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At least 469 records · Page 26

Initial study of notch sensitivity of Grade 91 using mechanisms motivated crystal plasticity finite element method

This report describes the development of a crystal plasticity finite element method (CPFEM) model for the multiaxial creep rupture of Grade 91 steel. The report demonstrates that core blocks in heat pipe reactor designs will see significantly different stress states than those typically found in conventional advanced reactor components where structures can often be represented as thin-walled pressure vessels. Current design practice uses effective stress measures calibrated to biaxial creep test data to account for the effect of stress multiaxiality on rupture life. Because these models rely on biaxial data they may not be accurate for the truly 3D, triaxial states found in heat pipe microreactor core blocks. A physically-based model, like the CPFEM model developed here, may be able to more accurately represent creep rupture under triaxial stresses when compared to conventional, empirical methods. This report describes the development, implementation, and validation of such a model and then applies the model to predict the effect of stress triaxiality on rupture in Grade 91 steel. The model results are used to assess the effective stress measures currently used in high temperature design codes and makes specific recommendations on improving these effective stresses to better account for the effect of 3D stress states on rupture in Grade 91. The validation and then implementation of these recommendations in design codes and standards could lead to safer, more effective heat pipe microreactor core block designs.

36 MATERIALS SCIENCE↗

Development, Implementation, and Verification of Partially-Ionized Collisional Multifluid Plasma Models in Drekar

We consider the development of multifluid models for partially ionized multispecies plasmas. The models are composed of a standard set of five-moment fluid equations for each species plus a description of electromagnetics. The most general model considered utilizes a full set of fluid equations for each charge state of each atomic species, plus a set of fluid equations for electrons. The fluid equations are coupled through source terms describing electromagnetic coupling, ionization, recombination, charge exchange, and elastic scattering collisions in the low-density coronal limit. The form of each of these source terms is described in detail, and references for required rate coefficients are identified for a diverse range of atomic species. Initial efforts have been made to extend these models to incorporate some higher-density collisional effects, including ionization potential depression and three- body recombination. Some reductions of the general multifluid model are considered. First, a reduced multifluid model is derived which averages over all of the charge states (including neutrals) of each atomic species in the general multifluid model. The resulting model maintains full consistency with the general multifluid model from which it is derived by leveraging a quasi-steady-state collisional ionization equilibrium assumption to recover the ionization fractions required to make use of the general collision models. Further reductions are briefly considered to derive certain components of a single-fluid magnetohydrodynamics (MHD) model. In this case, a generalized Ohm's law is obtained, and the standard MHD resistivity is expressed in terms of the collisional models used in the general multifluid model. A number of numerical considerations required to obtain robust implementations of these multifluid models are discussed. First, an algebraic flux correction (AFC) stabilization approach for a continuous Galerkin finite element discretization of the multifluid system is described in which the characteristic speeds used in the stabilization of the fluid systems are synchronized across all species in the model. It is demonstrated that this synchronization is crucial in order to obtain a robust discretization of the multifluid system. Additionally, several different formulations are considered for describing the electromagnetics portion of the multifluid system using nodal continuous Galerkin finite element discretizations. The formulations considered include a parabolic divergence cleaning method and an implicit projection method for the traditional curl formulation of Maxwell's equations, a purely- hyperbolic potential-based formulation of Maxwell's equations, and a mixed hyperbolic-elliptic potential-based formulation of Maxwell's equations. Some advantages and disadvantages of each formulation are explored to compare solution robustness and the ease of use of each formulation. Numerical results are presented to demonstrate the accuracy and robustness of various components of our implementation. Analytic solutions for a spatially homogeneous damped plasma oscillation are derived in order to verify the implementation of the source terms for electromagnetic coupling and elastic collisions between fluid species. Ionization balance as a function of electron temperature is evaluated for several atomic species of interest by comparing to steady-state calculations using various sets of ionization and recombination rate coefficients. Several test problems in one and two spatial dimensions are used to demonstrate the accuracy and robustness of the discretization and stabilization approach for the fluid components of the multifluid system. This includes standard test problems for electrostatic and electromagnetic shock tubes in the two-fluid and ideal shock-MHD limits, a cylindrical diocotron instability, and the GEM challenge magnetic reconnection problem. A one-dimensional simplified prototype of an argon gas puff configuration as deployed on Sandia's Z-machine is used as a demonstration to exercise the full range of capabilities associated with the general multifluid model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimization of Air-Gap Profile in Interior Permanent-Magnet Synchronous Motors for Torque Ripple Mitigation

Interior permanent magnet synchronous motors (IPMSMs) have been widely used due to their high efficiency and high power density. Minimization of torque pulsation resulting in vibration and acoustic noise is one of the important design considerations for IPMSMs. In this paper, a grid on/off search method for the rotor profile is proposed to mitigate torque pulsation. Selection of the rotor profile is due to the fact that air-gap is the most sensitive parameter in electric machines wherein changes in flux densities can cause substantial differences in the distribution of forces. A layer comprised of 20 partitions with a 0.1 mm thickness and 3 degrees wide grids have been introduced to the rotor surface for each pole and the possible geometries have been analyzed using finite element method (FEM) in ANSYS Maxwell. An optimal design was found that has the lowest torque ripple with a higher average torque compared to the original design. Genetic algorithm (GA) has also been applied to the method to automate the coupling between Maxwell and Matlab thereby saving the simulation time. Finally, complete structural analysis has been done for both of the original and optimal designs to verify the superiority and feasibility of the proposed design.

42 ENGINEERING↗

Finite-element analysis of top-casing electric source method for imaging hydraulically active fracture zones

Imaging hydraulically active fracture zones (HAFZ) is of paramount importance to subsurface resource extraction, geologic storage, and hazardous waste disposal. We have developed advanced 3D finite-element (FE) electrical imaging algorithms for HAFZ in the presence of a steel-cased well. The algorithms use tetrahedral FE meshes in the simulation domain and coarse rectangular finite-difference meshes in the imaging domain. This heterogeneous dual-mesh approach is well suited to modeling the multiscale earth model due to steel-cased wells. We find that the algorithms accurately and efficiently simulate surface electric field measurements over a 3D HAFZ at depth when one end point of a surface electric source is connected to a wellhead. For brevity, this configuration is called the top-casing electric source method. By replacing a hollow cased well with a solid prism, we improve our computational efficiency without affecting the solution accuracy. The sensitivity of the top-casing source method to HAFZ highly depends on the continuity of a steel-cased well because it makes currents preferentially flow to HAFZ. The sensitivity also depends on conductivity structures around the well because they control current leaking from the steel-cased well. We find that the method can image a localized HAFZ and detect changes in its width and height. Here, the imaging results are improved when a volume of the imaging domain is constrained from geomechanical perspectives. A primary advantage of the method is the fact that the sources and receivers are placed on the surface, thus not interrupting the well operation.

3D↗

An arbitrarily high-order three-dimensional Cartesian-grid method for reconstructing interfaces from volume fraction fields

Here Tthis work describes a newly developed, arbitrarily high-order Cartesian-grid method for reconstructing material interfaces from a volume fraction field. The method begins by identifying all of the grid cells in the volume fraction field that are intersected by the interface and need to be approximated by the reconstruction scheme. Finite-differences are used to calculate the gradient of the volume fraction field and provide an estimate of the surface normal in all of the interfacial grid cells. Groups of connected grid cells are then identified which all have the same dominant component of the normal vector. This grouping by orientation determines the proper dependent variable to use in the surface reconstruction (e.g. for a 2D curve, this step determines if the surface will be approximated by a function of x or y). A cumulative integral over the surface is constructed and fit using b-splines for two-dimensional problems or tensor-product b-splines for three-dimensional problems. This construction allows for the interface to be recovered through application of the second fundamental theorem of calculus. Fitting the cumulative integral with $\mathscr{N}$ th-order b-splines (or tensor-product b-splines) yields an ($\mathscr{N}$-1) th-order convergence rate of the interface shape. Differentiation of the b-spline interface function(s) allows for the high-order approximation of the normal vector and curvature to be obtained directly anywhere along b-spline. Together, the proposed reconstruction technique can achieve arbitrarily high mesh convergence rates. Validation tests are presented with mesh convergence rates ranging from fourth- to tenth-order.

97 MATHEMATICS AND COMPUTING↗

End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations

In this article, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in H(curl) and H(div) (e.g., for electromagnetic or radiation diffusion problems), a specially constructed interpolation–histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.

97 MATHEMATICS AND COMPUTING↗

Evaluation of the ring tension test (RTT) for robust determination of material strengths

The ring tension test (RTT) is an experimental method for determining mechanical behavior in a material’s circumferential or hoop direction. It is a crucial test for testing anisotropic materials with tube geometry, such as nuclear fuel cladding or irradiated pipes. Several RTT configurations exist, each with their own advantages and disadvantages. However, this test is significantly more complex than traditional tensile testing and can be especially sensitive to small differences and inconsistencies in the test setup and geometry, ultimately affecting the derived mechanical properties. Previous research has focused on method development, and little work has been done on understanding the subtle differences between an ideal test and experiments, specifically when the tests are performed on highly irradiated materials in hot cells. In this work, a finite element-based investigation of the RTT is conducted to fill this gap. The two most used test configurations are investigated, comparing their ability to determine accurate material strengths through plastic deformation. Several non-ideal conditions and uncontrollable effects which are likely to occur during experimental testing such as machining tolerances, variations of specimen geometry from nominal dimensions, rotation of specimens and fixturing, and other test setup discrepancies are studied. The sensitivity of measured strengths to these conditions is presented. A mechanics-based approach to describing and correcting raw data to determine actual strengths is also included for one of the configurations, resulting in a robust correction method with highly accurate material strength measurements. Finally, based on these analyses, the hemicylindrical mandrel configuration is recommended with a gauge region oriented at a 45° angle.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Numerical and Experimental Analysis of Dissimilar Repair Welding Residual Stress in P91 Steel Considering Solid-State Phase Transformation

Repair welding is a popular method to repair the cracked zones of pipes in power plants. However, residual stresses induced by repair welding are inevitably generated and have a significant effect on the performance of repair-welded components during service. The purpose of this research is to investigate the effects of solid-state phase transformation (SSPT) on the repair welding residual stress distribution of multi-layer and multi-pass welding in P91 steel. Based on thermal elastic-plastic theory, a three-dimensional thermal–metallurgical–mechanical finite element model considering the SSPT is established, and shielded metal arc welding (SMAW) heat input is modelled as one double elliptical heat source. The effect of phase transformation on residual stress is investigated by considering effects with and without phase transformation in the database of materials. The results show that transverse compressive stress and a low longitudinal stress area are generated in the final pass due to martensite transformation. Compared with different zones along the thickness direction, the effect of SSPT is greater around the outer surface than around the internal fusion zone. The rationality of the developed finite element model is verified by the experimental method, and good agreement is obtained between those results from the numerical analysis and experimental methods.

36 MATERIALS SCIENCE↗

Online Adaptive Hyperthermia Treatment Planning During Locoregional Heating to Suppress Treatment-Limiting Hot Spots

Background: Adequate tumor temperatures during hyperthermia are essential for good clinical response, but excessive heating of normal tissue should be avoided. This makes locoregional heating using phased array systems technically challenging. Online application of hyperthermia treatment planning could help to improve the heating quality. The aim of this study was to evaluate the clinical benefit of online treatment planning during treatment of pelvic tumors heated with the AMC-8 locoregional hyperthermia system. Methods: For online adaptive hyperthermia treatment planning, a graphical user interface was developed. Electric fields were calculated in a preprocessing step using our in-house–developed finite-difference–based treatment planning system. This allows instant calculation of the temperature distribution for user-selected phase-amplitude settings during treatment and projection onto the patient's computed tomographic scan for online visualization. Online treatment planning was used for 14 treatment sessions in 8 patients to reduce the patients' reports of hot spots while maintaining the same level of tumor heating. The predicted decrease in hot spot temperature should be at least 0.5°C, and the tumor temperature should decrease less than 0.2°C. These predictions were compared with clinical data: patient feedback about the hot spot and temperature measurements in the tumor region. Results: In total, 17 hot spot reports occurred during the 14 sessions, and the alternative settings predicted the hot spot temperature to decrease by at least 0.5°C, which was confirmed by the disappearance of all 17 hot spot reports. At the same time, the average tumor temperature was predicted to change on average −0.01°C (range, −0.19°C to 0.34°C). The measured tumor temperature change was on average only −0.02°C (range, −0.26°C to 0.31°C). In only 2 cases the temperature decrease was slightly larger than 0.2°C, but at most it was 0.26°C. Conclusions: Online application of hyperthermia treatment planning is reliable and very useful to reduce hot spots without affecting tumor temperatures.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Correspondence between neuroevolution and gradient descent

Abstract We show analytically that training a neural network by conditioned stochastic mutation or neuroevolution of its weights is equivalent, in the limit of small mutations, to gradient descent on the loss function in the presence of Gaussian white noise. Averaged over independent realizations of the learning process, neuroevolution is equivalent to gradient descent on the loss function. We use numerical simulation to show that this correspondence can be observed for finite mutations, for shallow and deep neural networks. Our results provide a connection between two families of neural-network training methods that are usually considered to be fundamentally different.

97 MATHEMATICS AND COMPUTING↗

PROTEUS-MOC User Manual

The PROTEUS-MOC code is a three-dimensional (3D) neutron transport code based on the finite element mesh and the method of characteristics (MOC) which combines a 2D MOC with the discontinuous Galerkin finite element method for the axial direction. Thus, for PROTEUS-MOC, a 3D geometry is represented with by the implicit extrusion of a single 2D planar geometry with different material assignments allowable on each plane. The code requires four input files for a steady-state calculation without the thermal feedback: a driver input, a mesh input, a cross section input, and a material assignment input. With thermal feedback, a T/H input file is needed. For kinetics, a kinetics driver input file is required. The PROTEUS-MOC software produces a text output file as well as a data file which includes integral and average quantities such on fluxes, powers, temperatures, densities, etc. The detailed output file can be converted to the VTK format using the post processing code so that the outputs can be visualized using a visualization software such as VisIt.

97 MATHEMATICS AND COMPUTING↗

Computationally Efficient AC Resistance Model for Stator Winding With Rectangular Conductors

The resistance of the electric machine’s windings is an important parameter when analyzing the machine’s performance, as conduction losses in the winding are often the largest loss component. However, this resistance changes with frequency due to the skin and proximity effects, making it challenging to accurately estimate these losses. In this article, a computationally efficient, general method of calculating the ac resistance of an electric machine winding with rectangular conductors is presented. The method uses a 1-D magnetoquasi-static model of the stator slot region to develop boundary transfer relations between individual turns. These relations are then used to create an impedance matrix from which the ac resistance can be calculated. This technique is more flexible than previous solutions since it can accommodate different winding configurations such as fractional-pitch windings. It is shown that a fractional-pitch winding has a lower ac resistance than a full-pitch winding. Finally, finite-element analysis simulations and experimental results are used to validate the proposed method.

42 ENGINEERING↗

PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method

Abstract A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time-integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.

36 MATERIALS SCIENCE↗

Exploring finite temperature properties of materials with quantum computers

Abstract Thermal properties of nanomaterials are crucial to not only improving our fundamental understanding of condensed matter systems, but also to developing novel materials for applications spanning research and industry. Since quantum effects arise at the nano-scale, these systems are difficult to simulate on classical computers. Quantum computers can efficiently simulate quantum many-body systems, yet current quantum algorithms for calculating thermal properties of these systems incur significant computational costs in that they either prepare the full thermal state on the quantum computer, or they must sample a number of pure states from a distribution that grows with system size. Canonical thermal pure quantum (TPQ) states provide a promising path to estimating thermal properties of quantum materials as they neither require preparation of the full thermal state nor require a growing number of samples with system size. Here, we present an algorithm for preparing canonical TPQ states on quantum computers. We compare three different circuit implementations for the algorithm and demonstrate their capabilities in estimating thermal properties of quantum materials. Due to its increasing accuracy with system size and flexibility in implementation, we anticipate that this method will enable finite temperature explorations of relevant quantum materials on near-term quantum computers.

36 MATERIALS SCIENCE↗

Modeling of Stick-Slip Behavior in Sheared Granular Fault Gouge Using the Combined Finite-Discrete Element Method

Sheared granular layers undergoing stick-slip behavior are broadly employed to study the physics and dynamics of earthquakes. In this paper, a two-dimensional implementation of the combined finite-discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), is used to explicitly simulate a sheared granular fault system including both gouge and plate, and to investigate the influence of different normal loads on seismic moment, macroscopic friction coefficient, kinetic energy, gouge layer thickness, and recurrence time between slips. In the FDEM model, the deformation of plates and particles is simulated using the FEM formulation while particle-particle and particle-plate interactions are modeled using DEM-derived techniques. The simulated seismic moment distributions are generally consistent with those obtained from the laboratory experiments. In addition, the simulation results demonstrate that with increasing normal load, (i) the kinetic energy of the granular fault system increases; (ii) the gouge layer thickness shows a decreasing trend; and (iii) the macroscopic friction coefficient does not experience much change. Analyses of the slip events reveal that, as the normal load increases, more slip events with large kinetic energy release and longer recurrence time occur, and the magnitude of gouge layer thickness decrease also tends to be larger; while the macroscopic friction coefficient drop decreases. Finally, the simulations not only reveal the influence of normal loads on the dynamics of sheared granular fault gouge, but also demonstrate the capabilities of FDEM for studying stick-slip dynamic behavior of granular fault systems.

58 GEOSCIENCES↗

Inverse design of plasma metamaterial devices with realistic elements

In an expansion of a previous study, we apply inverse design methods to produce two-dimensional plasma metamaterial devices with realistic plasma elements which incorporate quartz envelopes, collisionality (loss), non-uniform density profiles, and resistance to experimental error/perturbation. Finite difference frequency domain simulations are used along with forward-mode differentiation to design waveguides and demultiplexers operating under the transverse magnetic polarization. Additionally, optimal devices with realistic elements are compared to previous devices with idealized elements, and several parameter initialization schemes for the optimization algorithm are explored, yielding a robust procedure for producing such devices. Demultiplexing and waveguiding are demonstrated for microwave-regime devices composed of plasma elements with reasonable space-averaged plasma frequencies ~10GHz and a collision frequency ~1 GHz, allowing for future in-situ training and experimental realization of these designs.

42 ENGINEERING↗

Unbinned extraction of $γ$ from $B\to DK$ with normalizing flows

We introduce an unbinned method for extracting the CKM angle $γ$ from the decay chain $B^\pm \to (D \to K_S π^+ π^-) K^\pm$ using normalizing flows (NFs). The NFs, trained on $D$ decay data, learn a faithful continuous representation of the amplitude and strong phase variation over the $D\to K_Sπ^+π^-$ Dalitz plot whose fidelity improves with increased data sample sizes. With this input, the $B$ decay data can be used to extract the parameters $r_B$, $δ_B$, and $γ$. We test the method on Monte Carlo generated data, where it successfully recovers the injected value of $γ$ within uncertainties. The present implementation propagates statistical uncertainties from finite training data via an ensemble of independently trained flows, and does not attempt to capture the effects of systematic experimental errors. We explore two versions of the method that differ in how the trigonometric constraint on phase variation is encoded, and comment on the possible extension to Bayesian NFs, which would provide direct uncertainty estimates on the learned densities without requiring ensemble training.

Grossman, Yuval [Cornell U., LEPP]↗