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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Surrogate models for plasma displacement and current in 3D perturbed magnetohydrodynamic equilibria in tokamaks

Abstract A numerical database of over one thousand perturbed three-dimensional (3D) equilibria has been generated, constructed based on the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) computed plasma response to the externally applied 3D field sources in multiple tokamak devices. Perturbed 3D equilibria with the n = 1–4 ( n is the toroidal mode number) toroidal periodicity are computed. Surrogate models are created for the computed perturbed 3D equilibrium utilizing model order reduction (MOR) techniques. In particular, retaining the first few eigenstates from the singular value decomposition (SVD) of the data is found to produce reasonably accurate MOR-representations for the key perturbed quantities, such as the perturbed parallel plasma current density and the plasma radial displacement. SVD also helps to reveal the core versus edge plasma response to the applied 3D field. For the database covering the conventional aspect ratio devices, about 95% of data can be represented by the truncated SVD-series with inclusion of only the first five eigenstates, achieving a relative error (RE) below 20%. The MOR-data is further utilized to train neural networks (NNs) to enable fast reconstruction of perturbed 3D equilibria, based on the two-dimensional equilibrium input and the 3D source field. The best NN-training is achieved for the MOR-data obtained with a global SVD approach, where the full set of samples used for NN training and testing are stretched and form a large matrix which is then subject to SVD. The fully connected multi-layer perceptron, with one or two hidden layers, can be trained to predict the MOR-data with less than 10% RE. As a key insight, a better strategy is to train separate NNs for the plasma response fields with different toroidal mode numbers. It is also better to apply MOR and to subsequently train NNs separately for conventional and low aspect ratio devices, due to enhanced toroidal coupling of Fourier spectra in the plasma response in the latter case.

3D equilibrium↗
DOE OSTI2022

A New Model for Simulating the Imbibition of a Wetting-Phase Fluid in a Matrix-Fracture Dual Connectivity System

The imbibition experiment is an effective approach for measuring petrophysical properties of porous media, with many such experiments performed over the past decade. Quite some empirical, analytical, and numerical models have been developed to simulate spontaneous imbibition of the wetting phase fluid into porous media, but limitations still exist. In previous studies, the imbibition process has been considered to give a piston-like displacement or the porous medium modeled as multiply-sized pores linked with bonds; both approaches fail to yield comprehensive results due to their neglect of the presence of irregular fractures or nonuniform flow paths through the matrix. By building a numerical model for simulating laboratory-scale experimental data, we performed imbibition tests on several fractured Barnett Shale samples having fractures either parallel ( P ) or transverse ( T ) to the bedding plane and used MATLAB to build a new numerical model by combining the imbibition process in fractures and the matrix using concepts from percolation theory. The experimental data show that the rocks with P -direction fractures have a more steady increase of imbibition rates than the case of T -direction one. As the shale matrix with low pore connectivity hampers the upward water movement, the imbibition rate of shales with T -direction fractures will decrease suddenly after the bottom layer in contact with water is saturated during the initial period. This wetting phase movement (WPM) model can simulate 3D porous media with 2D fractures. The rate of imbibition by fractured porous media is associated with physical parameters such as porosity and fracture distribution (e.g., the number and angle of fractures). Using Monte Carlo methods, we examined fracture parameters and predicted elapsed time and cumulative water imbibition, for the Barnett Shale samples. The results show that the rate of imbibed water mass is sensitive to the number of fractures directly connected to water source, and the connectivity between two neighboring grid cells is a key parameter for the wetting-front progression. The findings of this study can help to better understand the imbibition process with multiple influencing processes and factors in fractured-matrix rocks. Although the experiments, data simulation, and prediction results are based only on Barnett Shale samples, the model is readily applicable to imbibition tests of other fractured rocks to show the spatial and temporal behavior during a dynamic imbibition process that are not easily captured experimentally.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Electromagnetic duality and D3-brane scattering amplitudes beyond leading order

We use on-shell methods to study the non-supersymmetric and supersymmetric low-energy S-matrix on a probe D3-brane, including both the 1-loop contributions of massless states as well as the effects of higher-derivative operators. Our results include: (1) A derivation of the duality invariance of Born-Infeld electrodynamics as the dimensional oxidation of the group of spatial rotations transverse to a probe M2-brane; this is done using a novel implementation of subtracted on-shell recursion. (2) The first explicit loop-level BCJ double-copy in a non-gravitational model, namely the calculation of the 4-point self-dual amplitude of non-supersymmetric Born-Infeld. (3) From previous results for n-point self-dual 1-loop BI amplitudes and the conjectured dimension-shifting relations in Yang-Mills, we obtain an explicit all-multiplicity, at all orders in E, expression for the 1-loop integrand of the MHV sector of N = 4 DBI. (4) For all n > 4, the explicitly integrated duality-violating 1-loop amplitudes (self-dual and next-to-self-dual in pure BI as well as MHV in N = 4 DBI) are shown to be removable at O(ε 0 ) by adding finite local counterterms; we propose that this may be true more generally at 1-loop order. (5) We find that in non-supersymmetric Born-Infeld, not all finite local counterterms needed to restore electromagnetic duality can be constructed using the double-copy with higher-derivative corrections, suggesting a fundamental tension between electromagnetic duality and color-kinematics duality at loop-level. Finally we comment on oxidation of duality symmetries in supergravity and the parallels it has to the M2-brane to D3-brane oxidation demonstrated in this paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

DECOVALEX-2023: Task F1 Final Report

DECOVALEX-2023 Task F is a comparison of models and methods for post-closure performance assessment (PA) of a deep geologic repository for radioactive waste. The general aims of Task F are to build confidence in the models, methods, and software used for PA and to stimulate additional research and development in PA methodologies. The task objectives are to motivate development of PA modelling skills and capabilities, to examine the influence of model choices on calculated repository performance, and to compare the uncertainties introduced by model choices to other sources of uncertainty. Task F involves no actual experiment or site. It is a PA modelling exercise that requires the conceptual development of hypothetical repository designs and geologic settings. Because three of the teams were interested in salt and the rest of the teams were interested in crystalline rock, Task F was split into two branches: Task F1 for crystalline rock and Task F2 for salt. This report is for Task F1, crystalline rock. Teams from seven countries (Canada, Czech Republic, Germany, Korea, Sweden, Taiwan, and United States) participated in Task F1. The teams worked together to define the features, events, and processes of the reference case repository and established a set of performance measures. In addition, they defined a set of benchmark problems designed to test and compare modelling capabilities for fracture flow and transport at different scales. The repository design and benchmark problems are documented in a Task Specification that evolved over time as the group honed the specifications. The benchmark problems verified that each team can aptly model flow and transport in fractured media in 1-, 2-, and 3-dimensions. Two general approaches were used for the 3-dimensional benchmarks: discrete fracture network (DFN) and equivalent continuous porous medium (ECPM). DFN modelling involves explicit meshing of each fracture while ECPM modelling aims to capture the effective porosity and directional permeability of each cell in a space-filling mesh as affected by intersecting fractures. In some models, a combination of the two is used, i.e., DFN for large known fractures and ECPM for the rest of the domain. Transport is solved by using either the advection-dispersion equation or particle tracking. Although some variation is observed among model breakthrough curves in the benchmark problems, there is strong agreement in breakthrough behaviour up to at least the 75 th percentile for all benchmarks. At the 90 th percentile, breakthrough results show larger differences, suggesting several models retain substantially higher fractions of tracer in regions of slower moving water. In addition to the flow and transport benchmarks, several teams completed the source term benchmark, verifying capabilities for modelling radionuclide decay and ingrowth, waste package breach, instant release fractions, fuel matrix degradation rates, and radionuclide solubility limitations. The reference case is conceptualized as a generic spent fuel repository at a depth of 450 m in fractured crystalline rock. The repository has 50 parallel backfilled drifts, each with 50 deposition holes 6 m apart. Each deposition hole contains a 4-PWR waste package and bentonite buffer. The rock domain is 5 km in length, 2 km in width, and 1 km in depth. It has 6 deterministic fractured deformation zones and a multitude of stochastic fractures. Teams generally used the ECPM approach for the entire rock or a hybrid approach in which the deterministic fracture zones are modelled with a DFN and the rest of the rock is modelled by ECPM. Of the reference case problems specified, only the results of the initial reference case problem are compared in this report. The initial problem focuses on transport from the deposition holes to the surface, i.e., it neglects waste package performance. Tracers are released at all waste package locations at time zero and tracked for their releases to the near field and ground surface. The water fluxes calculated at the ground surface entry and exit regions of the domain are similar for all models except for two that have considerably lower fluxes. For tracer transport, large differences are observed among models in the magnitude of tracer transported. Much of the difference appears to be due to how the repository is implemented and hence the different degrees of repository simplification. Models that exclude the drifts, buffer, and backfill from the domain tend to show greater release of tracers and radionuclides from the repository. The initial study presented here indicates that major differences in modelling important processes within the repository (e.g., diffusion through buffer and backfill) can produce broadly different release and transport results, especially when those processes are excluded. Even for the models that included all specified features, events, and processes, the results show significant differences and demonstrate the importance of examining multiple modelling approaches in performance assessment. The differences in results observed in this study are expected to motivate teams to either increase complexity in future versions of the reference case models or to improve methods to account for the effects of simplified features and processes. Either way, future improvements in these models are expected to produce results that more closely agree.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Linear and Nonlinear Solvers for Simulating Multiphase Flow within Large-Scale Engineered Subsurface Systems

Simulation of multiphase flow in the subsurface is well-known to be computationally challenging. While there have been many studies that have explored approaches to overcoming these challenges, they often utilize relatively simple case studies. In this paper, we focus on the unique numerical challenges posed by modeling large-scale engineered subsurface systems, characterized by discrete features embedded in a heterogeneous natural subsurface setting. The man-made features such as shafts, tunnels, and barriers often cause multiple challenges in modeling the domain for multiphase porous media flow. This flow scenario can have a wide range of applications such as nuclear waste repositories, enhanced recovery of a petroleum reservoir, geothermal engineering, and carbon sequestration. An example of these severe numerical challenges is the case of performance assessment (PA) for Waste Isolation Pilot Plant (WIPP), the only operating deep geological repository in the US, which simulates extreme material properties of bedded salt rock formation and extreme contrast due to open excavation next to the formation. The models have extremes not only of permeability and porosity but also of the constitutive models needed for multiphase flow; additionally, they have process models like salt creep closure reducing porosity over time, fracturing in clay and anhydrite interbeds of the bedded salt, gas generation from the waste materials, and unintentional human borehole intrusions in some scenarios. Numerical simulations require the solution of coupled systems of nonlinear PDEs; in our work, we use the open-source simulator PFLOTRAN which is based on Finite Volume discretization. The solution of the nonlinear equations requires use of the Newton-Raphson iteration at each time step, which entails the solution of the linearized Jacobian system at each iteration. The effects of all the processes (i.e., large number of unknowns, highly nonlinear constitutive relations, large contrasts in material properties in short distances) lead to an ill-conditioned Jacobian matrix that severely challenges traditional linear solver, i.e., stabilized biconjugate gradient with block Jacobi incomplete LU preconditioner (BCGS-ILU) leading to non-convergence for traditional Newton-Raphson nonlinear solver causing unacceptably long computation time for each model. This paper presents linear solvers such as constrained pressure residual (CPR) two-stage preconditioner with alternate-block-factorization (ABF) and quasi- implicit pressure and explicit saturation (QIMPES) decouplers and flexible generalized residual solver (FGMRES). The new general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), is also introduced to resolve extreme nonlinearities in the models. We demonstrate the effectiveness of each method relative to the default BCGS-Newton solver. The two best cases had nearly 50 times speed-up and achieved completion of a simulation in 14 hours that never completed due to non-convergence with the default solver. We also investigate the strong scalability of each method and discuss some of the deficiencies found for Block Jacobi preconditioner using parallel domain decomposition, and node packing effects of modern processor architecture.

Preconditioner, Nonlinear, Porous media, Multiphas↗
DOE OSTI2021

Development of NDE/NDT Tools for High-Volume & High-Speed Inspection of CFRP Structures in Automotive Manufacturing

Main advantages of the air-coupled ultrasound testing (ACUT) and electromagnetic testing (EMT) techniques for NDE of CFRP composites were non-contact sensing, scalability for high-speed inspection, cost-effectiveness, and non-hazardous operation. Despite these advantages, no systems that would satisfy the project requirements were commercially available. Hence, one of the major efforts of the Michigan State University (MSU) team at the initial stage of the project was to close this technological gap by developing, optimizing, and validating array sensors that would provide sufficient sensitivity, spatial coverage, and resolution for robust defect detection. Optimization of the ACUT and EMT sensor designs was performed using experimentally validated finite element models. Initial experiments using array probes were conducted on relatively flat CFRP samples. In parallel, the MSU team designed and assembled a portable platform with two robotic arms. The robots were equipped with newly designed sensors that enabled high-speed NDE of curved CFRP parts. Presently, the developed robotic platform can be used as a demo/template NDE system, which is easily adaptable to manufacturing environments and in-line NDE. The ACUT NDE system developed by the MSU team used a high-power 4-channel pulser receiver for parallel data acquisition. The array probes were designed by stacking commercially available ACUT transducers, which operated in the frequency range between 100 kHz and 500 kHz. MSU optimized the excitation procedure and developed wave focusing cones so as to reduce the crosstalk between the transducers and to provide higher pulse repletion frequency (PRF). The through-transmission (TT) and single-side access (SSA) inspection modes were successfully implemented. In the TT-ACUT, structural defects in CFRP were detected by passing ultrasonic waves through the test part. Hence, the ACUT transmitters and receivers needed to be placed on the opposite sides of the test part. In the SSA-ACUT, guided waves (GW) were excited in the test part using the transmitters and were sensed by the receivers from the same side. Multi-channel TT-ACUT and SSA-ACUT provided high-speed NDE, and were successfully validated on CFRP test samples with interlaminar delaminations and other embedded defects The EM techniques developed by the MSU team included: 1) eddy current testing (ECT), 2) capacitive imaging (CI) and hybrid dual-mode imaging. In ECT, structural damage was detected in CFRP using coils sensor arrays. In ECT, the excitation magnetic field is generated by passing an alternating current through a coil, which is placed above the test sample. The excitation field penetrates the conductive sample and induces the eddy currents in its transect. In turn, the eddy currents generate the reaction field, which affects the total field sensed by a coil. Hence, the presence of structural flaws will alter the eddy current flow and the picked-up signal. ECT is mostly sensitive to local changes of the electric conductivity of the test sample, and CFRPs are mostly conductive in the direction of carbon fibers. Hence, ECT was well suited for the detection of fiber damage/fiber irregularities. The MSU team developed printed circuit boards (PCB) with coil sensor arrays optimized for NDE of CFRP. Unlike most commercial probes designed for ECT of metallic structures, the MSU array probes were designed for operation in [1-10] MHz frequency range, which was optimal for low-conductive CFRP. Multiple sensing topologies (coil groups excitation/sensing arrangements) were implemented and successfully validated. Capacitive Imaging (CI) technique developed by MSU was complementary to ECT. In contrast to ECT, which was sensitive to local changes of the electrical conductivity, the CI was sensitive to local changes of the dielectric constant. Therefore, CI could provide information about matrix damage/matrix irregularities in CFRP. The MSU CI sensor arrays were made of multiple circular or rectangular open-plate capacitors printed on PCB. Sensors of this type are not commercially available. In addition to ECT and CI, the MSU team developed a hybrid (dual-mode) inductive/capacitive measurement technique that synergistically combined the benefits of inductive and capacitive sensing for rapid NDE of fiber reinforced polymer (FRP) composite structures. Fiber damage and fiber irregularities in FRPs were detected by configuring hybrid sensors as coil sensors. Similarly, matrix damage, matrix irregularities and interlaminar delaminations were detected by configuring hybrid sensors as capacitive sensors. ECT and CI were performed sequentially by means of electronic switching. Hence, eliminating the need for mounting two separate sensor arrays on the probe. Portable robotic platform was developed by MSU for multi-technique high-speed NDE of CFRP test parts. The platform had two 6-axis robots, which enabled inspection of curved parts in approximately a 6×6×6 ft 3 active scan area. On the software side, the MSU team integrated scripts for NDE hardware control with scripts for robot motion control. MSU also implemented automated path planning for the robots, reconstruction of part’s surfaces via stereovision, 3D rendering of inspection data, and image processing algorithms for enhanced defect detection. Automotive composite parts manufactured by Plasan Composites from Phase I were used to validate the ACUT and EMT techniques on representative testbeds. Among those parts were three X-braces for a Dodge Viper, one composite calibration plaque with known defects at known locations, and four other test sections, including sections from a front splitter, a corner section from a composite hood, and a high-pressure RTM panel made using non crimp fabric. Other test samples included CFRP and GFRP calibration plates with fiber/matrix defects fabricated at MSU/CVRC.

36 MATERIALS SCIENCE↗