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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Analysis of the thermal performance of heat pipe radiators

A comprehensive mathematical model and computational methodology are presented to obtain numerical solutions for the transient behavior of a heat pipe radiator in a space environment. The modeling is focused on a typical radiator panel having a long heat pipe at the center and two extended surfaces attached to opposing sides of the heat pipe shell in the condenser section. In the set of governing equations developed for the model, each region of the heat pipe - shell, liquid, and vapor - is thermally lumped to the extent possible, while the fin is lumped only in the direction normal to its surface. Convection is considered to be the only significant heat transfer mode in the vapor, and the evaporation and condensation velocity at the liquid-vapor interface is calculated from kinetic theory. A finite-difference numerical technique is used to predict the transient behavior of the entire radiator in response to changing loads.

Boo, J. H.↗
NASA NTRS1999

Analytical Assessment of a Gross Leakage Event Within the International Space Station (ISS) Node 2 Internal Active Thermal Control System (IATCS)

Results of the International Space Station (ISS) Node 2 Internal Active Thermal Control System (IATCS) gross leakage analysis are presented for evaluating total leakage flowrates and volume discharge caused by a gross leakage event (i.e. open boundary condition). A Systems Improved Numerical Differencing Analyzer and Fluid Integrator (SINDA/FLUINT) thermal hydraulic mathematical model (THMM) representing the Node 2 IATCS was developed to simulate system performance under steady-state nominal conditions as well as the transient flow effects resulting from an open line exposed to ambient. The objective of the analysis was to determine the adequacy of the leak detection software in limiting the quantity of fluid lost during a gross leakage event to within an acceptable level.

Holt, James M.↗
NASA NTRS2001

Analytical Assessment of a Gross Leakage Event Within the International Space Station (ISS) Node 2 Internal Active Thermal Control System (IATCS)

Results of the International Space Station (ISS) Node 2 Internal Active Thermal Control System (IATCS) gross leakage analysis are presented for evaluating total leakage flow rates and volume discharge caused by a gross leakage event (i.e. open boundary condition). A Systems Improved Numerical Differencing Analyzer and Fluid Integrator (SINDA85/FLUINT) thermal hydraulic mathematical model (THMM) representing the Node 2 IATCS was developed to simulate system performance under steady-state nominal conditions as well as the transient flow effect resulting from an open line exposed to ambient. The objective of the analysis was to determine the adequacy of the leak detection software in limiting the quantity of fluid lost during a gross leakage event to within an acceptable level.

Holt, James M.↗
NASA NTRS1976

Survey of computer programs for prediction of crash response and of its experimental validation

The author seeks to critically assess the potentialities of the mathematical and hybrid simulators which predict post-impact response of transportation vehicles. A strict rigorous numerical analysis of a complex phenomenon like crash may leave a lot to be desired with regard to the fidelity of mathematical simulation. Hybrid simulations on the other hand which exploit experimentally observed features of deformations appear to hold a lot of promise. MARC, ANSYS, NONSAP, DYCAST, ACTION, WHAM II and KRASH are among some of the simulators examined for their capabilities with regard to prediction of post impact response of vehicles. A review of these simulators reveals that much more by way of an analysis capability may be desirable than what is currently available. NASA's crashworthiness testing program in conjunction with similar programs of various other agencies, besides generating a large data base, will be equally useful in the validation of new mathematical concepts of nonlinear analysis and in the successful extension of other techniques in crashworthiness.

Kamat, M. P.↗
NASA NTRS1978

UNIX as an environment for producing numerical software

The UNIX operating system supports a number of software tools; a mathematical equation-setting language, a phototypesetting language, a FORTRAN preprocessor language, a text editor, and a command interpreter. The design, implementation, documentation, and maintenance of a portable FORTRAN test of the floating-point arithmetic unit of a computer is used to illustrate these tools at work.

Schryer, N. L.↗
NASA NTRS2010

Transforming Mean and Osculating Elements Using Numerical Methods

Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order

averaging↗
NASA NTRSDate not supplied

Numerical Fluxes and Shocks

Accurately describing shocks within numerical partial differential equation solvers has been a significant computational hurdle for the field of applied mathematics. In our work we present and discuss the background and history of how shocks have been dealt with. We have analyzed numerical schemes and fluxes for the purpose of education and improved computational speed and accuracy. We demonstrate the need for specific methods to deal with shocks by showcasing some methods in a simple one dimensional case for burger’s equation. We aim to extend our knowledge to the euler equations.

Partial Differential Equations↗
NASA NTRS1989

Motivating the sure bounds

Motivation is provided for a theorem that provides upper and lower bounds for the reliability of reconfigurable digital control systems. The reliability goals for these systems are too high to be established by natural life testing, which means the probability of system failure must be computed from mathematical models that capture the essential elements of fault occurence and system fault recovery. The upper and lower bound theorem shows that system recovery can be adequately described by its first two moments, provided component failure rate is low and system recovery is fast. This result greatly simplifies both the fault injection experiments that study system recovery and the numerical computations that estimate the probability of system failure from a mathematical model.

White, Allan L.↗
NASA NTRS1991

Solution of geometrically nonlinear statics problems by the p-version of the finite element method

This project is concerned with the possibility of using computers for the simulation of structural systems with the same degree of reliability as full scale physical experiments. Reliable numerical simulation will make it possible to reduce the costs of engineering and improve the quality of engineering decisions based on computed information. An error of idealization is an error between the actual physical quantities on which engineering decisions are based (e.g., maximum principal stress, first natural frequency, etc.) and the same data corresponding to the exact solution of the mathematical model. An error of discretization is an error between the quantities of interest corresponding to the exact and approximate solutions of a mathematical model. A high degree of reliability can be achieved in numerical simulation only if both the errors of idealization and errors of discretization can be shown to be small.

Szabo, Barna A.↗
NASA NTRS1993

Program Computes Flows Of Fluids And Heat

SINDA'85/FLUINT incorporates lumped-parameter-network and one-dimensional-flow mathematical models. System enables analysis of mutual influences of thermal and flow phenomena. Offers two finite-difference numerical solution techniques: forward-difference explicit approximation and Crank-Nicholson approximation. Enables simulation of nonuniform heating and facilitates mathematical modeling of thin-walled heat exchangers. Ability to model nonequilibrium behavior within two-phase volumes included. Recent changes in program improve modeling of real evaporator pumps and other capillary-assist evaporators. Written in FORTRAN 77.

Cullimore, Brent↗
NASA NTRS2001

Radiometry Measurements of Mars at 1064 nm Using the Mars Orbiter Laser Altimeter

Measurements by the Mars Orbiter Laser Altimeter (MOLA) on board the Mars Global Surveyor (MGS) may be used to provides a radiometric measurement of Mars in addition to the topographic measurement. We will describe the principle of operation, a mathematical model, and the receiver calibration in this presentation. MOLA was designed primarily to measure Mars topography, surface roughness end the bidirectional reflectance to the laser beam. To achieve the highest sensitivity the receiver detection threshold is dynamically adjusted to be as low as possible while keeping a predetermined false alarm rate. The average false alarm rate 29 monitored in real time on board MOLA via a noise counter, whose output is fed to the threshold control loop. The false alarm rate at a given threshold is a function of the detector output noise which is the sum of the photo detector, shot noise due to the background light seen by the detector and the dark noise. A mathematical model has been developed that can be used to numerically solve for the optical background power given the MOLA threshold setting and the average noise count. The radiance of Mars can then be determined by dividing the optical power by the solid angle subtended by the MOLA receiver, the receiver optical band-width, end the Mars surface area within the receiver field of view. The phase angle which is the sun-Mars-MOLA angle is available from the MGS database. MOLA also measures simultaneously the bidirectional reflectance of Mars vie its 106-lum loser beam at nadir with nearly zero phase angle. The optical bandwidth of the MOLA receiver is 2um full width at half maximum (FWHM) and centered at 106-lum. The receiver field of view is 0.95mrad FWHM. The nominated spacecraft altitude is 100km and the ground track speed is about 3km/s. Under normal operation, the noise counter are read and the threshold levels are updated at 1Hz. The receiver sensitivity is limited by the detector dark noise to about 0.1nW, which corresponds to less than 2% the maximum radiance during daytime from the brightest area on Mars. The results from the mathematical model agree well with the prelaunch measurements at several calibrated optical power levels. The radiance of sunlit Mars estimated with this technique correlates well with the measurement from the MGS. Thermal Emission Spectrometer (TES) and the Hubble Space Telescope at similar wavelength.

Sun, Xiao-Li↗
NASA NTRS1987

A generalized procedure for constructing an upwind based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some linear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to scalar nonlinear equations and a constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance in numerical experiments. The formulation is extended to the nonlinear system. It is demonstrated that the present procedure can easily convert existing central or upwind, and second- or higher-order differencing schemes to preserve monotonicity and yield physically admissible solutions. The formulation is simple mathematically as well as numerically; both matrix-vector multiplication and Riemann solver are avoided. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made.

Liou, Meng-Sing↗
NASA NTRS1982

A mathematical model of post-instability in fluid mechanics

Postinstability of fluids is eliminated in numerical models by introducing multivalued velocity fields after discarding the principle of impenetrability. Smooth functions are shown to be incapable of keeping the derivatives from going towards infinity when iterating solutions for the governing equations such as those defined by Navier-Stokes. Enlarging the class of functions is shown to be necessary to eliminate the appearance of imaginary characteristic roots in the systems of arbitrary partial differential equations, a condition which leads to physically impossible motions. The enlarging is demonstrated to be achievable by allowing several individual particles with different velocities to appear at the same point of space, and the subsequent multivaluedness of the solutions is purely a mathematical concern, rather than one of actual physical existence. Applications are provided for an inviscid fluid and for turbulence.

Zak, M. A.↗
NASA NTRS1978

Application of semianalytical satellite theories to precision orbit determination

Those factors which limit the usefulness of current implementations of the semianalytical approach are discussed. Numerical and analytical enhancements to the semianalytical approach are considered. A simple mathematical model is provided to estimate the computational speed of a semianalytical theory employing the suggested enhancements. The model can factor in current experience with semianalytical theories (integration stepsizes, quadrature orders, speed of recursive formulations, etc.) and the characteristics of the particular output requirement (observation span (or orbit determination interval), observation rate, observation model, etc.). Comparisons with numerical integration are suggested.

Cefola, P. J.↗
NASA NTRS1987

A generalized procedure for constructing an upwind-based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some nonlinear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to a scalar nonlinear equation and constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance to numerical experiments. Then the formulation is formally extended to the nonlinear system of equations. It is demonstrated that use of the present procedure allows easy conversion of existing central or upwind, and second- or higher-order differencing schemes so as to preserve monotonicity and to yield physically admissible solutions. The formulation is simple mathematically as well as numerically; neither matrix-vector multiplication nor Riemann solver is required. Roughly twice as much computational effort is needed as compared to conventional scheme. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made. Numerical examples including various ranges of problems show both time- and spatial-accuracy in comparison with exact solutions.

Liou, Meng-Sing↗
NASA NTRS1971

The lunar laser ranging experiment

With data from two or more well-located observing stations, the lunar range can be corrected accurately for the effects of polar motion and fluctuations in the earth's rotation rate. Very accurate corrections can be made for the earth tides at each station. It appears that the use of lasers giving roughly 0.1-msec pulse lengths is highly desirable. With them, single-shot ranging accuracies of about 3 cm are expected. The actual lunar range results will be analyzed by fitting a numerical integration for the lunar motion to the data. A mathematical model for lunar range is given. Tests of the theory of gravitation are considered.

Bender, P. L.↗