Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical continuation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Magnon heat transport in a two-dimensional Mott insulator

Whether or not anomalies in the thermal conductivity in insulating cuprates can be attributed to antiferromagnetic order and magnons in a 2D Mott insulator remains an intriguing open question. To shed light on this issue, we investigate the thermal conductivity $\kappa$ and its relationship with the specific heat $c_v$ in the half-filled 2D single-band Hubbard model, using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. At low temperatures where the charge degrees of freedom are gapped-out and $c_v$ exhibits a clear magnon peak, we observe that thermal conductivity $\kappa$ also tends to form a peak at similar temperatures. Reducing temperature further produces a sharp upturn in $\kappa$, associated with an increasing mean-free path. Here we identify this as the high-temperature side of the anomalous peak in insulating cuprates, where the mean-free path eventually is cut-off by other scattering effects, including phonons, disorder, and physical size. Different scattering effects in our model are identified and analyzed in the thermal diffusivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Ensuring planetary survival: the centrality of organic carbon in balancing the multifunctional nature of soils

Not only do soils provide 98.7% of the calories consumed by humans, they also provide numerous other functions upon which planetary survivability closely depends. However, our continuously increasing focus on soils for biomass provision (food, fiber, and energy) through intensive agriculture is rapidly degrading soils and diminishing their capacity to deliver other vital functions. These tradeoffs in soil functionality – the increased provision of one function at the expense of other critical planetary functions – are the focus of this review. Here, we examine how land-use change for biomass provision has decreased the ability of soils to regulate the carbon pool and thereby contribute profoundly to climate change, to cycle the nutrients that sustain plant growth and ecosystem health, to protect the soil biodiversity upon which many other functions depend, and to cycle the Earth’s freshwater supplies. We also examine how this decreasing ability of soil to provide these other functions can be halted and reversed. Despite the complexity and the interconnectedness of soil functions, we show that soil organic carbon plays a central role and is a master indicator for soil functioning and that we require a better understanding of the factors controlling the behavior and persistence of C in soils. Given the threats facing humanity and their economies, it is imperative that we recognize that Soil Security is itself an existential challenge and that we need to increase our focus on the multiple functions of soils for long-term human welfare and survivability of the planet.

Carboncarbon sequestration↗

The look-elsewhere effect from a unified Bayesian and frequentist perspective

When searching over a large parameter space for anomalies such as events, peaks, objects, or particles, there is a large probability that spurious signals with seemingly high signi ficance will be found. This is known as the look-elsewhere effect and is prevalent throughout cosmology, (astro)particle physics, and beyond. To avoid making false claims of detection, one must account for this effect when assigning the statistical significance of an anomaly. This is typically accomplished by considering the trials factor, which is generally computed numerically via potentially expensive simulations. In this paper we develop a continuous generalization of the Bonferroni and Sidak corrections by applying the Laplace approximation to evaluate the Bayes factor, and in turn relating the trials factor to the prior-to-posterior volume ratio. Here, we use this to define a test statistic whose frequentist properties have a simple interpretation in terms of the global p-value, or statistical significance. We apply this method to various physics-based examples and show it to work well for the full range of p-values, i.e. in both the asymptotic and non-asymptotic regimes. We also show that this method naturally accounts for other model complexities such as additional degrees of freedom, generalizing Wilks' theorem. This provides a fast way to quantify statistical significance in light of the look-elsewhere effect, without resorting to expensive simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

NUM-DAT File Format Specification: Used in M-9 Gun Experiment Data Archiving

The M-9 Shock and Detonation Physics group executes experiments on gun and explosive platforms with large numbers of oscilloscopes used for data acquisition. The data acquisition from these oscilloscopes was automated many years ago using a custom piece of software called RunDig . The default save format from this software is a custom structure referred to as "NUM-DAT" format. This file format includes a text ".DAT" file which is a header file used to interpret the binary ".NUM" file which contains the oscilloscope data. The data save format was originally developed by John Vorthman and has been in use by M-9 personnel for over 20 years. This data format has been used for archiving data from experiments performed by M-9 personnel at TA-40, TA-39, and the TA-55 Impact Test Facility. Numerous custom analysis and visualization programs have also been developed, and continue to be used, that utilize this data format. This document describes the NUM-DAT format and provides code examples for reading the format and converting it to other formats.

47 OTHER INSTRUMENTATION↗

Reducing NOx Emissions in Ammonia Combustors

Ammonia continues to attract growing interest as a carbonneutral replacement fuel, motivating numerous research efforts toward understanding fundamental ammonia combustion characteristics. A major challenge for the use of ammonia is the development of combustor technologies for mitigating potentially high NOx emissions from the fuel-bound nitrogen chemical pathways to acceptable levels. Our work focuses on a staged RQL combustor architecture for minimizing the NOx emission levels through burning fuel-rich in the primary stage to formcombustion products containing significant levels of hydrogen in addition to nitrogen and water with minimal NOx formation. The subsequent quench and burnout stages of the combustor must then quickly burn residual hydrogen with flame-temperatures moderated by nitrogen and water forming in the first stage. Chemical Reactor Network modeling was used to understand and identify optimal stoichiometry and residence times in each stage for minimizing NOx emissions and to quantify pressure and temperature effects. Reducing the overall NOx emissions requires relatively long residence times in the primary stage to achieve near equilibrium NO levels due to kinetically controlling processes. For conditions relevant to gas turbines (e.g., 30 atm), our work indicates that NOx emissions below 20 ppm are theoretically achievable in a staged RQL combustor architecture. However, these emission predictions significantly depend on the accuracies of currently available chemical kinetic mechanisms which have not been extensively validated under elevated pressure and temperature conditions relevant to gas turbines.

10 SYNTHETIC FUELS↗

Removing numerical pathologies in a turbulence parameterization through convergence testing

Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB's equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e. clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, this noise can be amplified by an advective term in CLUBB's background diffusion. Smoothing the limiters and removing the advective component of the background diffusion reduces the noise and restores the expected first-order convergence in CLUBB's solutions. These model reformulations improve the results at coarser, near-operational grid spacing and time step in cumulus cloud and dry turbulence tests. In addition, convergence testing is proved to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

Mathematics and Computing, Geosciences↗

Removing Numerical Pathologies in a Turbulence Parameterization Through Convergence Testing

Abstract Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB's equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e., clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, nonlinear artificial diffusion employed for improving numerical stability can introduce unintended small‐scale features into the solution of the model equations. Smoothing the limiters and using linear artificial diffusion reduces the noise and restores the expected first‐order convergence in CLUBB's solutions. These model reformulations enhance our confidence in the trustworthiness of solutions from CLUBB by eliminating the unphysical oscillations in high‐resolution simulations. The improvements in the results at coarser, near‐operational grid spacing and timestep are also seen in cumulus cloud and dry turbulence tests. In addition, convergence testing is proven to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

58 GEOSCIENCES↗

Oxygenated Fuel Blending Effects in a Mixing-Controlled Compression-Ignition Engine Equipped with Ducted Fuel Injection [Slides]

Continued creation of harmful emissions such as NO x and soot from compression-ignition engines utilizing mixing-controlled combustion systems (i.e., diesel engines) remains a problem and is the subject of on-going research. The inherently high efficiency, relatively low cost, and numerous other desirable attributes of such engines, coupled with a widely supported infrastructure, motivates their continued advancement. Recently, a scientifically distinct and mechanically simple technology called ducted fuel injection (DFI) has shown a robust ability to allow such engines to operate with simultaneously low engine-out soot and NO x emissions when it is employed with simulated exhaust-gas recirculation. To better understand the property ranges of sustainable, oxygenated-fuel blending stocks that will most improve engine performance, two oxygenated blendstocks were separately blended with a commercial diesel base fuel and tested within a heavy-duty diesel optical engine equipped with a four-duct DFI configuration. Conventional and crank-angle-resolved optical diagnostics were used to elucidate the effects of fuel ignition quality, oxygenate molecular structure, and overall oxygen content on engine performance.

33 ADVANCED PROPULSION SYSTEMS↗

Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

EERC Final Topical Report – Findings on Subtask 3.2 – Produced Water Management Through Geologic Homogenization, Conditions, and Reuse

The Energy & Environmental Research Center (EERC) was awarded a contract by the North Dakota Industrial Commission (NDIC) Oil and Gas Research Program (NDIC No. G-051-101) to conduct a study on the recycling of water used in oil and gas operations, also known as produced water, from oil- and gas-producing regions of North Dakota as directed by Section 19 of North Dakota House Bill 1014. This final report provides a compilation of results of the study, which include regulatory, scientific, technological, and feasibility methods and considerations associated with North Dakota produced water management. The report provides a synopsis of this project’s previously submitted produced water assessment report entitled “Produced Water Management and Recycling Options in North Dakota” (Energy & Environmental Research Center, 2020), with updated values provided as appropriate. The report provides the results from the investigation of a novel produced water management strategy, referred to as geologic homogenization, conditioning, and reuse (GHCR), which aims to use a subsurface geologic formation as a natural medium for managing produced water recycling and reuse. Water management is a significant technical and economic challenge for sustainable oil and gas production, and water volumes are intrinsically linked to oil production volumes. North Dakota oil production rose to over 1.5 million barrels (MMbbl)/day in 2019, and despite a downturn in oil price in early 2020, North Dakota oil production has recovered to 1.1 MMbbl/day as of August 2021. Bakken petroleum system development between 2008 and 2020 has resulted in a nearly fourfold increase in produced water volumes to 642 MMbbl/yr in 2020 after peaking at 740 MMbbl/yr in 2019 and a fivefold increase in saltwater disposal (SWD) volumes to 565 MMbbl/yr in 2020 after a peak of 682 MMbbl/yr in 2019. Produced water and SWD volumes are forecasted to double by 2030. SWD is the primary method of produced water management used in North Dakota, with approximately 95% of the SWD volume occurring through subsurface injection into sandstones of the Dakota Group (Dakota). Localized pressurization of the Dakota resulting from SWD and projected increases in produced water volumes could impact the economics of North Dakota oil production. As a result, there is an emerging need to pursue alternative produced water management approaches, including recycling and reuse. While produced water recycling is not yet widespread, commercial operators are making strides in overcoming the technical challenges of using high salinity produced water in completion operations (Marathon Oil, 2020). As water management continues to be a key focal point in companies’ environmental, social, and governance (ESG) initiatives, focus on water management, including recycling, will likely continue to increase. Laboratory column testing, field sample collection, geologic modeling and numerical simulation, and techno-economic analysis all indicate that GHCR could feasibly be implemented as a potential water management option. Laboratory column testing and field sample collection indicate that the Inyan Kara sandstone and native formation fluid are capable of homogenizing with the Bakken produced water to a point where the fluid composition appears to stabilize. Extracting that stabilized fluid could be considered homogeneous and capable of providing individual batches of hydraulic fracturing fluid. Numerical simulation results indicate that extraction of fluids from the Inyan Kara in a GHCR implementation scenario is capable of reducing formation pressure, which would help ease localized pressurization of the Inyan Kara and extend the available capacity for nearby existing SWD wells. Economic analysis indicates that there are scenarios where GHCR implementation can be a competitive or even lower-cost option than a conventional water management approach. Site-specific conditions will dictate the economic potential of GHCR, but potentially attractive sites for GHCR implementation will be those that are located above a pressurized zone of the Inyan Kara, need six or more Bakken infill wells, and face high costs for conventional SWD and/or freshwater. Based on the regulatory review, drilling into the Inyan Kara for SWD and to harness as a source water for industrial use have precedent in North Dakota, and a workable regulatory solution for GHCR seems likely. However, restrictions in the state regarding surface storage and transport of produced fluids may limit some activities, which will affect how GHCR could ultimately be implemented. In summary, this study reveals pursuing GHCR can be a viable approach to water management in North Dakota. The GHCR concept addresses some of the challenges that hinder the more traditional approaches to recycling in the industry. Furthermore, an assessment of the current landscape of water management within the state reveals the ongoing trend of increasing volumes of produced water and SWD. Projections reveal that the volumes of produced water that need to be managed are expected to double over the next decade (Energy & Environmental Research Center, 2020). With the continued development of the Bakken and continuing driving factors related to ESG initiatives, implementing a practice such as GHCR is a feasible approach to adding recycling of produced water to industry within the state. This subtask was cofunded through the EERC–U.S. Department of Energy Joint Program on Research and Development for Fossil Energy-Related Resources Cooperative Agreement No. DE-FE0024233. Nonfederal funding was provided by the North Dakota Industrial Commission Oil and Gas Research Program. References Energy & Environmental Research Center, 2020, Produced water management and recycling options in North Dakota: Final Report for North Dakota Legislative Management Energy Development and Transmission Committee and North Dakota Industrial Commission. Marathon Oil, 2020, Sustainability report: https://cdn.sanity.io/files/ghcnw9z2/website/ 91744eb6ef8fbe59505a911c6b8d2e8dd9a537fa.pdf?dl (accessed November 2021).

02 PETROLEUM↗

Light-ray wave functions and integrability

Using integrability, we construct (to leading order in perturbation theory) the explicit form of twist-three light-ray operators in planar $\mathcal{N}$ = 4 SYM. This construction allows us to directly compute analytically continued CFT data at complex spin. We derive analytically the “magic” decoupling zeroes previously observed numerically. Using the Baxter equation, we also show that certain Regge trajectories merge together into a single unifying Riemann surface. Perhaps more surprisingly, we find that this unification of Regge trajectories is not unique. If we organize twist-three operators differently into what we call “cousin trajectories” we find infinitely more possible continuations. We speculate about which of these remarkable features of twist-three operators might generalize to other operators, other regimes and other theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

OC6 Project Phase IV: Validation of Numerical Models for Novel Floating Offshore Wind Support Structures

The fourth phase of the Offshore Code Comparison, Collaboration, Continued, with Correlation and unCertainty (OC6) aims to assess the ability of the tools to model a novel floating wind design. The design that was selected for this project is the TetraSpar designed by Stiesdal Offshore Technologies. The platform is a unique design that features a spar like stability with a very low center of gravity, but does not require deep-water ports. This combination is achieved with a system made of two separate steel structures, a hull at the water’s surface that supports the wind turbine tower, and a keel that is suspended below the main body. This lower keel has a very high density and drives the total platform’s low center of gravity. Scaled model tests of the TetraSpar design were performed in 2018-2019 by the University of Maine. The tests were performed with 1:43 Froude scaling. The data collected in the model tests provide a detailed description of the response of the platform in various controlled and relatively well understood conditions. Comparison with these data provides a good opportunity for validation of numerical models. The OC6 Phase IV work will focus on the specific parameters used in these scaled model tests. The load cases (LC) considered in this project are as follows: LC 1.X - Equilibrium and Static Offset Tests LC 2.X - Platform Free Decays LC 3.X - Turbine Thrust (Wind Only) LC 4.X - Regular and Irregular Waves (Wave only) LC 5.X - Combined Wind and Wave Loading

17 WIND ENERGY↗

Tri‐Metallic Catalyst for Oxygen Evolution Reaction Enables Continuous Operation of Anion Exchange Membrane Electrolyzer at 1A cm −2 for Hundreds of Hours

Abstract Although numerous efforts are made to synthesize active electrocatalysts for green hydrogen production; catalyst stability, and facile synthesis to scale up the production are still challenging. Herein, the production of novel non‐PGM catalysts for the oxygen reduction reaction (OER) in an alkaline aqueous medium is reported, which is based on the synthesis of a trimetallic metal–organic framework (MOF) precursors. Fine‐tuning of the composition of the metal centers (Ni, Co, and Fe) shows a great effect on OER activity after the MOF undergoes dynamic chemical and structural transformations under OER conditions. In situ characterization reveals the origin of OER activity enhancement as metals’ oxidation state increases, inducing compressive mechanical strain on metal centers, enhancing the electronic conductivity through the formation of oxygen vacancies, and stronger metal–oxygen covalency. Catalysts are used in membrane electrode assembly (MEA) setup within an industrial full‐cell anion exchange membrane electrolyzer (AEMEC), showing a stable performance for 550 h without noticeable decay at 750 and 1000 mA cm −2 industrial level current densities.

Chemistry↗

Reassessing methods to close the nuclear fuel cycle

This paper presents the major takeaways from studies conducted over several years that were focused on transitioning the U.S. nuclear infrastructure from the current once-through fuel cycle to one in which fuel is continuously recycled in fast reactors. Furthermore, these studies involved simulating and analyzing numerous example scenarios of fuel cycle transition with various assumptions on technology, policy, and material utilization strategies. Among the many findings, perhaps the most important is that under certain conditions, the use of high-assay low-enriched uranium to start up a fleet of fast reactors may be more favorable compared to using recycled Pu from thermal reactors since it is less constrained by other technologies and may even be more economical.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Investigation of enhanced CO 2 storage in deep saline aquifers by WAG and brine extraction in the Minnelusa sandstone, Wyoming

Geological CO 2 sequestration in deep saline aquifers has been extendedly investigated to reach the goal of carbon neutral as large amount of CO 2 can be reduced in a short time. Here, this study investigates the feasibility of water-alternating-gas (WAG) injection and brine extraction on enhancing CO 2 storage in a target deep saline aquifer, Minnelusa Sandstone in the Powder River Basin (PRB) of Wyoming. An integrated numerical model is developed to account for four scenarios: (1) CO 2 continuous injection (CI) through one injection well, (2) WAG injection through one injection well, (3) CO 2 CI through one injection well and brine extraction through one producer, (4) WAG injection through one injection well and brine extraction through one producer. Simulation results suggest that WAG injection and brine extraction corporately make it possible to enhance CO 2 injectivity while securing CO 2 storage safety. For instance, WAG injection considerably reduces structural trapping contribution while enhances dissolved and residual trapping contributions. As for brine extraction, it can decrease the maximum averaged reservoir pressure by 37% and 22% for CI and WAG injection, respectively. Besides, sensitive analyses of the operational parameters for the fourth scenarios are performed. Results reveal that, when the amount of total CO 2 injection has been predetermined, CO 2 injection time and rate within each period of WAG should be small whereas it is preferable to have large water injection time and rate. This is to secure desirable dissolved and residual trapping contributions (store CO 2 with safety). Sensitive degree results confirm that CO 2 injection rate, water injection time, and CO 2 injection time of WAG injection exhibit significant effects on CO 2 storage whereas the impacts of producer bottom-hole pressure (BHP), water injection rate, and CO 2 -water injection time are relatively weaker. This study not only sheds light on achieving double-win goal: enhance CO 2 injectivity and store CO 2 with safety, but also can be a critical reference for other CO 2 storage in deep saline aquifers.

58 GEOSCIENCES↗

Adaptive Deep Reinforcement Learning Algorithm for Distribution System Cyber Attack Defense With High Penetration of DERs

With grid modernization, smart inverters are increasingly used to execute advanced controls for distribution network reliability. However, this also increases the cyber-attack space. Here this paper focuses on the defense approaches to restore the system to normal operation circumstances in the presence of cyber-attacks. A unique deep reinforcement learning (DRL) method is developed to minimize voltage violations and reduce power losses for impacted feeders. The defense problem is reformulated as a Markov decision-making process to dynamically control DERs while minimizing load shedding. This is achieved via an improved soft actor-critic (SAC)-based DRL algorithm, which can govern DER set points and load-shedding scenarios in discrete and continuous modes via the auto-tune entropy and Gaussian policy features. Numerical comparison results on the modified IEEE 123-node system with other control approaches, such as Volt-VAR (VV), Volt-Watt (VW), and model predictive control (MPC) show that the proposed method can eliminate voltage violations and provide feasible control actions that perform complete mitigation of cyber-threats.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Laser heating and evaporation of a single droplet

The laser technology is being abundantly studied for controlled energy deposition for a range of applications in aerodynamic flow control, material processing, ignition, and combustion. The absorption of laser radiation by liquid droplets affects further propagation of laser in the atmosphere and causes bleaching of suspended droplets while the ignition and combustion characteristics in combustors are influenced by the evaporation rate of the sprayed fuel. In this work, we present a multi-dimensional mathematical model built on OpenFOAM for laser heating and evaporation of a single droplet in the diffusion dominated regime taking into account absorption of the laser radiation, evaporation process and vapor flow dynamics. The developed solver is validated against available experimental and numerical data for the ethanol and water droplet heating and evaporation. For continuous heating the peak temperature is established by the balance of cooling, evaporation and heating and results in high temperature for larger droplets. It has been shown that for heating by a single laser pulse the maximum temperature of droplets depends only on the peak intensity of the laser radiation. Furthermore, for the peak irradiance close to the transition to the boiling regime, temporal dynamics of the droplet temperature is independent of the droplet size. With proper normalization of time, the dynamics of the droplet shrinkage and cooling is shown to be independent of droplet sizes and peak laser intensities. The influence of cooling and evaporation processes on droplet heating was found to be controlled by the pulse repetition rate for repeated pulse operation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

OC6 project Phase IV: validation of numerical models for novel floating offshore wind support structures

Abstract. This paper provides a summary of the work done within Phase IV of the Offshore Code Comparison Collaboration, Continued with Correlation and unCertainty (OC6) project, under International Energy Agency Wind Technology Collaboration Programme Task 30. This phase focused on validating the loading on and motion of a novel floating offshore wind system. Numerical models of a 3.6 MW horizontal-axis wind turbine atop the TetraSpar floating support structure were compared using measurement data from a 1:43-Froude-scale test performed in the University of Maine's Alfond Wind–Wave (W2) Ocean Engineering Laboratory. Participants in the project ran a series of simulations, including system equilibrium, surge offsets, free-decay tests, wind-only conditions, wave-only conditions, and a combination of wind and wave conditions. Validation of the models was performed by comparing the aerodynamic loading, floating support structure motion, tower base loading, mooring line tensions, and keel line tensions. The results show a relatively good estimation of the aerodynamic loading and a reasonable estimation of the platform motion and tower base fore–aft bending moment. However, there is a significant dispersion in the dynamic loading for the upwind mooring line. Very good agreement was observed between most of the numerical models and the experiment for the keel line tensions.

17 WIND ENERGY↗