computational fluid dynamics (CFD) analysis utilizing the Chimera-overset-grid method. For modeling flows with viscosity about geometrically complex bodies in relative motion, the Chimera-overset-grid method is among the most computationally cost-effective methods for obtaining accurate aerodynamic results. CGT contains a large collection of tools for generating overset grids, preparing inputs for computer programs that solve equations of flow on the grids, and post-processing of flow-solution data. The tools in CGT include grid editing tools, surface-grid-generation tools, volume-grid-generation tools, utility scripts, configuration scripts, and tools for post-processing (including generation of animated images of flows and calculating forces and moments exerted on affected bodies). One of the tools, denoted OVERGRID, is a graphical user interface (GUI) that serves to visualize the grids and flow solutions and provides central access to many other tools. The GUI facilitates the generation of grids for a new flow-field configuration. Scripts that follow the grid generation process can then be constructed to mostly automate grid generation for similar configurations. CGT is designed for use in conjunction with a computer-aided-design program that provides the geometry description of the bodies, and a flow-solver program.

Chan, William M.↗

Efficient Processing of Data for Locating Lightning Strikes

Two algorithms have been devised to increase the efficiency of processing of data in lightning detection and ranging (LDAR) systems so as to enable the accurate location of lightning strikes in real time. In LDAR, the location of a lightning strike is calculated by solving equations for the differences among the times of arrival (DTOAs) of the lightning signals at multiple antennas as functions of the locations of the antennas and the speed of light. The most difficult part of the problem is computing the DTOAs from digitized versions of the signals received by the various antennas. One way (a time-domain approach) to determine the DTOAs is to compute cross-correlations among variously differentially delayed replicas of the digitized signals and to select, as the DTOAs, those differential delays that yield the maximum correlations. Another way (a frequency-domain approach) to determine the DTOAs involves the computation of cross-correlations among Fourier transforms of variously differentially phased replicas of the digitized signals, along with utilization of the relationship among phase difference, time delay, and frequency.

Medelius, Pedro J.↗