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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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Parametric model-order reduction for radiation transport using multi-resolution proper orthogonal decomposition

For parametric high-fidelity simulations, it is often desirable to utilize a reduced-order model (ROM) to emulate, at a reduced computational cost, parametric solutions of the governing partial differential equations (PDEs) for unseen parameter values. One commonly employed option is to utilize a data-driven, projection-based ROM supplemented with subspace identification via proper orthogonal decomposition (POD). POD discovers the ROM subspace by computing the singular value decomposition (SVD) of a set of training data from the full-order model (FOM). In streaming-dominated radiation transport simulations with localized sources, solutions often greatly vary over the spatial domain by many orders of magnitude. In such cases, machine-precision arithmetic can be insufficient to obtain an accurate SVD, resulting in a poorly performing ROM. We present a method called multiresolution POD (mrPOD) that mitigates these inaccuracies. The mrPOD method works by decomposing the spatial domain into regions and performing proper orthogonal decomposition on the training dataset separately in each region. In conclusion, mrPOD is tested on single energy group and multigroup atmospheric shielding transport problems and is shown to outperform classic POD.

42 ENGINEERING↗

Latent Space Dynamics Identification

LaSDI is a data-driven physical simulation software that forms a latent space for a given high-fidelity model and discovers a set of ordinary differential equations for the latent space dynamics. It allows a fast and accurate solution process, which is useful for multi-query decision making applications, such as design optimization and uncertainty quantification. The performance of the LaSDI framework is demonstrated on four different problems, i.e., 1D and 2D Burgers equations, nonlinear heat conduction, and radial advection problems. Both linear and nonlinear compression techniques, such as neural network and proper orthogonal decomposition, are used to form a latent space. A concept of local dynamics identification procedure is introduced to enable a parametric model, which enhances the accuracy level over a given parameter space.

Fries, William↗

VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

Conditional VAEs↗

Conservative projection-based data-driven model order reduction of a fluid-kinetic spectral solver

Kinetic simulations are computationally intensive due to six-dimensional phase space discretization. Many kinetic spectral solvers use the asymmetrically weighted Hermite expansion due to its conservation and fluid-kinetic coupling properties, i.e., the lower-order Hermite moments capture and describe the macroscopic fluid dynamics, and higher-order Hermite moments describe the microscopic kinetic dynamics. We leverage this structure by developing a parametric data-driven reduced-order model based on the proper orthogonal decomposition, which projects the higher-order kinetic moments while retaining the fluid moments intact. We demonstrate analytically and numerically that the method ensures local and global mass, momentum, and energy conservation. The numerical results show that the proposed method effectively replicates the high-dimensional spectral simulations at a fraction of the computational cost and memory, as validated on the weak Landau damping and two-stream instability benchmark problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Local reduced-order modeling for electrostatic plasmas by physics-informed solution manifold decomposition

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.

Electrostatic plasmas↗

Parametric reduced-order modeling for component-oriented treatment and localized nonlinear feature inclusion

Abstract We propose coupling a physics-based reduction framework with a suited response decomposition technique to derive a component-oriented reduction (COR) approach, which is suitable for assembly systems featuring localized nonlinearities. Dependencies on influencing parameters are injected into the reduced-order model (ROM), thus ensuring robustness and validity over a domain of parametric inputs, while capturing nonlinear effects. The implemented approach employs individual component modes to capture localized features while additionally relying on reduced modes of a global nature to approximate the system’s dynamics accurately. The global modes are derived from a linear monolithic system, defined as a result of a coordinate separation scheme, which permits the proposed COR-ROM to naturally couple the response between linear and nonlinear subdomains. The derived low-order representation utilizes a proper orthogonal decomposition projection and is additionally reinforced with the inclusion of a hyper-reduction technique to capture the underlying high-fidelity model response while providing accelerated computations. The resulting approach is exemplified in the synthetic case studies of a four-story shear frame with multiple nonlinear regions driven by hysteresis and a large-scale kingpin connection featuring plasticity.

Vlachas, Konstantinos (ORCID:000000029124219X)↗

Augmented reduced order models for turbulence

The authors introduce an augmented-basis method (ABM) to stabilize reduced-order models (ROMs) of turbulent incompressible flows. The method begins with standard basis functions derived from proper orthogonal decomposition (POD) of snapshot sets taken from a full-order model. These are then augmented with divergence-free projections of a subset of the nonlinear interaction terms that constitute a significant fraction of the time-derivative of the solution. The augmenting bases, which are rich in localized high wavenumber content, are better able to dissipate turbulent kinetic energy than the standard POD bases. Several examples illustrate that the ABM significantly out-performs L 2 -, H 1 - and Leray-stabilized POD ROM approaches. The ABM yields accuracy that is comparable to constraint-based stabilization approaches yet is suitable for parametric model-order reduction in which one uses the ROM to evaluate quantities of interests at parameter values that differ from those used to generate the full-order model snapshots. Several numerical experiments point to the importance of localized high wavenumber content in the generation of stable, accurate, and efficient ROMs for turbulent flows.

Kaneko, Kento↗

On the interaction of a wind turbine wake with a conventionally neutral atmospheric boundary layer

In this work, we investigate the dynamics of wind turbine tip-vortex breakdown in a conventionally neutral atmospheric boundary layer (ABL). To this end, high-resolution data are collected from large-eddy simulations of a wind turbine operating within a neutral ABL and studied by means of proper orthogonal decomposition (POD) and Fourier analysis. The high resolution of the generated data in both space and time allows us to gain insight into the tip-vortex breakdown mechanisms by (i) capturing the energy modes of the coherent structures, (ii) studying their contribution to the tip-vortex breakdown through their power spectra functions and mean kinetic energy (MKE) flux, and (iii) analysing the growth rate of each contributing perturbation frequency along tip vortices. Our analysis shows that under a fully turbulent scenario, the growth rate of perturbations along the tip vortices is largest for low wave numbers, i.e. long-wave perturbations. Additionally, the MKE flux reaches its highest value at two diameters downstream of the rotor plane, a behaviour that can be attributed to the coexistence of multiple interacting POD modes, with the streamwise vortex roller mode being the primary contributor to the total MKE flux budget, contributing approximately . Finally, comparisons with a laminar, uniform flow scenario subject to a single-frequency perturbation highlight the differences between the two ambient flow conditions. In the non-turbulent, uniform flow scenario, the growth rate attains its maximum value at a wave number corresponding to the out-of-phase mutual-inductance mechanism, whereas the MKE flux exhibits local minima and maxima along the wake and at different downstream locations depending on the perturbation frequency. Our analyses suggest that the breakdown of the wind turbine tip vortices under a fully turbulent neutral ABL inflow is due to complex interactions across a range of excitation frequencies, in which the mutual-inductance instability may not be the dominant one.

17 WIND ENERGY↗

Do ambient shear and thermal stratification impact wind turbine tip-vortex breakdown?

Modern wind turbines experience uneven inflow conditions across the rotor, due to the ambient flow’s shear and thermal stratification. Such conditions alter the shape and length of turbine wakes and thus impact the loads and power generation of downstream turbines. To this end, understanding the spatial evolution of the individual wakes under different atmospheric conditions is key to controlling and optimising turbine arrays. With this numerical study we aim to obtain a better understanding of the fundamental physics governing the near-wake dynamics of wind turbines under shear and thermal stability, by examining their tip-vortex breakup mechanisms. Our approach considers scale-resolving simulations of a single turbine wake under a linear shear profile as well as the application of harmonic tip perturbations to trigger flow instabilities. For the subsequent analysis we use the proper orthogonal decomposition (POD) method to extract coherent structures from the flow, and we also calculate mean kinetic energy fluxes to quantify each coherent structure’s contribution to wake recovery. The wake’s helical spiral is found to hinder wake recovery for all studied ambient flow conditions, whereas the mutual inductance instability has positive MKE flux leading to an enhanced wake recovery. Finally, the ambient shear has the largest impact on the local MKE flux with respect to downstream location by changing the shape of the curve and location of extrema, whereas thermal stratification has only a minimal impact on the magnitude of the near-wake local MKE flux distribution.

17 WIND ENERGY↗

Greedy emulators for nuclear two-body scattering

Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. Here, in this paper, we develop, implement, and test two model-driven emulators based on the (Petrov-)Galerkin projection using the prototypical test case of two-body scattering with the Minnesota potential and a more realistic local chiral potential. The high-fidelity scattering equations are solved with the matrix Numerov method, a reformulation of the popular Numerov recurrence relation for solving special second-order differential equations as a linear system of coupled equations. A novel error estimator based on reduced-space residuals is applied to an active learning approach (a greedy algorithm) to choosing training samples (“snapshots”) for the emulator and contrasted with a proper orthogonal decomposition (POD) approach. Both approaches allow for computationally efficient offline-online decompositions, but the greedy approach requires many fewer snapshot calculations. These developments set the groundwork for emulating scattering observables based on chiral nucleon-nucleon and three-nucleon interactions and optical models, where computational speed-ups are necessary for Bayesian uncertainty quantification. Our emulators and error estimators are widely applicable to linear systems.

Bayesian methods↗

Neutron diffusion calculation in heterogeneous geometry based on local/global iteration using proper orthogonal decomposition

This study newly proposes a heterogeneous core calculation method based on local/global iteration using proper orthogonal decomposition (POD). By using the singular value decomposition (SVD) and the low-rank approximation, appropriate POD bases for expanding the neutron flux can be obtained from snapshot data of the neutron flux obtained by fine mesh calculations. By projection using the POD bases, the dimension of the target equation (e.g., discretized neutron diffusion equation) can be dramatically reduced. In the proposed method, POD is effectively applied to each single assembly calculation (local calculation). Furthermore, using the local/global iteration, the effective neutron multiplication factor and the neutron flux distribution in the whole core geometry can be obtained by combining the numerical results of the local calculation for each fuel assembly and the global calculation for the whole core. As a feasibility study, the proposed method is applied to a one-dimensional heterogeneous core analysis, and the accuracy is investigated by changing the total number of POD bases. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Anomalous compressible mode generation by global frame projections of pure Alfven mode

Alfven wave is the single most important physical phenomenon of magneto-hydrodynamic turbulence and has far-reaching impact to almost all studies related to astrophysical magnetic field. Yet the restoration of the Alfven wave fluctuations from a given magnetic field, aka the local Alfven wave problem, is never properly addressed in literature albeit its importance. Previous works model the Alfven wave fluctuation as the perturbation along a straight-line, constant magnetic field. However, Lazarian & Pogosyan (2012) suggested that the decomposition of Alfven wave along a straight line, aka. the global frame decomposition, has a factor of discrepancy to the true local Alfven wave fluctuation. Here, in this paper, we provide a geometric interpretation on how the local Alfven wave is related to the global frame through the use of vector frame formulation. We prove both analytically and numerically that the local frame Alfven wave is an orthogonal transformation of that of the global frame and related by the local Alfvenic Mach number. In other words, when we observe Alfven wave in the global frame of reference, some of the Alfven wave will be mistaken as compressible waves. The importance of frame choices have a far-reaching impact to the analytical studies of MHD turbulence. Combining the frame formalism and the new techniques we can have accurate measurement to some of the fundamental turbulence properties like the inclination angle of mean magnetic field relative to the line of sight.

79 ASTRONOMY AND ASTROPHYSICS↗

Machine Learning Assisted Safety Modeling and Analysis of Advanced Reactors

With the advances in computational power and numerical methods, analysts can now rely on first-principle simulations to predict ultra-fine details in a variety of applications. Advances in machine learning (ML) have produced algorithms that can now learn high-level abstractions via hierarchical models. This project aims to leverage advances in ML techniques and the available high-resolution simulation data to develop a novel modeling and simulation (M\&S) methodology for reactor safety analysis. While application-agnostic ML techniques are available, complex physics constraints need to be incorporated into ML techniques to build ML-based closures for computationally efficient predictive simulations. This project intends to develop a physics-guided data-driven multi-scale methodology for M\&S of advanced reactors. The project focuses on thermal fluid (T/F) phenomena, which play major roles in advanced reactor safety. Specifically, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor (SFR). The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data with Reynolds-averaged Navier-Stokes (RANS) turbulence model to ensure accuracy. Three different neural networks are developed and tested for loss-of-flow transients in the hot pool of SFR, i.e. the densely connected convolutional neural network (DCNN), long-short-term-memory network based on proper orthogonal decomposition (POD-LSTM), and the DCNN informed by LSTM (DCNN-LSTM). The performances of these three neural networks are evaluated based on baseline models. The DCNN-LSTM model has been chosen for further hyperparameter optimization. Furthermore, based on a simplified two-dimensional case, uncertainty quantification (UQ) of the developed ML-based closure are investigated with three methods, i.e. Monte Carlo dropout, deep ensemble, and Bayesian neural network. The developed ML-based turbulent viscosity closure relation based on deep ensemble is then integrated into the system analysis module SAM and serves as a term in the conservation equations. Such a SAM-ML based procedure guarantees that the obtained results are consistent with the physical constraints of the thermal-fluid system. The SAM-ML simulation on the same loss-of-flow transient showed comparable accuracy with the CFD simulation but with a much coarser mesh setup. Last but not least, the ML-based closure improvement with the support of higher-fidelity data from large eddy simulation (LES) is discussed. As a first step towards this direction, a baseline LES simulation is performed to obtain comparable data with RANS results. Based on the early results, future investigation on further improving the ML-based closure is discussed. We believe the developed approach that combines scientific machine learning with nuclear system analysis code can benefit the advanced reactor community as more accurate safety analyses will better characterize reactor safety margins and reduce licensing efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Flow structures of the cross-flow over a five-layer helically coiled steam generator geometry

The helically-coiled heat exchanger (HCSG) offers advantages over straight tubes such as compactness in geometry, increased heat transfer coefficients, and capability to absorb thermal expansion. In this study, the time-resolved velocity field data of shell-side crossflow over a five-layer helically coiled steam generator geometry was obtained using Particle Image Velocimetry (PIV) between adjacent rods in four regions with up to 5000 frames per second (5 kHz) at approximately Re u = 3600. The slant rod bundle created different flow patterns in different regions. Proper Orthogonal Decomposition (POD) revealed high-energy-mode flow structures. Due to the confined flow channel geometry, the large flow structures were not advected resulting in no strong POD mode paring. Continuous Wavelet Transform (CWT) visualized the characteristics of flow fluctuation in time and frequency domain simultaneously, which ranged in Strouhal number, S u , between 0.03 and 1.17. In the wake regions of the rods, flows changed in both pattern and magnitude over time. Once a pattern formed, it continued for relatively shorter than straight tube arrays, before changing the pattern again. The histograms of the POD time coefficients presented this multimodal flow characteristics. The current study focuses more on whole flow field analyses in the selected regions rather than local point-wise analyses. Finally, this study revealed that various Strouhal numbers can exist in the helically coiled heat exchanger geometry, which was not observed in straight tube arrays. In particular, Strouhal numbers smaller than 0.1 do not seem to be caused by vortex shedding but seem to be the result of the combination of complex geometry and possible multimodal trends. Based on the current observation, further works would involve intensive instantaneous point-wise analyses on the interactions between important locations such as separation points, stagnation points, shear layers, etc.

42 ENGINEERING↗

Turbulent flow characteristics in an 84-pin rod bundle for typical and damaged spacer grids

Hexagonal rod bundles arranged in a tightly packed triangular lattice are extensively used for heat transfer and energy generation applications. Staggered spacer grids are used to maintain the structural integrity of gas-cooled fast reactor (GFR) fuel assemblies, while inducing localized turbulence in flow. Damage to these spacer grids results in a disruption of flow fields within these hexagonal fuel bundles. Experimental flow visualizations are critical to identify the differences in local flow properties that the structural damage may cause. This experimental research investigates the flow-field characteristics at a near-wall and center plane in a prototypical 84-pin GFR fuel assembly. Newly installed typical spacers and spacers subject to naturally occurring damage due to material degradation over prolonged experimentation were investigated. Velocity fields were acquired by utilizing the matched-index-of-refraction method to obtain time-resolved particle image velocimetry measurements for a Reynolds number of 12 000. Reynolds decomposition statistical results divulged differences in the time-averaged velocity, velocity fluctuations, flow anisotropy, and Reynolds stress distributions. Galilean decomposition demarcated the influence of spacer grid damage on the velocity fields. To extract turbulent structures and elucidate mechanisms of flow instabilities, proper orthogonal decomposition analysis was employed. Reduced order flow reconstructions enabled the application of vortex identification algorithms to determine the spatial and statistical characteristics of vortices generated. This research work provides unique experimental data on the spacer grid condition-dependent flow. The results offer a deeper understanding of fluid dynamics behavior to support GFR rod bundle design efforts and computational fluid dynamics model validation.

36 MATERIALS SCIENCE↗