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At least 199 records · Page 11

All sources NASA NTRS DOE OSTI

DOE OSTI2019

Ceramic nuclear fuel fracture modeling with the extended finite element method

Ceramic fuel pellets used in nuclear light water reactors experience significant fracture due to the high thermal gradients experienced under normal operating conditions. This has important effects on the performance of the fuel system. Because of this, a realistic, physically based fracture modeling capability is essential to predict fuel behavior in a wide variety of normal and off-normal conditions. The extended finite element method (X-FEM) is a powerful method to represent arbitrary propagating discrete cracks in finite element models, and has many characteristics that make it attractive for nuclear fuel performance analysis. This paper describes the implementation of X-FEM in a multiphysics fuel performance code and presents applications of that capability. These applications include several thermal mechanics fracture benchmark problems, which demonstrate the accuracy of this approach. It also includes application of this capability to study nuclear fuel fracture, both on stationary and propagating cracks. The study on stationary cracks shows the effects that varying the number of radial cracks and the length of those cracks have on the energy release rate. Here, the propagating crack case demonstrates random initiation and subsequent propagation of interacting thermally induced cracks during an initial ramp to full power with fresh fuel.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1980

A new approach in cascade flow analysis using the finite element method

A new approach in analyzing the potential flow past cascades and single airfoils using the finite element method is developed. In this analysis the circulation around the airfoil is not externally imposed but is directly computed in the numerical solution. Different finite element discretization patterns, orders of piecewise approximation, and grid sizes are used in the solution. The results obtained are compared with existing experimental measurements and exact solutions in cascades and single airfoils.

Baskharone, E.↗

DOE OSTI2014

Stable finite element method of eight-band k·p model without spurious solutions and numerical study of interfaces in heterostructures

A Lagrange-Hermite finite element method for the eight-band k·p model is developed. We demonstrate that besides the incompletion of k·p basis functions, the ill representation of first-order derivatives can also bend the conduction band structure down and lead to the highly oscillatory solutions. Our method simultaneously solves these two problems and achieves robust stability and high accuracy in real-space numerical calculation. The more physical asymmetric operator ordering is employed and the connection problem in abrupt interface is resolved by using an approximately abrupt interface. The situation of smooth interface used to explain the discrepancies between experiment and simulation of abrupt interface is also calculated by our method, and the result suggests that the influence of the interface smoothing should be considered in the short period superlattices or quantum structures of the narrow well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Detailed finite element method modeling of evaporating multi-component droplets

The evaporation of sessile multi-component droplets is modeled with an axisymmetic finite element method. The model comprises the coupled processes of mixture evaporation, multi-component flow with composition-dependent fluid properties and thermal effects. Based on representative examples of water–glycerol and water–ethanol droplets, regular and chaotic examples of solutal Marangoni flows are discussed. Furthermore, the relevance of the substrate thickness for the evaporative cooling of volatile binary mixture droplets is pointed out. It is shown how the evaporation of the more volatile component can drastically decrease the interface temperature, so that ambient vapor of the less volatile component condenses on the droplet. Finally, results of this model are compared with corresponding results of a lubrication theory model, showing that the application of lubrication theory can cause considerable errors even for moderate contact angles of 40°. - Graphical abstract:.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

A simple finite element method for the Stokes equations

The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1979

On finite element methods for the Helmholtz equation

The numerical solution of the Helmholtz equation is considered via finite element methods. A two-stage method which gives the same accuracy in the computed gradient as in the computed solution is discussed. Error estimates for the method using a newly developed proof are given, and the computational considerations which show this method to be computationally superior to previous methods are presented.

Aziz, A. K.↗

NASA NTRS1984

An adaptive finite element method for high speed compressible flow

Compressible fluid flow problems were solved using an adaptive finite element method. Supersonic flow past a wedge and Prandtl-Meyer expansion were considered. Computational grids are presented.

Loehner, R.↗

NASA NTRS1986

A Petrov-Galerkin finite element method for the compressible Euler and Navier-Stokes equations

An overview of a new finite element method for the compressible Euler and Navier-Stokes equations is presented. The discretization is based on entropy variables. The method is developed within the framework of a Petrov-Galerkin formulation. Two perturbations are added to the weighting function; one is a generalization of the SUPG operator and the other is designed to enhance shock capturing capability. The treatment of boundary conditions and the consistent calculation of boundary fluxes are addressed. Results of numerical tests are presented which confirm the robustness and wide applicability of the method.

Franca, L. P.↗

NASA NTRS1989

Least-squares finite element method for fluid dynamics

An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.

Jiang, Bo-Nan↗

NASA NTRS1989

Least-squares finite element method for fluid dynamics

Jiang, Bo-Nan↗

DOE OSTI2019

A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion

In this paper we propose a space-time adaptive finite element method for the phase field model of pitting corrosion, which is a parabolic partial differential equation system consisting of a phase variable and a concentration variable. A major challenge in solving this phase field model is that the problem is very stiff, which makes the time step size extremely small for standard temporal discretizations. Another difficulty is that a high spatial resolution is required to capture the steep gradients within the diffused interface, which results in very large number of degrees of freedom for uniform meshes. To overcome the stiffness of this model, we combine the Rosenbrock–Euler exponential integrator with Crank–Nicolson scheme for the temporal discretization. Moreover, by exploiting the fact that the speed of the corroding interface decreases with time, we derive an adaptive time stepping formula. For the spatial approximation, we propose a simple and efficient strategy to generate adaptive meshes that reduces the computational cost significantly. Thus, the proposed method utilizes local adaptivity and mesh refinement for efficient simulation of the corrosive dissolution over long times in heterogeneous media with complex microstructures. We also present an extensive set of numerical experiments in both two and three dimensional spaces to demonstrate efficiency and robustness of the proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

A fast matrix-free approach to the high-order control volume finite element method with application to low-Mach flow

Here, a fast matrix-free formulation of the control volume finite element method is presented, requiring much less memory and computational work than previous efforts. The method is implemented and evaluated as a solver for low-Mach flow, including the evaluation of a preconditioning strategy for the pressure Poisson equation. The efficiency and scaling with polynomial order is evaluated on simple turbulent flows of interest, with appropriate solution quality metrics, and compared with a reference node-centered finite volume discretization. For a turbulent channel flow test, we show improvement in computational work for a given accuracy with the high-order scheme. The performance on a GPU accelerated platform is also investigated, with benefit shown for the matrix-free discretization.

42 ENGINEERING↗

NASA NTRS1987

Multiple-mode nonlinear free and forced vibrations of beams using finite element method

Multiple-mode nonlinear free and forced vibration of a beam is analyzed by the finite element method. The geometric nonlinearity is investigated. Inplane displacement and inertia (IDI) are also considered in the formulation. Harmonic force matrix is derived and explained. Nonlinear free vibration can be simply treated as a special case of the general forced vibration by setting the harmonic force matrix equal to zero. The effect of the higher modes is more pronouced for the clamped supported beam than the simply supported one. Beams without IDI yield more effect of the higher modes than the one with IDI. The effects of IDI are to reduce nonlinearity. For beams with end supports restrained from axial movement (immovable cases), only the hardening type nonlinearity is observed. However, beams of small slenderness ratio (L/R = 20) with movable end supports, the softening type nonlinearity is found. The concentrated force case yields a more severe response than the uniformly distributed force case. Finite element results are in good agreement with the solution of simple elliptic response, harmonic balance method, and Runge-Kutte method and experiment.

Mei, Chuh↗

NASA NTRS1985

Application of the finite element method in the calculation of transmission loss of flat and curved panels

This investigation represents an extension of a study of Roussos (1985) who considered the noise transmission loss of a rectangular plate in an infinite baffle. Roussos, who employed an analytical formulation, considered an unstiffened plate. While it is difficult to consider stiffeners by means of analytical methods, the difficulties can be avoided by employing a finite element procedure. For this reason, the present study is concerned with the implementation of a finite element method. The representation of the panel transmission loss is discussed, and the determination of the panel motion by means of the finite element technique is described, taking into account an isotropic flat panel, the exciting force, an eigenvalue problem, the radiation pressure, a plate element, and a cylindrical shell element. Numerical results are considered for a flat panel, a curved panel, and a stiffened flat panel.

Koval, L. R.↗

NASA NTRS1993

Helicopter trim analysis by shooting and finite element methods with optimally damped Newton iterations

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Achar, N. S.↗

NASA NTRS1985

Finite element methods for high speed flows

An explicit finite element based solution procedure for solving the equations of compressible viscous high speed flow is presented. The method uses domain splitting to advance the solution with different timesteps on different portions of the mesh. For steady inviscid flows, adaptive mesh refinement procedures are successfully employed to enhance the definition of discontinuities. Preliminary ideas on the application of adaptive mesh refinement to the solution of problems involving steady viscous flow are presented. Sample timings are given for the performance of the finite element code on modern supercomputers.

Loehner, R.↗

NASA NTRS1989

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

Chung, T. J.↗

NASA NTRS2018

An Efficient Inverse Finite Element Method for Shape and Stress Sensing of Laminated Composite and Sandwich Plates and Shells

The inverse Finite Element Method (iFEM) is a revolutionary methodology for real-time reconstruction of full-field structural displacements and stresses in structures that are instrumented with strain sensors. This inverse problem is commonly referred to as shape and stress sensing, which is well-recognized as an enabling technology for structural health monitoring systems. In this study, an improved iFEM formulation is proposed for shape and stress sensing of laminated composite and sandwich plates and shells. The formulation includes the kinematics of a shear deformation plate theory known as Refined Zigzag Theory (RZT) as its baseline. The present iFEM formulation is based upon the minimization of a weighted-least-squares functional that uses the complete set of section strains of RZT. The improved iFEM methodology is applicable for shape and stress sensing of thin and moderately thick plate and shell structures involving a relatively small number of strain gauges. The main advantage of the current formulation is that highly accurate through-the-thickness distributions of displacements, strains, and stresses are attainable using an element based on simple C0-continuous displacement interpolation functions. A three-node inverseshell element, named i3-RZT, is developed. Two example problems are examined in detail: (1) a simply supported rectangular laminated composite plate and (2) a wedge structure with a hole near one of the clamped ends. For both problems, the experimental strain data are generated numerically by the direct finite element analysis using high-fidelity discretizations. These strains are then regarded as the experimental strains obtained from surface mounted strain gauges or embedded fiber Bragg grating (FBG) sensors. The numerical results demonstrate the superior capability and potential applicability of the i3- RZT/iFEM methodology for performing accurate shape and stress sensing of complex composite structures.

Kefal, Adnan↗