Introduction to FLAG
The following guide is a tutorial-style introduction to the free Lagrange (FLAG) hydrocode for anyone who wants to get started with or learn more about FLAG.
97 MATHEMATICS AND COMPUTING↗
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Results for “Lagrange”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Non-Diffusive Volume Advection with A High Order Interface Reconstruction Method
We show that non-diffusive volume advection in two-dimensions is achieved with several benchmark problems using a newly developed high-order volume of fluids (VOF) interface reconstruction method. (1) A new VOF interface reconstruction method using circular/corner facets (linear facets are a degenerate case of arcs). We create a circular interface facet in each mixed zone by matching neighbor volume with a hybrid Newton’s-bisection method and the local solution is final. In the general case, the new VOF interface reconstruction has 3rd order accuracy and can be easily made seamless. The new method addresses intrinsic issues with Young’s method such as gaps between interface facets in the case of a curved interface, and inability to define curvature nor identify corners. (2) A non-diffusive volume advection scheme. In an ALE advection step, a well-defined interface can be carried over through a Lagrange step and used to compute volume distribution into a relaxed mesh. Then, an interface reconstruction step is performed to redefine the interface in the relaxed mesh. We must point out that the interface carried over is also a solution of interface reconstruction because all the volume fractions in the relaxed mesh are naturally matched. We provide an interface tracking method compatible with our reconstruction scheme, where it is granted to use the prior info as an initial guess to capture sub-mesh resolution features. As a result, we are able to treat multiple facets inside a single mixed cell and obtain highly accurate, non-diffusive solution for advection problems with rather coarse meshes. We show our solutions for two-dimensional incompressible flows with two materials with a) the X + O diagonal translation; b) the Zalesak rotational test; and c) the single vortex spiral test.
97 MATHEMATICS AND COMPUTING↗
Optimization-based algorithms for nonlinear mechanics and frictional contact
An optimization-based strategy for solving nonlinear mechanics problems is proposed. In contrast to typical nonlinear equation solver algorithms that aim to find zeros in the residual force function, we minimize an energy (or energy-like) function to encourage solutions which are locally stable equilibria. These smooth and potentially non-convex objective functions are minimized using a preconditioned conjugate-gradient trust-region algorithm. Contact is formulated as an inequality constrained minimization problem, and is solved with an augmented Lagrangian algorithm. Friction is included in the approach via a regularized quasi-potential energy, and other dissipative behavior is included through the use of variational constitutive updates. Finally, to accelerate convergence rates for the Lagrange multipliers, we propose a novel multiplier update algorithm utilizing the Fischer-Burmeister function, and demonstrate super-linear solver convergence for some applications.
42 ENGINEERING↗
Fission Product Yield Data Adjustment in a Prototype Version of TSURFER
The TSURFER (Tool for Sensitivity/Uncertainty analysis of Response Functionals using Experimental Results) module of Oak Ridge National Laboratory’s (ORNL’s) SCALE code system has been updated to perform nuclear data adjustments for fixed-source irradiation/depletion problems. TSURFER uses a generalized linear least squares (GLLS) approach to consolidate a prior set of measured responses and corresponding calculated values to create the most self-consistent set of nuclear data. Traditionally, TSURFER adjustments have been performed for multigroup nuclear data such as reaction cross sections. In this work, TSURFER is expanded to perform adjustments to independent fission product yields and branching ratios that need equality constraints. To preserve equality constraints after the data adjustment procedure, an updated GLLS formulation includes a new Lagrange multiplier that forces data adjustment to sum to 0 for a given fission yield/branching ratio parent. A test problem illustrates that the newly updated TSURFER module satisfies the required constraint that adjustments for fission yield data sum to 0.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Modeling the Nonlinear Rheology of Polymer Additive Manufacturing
This report summarizes molecular and continuum simulation studies focused on developing physics - based predictive models for the evolution of polymer molecular order during the nonlinear processing flows of additive manufacturing. Our molecular simulations of polymer elongation flows identified novel mechanisms of fluid dissipation for various polymer architectures that might be harnessed to enhance material processability. In order to predict the complex thermal and flow history of polymer realistic additive manufacturing processes, we have developed and deployed a high - performance mesh - free hydrodynamics module in Sandia's LAMMPS software. This module called RHEO – short for Reproducing Hydrodynamics and Elastic Objects – hybridizes an updated - Lagrange reproducing - kernel method for complex fluids with a bonded particle method (BPM) to capture solidification and solid objects in multiphase flows. In combination, our two methods allow rapid, multiscale characterization of the hydrodynamics and molecular evolution of polymers in realistic processing geometries.
36 MATERIALS SCIENCE↗
An Investigation of Variables Affecting Plutonium Hydriding (20210946DI): Surface Phase Transitions and Reactions
Tusas was originally developed for phase field simulation of solidification (see [33, 6, 32]) and evolution of polycrystalline solid mechanics (see [16]). Tusas is particularly developed for PDEs compatible with structured or unstructured Lagrange (nodal) finite element discretizations and explicit (Euler) or implicit (Euler, Trapezoid, BDF2) temporal discretizations.
97 MATHEMATICS AND COMPUTING↗
Electrodynamic Shaker Capability Estimation Through Experimental Dynamic Substructuring [Thesis]
Electrodynamic shaker systems are an essential tool in shock and vibration testing of dynamic environments. However, the specific performance capability of these systems is difficult to characterize. The dynamics of the shaker itself, the device under test and the specific test configuration used all couple to create a dynamic response unique to each test. Poorly predicted limitations in shaker capability affect the ability to achieve test specifications, delay testing schedules, and create difficulties for choosing test equipment. To predict shaker capability for a specific test configuration prior to setup, a lumped parameter model of the shaker system and a modal model of a device under test was developed. These models were then analytically coupled using LaGrange multiplier frequency based substructuring to estimate their coupled frequency response functions. The coupled frequency response functions were used to predict electrical inputs required to meet a given test specification. These input requirements were finally compared to a validation test using the specification and setup. Input requirements estimated using the substructuring estimated frequency response functions showed significant error. However, results using an ideal frequency response function showed very little error. These results indicate that with a better method of experimental dynamic substructuring employed it would be possible to accurately predict shaker capability for a given test configuration prior to setup.
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↗
NEAMS Technical Area Support in MOOSE
The Multiphysics Object-Oriented Simulation Environment (MOOSE) framework is a foundational capability used by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to create over 15 different simulation tools for advanced nuclear reactors. Due to this ubiquity, improvements to the framework in support of modeling and simulation goals are critical to the program. These improvements can take many forms, including optimization, improved user experience, streamlined application programming interfaces (APIs), parallelism, and new capabilities. The work transcribed in this report was conducted in direct support of the simulation tools and has already been deployed. The capabilities outlined in this report include addition of Times and Positions systems, redesign of mechanical contact constraints to enable the augmented Lagrange algorithm, overhaul of the restart system, and incorporation of p-refinement in MOOSE.
97 MATHEMATICS AND COMPUTING↗
High Fidelity CFD Simulations Supporting the KP-FHR
Kairos Power, LLC, is developing its version of the Fluoride-cooled High-temperature Reactor, the KP-FHR. The design uses a pebble bed core with fluoride salt as a coolant. The pebbles used in the KP-FHR have a diameter of 4 cm, with a shell fuel region where TRISO particles are embedded. A Pebble bed core design is adopted by several Gen IV reactors, They boast many benefits, such as fuel integrity, highly efficient heat transfer, and passive safety. However, it is challenging to accurately predict temperature and flow inside a pebble bed. Traditional approaches use the porous media model, which regards the pebble bed as a continuous medium, but with different temperature fields representing different levels, such as the fluid temperature, pebble surface temperature, and pebble center temperature. Empirical heat transfer correlations are adopted to calculate the heat transfer coefficient between different phases. However, empirical correlations are usually validated with experimental data, which usually lacks detail inside the pebble bed. The available experimental data is also generally at a high Reynolds number, which falls outside of the conditions of KP-FHR. Explicit computational fluid dynamics (CFD) simulations of randomly packed pebble beds have only become feasible recently. This is thanks to the rapid development of computational power and scalable algorithms. In this work, we used the Spectral Element Method (SEM) CFD code NekRS to simulate the randomly packed pebble bed in a cylindrical container. NekRS, which is the GPU variant of Nek5000, but refactored to utilize the computational power of GPUs using the OCCA library to run on hybrid architecture high performance computing systems. It was initially developed with the libParamunal library, but truncated and tuned for large-scale turbulence simulation. As a result, the SEM reaches higher precision with the same degrees of freedom by using a high-order Lagrange polynomial basis distributed on Gauss-Lobatto-Legendre quadrature inside each element, compared to lower-order methods, such the Finite Volume Method and Finite Element Method. The report is divided into five parts. We start with a general discussion of the pebble bed reactor, along with a specific investigation into the KP-FHR. The second part presents the numerical methodology. In the third part, we study a modular pebble bed with 1741 pebbles in a container of 7 pebble-diameter radius. Beyond LES simulations done by NekRS, we also leveraged the thermal radiation model in OpenFOAM to study heat transfer under no-forced-flow scenarios. Then, in the fourth part we simulated a pebble bed similar to the size of the Hermes Test Reactor. The total number of pebbles is in these simulations is 34,374. The container radius is 14 pebble-diameters. Finally, the report concludes in part five, with a discussion of future work.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Average Incremental Cost Pricing for the AC Unit Commitment Problem [Rev. 1]
Unit Commitment (UC) problems that consider the Alternating Current (AC) model of the transmission network have long been considered intractable to solve at scale by the power system community. Recently, the Grid-Optimization (GO) Competition held by the Advanced Research Project Agency-Energy (ARPA-E) has facilitated the development of the first algorithms to solve large-scale ACUC problems. This new capability opens a path towards the explicit consideration of the AC transmission network model in UC problems used to clear day-ahead electricity markets. This calls for the analysis of electricity market structures that accommodate both the continuous non-linearity of the AC transmission network and the discrete non-linearity of the UC problem simultaneously. This paper serves as an initial effort to do so by proposing an Average Incremental Cost (AIC) pricing structure that is designed around the ACUC problem. In particular, an AIC one-pass pricing problem is proposed that represents a continuously constrained variant of the ACUC problem and allows for the computation of Locational Incremental Prices (LIPs) for both real and reactive power as the local optimal Lagrange multipliers of the power balance constraints. To avoid degeneracy, the pricing problem includes a small parameter ϵ > 0. Under certain assumptions market participants are shown to realize profit that converges to a non-negative value as ϵ approaches zero, practically ensuring profitability for small values of ϵ. We additionally provide many simple and important examples that provide intuition and insights into the proposed prices. Examples illustrate the basic concept of AIC pricing, the derived profitability results, the existence of multiple LIPs, the importance of including reactive power in the dispatch and pricing problems, the need for reactive power prices, and the improved incentives exhibited by LIPs as compared to traditional Locational Marginal Prices (LMPs). We additionally indicate many directions for future work including analysis of larger test cases.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Predicting Cislunar Orbit Lifetimes from Initial Orbital Elements
The volume of space between Earth’s geosynchronous orbit out to the Moon’s sphere of influence, including the lunar Lagrange points, is crucial for the successful planning and execution of space missions, but not fully understood dynamically. This region is a part of cislunar space. Trajectories through cislunar space are influenced by the gravitational forces of the Sun, Earth, Moon, and other Solar System planets leading to typically unpredictable and chaotic trajectory behavior. It is therefore difficult to predict the stability of an trajectory through cislunar space from a set of initial conditions or orbital elements. We simulate one million cislunar orbits to train a self-organizing map (SOM) to cluster the trajectories and orbits into families based on how long they remain stable within the cislunar space. Using the trained SOM, we are able to predict the stable lifetime of a trajectory through cislunar space from a set of initial orbital elements to within an accuracy of 10% for 8% of simulated trajectories and within 50% for 43% of the simulated trajectories. Clustering in the SOM suggests that a variety of trajectory morphologies have similar lifetimes. Once trained, the SOM can predict the stable lifetime of a given cislunar trajectory within milliseconds. The methods developed in this work enable the rapid identification of stable cislunar orbits and trajectories that could be used for future space exploration. Moreover, the developed SOM method can generate orbital and trajectory lifetime estimates from minimal observational data, such as a single two line element, making it useful for early warning systems and large-scale sensor network operations.
79 ASTRONOMY AND ASTROPHYSICS↗
Determining SMEFT and PDF parameters simultaneously based on the CTEQ-TEA framework
The SM effective field theory (SMEFT) provides a model-independent and systematically improvable framework for new physics searches. In this talk, we outline our approach of simultaneously fitting SMEFT parameters and Probability Density Functions (PDFs) in an extension of the CT18 global analysis framework. To enhance the efficiency of our global fitting and Lagrange multiplier scans, we leverage machine-learning techniques. We focus on several representative operators relevant to top-quark pair production and jet production. Through this approach, we establish self-consistent limitations on the associated Wilson coefficients, and explore the correlations between these Wilson coefficients and the PDFs.
Shen, XiaoMin↗
Scaling Turbulent Combustion Fields in Explosions
We considered the topic of explosions from spherical high-explosive (HE) charges. We studied how the turbulent combustion fields scale. On the basis of theories of dimensional analysis by Bridgman and similarity theories of Sedov and Barenblatt, we found that all fields scaled with the explosion length scale r0. This included the blast wave, the mean and root mean squared (RMS) profiles of thermodynamic variables, combustion variables, velocities, vorticity, and turbulent Reynolds stresses. This was a consequence of the formulation of the problem and our numerical method, which both satisfied the similarity conditions of Sedov. We performed numerical simulations of 1 g charges and 1 kg charges; the solutions were identical (within roundoff error) when plotted in scaled variables. We also explored scaling laws related to three-phase pyrotechnic explosions. We show that although the scaling formally broke down, the fireball still essentially scaled with the explosion length scale r0. However, the discrete Lagrange particles (DLP) (phase 2) and the heterogeneous continuum model (HCM) of the DLP wakes (phase 3) did not scale with r0, and mean and RMS profiles could differ by a factor of 10 in some regions. This was because the DLP particles and wakes introduced an additional scale that broke the similarity conditions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
An MILP-Based Distributed Energy Management for Coordination of Networked Microgrids
An MILP-based distributed energy management for the coordination of networked microgrids is proposed in this paper. Multiple microgrids and the utility grid are coordinated through iteratively adjusted price signals. Based on the price signals received, the microgrid controllers (MCs) and distribution management system (DMS) update their schedules separately. Then, the price signals are updated according to the generation–load mismatch and distributed to MCs and DMS for the next iteration. The iteration continues until the generation–load mismatch is small enough, i.e., the generation and load are balanced under agreed price signals. Through the proposed distributed energy management, various microgrids and the utility grid with different economic, resilient, emission and socio-economic objectives are coordinated with generation–load balance guaranteed and the microgrid customers’ privacy preserved. In particular, a piecewise linearization technique is employed to approximate the augmented Lagrange term in the alternating direction method of multipliers (ADMM) algorithm. Thus, the subproblems are transformed into mixed integer linear programming (MILP) problems and efficiently solved by open-source MILP solvers, which would accelerate the adoption and deployment of microgrids and promote clean energy. The proposed MILP-based distributed energy management is demonstrated through various case studies on a networked microgrids test system with three microgrids.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Insights on the Effects of Magnetic Forces on the Efficiency of Vibration Energy Harvesting Absorbers in Controlling Dynamical Systems
This study investigates the effects of magnetic constraints on a piezoelectric energy harvesting absorber while simultaneously controlling a primary structure and harnessing energy. An accurate forcing representation of the magnetic force is investigated and developed. A reduced-order model is derived using the Euler–Lagrange principle, and the impact of the magnetic force is evaluated on the absorber’s static position and coupled natural frequency of the energy harvesting absorber and the coupled primary absorber system. The results show that attractive magnet configurations cannot improve the system substantially before pull-in occurs. A rigorous eigenvalue problem analysis is performed on the absorber’s substrate thickness and tip mass to effectively design an energy harvesting absorber for multiple initial gap sizes for the repulsive configurations. Then, the effects of the forcing amplitude on the primary structure absorber are studied and characterized by determining an effective design of the system for a simultaneous reduction in the primary structure’s motion and improvement in the harvester’s efficiency.
42 ENGINEERING↗
Explicit Form for the Most General Lorentz Transformation Revisited
Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.
Science & Technology - Other Topics↗
Flaring and Spot Activities on the Semi-detached Binary System KIC 06852488
The continuous and unbroken time-series photometry data of Kepler and the Transiting Exoplanet Survey Satellite (TESS) provide a good opportunity to study the continuous variations in the light curve of binary stars. This paper reports the discoveries of the correlation between the two maxima on the light curve of KIC 06852488 and the correlation between the O’Connell effect and the O – C curve. The Max I and Max II vary with a same cycle length of ~2000 days and a 180° phase difference, and the variation of the Max II coincides with the O – C curve of the primary light minima. After analyzing the Kepler and TESS light curves, it is detected that this binary is a semi-detached system with a mass ratio of 0.4622(±0.0036). The secondary component is filling its critical Roche lobe, while the primary component is only filling 12.25(±0.10)% of the lobe volume that contributes more than 85% luminosity of the total system. The variation of the O’Connell effect could be explained by an evolving hot spot on the primary component and an evolving cool spot on the secondary component. It is found that their positions are symmetrical with the inner Lagrange L1 point. After subtracting the binary brightness changes, six optical flares are detected that come from the cool secondary. We calculated the energy of flares and found that all of the flares are superflares. Both the flares and an evolving dark spot on the lobe-filling secondary component make the system a very interesting source to investigate the effects of binary interaction on the magnetic activities.
47 OTHER INSTRUMENTATION↗