Search NASA⌕ Search

SEARCH · Search NASA

Results for “Finite Volume methods”

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 847 records · Page 47

A Hybrid Numerical Analysis Method for Structural Health Monitoring

A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.

Forth, Scott C.↗

Effective thermoelastic and thermal properties of unidirectional fiber-reinforced composites and their sensitivity coefficients

Three-dimensional finite element models are used to assess the accuracy of the thermoelastic and thermal properties of unidirectional fiber-reinforced composites predicted by six different micromechanical models. The six models are: simple mechanics of materials type equations, fiber substructuring model, vanishing fiber diameter model, self-consistent model, Mori-Tanaka model, and method of cells. In addition, the finite element models are used to assess the accuracy of derivatives of the effective properties, with respect to each of the constituent material properties and fiber-volume ratio, computed using the six micromechanical models. The predictions of the micromechanical and finite element models for four advanced composite material systems are compared with experimental data. The results obtained in the present study show that the predictions of the Mori-Tanaka model and the method of cells are closer to those of the finite element models than those of all the other micromechanical models.

Noor, Ahmed K.↗

All-Materials-Inclusive Flash Spark Plasma Sintering

A new flash (ultra-rapid) spark plasma sintering method applicable to various materials systems, regardless of their electrical resistivity, is developed. A number of powders ranging from metals to electrically insulative ceramics have been successfully densified resulting in homogeneous microstructures within sintering times of 8–35 s. A finite element simulation reveals that the developed method, providing an extraordinary fast and homogeneous heating concentrated in the sample’s volume and punches, is applicable to all the different samples tested. The utilized uniquely controllable flash phenomenon is enabled by the combination of the electric current concentration around the sample and the confinement of the heat generated in this area by the lateral thermal contact resistance. The presented new method allows: extending flash sintering to nearly all materials, controlling sample shape by an added graphite die, and an energy efficient mass production of small and intermediate size objects. This approach represents also a potential venue for future investigations of flash sintering of complex shapes.

36 MATERIALS SCIENCE↗

A general multiblock Euler code for propulsion integration. Volume 3: User guide for the Euler code

This manual explains the procedures for using the general multiblock Euler (GMBE) code developed under NASA contract NAS1-18703. The code was developed for the aerodynamic analysis of geometrically complex configurations in either free air or wind tunnel environments (vol. 1). The complete flow field is divided into a number of topologically simple blocks within each of which surface fitted grids and efficient flow solution algorithms can easily be constructed. The multiblock field grid is generated with the BCON procedure described in volume 2. The GMBE utilizes a finite volume formulation with an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. This user guide provides information on the GMBE code, including input data preparations with sample input files and a sample Unix script for program execution in the UNICOS environment.

Chen, H. C.↗

A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems

The finite-volume approach is presently used to obtain a 2D, high-order accurate and basically nonoscillatory shock-capture method whose high-order spatial accuracy is obtained by means of a piecewise polynomial approximation of the solution from cell averages. Attention is given to a high-order spatial operator that is able to both retain high-order accuracy in smooth regions and avoid the oscillations that are associated with interpolations across steep gradients. The operator is extended to hyperbolic systems of equations and curvilinear meshes.

Casper, Jay↗

A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations

A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind matching scheme is employed at material interfaces and the Engquist-Majda non-reflecting boundary condition is implemented at the numerical outer boundaries. The staggered leapfrog scheme and the Runge-Kutta methods are utilized for the time integration. Excellent agreements are found between the numerical and analytical solutions.

Liu, Yen↗

Mutual coupling effects in antenna arrays, volume 1

Mutual coupling between rectangular apertures in a finite antenna array, in an infinite ground plane, is analyzed using the vector potential approach. The method of moments is used to solve the equations that result from setting the tangential magnetic fields across each aperture equal. The approximation uses a set of vector potential model functions to solve for equivalent magnetic currents. A computer program was written to carry out this analysis and the resulting currents were used to determine the co- and cross-polarized far zone radiation patterns. Numerical results for various arrays using several modes in the approximation are presented. Results for one and two aperture arrays are compared against published data to check on the agreement of this model with previous work. Computer derived results are also compared against experimental results to test the accuracy of the model. These tests of the accuracy of the program showed that it yields valid data.

Collin, R. E.↗

A full potential inverse method based on a density linearization scheme for wing design

A mixed analysis inverse procedure based on the full potential equation in conservation form was developed to recontour a given base wing to produce density linearization scheme in applying the pressure boundary condition in terms of the velocity potential. The FL030 finite volume analysis code was modified to include the inverse option. The new surface shape information, associated with the modified pressure boundary condition, is calculated at a constant span station based on a mass flux integration. The inverse method is shown to recover the original shape when the analysis pressure is not altered. Inverse calculations for weakening of a strong shock system and for a laminar flow control (LFC) pressure distribution are presented. Two methods for a trailing edge closure model are proposed for further study.

Shankar, V.↗

Unsteady hybrid vortex technique for transonic vortex flows and flutter applications

The well developed surface panel method is extended by adding a volume integral term allowing calculation of the full effect of compressibility. The full effect of compressibility is calculated by using mixed type finite difference scheme consistent with the mixed nature of transonic flow. The solution is obtained through successive iteration cycles for subcritical flows and for critical flows the solution is obtained through satisfying the Rankine-Hugoniot relations across the captured shock in addition to the captured shock. The method is applied to airfoils in subcritical and critical flows and the results are in good agreement with the experimental data and finite-difference solutions of the full-potential and Euler equations.

Kandil, Osama A.↗

Euler solutions for the flow around a hovering helicopter rotor

A method for computing the flow around a hovering helicopter rotor is presented. The solution procedure is divided into two parts. The first part is a finite volume solution of the Euler equations for the near field flow around a rotor blade. The second part is a free wake approach for determining the wake geometry and induced velocities. These two parts are solved in a coupled fashion. The rolled-up vortex wake of the rotor is included in the Euler computational domain through a nonlinear perturbation technique. This eliminates the numerical diffusion of the wake vorticity due to truncation error and artificial viscosity without the need for excessive grid resolution near the vortex core. The method is used to compute both hovering rotor and wing/vortex interaction flows, and the results are compared to experiment.

Roberts, T. W.↗

Developing a Macro-scale SiC-cladding Behavior Model Based on Localized Mechanical and Thermal Property Evaluation on Pre- and Post-Irradiation SiC-SiC Composites (Final Report)

Silicon carbide is being investigated for accident tolerant fuel cladding applications due to its good neutronic performance, high temperature strength, exceptional stability under irradiation, and reduced oxidation compared to Zircaloy under accident conditions. The development and investigation of these materials is particularly important in the light of the Fukushima event and subsequent emphasis in DOE on accident tolerant fuel (ATF) concepts. In this work, we propose to develop and improve upon existing small-scale mechanical and thermal characterization methods, including micro-cantilever bend tests and fiber push-out tests, and time-domain thermo-reflectance measurements. These techniques will be applied to evaluate micro-scale properties of SiC-SiC composite constituents (matrix, fibers, interphase). The results will be coupled with meso-scale fiber and void structural information and be used as input to develop a comprehensive, finite element-based model based on constituent properties. The goal of this multi-scale model is to be used to predict anisotropic mechanical and thermal cladding behaviors. The model will be benchmarked against measurements of bulk properties and validated for radiation-damaged materials by utilizing irradiated SiC-SiC composites available from General Atomics. The characterization approach developed under this program will have particular application in the property prediction of reactor irradiated materials, as only small volumes need to be tested, minimizing associated hazards and costs. The micro-scale test methods developed here will be used along with meso-scale structural data to inform a finite element model of the full SiC-based cladding system. This model will capture fabrication and irradiation effects and importantly include for the first-time separate material data for each system component. The incorporation of these micro-scale effects will lead to a more accurate model of SiC-SiC composite behavior, enabling further advancements in the development and design of SiC-based materials for improved fuel cladding performance. The aim of this work is to develop advanced localized material characterization techniques to directly measure mechanical and thermal properties of the individual constituents of SiC-based claddings at the relevant micro-scale. SiC-SiC composites will be evaluated before and after irradiation and these results will be coupled with macro-scale properties and microstructural information in order to provide the input parameters for a comprehensive finite element model, which will be developed in this program.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Higher order cumulants in colorless partonic plasma

Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume T{sub 0}(V), a new approach based on the finite-size cumulant expansion of the order parameter and the ℒ{sub m,n}-Method is used. We have shown that both cumulants of higher order and their ratios, associated to the thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Gradient-Based Aerodynamic Shape Optimization Using ADI Method for Large-Scale Problems

A gradient-based shape optimization methodology, that is intended for practical three-dimensional aerodynamic applications, has been developed. It is based on the quasi-analytical sensitivities. The flow analysis is rendered by a fully implicit, finite volume formulation of the Euler equations.The aerodynamic sensitivity equation is solved using the alternating-direction-implicit (ADI) algorithm for memory efficiency. A flexible wing geometry model, that is based on surface parameterization and platform schedules, is utilized. The present methodology and its components have been tested via several comparisons. Initially, the flow analysis for for a wing is compared with those obtained using an unfactored, preconditioned conjugate gradient approach (PCG), and an extensively validated CFD code. Then, the sensitivities computed with the present method have been compared with those obtained using the finite-difference and the PCG approaches. Effects of grid refinement and convergence tolerance on the analysis and shape optimization have been explored. Finally the new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4. Despite the expected increase in the computational time, the results indicate that shape optimization, which require large numbers of grid points can be resolved with a gradient-based approach.

Pandya, Mohagna J.↗

Conservative fourth-order finite-volume Vlasov–Poisson solver for axisymmetric plasmas in cylindrical (r,v r ,v θ ) phase space coordinates

In this paper, a fourth-order finite-volume Vlasov–Poisson algorithm is developed for simulating axisymmetric plasma configurations in ( r , v r , v θ ) phase space coordinates. The Vlasov equation for cylindrical phase space coordinates is cast into conservation-law form and is discretized on a structured grid. The conservative finite-volume discretization is based on fifth-order upwind reconstructions of the distribution function and a fourth-order quadrature rule that accounts for transverse variations of fluxes along control volume surfaces. High-order specular reflection boundary conditions enable high-fidelity treatment of plasma distribution functions at the axis and at wall boundaries. The numerical method is applied to simulate a confined uniform neutral gas to assess convergence properties for an equilibrium system in which effects of finite-temperature and acceleration due to centrifugal and Coriolis forces are present. The discretization is also applied to a Z-pinch configuration to study electrostatic ion confinement and the dynamics of the associated breathing mode. Simulations show that the ion distribution function exhibits non-Maxwellian features and that a temperature anisotropy develops and is sustained. Finally, the finite-volume implementation is demonstrated to converge at fourth-order for both applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Predicting the mechanical response of oligocrystals with deep learning

In this study, we employ data-driven homogenization approaches to predict the particular mechanical evolution of polycrystalline aggregates with tens of individual crystals. In these oligocrystals the differences in stress response due to microstructural variation is pronounced. Shell-like structures produced by metal-based additive manufacturing and the like make the prediction of the behavior of oligocrystals technologically relevant. The predictions of traditional homogenization theories based on grain volumes are not sensitive to variations in local grain neighborhoods. Direct simulation of the local response with crystal plasticity finite element methods is more detailed, but the computations are expensive. To represent the stress-strain response of a polycrystalline sample given its initial grain texture and morphology we have designed a novel neural network that incorporates a convolution component to observe and reduce the information in the crystal texture field and a recursive component to represent the causal nature of the history information. This model exhibits accuracy on par with crystal plasticity simulations at minimal computational cost per prediction.

36 MATERIALS SCIENCE↗

Euler calculations for wings using Cartesian grids

A method is presented for the calculation of transonic flows past wings using Cartesian grids. The calculations are based on a finite volume formulation of the Euler equations. Results are presented for a rectangular wing with a flat tip and the ONERA M6 wing. In general, the results are in good agreement with other computations and available experiment. However, Cartesian grids require a greater number of points than body fitted grids in order to resolve the flow properties near the leading edge of a swept wing.

Gaffney, R. L., Jr.↗

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

Slack, David C.↗