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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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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Aging Mechanisms of Broad Area High-Power ~800nm Laser Diodes

Improved lifetime of high-power broad area laser diodes will enhance their utility for manufacturing, scientific, and medical laser systems. However, factors contributing to gradual degradation of diode laser performance are not fully understood. Here we study the aging mechanisms of ~800 nm aluminum-free laser diodes grown by solid-source MBE. Oxygen was intentionally introduced at three different concentration levels into the quantum well (QW) and waveguide (WG) at concentrations <5×10 15 cm -3 . Diode power, slope efficiency (SE th ), threshold current (I th ), and device parameters such as QW and WG lifetimes were measured at discrete time steps throughout the aging run. The data show that lasing characteristics prior to aging are degraded by oxygen introduction, but the gradual power degradation rate of ~5% over 500 hours at current density 1.74 kA/cm 2 does not change with oxygen concentration. Aging-induced changes in nonradiative lifetimes and threshold were observed for shorter aging times, but stabilized after ~100 hrs. and cannot explain the observed power degradation. This suggests that gradual degradation in these devices is not due to nonradiative recombination at low levels of point defects. The data shows that this degradation results primarily from changes in slope efficiency, and simulation of these results suggests that the power degradation arises from increased intracavity absorption (ICA). Efforts to slow ICA growth, instead of efforts to control low levels of nonradiative recombination centers, may be the most fruitful path forward to improve laser diode lifetime.

42 ENGINEERING↗
DOE OSTI2025

CACTUS: CO 2 Aerogel Capture Towards Utilization and Sequestration

The CACTUS project aimed to develop a novel solid sorbent and sorption module prototype for direct air capture (DAC) of carbon dioxide, by a moisture-swing adsorption (MSA) mechanism. Because MSA uses changes in humidity, not temperature to switch the sorbent from capturing CO 2 to releasing concentrated CO 2 it is > 4X more energy-efficient than the thermal swing process. The goal was to develop a sorbent with a CO 2 capture capacity of 1 mmol CO 2 /g sorbent (or 0.75 mmol CO 2 /g structured sorbent), at a projected scaled cost of < $\$$15/kg sorbent and demonstration of a path to < $\$$100/ton CO 2 . At the end of the project, we achieved 0.8 mmol CO 2 /g sorbent powders, 0.37 mmol CO 2 /g structured sorbent (50% of target), at a projected cost of $\$$29/kg sorbent and an estimated cost of $\$$160/ton CO 2 . The key innovation was SRI’s patented polymer aerogel synthesis platform, which was adapted to produce a nanoporous aerogel with a high density of CO 2 -adsorbing quaternary ammonium groups. This research discovered a new ammonium polymer sorbent and identified a chemical path for its fabrication. The new process solved the monomer immiscibility challenge encountered with the initial method (ammonium is hydrophilic and the crosslinker is hydrophobic). The team fabricated structured sorbent sheets consisting of a non-woven porous substrate impregnated with ammonium polymer and demonstrated its operation in custom made breakthrough test setup MSA DAC built at SRI, and which operates similarly to the envisioned large-scale CO 2 capture plant, to provide data for techno-economic analysis (TEA). TEA sensitivity analysis indicated that ∼$\$$100/ton CO 2 can be achieved if the target capacity of 0.75 mmol CO 2 /g structured sorbent is met. Also identified routes to decrease sorbent manufacturing cost to ∼$\$$19/kg by reducing amounts and recycling the organic solvents. More work is needed on transitioning process manufacturing from powders (which showed a capacity of up to 0.8 mmol/g sorbent) to structured sheets which showed a capacity of 0.37 mmol CO 2 /g structured sorbent (or 0.44 mmol/g sorbent if one excludes the inert porous substrate). This is likely due to different micro/nano-structure of the sorbent and material processing constraints at the laboratory scale. Sorbent cycling studies (> 100 cycles) are needed to investigate its performance stability over time.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2022

Behavior and mechanisms of Doppler wind lidar error in varying stability regimes

Abstract. Wind lidars are widespread and important tools in atmospheric observations. An intrinsic part of lidar measurement error is due to atmospheric variability in the remote-sensing scan volume. This study describes and quantifies the distribution of measurement error due to turbulence in varying atmospheric stability. While the lidar error model is general, we demonstrate the approach using large ensembles of virtual WindCube V2 lidar performing a profiling Doppler-beam-swinging scan in quasi-stationary large-eddy simulations (LESs) of convective and stable boundary layers. Error trends vary with the stability regime, time averaging of results, and observation height. A systematic analysis of the observation error explains dominant mechanisms and supports the findings of the empirical results. Treating the error under a random variable framework allows for informed predictions about the effect of different configurations or conditions on lidar performance. Convective conditions are most prone to large errors (up to 1.5 m s−1 in 1 Hz wind speed in strong convection), driven by the large vertical velocity variances in convective conditions and the high elevation angle of the scanning beams (62∘). Range-gate weighting induces a negative bias into the horizontal wind speeds near the surface shear layer (−0.2 m s−1 in the stable test case). Errors in the horizontal wind speed and direction computed from the wind components are sensitive to the background wind speed but have negligible dependence on the relative orientation of the instrument. Especially during low winds and in the presence of large errors in the horizontal velocity estimates, the reported wind speed is subject to a systematic positive bias (up to 0.4 m s−1 in 1 Hz measurements in strong convection). Vector time-averaged measurements can improve the behavior of the error distributions (reducing the 10 min wind speed error standard deviation to <0.3 m s−1 and the bias to <0.1 m s−1 in strong convection) with a predictable effectiveness related to the number of decorrelated samples in the time window. Hybrid schemes weighting the 10 min scalar- and vector-averaged lidar measurements are shown to be effective at reducing the wind speed biases compared to cup measurements in most of the simulated conditions, with time averages longer than 10 min recommended for best use in some unstable conditions. The approach in decomposing the error mechanisms with the help of the LES flow field could be extended to more complex measurement scenarios and scans.

17 WIND ENERGY↗
DOE OSTI2020

Contaminant Migration Modeling to Support the In Situ Decommissioning of Hardened Nuclear Facilities - 20215

The decommissioning of hardened nuclear facilities provides a unique challenge in balancing current worker dose with exposure to future receptors and media. In situ decommissioning (ISD) is a cost-effective and safe option for the closure of such facilities but requires a detailed understanding of the threat that radioactive and hazardous constituents remaining in the facilities pose to groundwater and surrounding surface water. The Savannah River Site (SRS) extensively employs contaminant migration models within the decommissioning process to develop site-specific removal, grouting, and monitoring strategies in support of safe and effective final end states of nuclear facilities. This work discusses the use of contaminant migration modeling in the ISD process at SRS, including specific examples from the closure of P-Reactor and R-Reactor, Building 235-F, F-Canyon and F/H Laboratory Complex. Migration models developed during the closure of P-Reactor and R-Reactor were divided into four source areas: the reactor vessel, the process area, the disassembly basin, and the purification wing. Each source area was assigned a specific inventory and migration pathway and was then subject to varying hypothetical removal, capping, and grouting schemes. Modeling indicated that groundwater Maximum Concentration Limits (MCLs) might be exceeded if no action was taken for eleven and ten constituents of concern (COCs) at P-Reactor and R-Reactor, respectively. These exceedances could occur in as few as 200 to 500 years. Alternatively, the migration modeling demonstrated that the selected ISD actions reduced contaminant mobility which allowed for significant radioactive decay and resulted in fewer predicted exceedances of groundwater MCLs (five COCs for P-Reactor; eight COCs for R-Reactor). In response to the modeling results for P-Reactor and R-Reactor, effectiveness monitoring programs were developed to target contaminants, specific to each reactor, that may migrate to groundwater. Contaminant migration modeling also revealed that roof collapse was a large factor in the release of COCs to the environment, giving rise to roof improvements, and an inspection and vegetation control program to ensure roof stability over time. Contaminant migration modeling is also aiding in the closure planning for hardened facilities in F Area. Building 235-F housed the Actinide Billet Line, which produced Np-237 billets for irradiation in SRS reactors, and the Plutonium Fuel Form (PuFF) facility that produced Pu-238 heat sources for the space program. As a result of these missions, areas within Building 235-F contain considerable residual amounts of both Pu-238 and Np-237. Contaminant migration modeling of Building 235-F was originally performed in 2012 to identify the feasibility of ISD and the amount of radioactive material removal required to prevent the exceedance of groundwater MCLs. The original model indicated that a 60% reduction in the PuFF facility Pu-238 inventory could keep groundwater concentrations below standards, while Np-237 did not pose a threat to groundwater. However, updates to the model with an emphasis on source impact pathways revealed that, due to the orientation of the source areas relative to groundwater flow, no amount of reasonable removal of Pu-238 would keep groundwater concentrations below MCLs and that Np-237 could be a large contributor to localized MCL exceedances. With this insight, the refined 2019 model is being used to assist in the development of grouting plans specific to each facility source area, where bentonite may be utilized to slow the migration of Pu-238 and its daughter products from the PuFF facility and a reducing grout may decrease Np-237 transport by ensuring the nuclide remains in the less mobile +IV oxidation state. The beginning phases of contaminant migration modeling are underway for F-Canyon and associated facilities using lessons learned from the Reactors and Building 235-F. A contaminant migration pathway, similar to the pathway used for the reactor vessels, is being developed for the hot and warm canyons. The F-Canyon inventories are being spatially refined to identify specific and localized source zones, comparable to Building 235-F, that may impact groundwater. Contaminant migration modeling provides vital input within the ISD process, from facility investigation to post closure effectiveness monitoring, making it a valuable tool in the development of safe and effective end states for hardened nuclear facilities at SRS. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Quantifying the impact of climate change on erosion - 20397

The New York State Energy Research and Development Authority (NYSERDA) is the owner of the Western New York Nuclear Service Center (WNYNSC), a 1,351-ha (3,338-ac) site located approximately 48 km (30 mi) south of Buffalo, New York. In 1962, Nuclear Fuel Services, Inc. (NFS) entered into Agreements with the Atomic Energy Commission and New York State to construct the first commercial reprocessing plant of nuclear fuel in the United States. NFS, a private company, built and operated the spent fuel reprocessing plant and waste disposal facilities, processing 640 Mg (metric tons, or 705 short tons) of spent nuclear fuel from 1966 to 1972 under an Atomic Energy Commission license. Nuclear fuel reprocessing operations ended in 1972 and never reopened, leaving behind radioactive and chemical wastes. Erosion can play an important role in the fate and transport of waste at sites where disposal of long-lived waste is anticipated. The statistical characterization of key processes related to erosion is essential to the understanding of site stability through time. One of the key processes governing erosion is extreme precipitation and it is critical that trends in the distribution of extreme precipitation events through time be represented. The evidence of climate change is increasingly well documented and projected impacts on extreme precipitation events should be incorporated in performance assessment studies when relevant. Not evaluating future climate states in a performance assessment is contradictory to good modeling practice. Specifically, excluding climate change limits development of modeling information that could aid in effective decision making. The current climate literature provides both observational evidence and climate model projections of climate trends and/or climate change in the late 20. and early 21. centuries for North America and the northeast United States. In this work, this information was used to assess the impacts of potential changes in climate on erosion processes. The goal was to understand how projections of future climate relate to the performance of the WNYNSC through time. In the first stage of this work multi-temporal historical aerial images were analyzed in conjunction with orthophotography and Lidar data to develop probability distributions for variables representing important erosion processes. The information from these analyses was then used in conjunction with simulated data from the West Valley Erosion Working Group (EWG). Analysis of EWG simulations provides estimates for the change in erosion rates through time that is driven by changes in climate. The time-varying rates of erosion change were applied to the historical aerial imagery data in order to inform time-varying rates of erosion that are driven by changes in climate. Ultimately, this process resulted in the identification of locations for features like gully heads using both the Lidar dataset and projection of the estimated location from the historical aerial photo under consideration back to the Lidar dataset. The distance between the estimate of the location from the historical image and that of the Lidar dataset was the estimated distance the feature has moved. This distance was then divided by the number of years between the Lidar dataset and the year of the historical aerial image of interest to get a rate of movement through time. This was done for several dozen points on each historical aerial image. The analyses from the EWG were used to characterize the relative impact of climate change on the erosion rates. This relative impact was quantified by comparing the LEM based estimates of erosion that were derived using historical climate data with LEM based estimates of erosion that were derived using projections of future climate. The relative increase in the erosion rates was then applied to the historical estimates of erosion derived from the analysis of the historical aerial imagery. This approach was used since the LEM-based estimated of the historical erosion rates from the past century have a bias towards underestimating erosion. This underestimation is hypothesized to be a consequence of an inability of the LEMs to account for the impacts of land-use change (i.e. deforestation) which had been shown to significantly increase erosion in similar Northern hardwood forest ecosystems. In summary, gully head retreat rate and gully widening rate were characterized using statistical probability distributions from the historical aerial image analysis. Simulated data from the EWG was used to estimate the climatically-driven changes in erosion rates through time. The changes through time from the EWG were applied to the gully head retreat rate and gully widening rate characterized using the historical aerial image analysis. This information can be used to inform PPA models to project future risks from a given site. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

A Trade-Off Study Between the Primary and Transient Responses of Grid-Forming Inverters

The control parameters of the grid-forming (GFM) inverter-based resources (IBRs) directly impact power system dynamics. The primary control requires the GFM inverter to balance generation and load. It is also preferred that a GFM inverter maintain the terminal frequency after a power system fault. In this paper, we investigate the trade-off between the primary control objective and the transient response. To quantify the transient performance of the GFM inverter, we introduce a new real-time transient stability index (TSI). This index plays a crucial role in our investigation, as it allows us to compare the performance trade-offs of different sets of GFM control parameters.

Lin, Xuheng↗
DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Modeling and Feedback Compensator Design for Power-Hardware-in-the-Loop System for Medium-Voltage Grid-Connected Power Converters

Hardware-in-the-loop (HIL) evaluation is a method in which the test subject is split into a physical part and a simulated part, and these parts are connected with interfaces to form a combined physical-numerical system. Power-hardware-in-the-loop (PHIL) systems, where actual hardware is connected to a real-time model, can exhibit issues of instability, inaccuracy and errors when operating in a closed-loop. The challenges of generating a PHIL setup are that, first, because of the limited dynamic response of the different parts of the system, the test results might be inaccurate, and, second, because of the high frequency noise introduced by the sensors to the closed-loop system, it can be difficult to design a compensator for the real-time emulator response, while stabilizing the closed-loop system at the same time. In this paper, different parts of a PHIL system are characterized, and the feedback compensator system design is proposed for the stable operation of the closed-loop PHIL system. The issues as observed in a PHIL system without any compensator are demonstrated using experimental results, and the effectiveness of a first order phase lead compensator is validated.

compensator design↗
DOE OSTI2023

Bound-preserving finite element approximations of the Keller–Segel equations

We report this paper aims to develop numerical approximations of the Keller–Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a non-negative variable. We propose two algorithms, which combine a stabilized finite element method and a semi-implicit time integration. The stabilization consists of a nonlinear artificial diffusion that employs a graph-Laplacian operator and a shock detector that localizes local extrema. As a result, both algorithms turn out to be nonlinear and can generate cell and chemoattractant numerical densities fulfilling lower bounds. However, the first algorithm requires a suitable constraint between the space and time discrete parameters, whereas the second one does not. We design the latter to attain a discrete energy law on acute meshes. We report some numerical experiments to validate the theoretical results on blowup and nonblowup phenomena. In the blowup setting, we identify a locking phenomenon that relates the L ∞ (Ω)-norm to the L 1 (Ω)-norm limiting the growth of the singularity when supported on a macroelement.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Pedestal formation via different trajectories in the stability space in response to the timing scan of neutral beam heating in DIII-D

The frequency of type-I ELMs decreases as the initiation of the neutral beam injection (NBI) heating is delayed with respect to the time when plasma current (I p ) reaches flat-top in the ITER Baseline Scenario discharges in DIII-D. Henceforth, the time gap between the NBI initiation and I p flat-top will be referred to as “heating delay.” As the heating delay is modified, pedestal formation follows different trajectories in the edge current density–pedestal pressure gradient (j edge -∇p e ped ) space from the L-H transition toward the first ELM event. During the stationary phase after the first ELM, the ELM frequency (f ELM ) decreases by a factor of ~2 as the heating delay is increased. A longer pedestal recovery time in the inter-ELM period is observed for the low f ELM discharges as compared to the high f ELM discharges. Both low and high f ELM discharges show nearly identical profiles of electron density and temperature and have a similar MHD stability just before an ELM crash. However, a marked difference is observed in the magnetic spectrogram of the high and low f ELM discharges in response to the variation in the heating delay. The main difference is in the 200–400 kHz range of the magnetic spectra. A quasi-coherent mode (QCM) at 220 kHz and weaker broadband fluctuations are observed in the high f ELM discharges, while only strong broadband fluctuations are prevalent in the low f ELM discharges. ELM-synchronized analysis shows that the time evolution of these modes is different for the high and low f ELM discharges. The localization of both these modes is confirmed at the maximum gradient region of the pedestal. We hypothesize that these modes cause important pedestal transport and that the difference in the pedestal recovery of the high and low f ELM discharges is a result of the difference in transport driven by these modes, as they change with changes in the heating delay. It is demonstrated experimentally for the first time that discharges with similar pedestal parameters can carry the history of the heating delay into the stationary phase and that changes in turbulent-driven transport are a likely cause of changes in f ELM observed with variations of heating delay.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

ML-Based Power System Stability Assessment Considering Network Topology Changes: WECC 20,000+ Bus System Case Study

Modern power grids are fast-changing and thus require real-time monitoring and online stability assessment. With the rapid development of machine learning (ML) techniques, using data-driven models to provide fast and accurate estimations of power system stability marginal information, such as frequency nadir for frequency stability and critical clearing time (CCT) for transient stability, have become possible. However, despite the numerous research on ML-based methods for frequency nadir and CCT prediction, there is limited work on the impact of different network topology changes. Furthermore, most previous studies only focused on small or synthetic systems, and there is a lack of research on actual large power system models. In this paper, the above issues are addressed by studying the actual U.S. Western Electricity Coordinating Council (WECC) system model with more than 20,000 buses. Massive simulations are conducted in PowerWorld Simulator to study the impact of various topology change scenarios on both frequency stability and transient stability. System operating information is extracted from the success dispatch cases of various network topologies to generate a comprehensive dataset for ML-based models. Two ML methods, random forest (RF) and multilayer perceptron (MLP) neural network, are trained and tested for both frequency nadir prediction and CCT prediction. Test results have proven the models are capable of online stability assessment for large power networks such as the WECC system with sufficient accuracy.

critical clearing time↗
DOE OSTI2024

Topology property analysis and application of stable time-delay regions for linear multiple time-delay systems

This study examines the relationship between the topology of stable time-delay regions and the stability analysis of an linear multiple time delay system. To analyze the topology of stable time-delay regions, we construct a function with a value equal to zero for the time-delay points on the boundaries of stable time-delay regions. The function is continuous and differentiable in the whole defining field with a global minimum of zero so that we can locate the boundaries by minimizing the value of the function. Based on the topology analysis, we proposed a performance validation approach for controllers that are designed to stabilize the system using feedback signals with time delays. The method based on the topology analysis is simple and reliable so that can deal with a linear time-invariant system with high order and multiple time delays (more than 3). The example case study shows that the above method is reliable and enables ultra-low latency coordination and control for the future power grid with ubiquitous power electronics.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Noise-induced stabilization of dynamical states with broken time-reversal symmetry

Under a high frequency drive, Josephson junctions demonstrate Shapiro steps of quantized voltage. These are dynamically stabilized states in which the phase across the junction locks to the external drive. We explore the stochastic switching between two symmetric steps at $\frac{hw}{2e}$ and –$\frac{hw}{2e}$. Surprisingly, the switching rate exhibits a pronounced nonmonotonicity as a function of temperature, violating the general expectation that transitions should become faster with temperature. As a result, we explain this behavior by realizing that the system retains memory of the dynamic state from which it is switching, thereby breaking the conventional simplifying assumptions about separations of timescales.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Theoretical Understanding of the Linear Relationship between Convective Updrafts and Cloud-Base Height for Shallow Cumulus Clouds. Part II: Continental Conditions

This is the Part II of a two-part study that seeks a theoretical understanding of an empirical relationship for shallow cumulus clouds: subcloud updraft velocity covaries linearly with the cloud-base height. This work focuses on continental cumulus clouds that are more strongly forced by surface fluxes and more deviated from equilibrium than those over oceans (Part I). We use a simple analytical model for shallow cumulus that is well tested against a high-resolution (25 m in the horizontal) large-eddy simulation model. Consistent with a conventional idea, we find that surface Bowen ratio is the key variable that regulates the covariability of both parameters: under the same solar insolation, a drier surface allows for stronger buoyancy flux, triggering stronger convection that deepens the subcloud layer. We find that the slope of the Bowen-ratio-regulated relationship between the two parameters (defined as λ) is dependent on both the local time and the stability of the lower free atmosphere. The value of λ decreases with time exponentially from sunrise to early afternoon and linearly from early afternoon to sunset. The value of λ is larger in a more stable atmosphere. In addition, continental λ in the early afternoon more than doubles the oceanic λ. Validation of the theoretical results against ground observations over the Southern Great Plains shows a reasonable agreement. Physical mechanisms underlying the findings are explained from the perspective of different time scales at which updrafts and cloud-base height respond to a surface flux forcing.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Aeroelastic code comparison using the IEA 22MW reference turbine

Reference wind turbine designs and the associated aeroelastic models are widely used in both research and industry. Reference models representing future concepts are of particular interest. Current state of the art aeroelastic tools are relied upon to design the next generation of large wind turbines. However, modelling assumptions may be invalidated by upcoming very large turbines, and different aeroelastic tools may give inconsistent results. A 22MW turbine model has been defined as part of International Energy Agency (IEA) Wind Task 55 on Reference Wind Turbines and Farms to represent future turbines to be deployed in the 2030s. In this study, an aeroelastic model of this turbine has been created in four tools; Bladed, HAWC2, OpenFAST, and QBlade. Code comparisons are presented for steady state operation, linear stability analysis, and time domain power production simulations in steady and turbulent wind. Generally, the codes show a good agreement, but with some differences present in the linear stability analysis, periodic azimuthal variation, and time domain simulations. The models are a good basis for further study with the IEA 22MW turbine, and further code comparison exercises.

17 WIND ENERGY↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic framework for solving the nonlinear equations that arise from IRK methods (and discontinuous Galerkin discretizations in time) applied to nonlinear numerical PDEs, including PDEs with algebraic constraints. Several new linearizations of the nonlinear IRK equations are developed, offering faster and more robust convergence than the often-considered simplified Newton, as well as an effective preconditioner for the true Jacobian if exact Newton iterations are desired. Inverting these linearizations requires solving a set of block 2 x 2 systems. Under quite general assumptions, it is proven that the preconditioned 2 x 2 operator's condition number is bounded by a small constant close to one, independent of the spatial discretization, spatial mesh, and time step, and with only weak dependence on the number of stages or integration accuracy. Moreover, the new method is built using the same preconditioners needed for backward Euler-type time stepping schemes, so can be readily added to existing codes. The new methods are applied to several challenging fluid flow problems, including the compressible Euler and Navier--Stokes equations, and the vorticity-streamfunction formulation of the incompressible Euler and Navier--Stokes equations. Up to 10th-order accuracy is demonstrated using Gauss IRK, while in all cases fourth-order Gauss IRK requires roughly half the number of preconditioner applications as required by standard Singly diagonally implicit Runge--Kutta methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A comparison of Eulerian and semi-Lagrangian approaches for modeling stream water quality

This paper describes and compares some of the advantages and limitations of Eulerian and Lagrangian approaches to water quality modeling and introduces a mixed Eulerian-Lagrangian (or semi-Lagrangian) methodology that captures the strengths of both approaches. The semi-Lagrangian modeling approach is applied to advection-dominated rivers, and flexibly ensures unconditional stability for all time step durations and grid segmentations. The semi-Lagrangian modeling approach is demonstrated by applying it to estimate the dissolved oxygen concentrations in the Sava River in Slovenia, focusing on aspects of the methodology and findings that would be of broad interest to managers of water quality in fluvial water bodies. Results of comparisons of the semi-Lagrangian model with the Eulerian-based QUAL2K model in steady and non-steady scenarios demonstrate that while both models are fully capable of producing satisfactory results when optimally configured, the semi-Lagrangian approach offers accuracy and stability without sensitivity to the interaction of time step size and computational grid segmentation scheme.

Sava River↗
DOE OSTI2025

Regularizing the linearly extrapolated BDF2 scheme for incompressible flows with time relaxation

This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. Furthermore, we also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.

97 MATHEMATICS AND COMPUTING↗