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At least 649 records · Page 36

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NASA NTRS1983

Optimal trajectories for aeroassisted orbital transfer

Consideration is given to classical and minimax problems involved in aeroassisted transfer from high earth orbit (HEO) to low earth orbit (LEO). The transfer is restricted to coplanar operation, with trajectory control effected by means of lift modulation. The performance of the maneuver is indexed to the energy expenditure or, alternatively, the time integral of the heating rate. Firist-order optimality conditions are defined for the classical approach, as are a sequential gradient-restoration algorithm and a combined gradient-restoration algorithm. Minimization techniques are presented for the aeroassisted transfer energy consumption and time-delay integral of the heating rate, as well as minimization of the pressure. It is shown that the eigenvalues of the Jacobian matrix of the differential system is both stiff and unstable, implying that the sequential gradient restoration algorithm in its present version is unsuitable. A new method, involving a multipoint approach to the two-poing boundary value problem, is recommended.

Miele, A.↗

NASA NTRS1972

Modes of vibration in a circular plate with three simple support points.

The analytical solutions for the vibrational modes of a thin circular flat plate that is simply supported at three points on the circumference are presented. The mode shapes and corresponding eigenvalues are obtained. Results show that the modes can be grouped into four different types depending on the manner by which they receive the pressure at the supported points. The problem is of the mixed boundary value type in that some portion of the boundary is free while the other portion is simply supported.

Chi, C.↗

NASA NTRS1992

Sensitivity analysis of hydrodynamic stability operators

The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudoeigenvalues are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette, trailing line vortex flow and compressible Blasius boundary layer flow. Parametric studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the non-normality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.

Schmid, Peter J.↗

DOE OSTI2024

Strongly hyperbolic quasilinear systems revisited, with applications to relativistic fluid dynamics

We revisit the theory of first-order quasilinear systems with diagonalizable principal part and only real eigenvalues, what is commonly referred to as strongly hyperbolic systems. We provide a self-contained and simple proof of local well-posedness, in the Hadamard sense, of the Cauchy problem. Our regularity assumptions are very minimal. As an application, we apply our results to systems of ideal and viscous relativistic fluids, where the theory of strongly hyperbolic equations has been systematically used to study several systems of physical interest.

Mathematics↗

NASA NTRS1972

A critical discussion of theories of flame spread across solid and liquid fuels.

Mathematical descriptions of flames spreading over liquid and solid fuels are obtained, using basic assumptions derived from observations or physical reasoning. A review of existing theories shows that they are incomplete in that they either treat an uncoupled problem of the condensed phase where the spreading rate and heat flux at the surface are given, or they merely determine the spreading rate in terms of a new vaguely defined eigenvalue. An important difference between the liquid and solid cases, due to convection, is pointed out, and it is shown that solid-fuel flame-spread theories which claim to apply to the liquid case, in reality do not apply to it. A mathematical formulation and a method of solution are presented for the phenomenon of flame spread over solid fuels with forward heat conduction in both the solid and the gas. The method uses an energy integral over the field to determine the spreading rate in terms of the basic properties of the fuel and air.

Sirignano, W. A.↗

NASA NTRS1984

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, K.↗

NASA NTRS1987

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

Ito, Kazufumi↗

NASA NTRS1991

The stability of numerical boundary treatments for compact high-order finite-difference schemes

The stability characteristics of various compact fourth and sixth order spatial operators are assessed using the theory of Gustafsson, Kreiss and Sundstrom (G-K-S) for the semi-discrete Initial Boundary Value Problem (IBVP). These results are then generalized to the fully discrete case using a recently developed theory of Kreiss. In all cases, favorable comparisons are obtained between the G-K-S theory, eigenvalue determination, and numerical simulation. The conventional definition of stability is then sharpened to include only those spatial discretizations that are asymptotically stable. It is shown that many of the higher order schemes which are G-K-S stable are not asymptotically stable. A series of compact fourth and sixth order schemes, which are both asymptotically and G-K-S stable for the scalar case, are then developed.

Carpenter, Mark H.↗

NASA NTRS1992

Optimum design of a gearbox for low vibration

A computer program was developed for designing a low vibration gearbox. The code is based on a finite element shell analysis, a modal analysis, and a structural optimization method. In the finite element analysis, a triangular shell element with 18 degrees-of-freedom is used. In the optimization method, the overall vibration energy of the gearbox is used as the objective function and is minimized at the exciting frequency by varying the finite element thickness. Modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variable. The sensitivity is representative of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. The computer code is applied to a design problem derived from an experimental gearbox in use at the NASA Lewis Research Center. The top plate and two side plates of the gearbox are redesigned and the contribution of each surface to the total vibration is determined. Results show that optimization of the top plate alone is effective in reducing total gearbox vibration.

Inoue, Katsumi↗

NASA NTRS1968

Internal low Reynolds number turbulent heat transfer

The results of a semi-analytical and experimental study of adiabatic tube flow and an analytical and experimental investigation of the thermal entrance region for gas flowing through electrically heated circular tubes are presented. Emphasis is placed on the low Reynolds number turbulent flow regime--defined as fully turbulent flow at bulk Reynolds numbers from 3,000 to about 15,000. Adiabatic air velocity and friction data and localized heat transfer measurements for air and helium, at low heating rates, are presented for this range. The adiabatic data were obtained in a 1.61 inch 1D tube for flow at bulk Reynolds numbers from 3,000 to 15,000. A continuous, Reynolds number-dependent, profile is developed from the data by using a modification of Reichardts' wall and middle law eddy diffusivity expressions. The velocity profile satisfies continuity. It is valid for all Reynolds numbers in excess of 3,000 for which the flow is fully turbulent and the Blasius friction factor expression is valid. The thermal entrance problem for a fully developed velocity profile is solved analytically by the method of Sparrow, Hallman, and Siegel. The solution is based on the profile developed from the velocity study. Tabular values of the eigenvalues and normalized Nusselt numbers for gases are presented for it range of Reynolds numbers from 3,000 to 50,000. The axial variation of Nusselt number is found to be correlated by [Nu/Nu_(∞)] = 1 + 0.8 (1+ 70,000 Re^(-3/2)) ((x/D)^(-1)) to within ± 5 per cent for x/D ≥2. The fully developed value agrees with the Dittus - Boelter correlation, Nu_(∞) = 0.021 Re^(0.8) Pr^(0.4) For the eigenvalues, λ^(2)_(n), and the associated constants, A_(n), correlations of the form λ^(2)_(n) =A_(1,n) Re^(-b_(1,n) + C_(1,n) Re^(-d_(1,n)) A_(n) = -A_(2,n) Re^(-b_(2,n) + C_(2,n) Re^(-d_(2,n)) are obtained. The coefficients and powers are presented in tabular form. Heat transfer data are presented, primarily for helium, for the low Reynolds number turbulent range. A one-quarter inch, resistively heated, vertical, circular tube was used for the study. The data cover an axial range from 1.2 to 96 diameters; wall-to-bulk temperature ratios vary from 1 to 1.4. In the low Reynolds number turbulent regime, these data clearly support the present analytical solution rather than the prediction obtained by applying the eddy diffusivity distribution used by Sparrow, Hallman, and Siegel.

Harold C. Reynolds, Jr.↗

NASA NTRS1980

The 1980 summer research fellowship program

The problem of incorporating visual input into robot systems is described. The photochemistry of the stratosphere, particularly possible permutations of the ozone layer, is discussed. Photoelectrochemical properties of metal thio-hypodiphosphates are investigated. Extreme eigenvalues are computed by the Lancqos approach. The rotational Raman spectra of the molecular atmosphere is studied. A computer operated mathematical symbolic manipulation system is described. Preparation of polycrystalline semiconductor electrodes of tungsten and molybdenum dichalcogenides is received.

Darden, G. C.↗

NASA NTRS1983

Efficient linear and nonlinear heat conduction with a quadrilateral element

A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2, and 1 for the normalized stabilization parameter lead to the 5-point, 9-point finite difference, and fully integrated finite element operators, respectively, for rectangular meshes and have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.

Liu, W. K.↗

NASA NTRS1984

Efficient linear and nonlinear heat conduction with a quadrilateral element

A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5-point finite difference, 9-point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.

Liu, W. K.↗

NASA NTRS1985

Application of eigenspace techniques to design of aircraft control systems

Eigenspace techniques allow the control system designer to use feedback to place eigenvalues and shape eigenvectors so as to modify closed loop dynamic response characteristics to achieve performance objectives. In this paper the theory of eigenspace design is reviewed, extended and applied to several aircraft control problems.

Liebst, B. S.↗

NASA NTRS1990

Improving stability and strength characteristics of framed structures with nonlinear behavior

In this paper an optimal design procedure is introduced to improve the overall performance of nonlinear framed structures. The design methodology presented here is a multiple-objective optimization procedure whose objective functions involve the buckling eigenvalues and eigenvectors of the structure. A constant volume with bounds on the design variables is used in conjunction with an optimality criterion approach. The method provides a general tool for solving complex design problems and generally leads to structures with better limit strength and stability. Many algorithms have been developed to improve the limit strength of structures. In most applications geometrically linear analysis is employed with the consequence that overall strength of the design is overestimated. Directly optimizing the limit load of the structure would require a full nonlinear analysis at each iteration which would be prohibitively expensive. The objective of this paper is to develop an algorithm that can improve the limit-load of geometrically nonlinear framed structures while avoiding the nonlinear analysis. One of the novelties of the new design methodology is its ability to efficiently model and design structures under multiple loading conditions. These loading conditions can be different factored loads or any kind of loads that can be applied to the structure simultaneously or independently. Attention is focused on optimal design of space framed structures. Three-dimensional design problems are more complicated to carry out, but they yield insight into real behavior of the structure and can help avoiding some of the problems that might appear in planar design procedure such as the need for out-of-plane buckling constraint. Although researchers in the field of structural engineering generally agree that optimum design of three-dimension building frames especially in the seismic regions would be beneficial, methods have been slow to emerge. Most of the research in this area has dealt with the optimization of truss and plane frame structures.

Pezeshk, Shahram↗

NASA NTRS1993

Eigenvalue routines in NASTRAN: A comparison with the Block Lanczos method

The NASA STRuctural ANalysis (NASTRAN) program is one of the most extensively used engineering applications software in the world. It contains a wealth of matrix operations and numerical solution techniques, and they were used to construct efficient eigenvalue routines. The purpose of this paper is to examine the current eigenvalue routines in NASTRAN and to make efficiency comparisons with a more recent implementation of the Block Lanczos algorithm by Boeing Computer Services (BCS). This eigenvalue routine is now available in the BCS mathematics library as well as in several commercial versions of NASTRAN. In addition, CRAY maintains a modified version of this routine on their network. Several example problems, with a varying number of degrees of freedom, were selected primarily for efficiency bench-marking. Accuracy is not an issue, because they all gave comparable results. The Block Lanczos algorithm was found to be extremely efficient, in particular, for very large size problems.

Tischler, V. A.↗

NASA NTRS2008

Toward Optimal Transport Networks

Strictly evolutionary approaches to improving the air transport system a highly complex network of interacting systems no longer suffice in the face of demand that is projected to double or triple in the near future. Thus evolutionary approaches should be augmented with active design methods. The ability to actively design, optimize and control a system presupposes the existence of predictive modeling and reasonably well-defined functional dependences between the controllable variables of the system and objective and constraint functions for optimization. Following recent advances in the studies of the effects of network topology structure on dynamics, we investigate the performance of dynamic processes on transport networks as a function of the first nontrivial eigenvalue of the network's Laplacian, which, in turn, is a function of the network s connectivity and modularity. The last two characteristics can be controlled and tuned via optimization. We consider design optimization problem formulations. We have developed a flexible simulation of network topology coupled with flows on the network for use as a platform for computational experiments.

Alexandrov, Natalia↗

DOE OSTI2024

Sodium-Cooled Fast Reactor Reference Plant Model

This report details the progress of Idaho National Laboratory (INL) in creating a reference plant multiphysics model for the Advanced Burner Test Reactor (ABTR). This model was developed under Task 13 of the U.S. Nuclear Regulatory Commission project “Development and Modeling Support for Advanced Non-Light Water Reactors,” and is an extension of the reference plant model developed in Task 4b, which was improved upon in the following ways. (1) The discrete ordinates method was used in lieu of the super-homogenization (SPH)-corrected diffusion approximation in order to better capture the anisotropic scattering contribution and the neutron leakage change due to thermal expansion. (2) The novel neutronic spatial discretization approach, termed the ring-heterogeneous (RH) approximation, was conceptualized and introduced to capture the differential expansion of the materials in the core. This new technique proved capable of preserving fission rates and maintaining the eigenvalue within 2.5% and 266 pcm with 9 neutron energy groups, respectively. Separating the different materials in the core enables the differential expansion of materials to be explicitly accounted for, eliminating the need for problem-specific cross-section functionalization techniques. (3) The SAM model for the core and system thermal-hydraulics analysis was updated to include 61 channels instead of just four representative ones. This enables users to obtain improved spatial resolution for sodium temperature and density scalar fields. (4) All the mesh files were created via the Multiphysics Object-Oriented Simulation Environment (MOOSE) Reactor module, eliminating all reliance on external tools for mesh creation. (5) Finally, the fuel axial expansion now leverages the HT9 and UPuZr material properties that have been validated against experimental data. The reference plant model was used to perform a full-core unprotected loss of flow (ULOF) transient calculation, including neutronics, thermal and mechanical feedback mechanisms. Future work will be devoted to further enhancements of the model. Potential improvements to the model include the addition of the control rod driveline expansion feedback and the upgrading of the support plate model so as to explicitly include 3D effects. Additionally, a Nuclear Energy Advanced Modeling and Simulation funded parallel effort has completely automated the creation of the ring-heterogeneous (RH) mesh from the fully heterogeneous (FH) geometry, thus maximizing user friendliness for the sodium fast reactor sodium-cooled fast reactor (SFR) workflow and will be incorporated in future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗