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At least 577 records · Page 32

A thermodynamics-based damage model for the non-linear mechanical behavior of SiC/SiC ceramic matrix composites in irradiation and thermal environments

A damage model is developed and validated with experimental data for the non-linear mechanical behavior of SiC/SiC composite materials in nuclear applications. Cyclic thermal and mechanical loading associated with neutron irradiation effects of these composites leads to wide-spread and progressive micro-cracking that leads to loss of thermal conductivity and further enhancement of thermo-mechanical damage. A physics-based model of wide-spread micro-cracking is developed within the thermodynamic framework of continuum damage mechanics. Evolution equations for damage parameters that describe the growth of continuum damage are developed, where the material variables are obtained from experiments. The model novelty is in coupling mechanical, thermal, and irradiation damage through a consistent thermodynamic framework, including loss of thermal conductivity due to the evolution of mechanically induced micro-cracks. A number of thermo-mechanical experiments were conducted to confirm model assumptions. The model is shown to be validated with out-of-pile experiments, and then implemented using commercial finite element code COMSOL to the fuel cladding problem with normal and high radiation dose cases.

Materials Science↗

Space-energy separated representations for multigroup neutron diffusion using proper generalized decompositions

Proper generalized decomposition (PGD) can be described as a numerical extension of separation of variables and thus be employed as a solution technique for multi-dimensional problems, where dimensions should be understood in the phase-space context of the governing law at hand. This paper presents a PGD approach on efficiently solving problems involving multigroup neutron diffusion. Two PGD approaches are described: space-only and space-energy decompositions. Numerical results include 2-D and 3-D examples with two-, seven-, and 145-group structures. The PGD solutions are compared against traditional multi-dimensional finite element discretization. For few-group problems, both PGD approaches prove effective for mildly heterogeneous geometries, but showed reduced performance with increasing heterogeneity. The space-energy representation was found to be slower than the space-only approach for two-group problems, but proved more effective for seven-group problems. For even larger numbers of groups, the space-energy PGD decomposition was very effective at reducing the computational time.

42 ENGINEERING↗

Implement and Test 3D Mortar Contact in BISON

We leverage the extension of the generation of mortar segment meshes to three dimensions in MOOSE’s framework to extend thermomechanical modeling capabilities to problems with three dimensions. A modular approach to gap heat transfer physics using the mortar finite element method was created and documented, mechanical contact was extended to three dimensions—including frictional behavior, performance and ease of use were improved, and steps towards scalability of solid mechanics problems involving contact were taken. Many of these new developments are demonstrated in the simulation of 3D light-water reactor (LWR) problems, where the thermomechanical interface problem is solved using the mortar finite element method. Usage of the mortar framework has improved convergence in 2D problems and has enabled employing friction in 3D problems, of which we show results of a short, local stack of 3D pellets. Consequently, the benefits of mortar in terms of solution convergence and quality are extended to three dimensions. Section 2 discusses fundamental developments that enabled the simulation of practical mortar problems in three dimensions and other general improvements, including the reduction of the derivative container size, the modification of dual basis computations when edge dropping (lack of secondary element projection) takes place, the improvement of conditioning when employing the VCP in-edge dropping conditions, and code usability and quality improvements. These latter code enhancements include the migration of tests using “old” mortar contact constraints to using dual mortar with a semi-smooth Newton solution strategy and the reuse of lower dimensional domains for straightforwardly setting up a mortar thermomechanical LWR problem, i.e. the MOOSE action is employed for mechanical contact and the thermal LWR action is employed to capture the gas conductance, contact, and radiation components of gap heat transfer physics. Independently of the mortar LWR thermal action, we developed a modular approach to gap heat transfer that resides in MOOSE and can be leveraged, e.g., in metallic fuel problems. This approach, whose code design based on MOOSE’s user objects to model specific physics was proposed by the maintenance activity, is detailed in Section 3. Based on the dual mortar finite element method, the frictional contact constraints were extended to three dimensions. A block sheared in two directions in and out of contact with a rigid plane is employed in Section 4 to show the way the approach handles changes in frictional states (e.g. stick to slip) within a competitive number of Newton iterations. Equations and numerical results on the use of the VCP with Cartesian Lagrange multipliers, whose combination enables their direct condensation, are described in Section 5.3. Two-dimensional and three-dimensional BISON LWR simulations are discussed in Section 6. Particularly, a stack of five eccentric pellets with a surface defect is simulated and the effect of pellet-cladding friction is assessed. Finally, conclusions are outlined in Section 7.

42 ENGINEERING↗

Computational aspects of heat transfer in structures via transfinite element formulations

The paper presents a generalized Transform Method based Finite Element methodology for thermal analysis with emphasis on the computational aspects of heat transfer in structures. The purpose of this paper is to present an alternate methodology for thermal analysis of structures and therein outline the advantages of the approach in comparison with conventional finite element schemes and existing practices. The overall goals of the research, however, are aimed first toward enhanced thermal formulations and therein to provide avenues for subsequent interdisciplinary thermal/structural analysis via a common numerical methodology. Basic concepts of the approach for thermal analysis is described with emphasis on a Laplace Transform based finite element methodology. Highlights and characteristic features of the approach are described via generalized formulations and applications to several problems. Results obtained demonstrate excellent agreement in comparison with analytic and/or conventional finite element solutions with savings in computational times and model sizes. Potential of the approach for interdisciplinary thermal/structural problems are also identified.

Tamma, K. K.↗

Vibrations of cantilevered shallow cylindrical shells of rectangular planform

A cantilevered, shallow shell of circular cylindrical curvature and rectangular planform exhibits free vibration behavior which differs considerably from that of a cantilevered beam or of a flat plate. Some numerical results can be found for the problem in the previously published literature, mainly obtained by using various finite element methods. The present paper is the first definitive study of the problem, presenting accurate non-dimensional frequency parameters for wide ranges of aspect ratio, shallowness ratio and thickness ratio. The analysis is based upon shallow shell theory. Numerical results are obtained by using the Ritz method, with algebraic polynomial trial functions for the displacements. Convergence is investigated, with attention being given both to the number of terms taken for each co-ordinate direction and for each of the three components of displacement. Accuracy of the results is also established by comparison with finite element results for shallow shells and with other accurate flat plate solutions.

Leissa, A. W.↗

On minimal surfaces, membranes and compressible flows

The theory, variational formulation and finite element analysis of a class of nonlinear problems arising in optimization, thin membrane deflection and compressible flows are developed. Error estimates are summarized, and representative numerical results are presented. Particular theoretical questions pertaining to the existence and uniqueness of solutions are addressed, and their implications for such applications of finite element analysis as the study of compressible flows indicated.

Carey, G. F.↗

A comparative study of an ABC and an artificial absorber for truncating finite element meshes

The type of mesh termination used in the context of finite element formulations plays a major role on the efficiency and accuracy of the field solution. The performance of an absorbing boundary condition (ABC) and an artificial absorber (a new concept) for terminating the finite element mesh was evaluated. This analysis is done in connection with the problem of scattering by a finite slot array in a thick ground plane. The two approximate mesh truncation schemes are compared with the exact finite element-boundary integral (FEM-BI) method in terms of accuracy and efficiency. It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture. However, the artificial absorber termination method leads to a substantially more efficient solution. Moreover, it is shown that the FEM-BI method remains quite competitive with the FEM-artificial absorber method when the FFT is used for computing the matrix-vector products in the iterative solution algorithm. These conclusions are indeed surprising and of major importance in electromagnetic simulations based on the finite element method.

Oezdemir, T.↗

Numerical solution of fluid flow and heat tranfer problems with surface radiation

This paper presents a numerical scheme, based on the finite element method, to solve strongly coupled fluid flow and heat transfer problems. The surface radiation effect for gray, diffuse and isothermal surfaces is considered. A procedure for obtaining the view factors between the radiating surfaces is discussed. The overall solution strategy is verified by comparing the available results with those obtained using this approach. An analysis of a thermosyphon is undertaken and the effect of considering the surface radiation is clearly explained.

Ahuja, S.↗

A 3D finite element ALE method using an approximate Riemann solution

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented.

97 MATHEMATICS AND COMPUTING↗

Uncertainty Analysis of Slug Calorimeters in the HyMETS Arc-Jet Facility

The objective of this work is to perform an uncertainty analysis of the deduced stagnation heat flux environment on a slug calorimeter for conditions that span the performance envelope of the Hypersonic Materials Environmental Test System arc-jet facility located at NASA Langley Research Center. Analytical solutions are developed for boundary-value problems on the slug element accounting for non-ideal effects, including spatial variation in the slug heat flux, multi-dimensional thermal conduction, and back-face losses, which departs from the state-of-the-art method derived from the American Society of Testing and Materials. Boundary-value problem definitions are informed by preliminary finite element thermal analysis of the slug calorimeter assembly (including both slug and housing) and just the slug element. The analytical solutions are presented in a general sense and in a truncated form from error analysis. Results are shown in optimizing and validating the analytical models against available slug back-face thermal data. The optimization results indicate that the appropriate epistemic uncertainty of the deduced stagnation heat flux on the slug calorimeter is at most±2.5% for both a high-and low-enthalpy test condition. In addition, a numerical approach is used to determine the aleatory (probabilistic) uncertainty component in the slug stagnation heat flux by applying a marching least-squares slope routine through the steady-state portion of the slug back-face thermal response. Results indicate a compromise between the number of samples and the filter frequency of slug back-face thermal data points when evaluating the standard deviation of the deduced stagnation heat flux statistics. When combining the mixed uncertainty, both aleatory and epistemic, the interval of uncertainty in the deduced stagnation heat flux is determined to be up to ±4%, which is at least a 60% reduction from the standard uncertainty used in the state-of-the-art method.

uncertainty↗

A Finite-Element Formulation for Subsonic Flows Around Complex Configurations

The problem of potential steady subsonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element. This yields a set of linear algebraic equations. The coefficients of the equation are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented.

Morino, L.↗

A finite element formulation for supersonic flows around complex configurations

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element are assumed to be constant and equal to its value at the centroid of the element. This yields a set of linear algebraic equations whose coefficients are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented.

Morino, L.↗

The simulation of 2D compressible viscous high speed flow by the finite element method

Am implicit/explicit procedure for the solution of problems of two-dimensional steady compressible viscous high-speed flows is presented. In the vicinity of solid walls, a grid which need only exhibit structure in the normal direction is employed while, away from this region, the grid is totally unstructured. The implicit form of the algorithm is used near solid walls, with the grid structure being utilized in an equation solution approach, based upon line relaxation. The explicit form of the algorithm is used elsewhere. Grid adaptation is achieved by means of adaptive remeshing. To illustrate the performance of the proposed method, problems of shock-boundary layer interaction and flow over a simulated forebody at high Mach number are included.

Hassan, O.↗

A Continuous-Discontinuous Hybrid Finite Element Method for S{sub N} Transport

Particle transport phenomenon for neutral particles, such as neutrons and photons, is governed by the linear Boltzmann equation, which is a first-order partial differential equation (PDE). In order to solve the transport equation, discontinuous finite element method (DFEM) is heavily developed. However, the large memory consumption due to the extra degrees of freedom is problematic in multi-D calculations. Another path is to recast the transport equation to a second-order form, such as the well-known self-adjoint angular flux equation (SAAF) and the even parity equations, and spatially discretize the equation using continuous finite element method (CFEM). Yet, such forms generally have problems in void situation as the streaming operator contains a 1/σ{sub t} term and becomes singular in void, which draws numerous efforts on developing void-treatment methods. An intuition to mitigate the shortcomings of both methods is then to develop a method that utilizes DFEM in part of the problem where CFEM has issues while in the other part, CFEM is employed to avoid DFEM's high cost. In this work, we present a novel continuous-discontinuous finite element method (CDFEM) for solving the discrete-ordinates (S{sub N}) transport equations. We perform the hybridization between 1/σ{sub t}-weighted least-squares finite element methods (1/σ{sub t}-LSFEM), with continuous basis functions, and first-order solver. Different solvers are defined in different regions, or subdomains, of the problem. The resulting scheme is such that CFEM-SAAF is performed in subdomains with continuous basis functions while upwinding based DFEM solver is utilized in subdomains with discontinuous basis functions. The connection between subdomains is through an upwinding operation on the interface, which can be performed via the sweep procedure. A foreseeable benefit is such a scheme is compatible with void as first-order DFEM solver can be used in void. On the other hand, as DFEM is only used in part of the problem, CDFEM can effectively avoid the notorious memory consumption of DFEM in multi-D calculation for the future work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Elasto visco-plastic flow with special attention to boundary conditions

A simple but nontrivial steady-state creeping elasto visco-plastic (Maxwell fluid) radial flow problem is analyzed, with special attention given to the effects of the boundary conditions. Solutions are obtained through integration of a governing equation on stress using the Runge-Kutta method for initial value problems and finite differences for boundary value problems. A more general approach through the finite element method, an approach that solves for the velocity field rather than the stress field and that is applicable to a wide range of problems, is presented and tested using the radial flow example. It is found that steady-state flows of elasto visco-plastic materials are strongly influenced by the state of stress of material as it enters the region of interest. The importance of this boundary or initial condition in analyses involving materials coming into control volumes from unusual stress environments is emphasized.

Shimazaki, Y.↗

Generalized Multiscale Inversion for Heterogeneous Problems

In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a coarse-grid medium properties, e.g., permeability and conductivity, and by doing so, they assume that there exists a homogenized representation of the underlying fine-scale permeability field on a coarse grid. Generally such assumptions do not hold for highly heterogeneous fields, e.g., fracture media or channelized fields, where the width of channels are very small compared to the scale of coarse grids. In these cases, grid refinement can lead to many degrees of freedom, and thus numerically unattractive to apply. The proposed algorithm is based on the Generalized Multiscale Finite Element Method (GMsFEM), which uses local spectral problems to identify non-localized features, i.e., channels (high-conductivity inclusions that connect the boundaries of the coarse-grid block). The inclusion of these features in the coarse space enables one to achieve a good accuracy. The approach is valid under the assumption that the solution can be well represented in a reduced-dimensional space spanned by multiscale basis functions. In practice, these basis functions are non-observable as we do not identify the fine-scale features of the permeability field. Our inversion algorithm finds the discretization parameters of the resulting system on the coarse grid. By doing so, we identify the appropriate coarse-grid parameters representing the permeability field instead of fine-grid permeability field. We illustrate the potential of the approach by numerical results for fractured media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Parallel Domain Decomposition Formulation and Software for Large-Scale Sparse Symmetrical/Unsymmetrical Aeroacoustic Applications

The overall objectives of this research work are to formulate and validate efficient parallel algorithms, and to efficiently design/implement computer software for solving large-scale acoustic problems, arised from the unified frameworks of the finite element procedures. The adopted parallel Finite Element (FE) Domain Decomposition (DD) procedures should fully take advantages of multiple processing capabilities offered by most modern high performance computing platforms for efficient parallel computation. To achieve this objective. the formulation needs to integrate efficient sparse (and dense) assembly techniques, hybrid (or mixed) direct and iterative equation solvers, proper pre-conditioned strategies, unrolling strategies, and effective processors' communicating schemes. Finally, the numerical performance of the developed parallel finite element procedures will be evaluated by solving series of structural, and acoustic (symmetrical and un-symmetrical) problems (in different computing platforms). Comparisons with existing "commercialized" and/or "public domain" software are also included, whenever possible.

Nguyen, D. T.↗

Enriched immersed finite element and isogeometric analysis: algorithms and data structures

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.

Computer implementation↗