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At least 271 records · Page 15

Ensemble Kalman filter for data assimilation coupled with low-resolution computations techniques applied in fluid dynamics

This paper presents an innovative Reduced-order model (ROM) for merging experimental and simulation data using data assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our methodology introduces a novel approach by implementing the ensemble Kalman filter (EnKF) within a reduced-dimensional framework, grounded in a robust theoretical foundation and applied to fluid dynamics. To address the substantial computational demands of DA, the proposed ROM employs low-resolution (LR) techniques to drastically reduce computational costs. This innovative approach involves downsampling datasets for DA computations, followed by an advanced reconstruction technique based on low-cost singular value decomposition (lcSVD). The lcSVD method, a key innovation in this paper, has never been applied to DA before and offers a highly efficient way to enhance resolution with minimal computational resources. Our results demonstrate significant reductions in both computation time and RAM usage through these LR techniques without compromising the accuracy of the estimations. For instance, in a turbulent test case, for a data compression rate of 15.9, the LR approach can achieve a speed-up of 13.7 and a RAM compression of 90.9% while maintaining a low relative root mean square error (RRMSE) of 2.6%, compared to 0.8% in the high-resolution (HR) reference. Furthermore, we highlight the effectiveness of the EnKF in estimating and predicting the state of fluid flow systems based on limited observations and given low-fidelity numerical data. This paper highlights the potential of the proposed DA method in fluid dynamics applications, particularly for improving computational efficiency in CFD and related fields. Its ability to balance accuracy with low computational and memory costs makes it especially suitable for large-scale and real-time applications, such as environmental monitoring or engineering design. This method will be incorporated into ModelFLOWs-app.

Data Assimilation↗

Linking classical PRA models to a dynamic PRA

Here, this paper presents a series of methods designed to incorporate classical Probabilistic Risk Assessment (PRA) models such as Event Trees (ETs) and Fault Trees (FTs) into dynamic PRA. In contrast to classical PRA, dynamic PRA couples stochastic methods with system simulators to determine the risks associated with complex systems such as nuclear power plants. Compared with classical PRA methods, they can evaluate with higher resolution the safety impact of timing and sequencing of events on the progression of the accident. As part of a dynamic PRA analysis, it is not uncommon that parts of the system to be analyzed might not require a computationally expensive simulation model. These parts could be in fact modeled by employing classical PRA models (e.g., a FT). Here, we present a set of methods and tools that can be used to link the most common classical PRA models (ETs, FTs, reliability block diagrams and Markov models) to simulation codes such as RELAP5-3D: creating a “hybrid PRA.” In order to show the potential of such an hybrid PRA we employ this method to verify ET modeling assumptions (e.g., success criteria) using a large break loss of coolant accident initiating event as a test case. In this respect, we link a set of FTs from the original PRA to the RELAP5-3D code and perform a hybrid PRA. The FTs are employed to model the control logic of several safety systems and to propagate component failures throughout the system. Provided the generated dynamic PRA data, we show how conservative assumptions in the original PRA can be identified and how such original PRA can be modified by updating success criteria captured by the set of RELAP5-3D simulation runs.

97 - MATHEMATICS AND COMPUTING↗

Scalable modular dynamic molten salt reactor system model with decay heat

Nodal dynamic models allow rapid reduced-order simulations of complex systems. This paper presents a publicly available system dynamic model of a molten salt reactor system with a topology of the Molten Salt Reactor Experiment (MSRE), in MATLAB/Simulink, building upon a model previously published and validated with MSRE data. It adds scaling of nominal power, dynamic representation of decay heat generation, a generic decay heat removal system, improved documentation, modularity, and test cases. One hour of system transient runs in less than 10 min on a laptop. This model is intended for first order engineering calculations, developing insights into system transient behavior, equipment sizing, parameter sensitivity studies. The model contains an easy to use toolkit which can be customized and expanded to describe any molten salt reactor system. Finally, scenarios involving off-normal transients are presented. Relation between shutdown reactivity insertions, decay heat removal, core recriticality, and safe shutdown conditions are discussed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Simulation-based methodology to assess the lattice defects creation as energy storing process

In nuclear industry, damages caused to in-core structural materials by high-energy neutrons have been studied for years. Recently, the possibility of storing energy through the creation of defects in crystalline materials via heavy particle bombardment was investigated. To evaluate the potential of the Wigner effect as energy-storing process, a graphite-moderated Molten Salt Reactor was adopted as a test case. Neutronics simulations performed with OpenMC Monte Carlo code allowed estimating the amount of energy released during fission events, the fraction that is deposited in graphite, and the fraction that has the potential to cause radiation damages. Additionally, molecular dynamics simulations were then performed to study the evolution of cascades triggered by high-energy neutrons. As a major outcome, a more accurate estimate of the radiation damage with respect to the traditional approaches was obtained, and the fraction of the deposited neutron energy that can be stored through long-lived defects was quantified.

25 ENERGY STORAGE↗

A digital twin approach to system-level fault detection and diagnosis for improved equipment health monitoring

Automating the task of fault detection and diagnosis is crucial in the effort to reduce the operation and maintenance cost in the nuclear industry. This paper describes a physics-based approach for system-level diagnosis in thermal-hydraulic systems in nuclear power plants. The inclusion of physics information allows for the creation of virtual sensors, which provide improved fault diagnosis capability. The physics information also serves to better constrain diagnostic solutions to the physical domain. As a demonstration, various test cases for fault diagnosis in a high-pressure feedwater system were considered. The use of virtual sensors allows constructing performance models for two first-point feedwater heaters which would not have been possible otherwise due to the limited sensor set. Real-time plant data provided by a utility partner were used to assess the diagnostic approach. The detection of an abnormal event immediate after a plant startup pointed to faulty behaviors in the two first-point feedwater heaters. Further, this double-blind fault diagnosis was subsequently confirmed by the plant operator. In addition, several simulated sensor fault events demonstrated the capability of our algorithms in detecting and discriminating sensor faults.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

SCALE depletion capabilities for molten salt reactors and other liquid-fueled systems

Nuclear reactor systems that use fuel dissolved in a liquid have the potential for enhanced safety characteristics, improved fuel-cycle outcomes, and more efficient isotope-production configurations. In these reactor systems, the fueled liquid may simultaneously undergo irradiation, physical and chemical removal processes, and fueling. The modeling and simulation of this transmutation and decay with material additions and removals is an ongoing research area. An accurate simulation tool is critical to the reactor and fuel-cycle design, reactor deployment, and source-term characterization for these advanced reactor systems. The work described herein involved implementing, testing, and applying the capability to perform reactor physics simulations within the Oak Ridge National Laboratory-developed SCALE suite for nuclear systems analyses and design, leveraging much of its pedigree in quality-assurance and reactor-analysis capabilities. The functionalities to simulate irradiation with material feeds and removals had been added in ORIGEN, and the TRITON reactor physics sequence was extended to calculate the total removed material and track external nonirradiated mixtures to estimate separate processing or waste streams. Results from these capabilities align with analytical expectations obtained from ORIGEN for simplified test cases and with expectations for a molten salt reactor application. This implementation, available with the SCALE 6.3 release, provides for a more efficient and accurate material accountability methodology, allowing for the characterization, design, and analysis of the complete isotopic material inventory of advanced liquid-fueled systems for a variety of applications.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A Model for Evaluating the Configuration and Dispatch of PV Plus Battery Power Plants

An open-source model was developed to optimize energy storage operation for photovoltaic- (PV-) plus-battery systems with AC-coupled and DC-coupled configurations. It includes the ability to use forecast energy prices to optimize battery charge and discharge on a rolling time horizon. The model allows for exploration of different configurations, including capital costs, inverter performance, dispatch flexibility, and capturing otherwise clipped energy for the DC-coupled system. The model can run 20 full years of hourly data in approximately two seconds, allowing comparison of a large number of configurations. We applied the model in a test case demonstrating reduced inverter clipping for DC-coupled systems and yielded slightly higher overall value than AC-coupled systems, with an approximately 2 percent increase in internal rate of return or benefit/cost ratio. Our results show that at current estimated prices for lithium-ion battery systems, large-scale PV-plus-battery plants are economically viable under the right conditions, with the configuration playing a role in system flexibility and performance. This model provides the ability for project developers, industry professionals, and researchers to use readily available software to quickly evaluate and design these systems.

41 EE - Solar Energy Technologies Office (EE-4S)↗

Validation of the TOPAS Monte Carlo toolkit for HDR brachytherapy simulations

The goal of this work is to validate the user-friendly Geant4-based Monte Carlo toolkit TOol for PArticle Simulation (TOPAS) for brachytherapy applications. Brachytherapy simulations performed with TOPAS were systematically compared with published TG-186 reference data. The photon emission energy spectrum, the air-kerma strength, and the dose-rate constant of the model-based dose calculation algorithm (MBDCA)-WG generic Ir-192 source were extracted. For dose calculations, a track-length estimator was implemented. Additionally, the four Joint AAPM/ESTRO/ABG MBDCA-WG test cases were evaluated through histograms of the local and global dose difference volumes. A prostate, a palliative lung, and a breast case were simulated. For each case, the dose ratio map, the histogram of the global dose difference volume, and cumulative dose-volume histograms were calculated. The air-kerma strength was (9.772 ± 0.001) × 10 -8 U Bq -1 (within 0.3% of the reference value). The dose-rate constant was 1.1107 ± 0.0005 cGy h -1 U -1 (within 0.01% of the reference value). For all cases, at least 96.9% of voxels had a local dose difference within [-1%, 1%] and at least 99.9% of voxels had a global dose difference within [-0.1%, 0.1%]. The implemented track-length estimator scorer was more efficient than the default analog dose scorer by a factor of 237. For all clinical cases, at least 97.5% of voxels had a global dose difference within [-1%, 1%]. Dose-volume histograms were consistent with the reference data. TOPAS was validated for high-dose-rate brachytherapy simulations following the TG-186 recommended approach for MBDCAs. Built on top of Geant4, TOPAS provides broad access to a state-of-the-art Monte Carlo code for brachytherapy simulations.

59 BASIC BIOLOGICAL SCIENCES↗

Mesh refinement for anisotropic diffusion in magnetized plasmas

Highly accurate simulation of plasma transport is needed to drive the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers that are expensive to resolve. Here, this work investigates how various mesh refinement strategies might reduce that expense to allow for more efficient simulation by comparing standard variable refinement approaches that use a field quantity to an adaptive approach that uses an error estimator. It is first verified that higher order discretization only realizes the proper rate of convergence once the mesh resolves the thin boundary layer, therefore motivating the focusing of refinement on the boundary layer. For three two-dimensional test cases that contain characteristic features of tokamak magnetic fields, an exponential refinement strategy based on the magnetic flux function, which is the standard refinement approach in the field, is compared to an adaptive strategy utilizing the established Zienwiekicz and Zhu error estimator. The adaptive mesh refinement strategy consistently achieves the same accuracy using orders of magnitude less degrees of freedom than either exponential or uniform refinement. This result makes the adaptive refinement strategy more efficient than the exponential refinement strategy while also being more generalizable to problems with complex magnetic geometries. Scaling laws are derived that quantify the improvement in cost of the adaptive refinement strategy over other refinement approaches in 2D and 3D.

97 MATHEMATICS AND COMPUTING↗

Forward sensitivity analysis and mode dependent control for closure modeling of Galerkin systems

Model reduction by projection-based approaches is often associated with losing some of the important features that contribute towards the dynamics of the retained scales. As a result, a mismatch occurs between the predicted trajectories of the original system and the truncated one. We put forth a framework to apply a continuous time control signal in the latent space of the reduced order model (ROM) to account for the effect of truncation. We set the control input using parameterized models by following energy transfer principles. Our methodology relies on observing the system behavior in the physical space and using the projection operator to restrict the feedback signal into the latent space. Then, we leverage the forward sensitivity method (FSM) to derive relationships between the feedback and the desired mode-dependent control. We test the performance of the proposed approach using two test cases, corresponding to viscous Burgers and vortex merger problems at high Reynolds number. Results show that the ROM trajectory with the applied FSM control closely matches its target values in both the data-dense and data-sparse regimes.

97 MATHEMATICS AND COMPUTING↗

Lagrange-Remap strategy for multi-material fluid-solid simulations using compressive limiters

In the present work, the Lagrange-Remap strategy proposed in [1] is extended to multi-material fluid-solid simulations. Both hypo-elastic and hyper-elastic material models are considered to describe the mechanical behavior of the solids. In practice, the deviatoric stress tensor (for hypo-elastic materials) and the left Cauchy-Green tensor (for isotropic hyper-elastic materials) are remapped, while the use of compressive limiters effectively reduces numerical diffusion during the remapping step. The simplicity of this diffuse interface approach is emphasized in the context of multi-material fluid-solid simulations. A series of Lagrange-Remap test cases, involving both solids and fluids, are conducted and compared with reference Lagrangian simulations, demonstrating the robustness and accuracy of the overall numerical strategy.

Compressive limiters↗

Data-driven variational multiscale reduced order models

We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost. The VMS methodology is a natural fit for the hierarchical structure of the ROM basis: In the first step, we use the ROM projection to separate the scales into three categories: (i) resolved large scales, (ii) resolved small scales, and (iii) unresolved scales. In the second step, we explicitly identify the VMS–ROM closure terms, i.e., the terms representing the interactions among the three types of scales. In the third step, we use available data to model the VMS–ROM closure terms. Thus, instead of phenomenological models used in VMS for standard numerical discretizations (e.g., eddy viscosity models), we utilize available data to construct new structural VMS–ROM closure models. Specifically, we build ROM operators (vectors, matrices, and tensors) that are closest to the true ROM closure terms evaluated with the available data. We test the new data-driven VMS–ROM in the numerical simulation of four test cases: (i) the 1D Burgers equation with viscosity coefficient v = 10 -3 ; (ii) a 2D flow past a circular cylinder at Reynolds numbers, Re = 100, Re = 500, and Re= 1000; (iii) the quasi-geostrophic equations at Reynolds number Re = 450 and Rossby number Ro = 0.0036; and (iv) a 2D flow over a backward facing step at Reynolds number Re = 1000. The numerical results show that the data-driven VMS–ROM is significantly more accurate than standard ROMs.

42 ENGINEERING↗

Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting

In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using subcell flux corrections and convex limiting. These methods are based on a subcell flux corrected transport (FCT) methodology that involves blending a high-order target scheme with a robust, low-order invariant domain preserving method that is obtained using a graph viscosity technique. Furthermore, the new low-order discretizations are based on sparse stencils which do not increase with the polynomial degree of the high-order DG method. As a result, the accuracy of the low-order method does not degrade when used with high-order target methods. The method is applied to both scalar conservation laws, for which the discrete maximum principle is naturally enforced, and to systems of conservation laws such as the Euler equations, for which positivity of density and a minimum principle for specific entropy are enforced. Numerical results are presented on a number of benchmark test cases.

97 MATHEMATICS AND COMPUTING↗

A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems

This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. In conclusion, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field.

97 MATHEMATICS AND COMPUTING↗

$\mathrm{IH}$-$\mathrm{GAN}$: A conditional generative model for implicit surface-based inverse design of cellular structures

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignoring the effects of unit cell geometry on properties, or considers the geometry–property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from properties to geometries. Here we further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (R 2 -scores between target properties and properties of generated unit cells >98%) and 2) improve the optimized structural performance over the conventional variable-density single-type structure. In the minimum compliance example, our IH-GAN generated structure achieves a 79.7% reduction in concentrated stress and an extra 3.03% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 86.4% and 79.6% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending.

42 ENGINEERING↗

Non-intrusive reduced-order modeling for dynamical systems with spatially localized features

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.

42 ENGINEERING↗

A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM

Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.

Automatic differentiation↗

Preheating and premixing effects on NO x emissions in a high-pressure axially staged combustor

NO x emissions remain a primary concern for modern and future gas turbines, particularly as we progress towards a net-zero carbon future. It is critical to identify novel strategies to mitigate environmental pollutants for both modern turbines operated on natural gas and future turbines projected to use carbon-free fuels (such as hydrogen). In the current study, NO x emissions of a reacting methane-air jet in a vitiated crossflow are experimentally investigated in a model axially staged combustor at 5 atm. The combustion products from the main stage combustor flow into the axial stage at temperatures ranging from 1580 to 1650 °C. The axial stage contains a reacting jet in crossflow, which provides an overall temperature rise ranging from 50 to 220 °C to generate exit temperatures similar to gas turbine engines. The focus of this paper is to explore the effects of flame liftoff and ignition timescales on the NO x contribution of this secondary jet. This is done by varying the premixed level and preheat temperature of the axial jet. The effects are explored at different momentum flux ratios (J), jet equivalence ratios (φ jet ), exit temperatures (T exit ), and main stage (headend) temperatures (T HE ). High-speed CH* chemiluminescence imaging is employed for each test case to determine the flame stabilization point. For a given temperature rise and combustor exit temperature, an increase in ignition delay was observed with a decrease in jet temperature. This provided a NO x benefit, particularly for jets that are injected at or close to an ignitable mixture fraction. Similarly, the coaxial injector caused a significant ignition delay compared to the fully premixed injector; this also led to a NO x benefit. Overall, the results show that a thermally driven delay in the axial stage provides a greater NO x reduction than a mixing delay.

03 NATURAL GAS↗