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DOE OSTI2024

Collisional simulations of the modulator section in coherent electron cooling

The first section of any coherent electron cooling (CeC) system is the modulator, where the density of the electron beam is modulated by the copropagating ion beam. This density modulation is a result of Coulomb collisions between the individual particles of the two beams. The pairwise, stochastic part of the interactions impacts the overall performance of the CeC process. We present the first simulations of the density modulations of the electron beams from a collisional picture of the dynamics, considering the proof-of-principle CeC experiments at Brookhaven National Laboratory. These simulations were performed using PHAD, which is the first efficient, large-scale collisional numerical method in beam physics that we have previously developed and benchmarked. Realistic beam distributions and external fields have been optimized to provide strong modulation signals necessary for variations of coherent electron cooling systems. Cooling performance limits and potential collisionless simulation pitfalls are pointed out. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Short-Term Probabilistic Solar Forecasting via Reinforcement Learning over ECMWF

In this paper, we present an innovative reinforcement learning approach for short-term solar forecasting, leveraging data from the European Centre for Medium-Range Weather Forecasts (ECMWF). The methodology begins with the application of the System Advisor Model (SAM) to transform various ECMWF numerical weather prediction members into predictive photovoltaic power generation. To enhance the precision of deterministic forecasting, we introduce a dynamic model selection algorithm based on Q-learning. This algorithm dynamically identifies and utilizes the most accurate ensemble member for forecasting purposes. Furthermore, we employ a support vector regression surrogate model with a Gaussian distribution to generate probabilistic forecasts, providing a holistic view of solar energy generation uncertainty. To expedite the training process and make it more practical for real-world applications, we integrate a rolling update workflow. This innovative workflow reduces the training period from months to a mere 19 days, making our method highly efficient. Numerical results of the case study show that in comparison to benchmark models, the proposed method improves the deterministic and probabilistic solar forecasting accuracy by up to 40.84% and 48.42%, respectively.

ensemble forecasting↗

DOE OSTI2012

Research and Development of a Low Cost Solar Collector

This is a Final Technical Report on the Research and Development completed towards the development of a Low Cost Solar Collector conducted under the DOE cost-sharing award EE-0003591. The objective of this project was to develop a new class of solar concentrators with geometries and manufacturability that could significantly reduce the fully installed cost of the solar collector field for concentrated solar thermal power plants. The goal of the project was to achieve an aggressive cost target of $\$$170/m 2 , a reduction of up to 50% in the total installed cost of a solar collector field as measured against the current industry benchmark of a conventional parabolic trough. The project plan, and the detailed activities conducted under the scope of the DOE Award project addressed all major drivers that affect solar collector costs. In addition to costs, the study also focused on evaluating technical performance of new collector architectures and compared them to the performance of the industry benchmark parabolic trough. The most notable accomplishment of this DOE award was the delivery of a full-scale integrated design, manufacturing and field installation solution for a new class of solar collector architecture which has been classified as the Bi-Planar Fresnel Collector (BPFC) and may be considered as a viable alternative to the conventional parabolic trough, as well as the conventional Fresnel collectors. This was in part accomplished through the design and development, all the way through fabrication and test validation of a new class of Linear Planar Fresnel Collector architecture. This architecture offers a number of key differentiating features which include a planar light-weight frame geometry with small mass-manufacturable elements utilizing flat mirror sections. The designs shows significant promise in reducing the material costs, fabrication costs, shipping costs, and on-site field installation costs compared to the benchmark parabolic trough, as well as the conventional Fresnel collector. The noteworthy design features of the BPFC architecture include the use of relatively cheaper flat mirrors and a design which allows the mirror support beam sections to act as load-bearing structural elements resulting in more than a 36% reduction in the overall structural weight compared to an optimized parabolic trough. Also, it was shown that the utilization of small mass-produced elements significantly lowers mass-production and logistics costs that can more quickly deliver economies of scale, even for smaller installations while also reducing shipping and installation costs. Moreover, unlike the traditional Fresnel trough the BPFC architecture does not require complex articulating drive mechanisms but instead utilizes a standard parabolic trough hydraulic drive mechanism. In addition to the development of the Bi-Planar Fresnel Collector, an optimized conventional space-frame type parabolic trough was also designed, built, analyzed and field-tested during the first phase of this award. The design of the conventional space-frame parabolic collector was refined with extensive FEA and CFD analysis to reduce material costs and re-designed for simpler fabrication and more accurate lower-cost field assembly. This optimized parabolic trough represented an improvement over the state-of-the art of the traditional parabolic trough architecture and also served as a more rigorous and less subjective benchmark that was used for comparison of new candidate design architectures. The results of the expanded 1 st phase of the DOE award project showed that both the Optimized Parabolic Trough and the new Bi-Planar Fresnel Collector design concepts failed to meet the primary objectives for the project of achieving a 50% cost reduction from the industry reference total installed cost of $\$$350/m 2 . Results showed that the BPFC came in at projected total installed cost of $\$$237/m 2 representing a 32% savings compared to the industry benchmark conventional parabolic trough. And the cost reduction obtained by the Optimized Parabolic Trough compared to the industry benchmark reference was approximately 16.5% against the industry benchmark. The new BPFC design showed a weight savings of almost 36% compared to the optimized parabolic trough and a 50% reduction in field assembly labor and a 13% reduction in shipping volume. The BPFC design showed only a marginal improvement of 16% over the fully projected installed cost of the optimized parabolic trough benchmark developed as Concept One. During the course of the investigation numerous sensitivity analyses and other analytical studies were conducted to assess potential improvement opportunities, and further optimizations that could lead to cost reductions and performance improvements. Factors that could have a significant impact on high-volume costs were related to production and further improvements in design for manufacturability, automation, assembly jigs, and fixtures, and robotic welding etc. The wind modeling analysis showed that the Fresnel design concept did not reduce the wind load in a significant manner. The stress analysis showed that the design concept with almost a 36% lower weight than the parabolic trough and it was strong enough to withstand the expected wind loads and maintain targeting accuracy. The Initial on-sun optical testing showed that the Fresnel Trough was capable of concentrating sunlight effectively to the desired target and yielding an optical efficiency slightly lower than a parabolic trough.

14 SOLAR ENERGY↗

DOE OSTI2012

LU Factorization with Partial Pivoting for a Multi-CPU, Multi-GPU Shared Memory System

LU factorization with partial pivoting is a canonical numerical procedure and the main component of the High Performance LINPACK benchmark. This article presents an implementation of the algorithm for a hybrid, shared memory, system with standard CPU cores and GPU accelerators. Performance in excess of one TeraFLOPS is achieved using four AMD Magny Cours CPUs and four NVIDIA Fermi GPUs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Preliminary Study on the Suitability of a Second-Order Reconstructed Discontinuous Galerkin Method for RELAP-7 Thermal-Hydraulic Modeling

This document presents a preliminary study on the suitability of a second-order reconstructed discontinuous Galerkin (rDG) method for RELAP-7 thermal-hydraulic modeling. The document begins with a brief description of the governing equations for compressible, two-phase vapor and liquid flow, with a presentation of the seven-equation formulation details. A comparative study between the second-order rDG method and the RELAP-7's finite element method (FEM) with a entropy viscosity method (EVM) based numerical stabilization scheme (namely FEM-EVM) over a series of benchmark test problems is demonstrated. The intent for this suite of test problems is to provide baseline comparison data that demonstrate the performance of 1) the rDG solution and 2) the RELAP-7's FEM-EVM solution (with RELAP-7 code version dated August 15, 2017), on problems from single- to specific, limited two-phase flows. For all the test problems in this document, the rDG solutions were obtained with a second-order, two-step, explicit strong stability preserving Runge-Kutta time integration method. The computational results clearly indicate that the performance of the rDG method is superior to that of the RELAP-7's FEM-EVM method in all the test problems presented. Therefore, as far as the test problems in this document are considered, the second-order rDG method is recommended as an improved solution method option for RELAP-7.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Uncertainty-Guided Prediction Horizon of Phase-Resolved Ocean Wave Forecasting Under Data Sparsity: Experimental and Numerical Evaluation

Accurate short-term wave forecasting is critical for the safe and efficient operation of marine structures that rely on real-time, phase-resolved ocean wave information for control and monitoring purposes (e.g., digital twins). These systems often depend on environmental sensors (e.g., waverider buoys, wave-sensing LIDAR). Challenges arise when upstream sensor data are missing, sparse, or phase-shifted due to drift. This study investigates the performance of two machine learning models, time-series dense encoder (TiDE) and long short-term memory (LSTM), for forecasting phase-resolved ocean surface elevations under varying degrees of data degradation. We introduce the τ-trimming algorithm, which adapts the prediction horizon based on uncertainty thresholds derived from historical forecasts. Numerical wave tank (NWT) and wave basin experiments are used to benchmark model performance under short- and long-term data masking, spatially coarse sensor grids, and upstream phase shifts. Results show under a 50% probability of upstream data loss, the τ-trimmed TiDE model achieves a 46% reduction in error at the most upstream target, compared to 22% for LSTM. Furthermore, phase misalignment in upstream data introduces a near-linear increase in forecast error. Under moderate model settings, a ±3 s misalignment increases the mean absolute error by approximately 0.5 m, while the same error is accumulated at ±4 s using the more conservative approach. These findings inform the design of resilient, uncertainty-aware wave forecasting systems suited for realistic offshore sensing environments.

42 ENGINEERING↗

DOE OSTI2016

Large Eddy Simulation of Autoignition Transients in a Model Diesel Injector Configuration

Developing an improved understanding of transient mixing and combustion processes inherent in diesel injection is an important element in the design of advanced engines. This paper provides a detailed analysis of these processes using an idealized benchmark configuration designed to facilitate precise comparisons between different models and numerical methods. The computational domain is similar to the Engine Combustion Network (www.sandia.gov/ECN) Spray-A injector with n-dodecane as the fuel. Quantified idealizations are made in the treatment of boundary conditions to eliminate ambiguities and unknowns associated with the actual injector(s) used in the experiment. These ambiguities hinder comparisons aimed at understanding the accuracy of different models and the coupled effects of potential numerical errors. Prior to understanding the impact of injector imperfections on their performance, it is first necessary to understand how models perform in a well-controlled environment with well-defined boundary conditions. Here, we focus on the latter while accurately matching the operating conditions used in the experiments. Relevant high-pressure phenomena are treated with real-fluid thermodynamics and transport for multicomponent mixtures. A highly resolved calculation is performed to study both scalar-mixing and initiation of combustion. Results are assembled into a database that can facilitate one-to-one comparisons between codes. The combined set of results is analyzed to provide physical insights related to localized broadband transient mixing and combustion processes that are typically not available from experiments.

Hakim, Layal↗

NASA NTRS1984

Algorithms for elasto-plastic-creep postbuckling

This paper considers the development of an improved constrained time stepping scheme which can efficiently and stably handle the pre-post-buckling behavior of general structure subject to high temperature environments. Due to the generality of the scheme, the combined influence of elastic-plastic behavior can be handled in addition to time dependent creep effects. This includes structural problems exhibiting indefinite tangent properties. To illustrate the capability of the procedure, several benchmark problems employing finite element analyses are presented. These demonstrate the numerical efficiency and stability of the scheme. Additionally, the potential influence of complex creep histories on the buckling characteristics is considered.

Padovan, J.↗

NASA NTRS1991

Ground-based PIV and numerical flow visualization results from the surface tension driven convection experiment

The Surface Tension Driven Convection Experiment (STDCE) is a Space Transportation System flight experiment to study both transient and steady thermocapillary fluid flows aboard the United States Microgravity Laboratory-1 (USML-1) Spacelab mission planned for June, 1992. One of the components of data collected during the experiment is a video record of the flow field. This qualitative data is then quantified using an all electric, two dimensional Particle Image Velocimetry (PIV) technique called Particle Displacement Tracking (PDT), which uses a simple space domain particle tracking algorithm. Results using the ground based STDCE hardware, with a radiant flux heating mode, and the PDT system are compared to numerical solutions obtained by solving the axisymmetric Navier Stokes equations with a deformable free surface. The PDT technique is successful in producing a velocity vector field and corresponding stream function from the raw video data which satisfactorily represents the physical flow. A numerical program is used to compute the velocity field and corresponding stream function under identical conditions. Both the PDT system and numerical results were compared to a streak photograph, used as a benchmark, with good correlation.

Pline, Alexander D.↗

NASA NTRS1991

Ground-based PIV and numerical flow visualization results from the Surface Tension Driven Convection Experiment

Pline, Alexander D.↗

NASA NTRS1995

Acoustic scattering from ellipses by the modal element method

The modal element method is used to study acoustic scattering from ellipses, which may be acoustically soft (absorbing) or hard (reflecting). Because exact solutions are available, the results provide a benchmark for algorithm performance for scattering from airfoils and similar shapes. Numerical results for scattering from rigid ellipses are presented for a wide variety of eccentricities at moderate frequencies. These results indicate that the method is practical.

Kreider, Kevin L.↗

NASA NTRS2005

Capillary Driven Flows Along Differentially Wetted Interior Corners

Closed-form analytic solutions useful for the design of capillary flows in a variety of containers possessing interior corners were recently collected and reviewed. Low-g drop tower and aircraft experiments performed at NASA to date show excellent agreement between theory and experiment for perfectly wetting fluids. The analytical expressions are general in terms of contact angle, but do not account for variations in contact angle between the various surfaces within the system. Such conditions may be desirable for capillary containment or to compute the behavior of capillary corner flows in containers consisting of different materials with widely varying wetting characteristics. A simple coordinate rotation is employed to recast the governing system of equations for flows in containers with interior corners with differing contact angles on the faces of the corner. The result is that a large number of capillary driven corner flows may be predicted with only slightly modified geometric functions dependent on corner angle and the two (or more) contact angles of the system. A numerical solution is employed to verify the new problem formulation. The benchmarked computations support the use of the existing theoretical approach to geometries with variable wettability. Simple experiments to confirm the theoretical findings are recommended. Favorable agreement between such experiments and the present theory may argue well for the extension of the analytic results to predict fluid performance in future large length scale capillary fluid systems for spacecraft as well as for small scale capillary systems on Earth.

Golliher, Eric L.↗

DOE OSTI2022

DFT-FE 1.0: A massively parallel hybrid CPU-GPU density functional theory code using finite-element discretization

In this work, we present DFT-FE 1.0, building on DFT-FE 0.6 [Comput. Phys. Commun. 246, 106853 (2020)], to conduct fast and accurate large-scale density functional theory (DFT) calculations (reaching ~ 100,000 electrons) on both many-core CPU and hybrid CPU-GPU computing architectures. This work involves improvements in the real-space formulation—via an improved treatment of the electrostatic interactions that substantially enhances the computational efficiency—as well high-performance computing aspects, including the GPU acceleration of all the key compute kernels in DFT-FE. We demonstrate the accuracy by comparing the ground-state energies, ionic forces and cell stresses on a wide-range of benchmark systems against those obtained from widely used DFT codes. Further, we demonstrate the numerical efficiency of our implementation, which yields ~ 20× CPU-GPU speed-up by using GPU acceleration on hybrid CPU-GPU nodes. Notably, owing to the parallel-scaling of the GPU implementation, we obtain wall-times of 80–140 seconds for full ground-state calculations, with stringent accuracy, on benchmark systems containing ~ 6, 000 – 15,000 electrons.

pseudopotential↗

DOE OSTI2014

Numerical Simulation of Carbon Dioxide Injection in the Western Section of the Farnsworth Unit

Numerical simulation is an invaluable analytical tool for scientists and engineers in making predictions about of the fate of carbon dioxide injected into deep geologic formations for long-term storage. Current numerical simulators for assessing storage in deep saline formations have capabilities for modeling strongly coupled processes involving multifluid flow, heat transfer, chemistry, and rock mechanics in geologic media. Except for moderate pressure conditions, numerical simulators for deep saline formations only require the tracking of two immiscible phases and a limited number of phase components, beyond those comprising the geochemical reactive system. The requirements for numerically simulating the utilization and storage of carbon dioxide in partially depleted petroleum reservoirs are more numerous than those for deep saline formations. The minimum number of immiscible phases increases to three, the number of phase components may easily increase fourfold, and the coupled processes of heat transfer, geochemistry, and geomechanics remain. Public and scientific confidence in the ability of numerical simulators used for carbon dioxide sequestration in deep saline formations has advanced via a natural progression of the simulators being proven against benchmark problems, code comparisons, laboratory-scale experiments, pilot-scale injections, and commercial-scale injections. This paper describes a new numerical simulator for the scientific investigation of carbon dioxide utilization and storage in partially depleted petroleum reservoirs, with an emphasis on its unique features for scientific investigations; and documents the numerical simulation of the utilization of carbon dioxide for enhanced oil recovery in the western section of the Farnsworth Unit and represents an early stage in the progression of numerical simulators for carbon utilization and storage in depleted oil reservoirs.

carbon sequestration↗

DOE OSTI2019

What Is the Fractional Laplacian? A Comparative Review with New Results

The fractional Laplacian in $\mathbb{R}^{d}$, which we write as (–Δ) α/2 with, α ϵ (0, 2) has multiple equivalent characterizations. Furthermore, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ways, and there is currently no consensus in the literature as to which definition of the fractional Laplacian in bounded domains is most appropriate for a given application. The Riesz (or integral) definition, for example, admits a nonlocal boundary condition, where the value of a function must be prescribed on the entire exterior of the domain in order to compute its fractional Laplacian. Yet, the spectral definition requires only the standard local boundary condition. These differences, among others, lead us to ask the question: “What is the fractional Laplacian?” Beginning from first principles, we compare several commonly used definitions of the fractional Laplacian theoretically, through their stochastic interpretations as well as their analytical properties. Next, we present quantitative comparisons using a sample of state-of-the-art methods. We discuss recent advances on nonzero boundary conditions and present new methods to discretize such boundary value problems: radial basis function collocation (for the Riesz fractional Laplacian) and nonharmonic lifting (for the spectral fractional Laplacian). In our numerical studies, we aim to compare different definitions on bounded domains using a collection of benchmark problems. We consider the fractional Poisson equation with both zero and nonzero boundary conditions, where the fractional Laplacian is defined according to the Riesz definition, the spectral definition, the directional definition, and the horizon-based nonlocal definition. We verify the accuracy of the numerical methods used in the approximations for each operator, and we focus on identifying differences in the boundary behaviors of solutions to equations posed with these different definitions. Through our efforts, we aim to further engage the research community in open problems and assist practitioners in identifying the most appropriate definition and computational approach to use for their mathematical models in addressing anomalous transport in diverse applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Neutronic-Thermal Hydraulic Benchmark using the SKINATH Point Kinetics Model

The SKINATH point kinetics program, whose name comes from: A Computer Program for Solving the Reactor Point Kinetics Equations with Simple Thermal Hydraulic-Feedback, had its origins at ORNL. The authors were interested in investigating low-level criticality events such as might occur in a waste repository of 55 gallon drums. We assume a relatively realistic thermal feedback for fissionable material in a container (called a reactor here), either critical or subcritical, with the potential to undergo a further excursion. The system is a homogeneous fissile fluid (mostly water), increasing in temperature as it absorbs all heat from the excursion. An ideal gas eternally cools the reactor at constant temperature T{sub c}. The SKINATH numerical concept in 1984 was to use an off-the-shelf Livermore ODE solver LSODE to solve the kinetic equations, much as one does today with MATLAB{sup TM}. Here, we develop a novel solver that uses the simplest of numerical methods including convergence acceleration. This work represents the initiation of a Multiphysics benchmark effort at INL. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2000

Effects of Melt Convection and Solid Transport on Macrosegregation and Grain Structure in Equiaxed Al-Cu Alloys

Macrosegregation in metal casting can be caused by thermal and solutal melt convection, and the transport of unattached solid crystals resulting from nucleation in the bulk liquid or dendrite fragmentation. To develop a comprehensive numerical model for the casting of alloys, an experimental study has been conducted to generate benchmark data with which such a solidification model could be tested. The objectives were: (1) experimentally study the effects of solid transport and thermosolutal convection on macrosegregation and grain size; and (2) provide a complete set of boundary conditions temperature data, segregation data, and grain size data - to validate numerical models. Through the control of end cooling and side wall heating, radial temperature gradients in the sample and furnace were minimized. Thus the vertical crucible wall was adiabatic. Samples at room temperature were 24 cc and 95 mm long. The alloys used were Al-1 wt. pct. Cu, and Al- 10 wt. pct. Cu; the starting point for solidification was isothermal at 710 and 685 C respectively. To induce an equiaxed structure various amounts of the grain refiner TiB2 were added. Samples were either cooled from the top, or the bottom. Several trends in the data stand out. In attempting to model these experiments, concentrating on these trends or differences may be beneficial.

Rerko, Rodney S.↗

DOE OSTI2015

Numerical studies of electron cyclotron wave current drive on HL-2A tokamak

The electron cyclotron wave (ECW) current drive (CD) for the HL-2A tokamak is investigated numerically with a new ray-tracing and Fokker-Planck code. The code is benchmarked with other well-tested linear and quasilinear codes and is then used to study the electron cyclotron current drive on the HL-2A tokamak. The wave propagation, power deposition, and driven-current profiles are presented. The effect of electron trapping is also assessed. It is found that quasilinear effects are negligible at the present ECW power levels and that when both waves are injected at an angle of 20° on the plasma equatorial plane, the CD efficiency for the HL-2A saturates at ∼0.029 × 10{sup 20 }A/W/m{sup 2} and ∼0.020 × 10{sup 20 }A/W/m{sup 2} for the 0.5 MW/68 GHz first harmonic ordinary (O1) and 1 MW/140 GHz second harmonic extraordinary (X2) modes, respectively. The effects of the plasma density, temperature, and wave-launching position on the driven current are also investigated analytically and numerically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗