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DOE OSTI2018

An effective numerical algorithm for intra-granular fission gas release during non-equilibrium trapping and resolution

Both fission gas release and gaseous swelling in nuclear fuel are driven by the transport of fission gas from within the fuel grains to grain boundaries (intra-granular fission gas release). The process involves gas atom diffusion in conjunction with trapping in and resolution from intra-granular bubbles, and is described mathematically by a system of two partial differential equations (PDE). Following Speight, under the assumption of equilibrium between trapping and resolution (quasi-stationary approximation) the system can be reduced to a single diffusion equation with an effective diffusion coefficient. Numerical solutions used in engineering fuel performance calculations invariably rely on this simplification. First, we investigate the validity of the quasi-stationary approximation compared to the solution of the general system of PDEs. Results demonstrate that the approximation is valid under most conditions of practical interest, but is inadequate to model intra-granular fission gas release during rapid transients to relatively high temperatures such as postulated reactivity initiated accidents (RIA). Then, we develop a novel numerical algorithm for the solution of the general problem in time-varying conditions. We verify the PolyPole-2 algorithm against a reference finite difference solution for a large number of randomly generated operation histories including prototypical RIA transients. Results demonstrate that PolyPole-2 captures the solution of the general PDE system with a high accuracy and a low computational cost. As a result, the PolyPole-2 algorithm overcomes the quasi-stationary approximation and the concept of an effective diffusion coefficient for the solution of the intra-granular fission gas release problem in nuclear fuel analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials

Under compressive creep, viscoplastic solids experiencing internal mass transfer processes can accommodate singular cnoidal wave solutions as material instabilities at the stationary wave limit. These instabilities appear when the loading rate is significantly faster than the material's capacity to diffusive internal perturbations, leading to localized failure features (e.g., cracks and compaction bands). These cnoidal waves, generally found in fluids, have strong nonlinearities that produce periodic patterns. Due to the singular nature of the solutions, the applicability of the theory is currently limited. Additionally, practical simulation tools require proper regularization to overcome the challenges that singularity induces. We focus on the numerical treatment of the governing equation using a nonlinear approach building on a recent adaptive stabilized finite element method. This automatic refinement method provides an error estimate that drives mesh adaptivity, a crucial feature for the problem at hand. We compare the performance of this adaptive strategy against analytical and standard finite element solutions. We then investigate the sensitivity of the diffusivity ratio, the parameter controlling the process, and identify multiple possible solutions with several stress peaks. We also show the evolution of the spacing between peaks for all solutions as a function of that parameter.

42 ENGINEERING↗

DOE OSTI2022

Verification of the AGREE and Serpent for the steady state HTR-10 benchmark problems

This paper provides results from steady state HTR-10 benchmark calculations performed using AGREE and Serpent that are compared to experimental results as well as calculations performed by INET. The purpose of completing this benchmark is to validate AGREE and Serpent for the prediction of HTGR operation so that they may ultimately be used to support licensing and deployment efforts of advanced reactors. The benchmark consists of several problems ranging from control rod worth calculations to k{sub eff} calculations at various temperatures. Overall, AGREE and Serpent show good agreement with the reference solutions and are effectively able to predict HTGR operation for a variety of steady state cases. The largest difference from the reference was for the initial core single rod worth, which is possibly due to the larger core helium cavity causing inaccuracies in the diffusion calculation whereas the control rod worth determined by Serpent and AGREE is much closer to the reference result for the full core loading. Moreover, in every benchmark problem, increasing the number of energy groups in the cross sections results in improved agreement of the AGREE result with the reference, although it also causes an increase in computation time. For problems with experimental data available, the accuracy of results generated by Serpent and AGREE is comparable to results obtained by other benchmark participants. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Connectivity‐based parcellation of normal and anatomically distorted human cerebral cortex

Abstract For over a century, neuroscientists have been working toward parcellating the human cortex into distinct neurobiological regions. Modern technologies offer many parcellation methods for healthy cortices acquired through magnetic resonance imaging. However, these methods are suboptimal for personalized neurosurgical application given that pathology and resection distort the cerebrum. We sought to overcome this problem by developing a novel connectivity‐based parcellation approach that can be applied at the single‐subject level. Utilizing normative diffusion data, we first developed a machine‐learning (ML) classifier to learn the typical structural connectivity patterns of healthy subjects. Specifically, the Glasser HCP atlas was utilized as a prior to calculate the streamline connectivity between each voxel and each parcel of the atlas. Using the resultant feature vector, we determined the parcel identity of each voxel in neurosurgical patients ( n = 40) and thereby iteratively adjusted the prior. This approach enabled us to create patient‐specific maps independent of brain shape and pathological distortion. The supervised ML classifier re‐parcellated an average of 2.65% of cortical voxels across a healthy dataset ( n = 178) and an average of 5.5% in neurosurgical patients. Our patient dataset consisted of subjects with supratentorial infiltrating gliomas operated on by the senior author who then assessed the validity and practical utility of the re‐parcellated diffusion data. We demonstrate a rapid and effective ML parcellation approach to parcellation of the human cortex during anatomical distortion. Our approach overcomes limitations of indiscriminately applying atlas‐based registration from healthy subjects by employing a voxel‐wise connectivity approach based on individual data.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Real-Time Control of an Ensemble of Heterogeneous Resources

This paper focuses on the problem of controlling an ensemble of heterogeneous resources connected to an electrical grid at the same point of common coupling (PCC). The controller receives an aggregate power setpoint for the ensemble in real time and tracks this setpoint by issuing individual optimal setpoints to the resources. The resources can have continuous or discrete nature (e.g., heating systems consisting of a finite number of heaters that each can be either switched on or off) and/or can be highly uncertain (e.g., photovoltaic (PV) systems or residential loads). A naive approach would lead to a stochastic mixed-integer optimization problem to be solved at the controller at each time step, which might be infeasible in real time. Instead, we allow the controller to solve a continuous convex optimization problem and compensate for the errors at the resource level by using a variant of the well-known error diffusion algorithm. We give conditions guaranteeing that our algorithm tracks the power setpoint at the PCC on average while issuing optimal setpoints to individual resources. We illustrate the approach numerically by controlling a collection of batteries, PV systems, and discrete loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2018

Density-Equalizing Maps for Simply Connected Open Surfaces

Here in this paper, we are concerned with the problem of creating flattening maps of simply connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing maps with any prescribed density distribution. By varying the initial density distribution, a large variety of flattening maps with different properties can be achieved. For instance, area-preserving parameterizations of simply connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Light Water Reactor Sustainability Program Modeling of Cu Precipitate Contributions to Reactor Pressure Vessel Steel Microstructure Evolution and Embrittlement

This report summarizes the lower-length-scale effort during FY 2017 in developing simulation capabilities for the mesoscale: models for microstructure evolution and plasticity in reactor pressure vessel steels. During operation, reactor pressure vessels undergo hardening and embrittlement caused by irradiation induced defect accumulation and irradiation enhanced solute precipitation. Both defect production and solute precipitation initiate on the atomic scale and manifest their eventual effects as degradation in the engineering scale properties. To predict the engineering scale property degradation, multiscale modeling and simulation capabilities are needed to better understand the microstructure evolution and to connect the microstructure feature evolution to the engineering scale material properties. In this report the development of coupling across different length scale models to understand the multi-physics property dedgration problem is discussed. The development of coupling a lattice kinetic Monte Carlo code to cluster dynamics to capture irradiation enhanced diffusion in the formation of defects is summarized. The implementation of a cluster dynamics model with Grizzly to predict Cu percipitate formation is discussed. A summary of the coupling of crystal plasticity and cluster dynamics to predict the effect on reactor pressure steel hardening is given.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

Cosmic-Ray Diffusion Coefficients throughout the Inner Heliosphere from a Global Solar Wind Simulation

We use a three-dimensional magnetohydrodynamic simulation of the solar wind to calculate cosmic-ray diffusion coefficients throughout the inner heliosphere (2 R{sub ⊙}−3 au). The simulation resolves large-scale solar wind flow, which is coupled to small-scale fluctuations through a turbulence model. Simulation results specify background solar wind fields and turbulence parameters, which are used to compute diffusion coefficients and study their behavior in the inner heliosphere. The parallel mean free path (mfp) is evaluated using quasi-linear theory, while the perpendicular mfp is determined from nonlinear guiding center theory with the random ballistic interpretation. Several runs examine varying turbulent energy and different solar source dipole tilts. We find that for most of the inner heliosphere, the radial mfp is dominated by diffusion parallel to the mean magnetic field; the parallel mfp remains at least an order of magnitude larger than the perpendicular mfp, except in the heliospheric current sheet, where the perpendicular mfp may be a few times larger than the parallel mfp. In the ecliptic region, the perpendicular mfp may influence the radial mfp at heliocentric distances larger than 1.5 au; our estimations of the parallel mfp in the ecliptic region at 1 au agree well with the Palmer “consensus” range of 0.08–0.3 au. Solar activity increases perpendicular diffusion and reduces parallel diffusion. The parallel mfp mostly varies with rigidity (P) as P{sup .33}, and the perpendicular mfp is weakly dependent on P. The mfps are weakly influenced by the choice of long-wavelength power spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

An Integrated Approach to Parameter Learning in Infinite-Dimensional Space

The availability of sophisticated modern physics codes has greatly extended the ability of domain scientists to understand the processes underlying their observations of complicated processes, but it has also introduced the curse of dimensionality via the many user-set parameters available to tune. Many of these parameters are naturally expressed as functional data, such as initial temperature distributions, equations of state, and controls. Thus, when attempting to find parameters that match observed data, being able to navigate parameter-space becomes highly non-trivial, especially considering that accurate simulations can be expensive both in terms of time and money. Existing solutions include batch-parallel simulations, high-dimensional, derivative-free optimization, and expert guessing, all of which make some contribution to solving the problem but do not completely resolve the issue. In this work, we explore the possibility of coupling together all three of the techniques just described by designing user-guided, batch-parallel optimization schemes. Our motivating example is a neutron diffusion partial differential equation where the time-varying multiplication factor serves as the unknown control parameter to be learned. We find that a simple, batch-parallelizable, random-walk scheme is able to make some progress on the problem but does not by itself produce satisfactory results. After reducing the dimensionality of the problem using functional principal component analysis (fPCA), we are able to track the progress of the solver in a visually simple way as well as viewing the associated principle components. This allows a human to make reasonable guesses about which points in the state space the random walker should try next. Thus, by combining the random walker's ability to find descent directions with the human's understanding of the underlying physics, it is possible to use expensive simulations more efficiently and more quickly arrive at the desired parameter set.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Accelerated coupled Monte Carlo-Thermal hydraulic calculations using a hybrid GTF-diffusion-based prediction block: first results

Accurate predictions of spatial power and temperature distributions require the coupling of a neutron transport solver with a thermal-hydraulic (TH) feedback. Nowadays, Monte Carlo (MC) codes are widely coupled to TH solvers, typically via a Picard iteration (PI) method, due to the higher fidelity that such frameworks can produce. To speed up a PI, a prediction step can produce an improved initial guess for a source distribution and feed it to the MC code. Recent work investigated a prediction step that uses generalized transfer functions (GTFs) to predict the macroscopic cross sections' variations following a perturbation in TH properties, such as coolant density. The previous method also relied on first order perturbation (FOP) theory to predict perturbed power profiles, rather than using an expensive MC iterate. The implemented FOP method relied on generating a fission matrix from which the forward and adjoint Eigenmodes were extracted and later used to for power calculations. The generation of the fission matrix can introduce a significant computational overhead, therefore undermining the performance of the proposed hybrid technique when applied to high-dimensional problems, e.g., full core calculations. This work attempts to improve the GTF-FOP prediction step by replacing the FOP solver with a nodal diffusion solver, thus eliminating the need to calculate a fission matrix. The GTF-diffusion step was tested for various moderator density perturbations. In each case, the predicted power distribution showed good agreement with the reference case. The latter is attributed to the generally good prediction of most spatially distributed macroscopic cross sections, except the transport cross section, which will become the focus of future work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Accelerated Coupled Monte Carlo-Thermal Hydraulic Calculations using a Hybrid GTF-Diffusion-based Prediction Block: First Results

Accurate predictions of spatial power and temperature distributions require the coupling of a neutron transport solver with a thermal-hydraulic (TH) feedback. Nowadays, Monte Carlo (MC) codes are widely coupled to TH solvers, typically via a Picard iteration (PI) method, due to the higher fidelity that such frameworks can produce. To speed up a PI, a prediction step can produce an improved initial guess for a source distribution and feed it to the MC code. Recent work [1, 2] investigated a prediction step that uses generalized transfer functions (GTFs) to predict the macroscopic cross sections’ variations following a perturbation in TH properties, such as coolant density. The previous method also relied on first order perturbation (FOP) theory to predict perturbed power profiles, rather than using an expensive MC iterate. The implemented FOP method relied on generating a fission matrix from which the forward and adjoint eigenmodes were extracted and later used to for power calculations. The generation of the fission matrix can introduce a significant computational overhead, therefore undermining the performance of the proposed hybrid technique when applied to high-dimensional problems, e.g., full core calculations. This work attempts to improve the GTF-FOP prediction step by replacing the FOP solver with a nodal diffusion solver, thus eliminating the need to calculate a fission matrix. The GTF-diffusion step was tested for various moderator density perturbations. In each case, the predicted power distribution showed good agreement with the reference case. The latter is attributed to the generally good prediction of most spatially distributed macroscopic cross sections, except the transport cross section, which will become the focus of future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Molecular Viscosity and Diffusivity Effects in Transitional and Shock-Driven Mixing Flows

Here, this paper investigates the importance of molecular viscosity and diffusivity for the prediction of transitional and shock-driven mixing flows featuring high and low Reynolds and Mach number regions. Two representative problems are computed with implicit large-eddy simulations using the inviscid Euler equations (EE) and viscous Navier-Stokes equations (NSE): the Taylor-Green vortex at Reynolds number Re = 3000 and initial Mach number Ma = 0.28, and an air- SF 6 -air gas curtain subjected to two shock waves at Ma = 1.2. The primary focus is on differences between NSE and EE predictions due to viscous effects. The outcome of the paper illustrates the advantages of utilizing NSE. In contrast to the EE, where the effective viscosity decreases upon grid refinement, NSE predictions can be assessed for simulations of flows with transition to turbulence at prescribed constant Re. The NSE can achieve better agreement between solutions and reference data, and the results converge upon grid refinement. On the other hand, the EE predictions do not converge with grid refinement, and can only exhibit similarities with the NSE results at coarse grid resolutions. We also investigate the effect of viscous effects on the dynamics of the coherent and turbulent fields, as well as on the mechanisms contributing to the production and diffusion of vorticity. The results show that nominally inviscid calculations can exhibit significantly varying flow dynamics driven by changing effective resolution-dependent Reynolds number, and highlight the role of viscous processes affecting the vorticity field. These tendencies become more pronounced upon grid refinement. The discussion of the results concludes with the assessment of the computational cost of inviscid and viscous computations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Lab-scale Development of a Hybrid Capture System with Advanced Membrane, Solvent system, and Process Integration

The objective of the project is to achieve lab-scale demonstration of a transformational hybrid membrane/solvent system for the capture of CO 2 from flue gas. A novel process integration scheme was proposed to overcome the low partial pressure of CO 2 present in flue gas. This scheme takes advantage of the potential synergies inherent in the membrane and solvent capture systems. The proposed hybrid technology replaces the second-stage membrane with a solvent capture process. The combustion air is used as a sweeping gas in the solvent stripper. This overall configuration has the major advantages of requiring much less air and eliminating the problems associated with oxygen slip in the membrane-based systems. Even more importantly, because of the presence of the air sweep in the stripper, much lower temperatures are required for solvent regeneration, which enables heat integration to the point that no process steam is required. This project was to perform lab-scale demonstration of Liquid Ion Solutions (LIS) transformational hybrid membrane/solvent system for post-combustion CO 2 capture while demonstrating significant progress toward achievement of the overall fossil energy performance goals of 90% CO 2 capture rate with 95% CO 2 purity at a cost of electricity 30% less than baseline capture approaches. This report is written chronologically based on budget periods. Each budget period discusses the work performed and its results. At the end of each budget period the milestone charts are provided to show the progress. This project was not able to meet its stated goals. The performances of the power plant equipped with the hybrid process and Baseline Case B12B were compared. The simulation results showed that the power plant equipped with hybrid CO2 capture process has an improved thermal efficiency of 33.4% compared to the Baseline Case B12B, which is 32.5%. However, the COE for the hybrid process is $146.3/MWh which is higher than the $142.8/MWh for Case B12B. If this process were to be applied as a retrofit, it may make sense to use this configuration as it does not require any change in an existing plant configuration and steam cycle. However, for a new powerplant the capital cost is higher than the Case B12B. On the membrane development side, we successfully showed that interfacially-controlled envelope (ICE) membranes work. The inclusion of surface modified nano-particles results in much higher gas diffusivities. The Gen-1 ICE membrane developed under this project showed exceptional improved permeability for CO 2 . However, we ran into major problems which were associated with the scalability and reproducibility of the poly(phosphozene) polymers. The issues with scale-up are and batch to batch variability is also discussed. At the end of this report we have provided our recommendations on materials development for better membrane materials and alluded to the use of much simpler chemistry while keeping the concept of ICE membrane intact. It is also clear that vacuum and compression equipment is costly. If a process which can eliminate the use of vacuum and compression equipment would significantly decrease the overall cost of capture. Some thoughts regarding such system is also provided in the outlook portion of this report.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2020

Source identification by non-negative matrix factorization combined with semi-supervised clustering

Machine-learning methods and apparatus are provided to solve blind source separation problems with an unknown number of sources and having a signal propagation model with features such as wave-like propagation, medium-dependent velocity, attenuation, diffusion, and/or advection, between sources and sensors. In exemplary embodiments, multiple trials of non-negative matrix factorization are performed for a fixed number of sources, with selection criteria applied to determine successful trials. A semi-supervised clustering procedure is applied to trial results, and the clustering results are evaluated for robustness using measures for reconstruction quality and cluster separation. The number of sources is determined by comparing these measures for different trial numbers of sources. Source locations and parameters of the signal propagation model can also be determined. Disclosed methods are applicable to a wide range of spatial problems including chemical dispersal, pressure transients, and electromagnetic signals, and also to non-spatial problems such as cancer mutation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Source identification by non-negative matrix factorization combined with semi-supervised clustering

Alexandrov, Boian S.↗

DOE OSTI2021

Parallel-In-Time Integration for Hyperbolic Problems (Final Report)

The work for the subcontract was situated in the area of parallel-in-time integration for advection-dominated and hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. Over the past two decades, much progress has been made in this area; however, this progress has largely been limited to non-hyperbolic, diffusion-dominated PDEs. Given the ubiquity of numerical simulations of advection-dominated hyperbolic PDEs throughout the sciences, there is a strong need to develop efficient parallel-in-time techniques for hyperbolic problems, which was the main topic of this subcontract.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

The “Fresnel Equations” for Diffuse radiation on Inclined photovoltaic Surfaces (FEDIS)

Here the well-known Fresnel equations solve for the reflection and transmission of light for precise incident angles. The transmission of diffuse radiation incident on a planar or domed surface is often needed for real-world applications. Due to the complexity of the Fresnel equations, the analytical solution of the integration has hitherto been unobtainable over the last centuries. Therefore, this problem was numerically solved by integrating the angular transmittances in space often leading to substantial computing burden and bias in the results. To efficiently estimate the solar energy resource for a glass-covered photovoltaic (PV) module, we derive an analytical solution of diffuse transmission based on the rigorous integration of an alternate form of the Fresnel equations. The approach leads to a simple yet accurate relative transmittance model that reconciles the solar energy sensed by pyranometers and PV panels. With limited and clearly stated approximations, the complex mathematical derivation resulted in an elegant solution. An experiment using 1-year of data at the National Renewable Energy Laboratory's (NREL's) Solar Radiation Research Laboratory (SRRL) shows that the new model dramatically decreases the disparity between the solar radiation measurements by a Kipp and Zonen CM Pyranometer 22 (CMP22) and an IMT reference cell on a 1-axis tracking system. The solution in this paper can be widely used in scientific and engineering research, development, and applications wherever the Fresnel equations are used.

14 SOLAR ENERGY↗

DOE OSTI2022

FEDIS (The “Fresnel Equations” for Diffuse radiation on Inclined photovoltaic Surfaces) [SWR-22-64]

The well-known Fresnel equations solve for the reflection and transmission of light for precise incident angles. The transmission of diffuse radiation incident on a planar or domed surface is often needed for real-world applications. Due to the complexity of the Fresnel equations, the analytical solution of the integration has hitherto been unobtainable over the last centuries. Therefore, this problem was numerically solved by integrating the angular transmittances in space often leading to substantial computing burden and bias in the results. To efficiently estimate the solar energy resource for a glass-covered photovoltaic (PV) module, we derive an analytical solution of diffuse transmission based on the rigorous integration of an alternate form of the Fresnel equations. The approach leads to a simple yet accurate relative transmittance model that reconciles the solar energy sensed by pyranometers and PV panels. With limited and clearly stated approximations, the complex mathematical derivation resulted in an elegant solution.

Xie, Yu↗