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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Simulation and testing of digital control on a flexible beam

Large space structures are expected to have control problems due to low stiffness and damping, and control laws for these structures must deal with shape and configuration control as well as attitude and orbit maintenance. In general, these control tasks must be accomplished without adversely interacting with the lightly damped and low frequency vibration modes of the structure. Modal control schemes have been proposed to deal with these problems. A discrete time parameter adaptive control scheme which uses modal control has been proposed by Montgomery and Johnson (1978). In the present investigation the method considered by Montgomery and Johnson is applied to a homogeneous free-free beam in both numerical simulation and laboratory experimentation. Mathematical modeling of the beam is treated in a manner expedient for digital simulation and control implementation.

Williams, J. P.↗
NASA NTRS1983

Propagation of solar disturbances - Theories and models

Recent theoretical developments and construction of several models for the propagation of solar disturbances from the sun and their continuation throughout heliospheric space are discussed. Emphasis centers on physical mechanisms as well as mathematical techniques (i.e., analytical and numerical methods). This outline will lead to a discussion of the state-of-the-art of theoretically based modeling efforts in this area. It is shown that the fundamental theory for the study of propagation of disturbances in heliospheric space is centered around the self-consistent analysis of wave and mass motion within the context of magnetohydrodynamics in which the small scale structures will be modified by kinetic effects. Finally, brief mention is made of some interesting problems for which attention is needed for advancement of the understanding of the physics of large scale propagation of solar disturbances in heliospheric space.

Wu, S. T.↗
NASA NTRS1985

Generation of Surface Coordinates by Elliptic Partial Differential Equations

The problem of generating spatial coordinates by numerical methods through carefully selected mathematical models is of current interest both in mechanics and physics. The problem of generation of a desired system of coordinates in a given surface was considered, which essentially is an effort directed to the problem of grid generation in a two-dimensional non-Euclidean space. The mathematical model selected for this purpose is based on the formulae of Gauss for a surface. The proposed equations can be used to generate a new coordinate system from the data of an already given coordinate system in a surface. If the coefficients of the first and second fundamental forms have been given, then the proposed equations can be used to generate a surface satisfying the given data (surface fitting). The proposed equations can also be used to generate surfaces in the space between two arbitrary given surfaces, thus providing 3D grids in an Euclidean space.

Warsi, Z. U. A.↗
NASA NTRS1986

Variable-Conductance Heat Pipes

In response to need to accurately and efficiently predict performance of variable-conductance heat pipes (VCHP's) incorporated in spacecraft thermalcontrol systems, computer code VCHPDA developed to interact with thermal analyzer programs such as SINDA (Systems Improved Numerical Differencing Analyzer). Calculates length of gas-blocked region and vapor temperature in active portion. Advantages of VCHPDA over prior programs improved accuracy, unconditional stability, and increased efficiency of solution resulting from novel approach and use of state-of-the-art numerical techniques for solving VCHP mathematical model. Code valuable tool in design and evaluation of advanced thermal-control systems using variable-conductance heat pipes. Written in FORTRAN IV for use on CDC 600 computers.

Antoniuk, D.↗
NASA NTRS1989

Bending rate damping in elastic systems

Preliminary results of an investigation of the bending rate damping model for elastic structures are presented. A model for which the internal damping term is physically plausible and which can accomodate cantilevered boundary conditions is discussed. The model formulation and mathematical foundations are given, and numerical results are discussed.

Banks, H. T.↗
NASA NTRS1991

Identification of linear multivariable systems from a single set of data by identification of observers with assigned real eigenvalues

A formulation is presented for identification of linear multivariable from a single set of input-output data. The identification method is formulated with the mathematical framework of learning identifications, by extension of the repetition domain concept to include shifting time intervals. This method contrasts with existing learning approaches that require data from multiple experiments. In this method, the system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded real eigenvalue assignment procedure. Through this relationship, the Markov parameters of the observer are identified. The Markov parameters of the actual system are recovered from those of the observer, and then used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and numerical examples presented to illustrate.

Phan, Minh↗
NASA NTRS1991

Identification of linear multivariable systems from a single set of data by identification of observers with assigned real eigenvalues

This paper presents a formulation for identification of linear multivariable systems from a single set of input-output data. The identification method is formulated with the mathematical framework of learning identification, by extension of the repetition domain concept to include shifting time intervals. This contrasts existing learning approaches that require data from multiple experiments. In this method, the system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded real eigenvalue assignment procedure. Through this relationship, the Markov parameters of the observer are identified. The Markov parameters of the actual system are recovered from those of the observer, and then used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and numerical examples presented to illustrate the proposed method.

Phan, Minh↗
NASA NTRS1991

Linear system identification via an asymptotically stable observer

This paper presents a formulation for identification of linear multivariable systems from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero. In this formulation, the Markov parameters of the observer are identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer, and used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and numerical examples using simulated noise-free data are presented to illustrate the proposed method.

Phan, Minh↗
NASA NTRS1952

Analysis of temperature distribution in liquid-cooled turbine blades

The temperature distribution in liquid-cooled turbine blades determines the amount of cooling required to reduce the blade temperature to permissible values at specified locations. This report presents analytical methods for computing temperature distributions in liquid-cooled turbine blades, or in simplified shapes used to approximate sections of the blade. The individual analyses are first presented in terms of their mathematical development. By means of numerical examples, comparisons are made between simplified and more complete solutions and the effects of several variables are examined. Nondimensional charts to simplify some temperature-distribution calculations are also given.

Livingood, John N B↗
NASA NTRS1993

A local dynamic model for large eddy simulation

The dynamic model is a method for computing the coefficient C in Smagorinsky's model for the subgrid-scale stress tensor as a function of position from the information already contained in the resolved velocity field rather than treating it as an adjustable parameter. A variational formulation of the dynamic model is described that removes the inconsistency associated with taking C out of the filtering operation. This model, however, is still unstable due to the negative eddy-viscosity. Next, three models are presented that are mathematically consistent as well as numerically stable. The first two are applicable to homogeneous flows and flows with at least one homogeneous direction, respectively, and are, in fact, a rigorous derivation of the ad hoc expressions used by previous authors. The third model in this set can be applied to arbitrary flows, and it is stable because the C it predicts is always positive. Finally, a model involving the subgrid-scale kinetic energy is presented which attempts to model backscatter. This last model has some desirable theoretical features. However, even though it gives results in LES that are qualitatively correct, it is outperformed by the simpler constrained variational models. It is suggested that one of the constrained variational models should be used for actual LES while theoretical investigation of the kinetic energy approach should be continued in an effort to improve its predictive power and to understand more about backscatter.

Ghosal, Sandip↗
NASA NTRS1994

Crystal growth and fluid mechanics problems in directional solidification

Broadly speaking, our efforts have been concentrated in two aspects of directional solidification: (A) a more complete theoretical understanding of convection effects in a Bridgman apparatus; and (B) a clear understanding of scalings of various features of dendritic crystal growth in the sensitive limit of small capillary effects. For studies that fall within class A, the principal objectives are as follows: (A1) Derive analytical formulas for segregation, interfacial shape and fluid velocities in mathematically amenable asymptotic limits. (A2) Numerically verify and extend asymptotic results to other ranges of parameter space with a view to a broader physical understanding of the general trends. With respect to studies that fall within class B, the principal objectives include answering the following questions about dendritic crystal growth: (B1) Are there unsteady dendrite solutions in 2-D to the completely nonlinear time evolving equations in the small surface tension limit with only a locally steady tip region with well defined tip radius and velocity? Is anisotropy in surface tension necessary for the existence of such solutions as it is for a true steady state needle crystal? How does the size of such a local region depend on capillary effects, anisotropy and undercooling? (B2) How do the different control parameters affect the nonlinear amplification of tip noise and dendritic side branch coarsening?

Tanveer, Saleh↗
NASA NTRS1993

Kinetic theory model predictions compared with low-thrust axisymmetric nozzle plume data

A system of nonlinear integral equations equivalent to the steady-state Krook kinetic equation was used to model the flow from a low-thrust axisymmetric nozzle. The mathematical model was used to numerically calculate the number density, temperature, and velocity of a simple gas as it expands into a near vacuum. With these quantities the gas pressure and flow directions of the gas near the exit plane were calculated and compared with experimental values for a low-thrust nozzle of the same geometry and mass flow rate.

Riley, B. R.↗
NASA NTRS2004

A Model for the Oxidation of Carbon Silicon Carbide Composite Structures

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.

Sullivan, Roy M.↗
NASA NTRS1999

Data Structure and Parallel Decomposition Considerations on a Fibonacci Grid

The Fibonacci grid, proposed by Swinbank and Purser (see companion abstract), provides attractive properties for global numerical atmospheric prediction by offering an optimally homogeneous, geometrically regular, and approximately isotropic discretization, with only the polar regions requiring special numerical treatment. It is a mathematical idealization, applied to the sphere, of the multi-spiral patterns often found in botanical structures, such as in pine cones and sunflower heads. Computationally, it is natural to organize the domain, into zones, in each of which the same pair, or triple, of "Fibonacci spirals" dominate. But the further subdivision of such zones into "tiles" of a shape and size suitable for distribution to the processors of a massively parallel computer requires very careful consideration if the subsequent spatial computations along the respective spirals, especially those computations (such as compact differencing schemes) that involve recursion, can be implemented in an efficient "load-balanced "manner without requiring excessive amounts of inter-processor communications. In this paper we show how certain "number theoretic" properties of the Fibonacci sequence (whose numbers prescribe the multiplicity of successive spirals) may be exploited in the decomposition of grid zones into tidy arrangements of triangular grid tiles, each tile possessing one side approximately parallel to the constant-latitude zone boundary. We also describe how the spatially recursive processes may be decomposed across such a tiling, and the directionality of the recursions reversed on alternate grid lines, to ensure a very high degree of load balancing throughout the execution of the computations required for one time step of a global model.

Michalakes, John↗
NASA NTRS2007

Asset surveillance system: apparatus and method

System and method for providing surveillance of an asset comprised of numerically fitting at least one mathematical model to obtained residual data correlative to asset operation; storing at least one mathematical model in a memory; obtaining a current set of signal data from the asset; retrieving at least one mathematical model from the memory, using the retrieved mathematical model in a sequential hypothesis test for determining if the current set of signal data is indicative of a fault condition; determining an asset fault cause correlative to a determined indication of a fault condition; providing an indication correlative to a determined fault cause, and an action when warranted. The residual data can be mode partitioned, a current mode of operation can be determined from the asset, and at least one mathematical model can be retrieved from the memory as a function of the determined mode of operation.

Bickford, Randall L.↗
NASA NTRSDate not supplied

A Numerical Method for Computing the State Transition Matrix Using Poincare Integral Invariants

The Poincare integral invariants describe the volumes of sets in Hamiltonian phase space. We use these invariants to derive a new numerical procedure for obtaining the state transition matrix (STM), which can be applied to both conservative and nonconservative systems. The method is analogous to a finite difference approximation of the STM, where perturbed states are numerically propagated along with the reference trajectory. We discuss the mathematical similarities between this new STM and existing methods, show numerical results for orbital motion and uncertainty propagation, and discuss new insights afforded by the Hamiltonian properties of phase flow.

state transition matrix↗
NASA NTRS1981

Global function approach in structural analysis: Basic approach, numerical results

The structural response to a given environment is described by the differential equations of motion of deformable bodies. Analytic solutions of such problems for a reasonably large class of structural configurations are not within the realm of the possible. Consequently, the mathematical problem is recast into a numerical problem for solution on the computer. New technology in the space and energy fields led to a growing demand for accurate analysis which at times cannot be met due to the limits set by available budgets for computer time. In response to this need for more efficient numerical analysis, the possibilities of reducing the number of freedoms in the system through a revival of the global function approach were explored.

Almroth, B. O.↗
DOE OSTI2022

Verification of MOOSE/Bison's Heat Conduction Solver Using Combined Spatiotemporal Convergence Analysis

Bison is a computational physics code that uses the finite element method to model the thermo-mechanical response of nuclear fuel. Since Bison is used to inform high-consequence decisions, it is important that its computational results are reliable and predictive. One important step in assessing the reliability and predictive capabilities of a simulation tool is the verification process, which quantifies numerical errors in a discrete solution relative to the exact solution of the mathematical model. One step in the verification process—called code verification—ensures that the implemented numerical algorithm is a faithful representation of the underlying mathematical model, including partial differential or integral equations, initial and boundary conditions, and auxiliary relationships. In this paper, the code verification process is applied to spatiotemporal heat conduction problems in Bison. Simultaneous refinement of the discretization in space and time is employed to reveal any potential mistakes in the numerical algorithms for the interactions between the spatial and temporal components of the solution. For each verification problem, the correct spatial and temporal order of accuracy is demonstrated for both first- and second-order accurate finite elements and a variety of time-integration schemes. Furthermore, these results provide strong evidence that the Bison numerical algorithm for solving spatiotemporal problems reliably represents the underlying mathematical model in MOOSE. The selected test problems can also be used in other simulation tools that numerically solve for conduction or diffusion.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗