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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Numerical studies of 2-dimensional flows

A formulation of the lambda scheme for the analysis of two dimensional inviscid, compressible, unsteady transonic flows is presented. The scheme uses generalized Riemann variables to determine the appropriate two point, one sided finite difference approximation for each derivative in the unsteady Euler equations. These finite differences are applied at the predictor and corrector levels with shock updating at each level. The weaker oblique shocks are captured, but strong near normal shocks are fitted into the flow using the Rankine-Hugoniot relations. This code is demonstrated with a numerical example of a duct flow problem with developing normal and oblique shock waves. The technique is implemented in a code which has been made efficient by streamlining to a minimal number of operations and by eliminating branch statements. The scheme is shown to provide an accurate analysis of the flow, including formation, motions, and interactions of shocks; the results obtained on a relatively coarse mesh are comparable to those obtained by other methods on much finer meshes.

Moretti, G.↗
NASA NTRS1984

Assessment of a 3-D boundary layer code to predict heat transfer and flow losses in a turbine

Zonal concepts are utilized to delineate regions of application of three-dimensional boundary layer (DBL) theory. The zonal approach requires three distinct analyses. A modified version of the 3-DBL code named TABLET is used to analyze the boundary layer flow. This modified code solves the finite difference form of the compressible 3-DBL equations in a nonorthogonal surface coordinate system which includes coriolis forces produced by coordinate rotation. These equations are solved using an efficient, implicit, fully coupled finite difference procedure. The nonorthogonal surface coordinate system is calculated using a general analysis based on the transfinite mapping of Gordon which is valid for any arbitrary surface. Experimental data is used to determine the boundary layer edge conditions. The boundary layer edge conditions are determined by integrating the boundary layer edge equations, which are the Euler equations at the edge of the boundary layer, using the known experimental wall pressure distribution. Starting solutions along the inflow boundaries are estimated by solving the appropriate limiting form of the 3-DBL equations.

Anderson, O. L.↗
NASA NTRS1989

A direct procedure for interpolation on a structured curvilinear two-dimensional grid

A direct procedure is presented for locally bicubic interpolation on a structured, curvilinear, two-dimensional grid. The physical (Cartesian) space is transformed to a computational space in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. Required partial derivative information is obtained by finite differences in the computational space. The partial derivatives in physical space are determined by repeated application of the chain rule for partial differentiation. A bilinear transformation is used to analytically transform the individual quadrilateral cells in physical space into unit squares. The interpolation is performed within each unit square using a piecewise bicubic spline.

Zingg, David W.↗
NASA NTRS1989

Euler flutter analysis of airfoils using unstructured dynamic meshes

Modifications to a two-dimensional unsteady Euler code for the aeroelastic analysis of airfoils are described. The modifications involve including the structural equations of motion and their simultaneous time-integration with the governing flow equations. A novel aspect of the capability is that the solutions are obtained using unstructured grids made up of triangles. Comparisons are made with parallel calculations performed using linear theory and a structured grid Euler code to assess the accuracy of the unstructured grid Euler results. Results are presented for a flat plate airfoil and the NACA 0012 airfoil to demonstrate applications of the Euler code for generalized force computations and aeroelastic analysis. In these comparisons, two different finite-volume discretizations of the Euler equations on unstructured meshes were employed. Sensitivity of the Euler results to changes in numerical parameters were also investigated.

Rausch, Russ D.↗
NASA NTRS2003

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows: Minimization of Delta * B Numerical Error - II

The generalization of a class of low-dissipative high order filter finite difference schemes for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been developed. The new scheme consists of a divergence free preserving high order spatial base scheme with a filter approach which can be divergence-free preserving depending on the type of filter operator being used, the method of applying the filter step, and the type of flow problem to be considered. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field (Delta * B) numerical error in the sense that no standard divergence cleaning is required. Performance evaluation of these variants, and the key role that the proper treatment of their corresponding numerical boundary conditions can play will be illustrated. Many levels of grid refinement and detailed comparison with several commonly used compressible MHD shock-capturing schemes will be sought. For certain MHD 2-D test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.

Sjoegreen, Bjoern↗
NASA NTRS2003

Divergence Free High Order Filter Methods for the Compressible MHD Equations

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard diver- gence cleaning is not required by the present filter approach. For certain MHD test cases, divergence free preservation of the magnetic fields has been achieved.

Yea, H. C.↗
NASA NTRS2003

High Order Filter Methods for the Non-ideal Compressible MHD Equations

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard divergence cleaning is not required by the present filter approach. For certain non-ideal MHD test cases, divergence free preservation of the magnetic fields has been achieved.

Yee, H. C.↗
DOE OSTI2018

Development of a layered two-dimensional approach for modelling fuel rod behaviour

Historically, light water reactor (LWR) fuel performance codes have been developed using layered one-dimensional (1D) or two-dimensional (2D) axisymmetric approaches. In a layered 1D analysis the fuel rod is divided into a number of axial layers, each of which is represented using a 1D axisymmetric model with generalized plane strain assumptions. These simulations are typically solved using a finite difference technique. A limited set of data such as fission gas behaviour, has an effect on all layers. The 2D axisymmetric approach improves the axial fidelity of the simulation by employing a finite element representation of the fuel rod geometry, and more readily allows for phenomena such as axial heat transfer to be represented. Depending upon the fuel rod analysis being investigated the assumptions made in layered 1D or 2D axisymmetric approaches can result in important physics not being adequately captured. Therefore, the Bison fuel performance code has been developed over the last 10 years to provide flexibility in modelling of fuel behaviour. The code is capable of investigating fuel behaviour in 1D, layered 1D, 2D, 2D-axisymmetric, and 3D geometric representations depending upon the fidelity required for a particular analysis. Recently, a new layered 2D approach has been developed and implemented. This approach utilizes a similar technique to layered 1D except the thermo-mechanical analysis in each layer is solved on layered disks that can have azimuthally varying boundary conditions. These azimuthally varying conditions are important for a variety of fuel rod applications including discrete fuel fracture and rod behaviour during Loss of Coolant Accidents (LOCA). This paper describes the development of the layered 2D approach and the types of analyses for which it is applicable. Results are presented that illustrate the improvement in model predictions provided by this approach over layered 1D and 2D-axisymmetric approaches for the LOCA rod behaviour.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2018

Optimal Control of a Degenerate PDE for Surface Shape

Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape in this paper. Specifically, we consider an objective (tracking) functional for surface shape with the prescribed mean curvature equation in graph form as a state constraint. The control variable is the prescribed curvature. We prove existence of an optimal control, and using improved regularity estimates, we show sufficient differentiability to make sense of the first order optimality conditions. This allows us to rigorously compute the gradient of the objective functional for both the continuous and discrete (finite element) formulations of the problem. Numerical results are shown to illustrate the minimizers and optimal controls on different domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1989

Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables

Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter.

Fenyes, Peter A.↗
NASA NTRS1991

A study of the response of nonlinear springs

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

Hyer, M. W.↗
DOE OSTI2019

Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. II. Implicit Methods

We consider specific realizations of different implicit generalized Runge–Kutta methods as applied to the numerical integration with respect to time of initial-boundary-value problems for the second-order parabolic equations and investigate their spectral stability. It is shown that all implicit generalized Runge–Kutta methods are unconditionally spectrally stable but some of them have the conditional property of monotonicity of the numerical solution with respect to time. The functions of spectral stability of the implicit generalized Runge–Kutta methods are rational. We compare the analytic solution of the nonstationary one-dimensional problem of heat conduction with the numerical solutions of this problem obtained by different implicit generalized Runge–Kutta methods. It is shown that, in this case, the application of the one-stage Radau methods with subsequent discretization of the problem with respect to the space variable leads to the classical forward finite difference scheme (Laasonen scheme), whereas the use of the one-stage Gauss–Legendre method leads to a six-point symmetric scheme (Crank–Nicolson scheme). It is shown that diagonally implicit generalized Nørsett and Burrage methods are realized in almost the same way as the one-stage Radau and Gauss–Legendre methods but their accuracy in the time step is 10–1000 times higher. On the basis of comparison of the numerical and analytic solutions, we conclude that, in order to get practically suitable numerical solutions without any restrictions on the time step, it is reasonable to use one- and three-stage generalized Radau methods or two- and four-stage Lobatto IIIC methods. All other explicit and implicit generalized Runge–Kutta methods require certain restrictions imposed on the time step.

42 ENGINEERING↗
DOE OSTI2017

Theoretical Analysis of Photoelectron Spectra of Pure and Mixed Metal Clusters: Disentangling Size, Structure, and Composition Effects

A theoretical/computational description and analysis of the spectra of electron binding energies of Al 12 - , Al 13 - and Al 12 Ni- clusters, which differ in size and/or composition by a single atom yet possess strikingly different measured photoelectron spectra, is presented. It is shown that the measured spectra can not only be reproduced computationally with quantitative fidelity – this is achieved through a combination of state-of-the-art density functional theory with a highly accurate scheme for conversion of the Kohn-Sham eigenenergies into electron binding energies – but also explained in terms of the effects of size, structure/symmetry and composition. Furthermore, a new methodology is developed and applied that provides for disentanglement and differential assignment of the separate roles played by size, structure/symmetry and composition in defining the observed differences in the measured spectra. The methodology is general and applicable to any finite system, homogeneous or heterogeneous. Finally, we project that in combination with advances in synthesis techniques this methodology will become an indispensable computation-based aid in the design of controlled synthesis protocols for manufacture of nanosystems and nanodevices with precisely desired electronic and other characteristics.

36 MATERIALS SCIENCE↗
DOE OSTI2018

A numerical hybrid model for outdoor sound propagation in complex urban environments

Noise mapping in large and dense urban areas is computationally challenging, if not impossible, with the use of conventional numerical techniques. Recently, promising results have shown the potential of energy-based models to compete with conventional numerical techniques. In this study, a hybrid full-wave/diffusion propagation model is proposed to address some of the flaws of the traditional diffusion model. The full-wave model is used for predicting sound propagation (i) near the source, where interactions between waves are important, and (ii) outside the cluttered environment, where free-field-like conditions apply. Finally, the diffusion model is used in regions where diffusion conditions are met.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

High-precision quantum algorithms for partial differential equations

Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity poly(1/ϵ), where ϵ is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms for linear PDEs to be poly(d,log(1/ϵ)), where d is the spatial dimension. Our algorithms apply high-precision quantum linear system algorithms to systems whose condition numbers and approximation errors we bound. We develop a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

Generalization of analytical tools for helicopter-rotor airfoils

A state-of-the-art finite difference boundary-layer program incorporated into the NYU Transonic Analysis Program is described. Some possible treatments for the trailing edge region were investigated. Findings indicate the trailing edge region, still within the scope of an iterative potential flow, boundary layer program, appears feasible.

Gibbs, E. H.↗
NASA NTRS1984

Simulating Atmospheric Turbulence

Dimensionless time series for gusts and gradients calculated with model. Single-sided one-dimensional spectra obtained from Fourier analysis of simulated vertical gust. Each of four plots represents spectrum in one of four altitude bands ranging from 0 to 10 km. Model differs from most models; is nondimensional for greater generality and uses spectra with finite wave number limits. Developed to predict effects of atmospheric turbulence in horizontal and near-horizontal flight also applicable to commercial aviation.

Tatom, F. B.↗
NASA NTRS1986

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

Chen, Y. S.↗