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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 433 records · Page 24

TEAMER: Electrically Engaged Undulation (EEL) System

The Electrically Engaged UnduLation (EEL) system is a buoyancy-driven submersible device for powering oceanographic instruments. Physically, EEL is a slender body whose flexible spine is made up of energy units interconnected by uniaxial hinges. Each unit consists of a pair of piezoelectric elements that converts the bending stress into electrical current to a battery charging circuit. An outer plastic skin forms a seal against water and allows for flexibility at hinge locations. At the top is a bluff body with electronics that holds a ballast for buoyancy adjustment. The bluff body is also responsible for creating fluid instabilities in its wake. When gliding through the water (mode 2), the spine will flex in response to the alternating vortices that shed from the head. This "lock-in" phenomenon occurs when the frequency at which vortices shed resonates with the EEL natural frequency, during which the efficient gaits were found in species of sea snake, eels, and fish. For active propulsion, a single motor can be placed at the first segment and provide the oscillatory input for propulsion similar to a dolphin's kick. Such anguilliform swimming is both efficient and nearly silent compared to a spinning propeller. Ultimately, mimicking bio-locomotion provides a viable path to a drag-reduced, self-propelled energy harvesting system for ocean monitoring.

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Flexoelectricity and New Phenomena

It is easy to miss the scientific implications of our recent work on Triboelectricity. Everyone knows that rubbing and contact can produce static electricity; less appreciated is that the thermodynamic driver has been an open question since static electricity was first observed by Thales of Miletus around 585 BC. People think they understand it, for instance one common explanation that can still be found in the current literature is that differences in the work function drives charge transfer, often called the Volta-Helmholtz hypothesis. As summarized in 1967 by Harper, this fails to explain many experimental observations, for instance that charging can occur when two pieces of the same material are rubbed against each other. We are the first to place triboelectricity on a solid foundation rooted in quantum mechanics – the flexoelectric effect. We were able to explain a significant number of previously unexplained phenomena: 1) Bipolar tribocurrents associated with stick-slip, due to the change in sign of the strain gradients. 2) A one-third power scaling of tribocurrents with indentation force. 3) Tribocharging when two identical materials are used, these being due to local variations in the asperities so there are usually local potential differences. 4) Inhomogeneous charging of insulators, related to the statistical nature of asperities. 5) An experimentally observed reversal in the sign of charge transfer for negative and positive curvature, which is related to a change in the sign of the strain gradient. Exploiting our DOE prior funded work on flexoelectricity, we obtained semi-quantitative matching to existing experimental measurements of the surface charge in triboelectric experiments. The work has been well received in the literature. The work has been the focus of a number of popular science press articles, and also formed the basis for a Podcast for children 6-10 “The Rise and Fall of Static Man” posted in December 2019 by NPR as part of their “Wow in the World” series. I was also briefly interviewed by the Chicago PBS station in January 2020. This work are significant for a wide range of energy applications; to quote from an independent source: "Triboelectric power has plenty of potential, says Wenzhuo Wu, an assistant professor of engineering at Purdue. If the basics of static electricity are better understood, we could maximize the efficiency of wind or wave power generators, Wu says. The body's own movement could be used to power internal medical devices. Imagine being able to create a roof shaped to harness the power of a raindrop — the friction of the rain passing over the surface — to generate triboelectricity, powering the building below it." This is the start of new science, some of which we already partially understand such as the role of band bending in charge transfer. We need to understand charge transfer combining elasticity, quantum mechanics, band bending and defect states. These directly involve several of the DOE Grand Challenges: "How do we control material processes at the level of electrons? How do remarkable properties of matter emerge from complex correlations of the atomic or electronic constituents and how can we control these properties? How do we characterize and control matter away—especially very far away— from equilibrium?" I will argue that this work truly falls into the class of disruptive science; it is not just a simple extension, linear science. Not everyone will accept the approach. Since we explain far more about triboelectricity than anyone before, the preponderance of evidence supports the model. The feedback I have received is that many agree with the work, to quote: "The model makes sense, says Michael McAlpine, a professor of engineering at the University of Minnesota. "It's such a simple explanation, I was surprised I didn't put my finger on that," McAlpine says." The proposal received strong reviews. It was also publicized on the Department of Energy Web Site.

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Biological Consequences of Marine Energy Development on Marine Animals

Marine energy devices harness power from attributes of ocean water to form a sustainable energy source. Knowledge gaps remain about whether marine energy systems can affect the environment, adding another threat to animal populations and habitats already under pressure from climate change and anthropogenic activities. To date, potential environmental effects have been studied under the scope of stressor–receptor interactions, where moving parts of, or emissions from, a system could harm the animals, habitats, and natural processes. While crucial for understanding effects and identifying knowledge gaps, this approach misses a holistic view of what animals may experience in the presence of marine energy systems. We look at six biological consequences and forces that drive the health of an animal population and the effects expected from marine energy development: success of early life stages; changes in competitive capabilities; growth and survival based on food availability; susceptibility to predators; injury or death; and reproductive success. We use case studies to develop this approach, focusing on a variety of marine animals. An approximate level of risk is assigned for each interaction based on the biological consequences. This work highlights the need to examine the effects of marine energy development on animal populations within their natural habitats.

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A compact mechanical power take-off for wave energy converters: Design, analysis, and test verification

Power Take-off (PTO) is one of the most critical components in the ocean wave conversion. This paper introduces an innovative compact mechanical PTO using a ball screw mechanism and a Mechanical Motion Rectifier (MMR) to improve the energy conversion performance. The proposed MMR PTO converts bidirectional oscillatory motion of the ocean waves into unidirectional rotation. The detailed design and working principle of the MMR PTO are explicitly explained. Dynamic analysis is presented for the three most important factors that influence the performance, including the equivalent mass, the equivalent damping, and the excitation frequency. The analytical relationship between these factors and the disengaged freewheeling motion caused by the MMR mechanism is derived, and the analytical solution is verified through dry lab testing. Experimental results in bench tests show that compared with the traditional linear PTO which use the ball screw to drive the generator directly, the MMR PTO is more efficient because of the unique freewheeling motion, achieving a maximum 81.2% energy transfer efficiency. After integrating the prototype PTO with a single-body point absorber type of wave energy converter, testing in a water tank yields total PTO efficiency up to 62.4%, showing a very promising potential for real applications.

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PacWave South SeaRAY k2 Risk Registers

The SeaRAY is a deployable power system for maritime sensors, monitoring equipment, communications, unmanned underwater vehicles, and other similar payloads. This project is to design, deliver, and test a prototype low-power WEC that lowers the total cost of ownership and provides robust, new capabilities for customers in the maritime environment. Failure Modes, Effects, and Criticality Analysis (FMECA) is conducted to systematically identify all potential failure modes and their effects on the system, and to analyze the criticality of each risk based on the likelihood of the event and the severity of the impact. Actions may then be recommended to mitigate the criticality of a risk, either by reducing the likelihood of the risk or the severity of its impact. Risk assessment is executed iteratively as an integral part of the design process. By incorporating risk assessment early in the development cycle, mitigation of risk can be achieved cost effectively. The actions recommended to mitigate risk may be subsequently executed, and as the design progresses the risk assessment is reviewed and revised. Review of the risk assessment is integrated into structured design reviews, ensuring that critical risks are comprehended and that the Project will not progress to e.g. fabrication while intolerable risks remain. The risk assessment process results in the population and maintenance of Risk Registers (RRs). Each major system (and as needed, subsystem) will have a distinct RR. This allows each system or subsystem to be assessed individually, rendering the RRs to a manageable size for review.

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The Design, Fabrication, and Test Program for NREL's Wave-Powered Desalination System

Starting in 2018, the U.S. Department of Energy's Water Power Technologies Office (WPTO), initiated the development of a prize competition as a foundational investment of Powering the Blue Economy, the prize encouraged the development of small, modular, cost-competitive wave-powered desalination systems. The National Renewable Energy Laboratory (NREL) was tasked with managing the prize, known as the Waves to Water Prize (W2W), and providing technical input based on prior desalination research performed at the lab. NREL partnered with the Coastal Studies Institute (CSI) and Jennette's Pier in North Carolina for their expertise in deploying research articles at the Jennette's Pier research facility. The prize consisted of five stages that included high-level concept proposals, numerical modelling, site-specific design, subsystem prototyping, and a final ocean demonstration. Due to the logistical risks of installing numerous prototypes in the ocean at the same time, NREL was tasked with designing and building a test article to de-risk the final event. The test article design needed to represent the technologies expected in the final stage of the prize. This meant that the design was expected to follow the same rules as the competitors, providing CSI with an opportunity to practice installations and develop a final logistics plan prior to the final event. After concluding the W2W event in April 2022, the NREL test article was redeployed in August 2022 to better understand the challenges of anchoring wave energy converters (WECs) in shallow water conditions with breaking waves.

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Testing and Expertise for Marine Energy (TEAMER) Program Support - Numerical Modeling Assistance for iProTech's "PIP" WEC Device: Cooperative Research and Development Final Report, CRADA Number CRD-20-17303

Develop a time-domain, 3 degree of freedom numerical model of IProTech's PIP device, including power take-off (PTO), that can be used to develop control algorithms and establish a baseline technology performance level (TPL). This is important to IProTech because having a good numerical model allows IProTech to optimize design and control algorithms on an ongoing basis. A baseline TPL enables the PIP technology to be benchmarked against other wave energy converter (WEC) concepts, providing (i) justification (or not) for investment in wave tank model testing, (ii) identifying optimum design parameters and control algorithms for the test model, (iii) specifying test conditions and (iv) interpreting wave tank test results. An accredited WEC-Sim model of the PIP device is an essential tool for further development of the technology. 1) The development of numerical models of the PIP concept will enable iProTech to evaluate the potential performance of this concept, and to investigate how sensitive the device is to different variables within the system (e.g. hydraulic components, geometry dimensions, etc.) 2) The numerical models were developed with WEC-Sim and PTO-Sim -- the de-facto industry standard WEC numerical modeling tools. A detailed model of the system's hydraulic circuit was developed with PTO-Sim. However, WEC-Sim is based on linear hydrodynamics and has several limitations; validation against high fidelity models/physical scale models would help to build confidence in the results.

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HERO WEC V1: Design and Experimental Data Collection Efforts

The Hydraulic and Electric Reverse Osmosis Wave Energy Converter (HERO WEC) is a research platform aimed at developing a modular, small-scale wave-powered desalination system for remote and disaster-response applications. Funded by the Department of Energy (DOE)'s Water Power Technologies Office (WPTO), the project aims to advance wave-powered desalination by developing and testing a small-scale, modular wave energy converter (WEC). The insights gained from this project will help guide the design and development of larger-scale wave energy devices as well as the integration of marine energy and reverse osmosis (RO) desalination. The HERO WEC was initially developed to derisk the Waves to Water prize, enabling the staff to practice WEC deployment and recovery, while optimizing installation protocols ologies, aiming to advance the broader fields of marine energy and water treatment.

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The Design, Fabrication, and Test Program for NREL's Wave-Powered Desalination System: Preprint

Starting in 2018, the U.S. Department of Energy's Water Power Technologies Office (WPTO), initiated the development of a prize competition as a foundational investment of Powering the Blue Economy, The prize encouraged the development of small, modular, cost-competitive wave-powered desalination systems. The National Renewable Energy Laboratory (NREL) was tasked with managing the prize, known as the Waves to Water Prize (W2W), and providing technical input based on prior desalination research performed at the lab. NREL partnered with the Coastal Studies Institute (CSI) and Jennette's Pier in North Carolina for their expertise in deploying research articles at the Jennette's Pier research facility. The prize consisted of five stages that included high-level concept proposals, numerical modelling, site- specific design, subsystem prototyping, and a final ocean demonstration. Due to the logistical risks of installing numerous prototypes in the ocean at the same time, NREL was tasked with designing and building a test article to de- risk the final event. The test article design needed to represent the technologies expected in the final stage of the prize. This meant that the design was expected to follow the same rules as the competitors, providing CSI with an opportunity to practice installations and develop a final logistics plan prior to the final event. After concluding the W2W event in April 2022, the NREL test article was redeployed in August 2022 to better understand the challenges of anchoring wave energy converters (WECs) in shallow water conditions with breaking waves. For the Spanish version of this report, see NREL/CP-5700-88482 (https://www.nrel.gov/docs/fy24osti/88482.pdf).

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Ocean Energy Systems Wave Energy Modeling Task 10.4: Numerical Modeling of a Fixed Oscillating Water Column

This paper reports on an ongoing international effort to establish guidelines for numerical modeling of wave energy converters, initiated by the International Energy Agency Technology Collaboration Program for Ocean Energy Systems. Initial results for point absorbers were presented in previous work, and here we present results for a breakwater-mounted Oscillating Water Column (OWC) device. The experimental model is at scale 1:4 relative to a full-scale installation in a water depth of 12.8 m. The power-extracting air turbine is modeled by an orifice plate of 1–2% of the internal chamber surface area. Measurements of chamber surface elevation, air flow through the orifice, and pressure difference across the orifice are compared with numerical calculations using both weakly-nonlinear potential flow theory and computational fluid dynamics. Both compressible- and incompressible-flow models are considered, and the effects of air compressibility are found to have a significant influence on the motion of the internal chamber surface. Recommendations are made for reducing uncertainties in future experimental campaigns, which are critical to enable firm conclusions to be drawn about the relative accuracy of the numerical models. It is well-known that boundary element method solutions of the linear potential flow problem (e.g., WAMIT) are singular at infinite frequency when panels are placed directly on the free surface. This is problematic for time-domain solutions where the value of the added mass matrix at infinite frequency is critical, especially for OWC chambers, which are modeled by zero-mass elements on the free surface. A straightforward rational procedure is described to replace ad-hoc solutions to this problem that have been proposed in the literature.

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Exploring Novel Configuration Designs Alternatives for Lazy Wave Submarine Power Cables

Floating offshore wind turbines require a complex integrated design to balance the platform response and station-keeping requirements in a highly dynamic environment. Dynamic subsea power cables are one of the critical components that have to be considered in detail to ensure both extreme, as well as repeated operational conditions do not exceed the cable design limits. This paper presents the design feasibility limits of a 66kV dynamic cable for a lazy wave configuration. The work explores an innovative staggered cable configuration that has the potential to provide additional compliance in shallow water conditions. Both configurations are evaluated using the motions of a representative floating wind platform under development for deployment in relatively shallow water depth of 150m. The assessment was conducted using the hydrodynamic software Orcaflex, incorporating a range of design inputs and design variations. Key parameters analysed include cable curvature and effective tension and bending stress. The alternative cable configuration provides a more gradual crossing of the water column, which would allow to support increased platform excursions in shallow water depths. The design uses a combined buoyancy and bend protection element, offering designers additional options for challenging operational conditions. The paper will be of interest to designers and developers of floating wind projects, providing a comparative assessment between the conventional lazy wave configuration and an innovative alternative that enables larger cable and mooring excursion envelopes in challenging conditions.

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Triton Initiative: FY 2024 Communications, Outreach, and Engagement End-of-Year Report

The Department of Energy (DOE) Water Power Technologies Office (WPTO) Triton Initiative works to reduce barriers to permitting of marine energy testing and installation through environmental monitoring research that can help inform decision-makers on potential environmental effects associated with these systems. Communications, outreach, and engagement efforts are critical to Triton's success, which involves facilitating the effective communication and dissemination of environmental monitoring research information and results to end-users and fostering collaborations between researchers and industry partners to address the most pressing needs of this emerging industry. The Triton Initiative's communications, outreach, and engagement (TCOE) foundational goals are to educate and raise awareness of ME and the role of Triton's environmental monitoring research in supporting the industry, build trust with audiences through transparent communications and outreach, and evaluate and refine TCOE tactics based on feedback and metrics. The TCOE FY 2024-specific objectives were to (1) refine and grow Triton's audience network by reaching new individuals and communities within Triton's target audience base, and (2) improve the strategy and evaluation of TCOE efforts to demonstrate the value of communications and outreach for the ME community. This report presents the results and analysis of communications activities from September 1, 2023 through August 31, 2024. We assess the TCOE target audiences, highlight notable successes and lessons learned from FY2024, and identify the most effective channels and activities used to connect with those audiences to achieve the TCOE goals.

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Polymer Additive Manufacturing for Marine Renewable Energy Applications: Best Practices, Research Trends, and Current Challenges

Additive manufacturing (AM) is a rapidly growing technology space, not only for prototyping, but is also becoming more feasible at larger scales and increasing component quantities. There are a large variety of AM processes and materials available to users and effectively applying those processes and materials to a specific use case can be challenging. One specific area where AM could be particularly beneficial is marine renewable energy (MRE). Not only is MRE a relatively nascent industry with a near-term need for rapid deployments and prototype testing, but developers could also see long-term benefits from the broad variety of environmentally resistant materials available and the ability to manufacture complex geometries that AM technologies offer. Over the past 4 years, AM materials have played an increasing role in the Advanced Materials project; a multi-year, multi-laboratory research project funded by the U.S. Department of Energy's Water Power Technologies Office, with the main goal of reducing barriers to the adoption of complex materials in the MRE industry. The primary focus of this project is to develop test methods and generate datasets to understand the long-term performance of advanced materials in marine environmental and address specific material challenges as they arise. This report provides an extensive overview of the research that has been performed specific to AM polymers as part of the Advanced Materials project. The intention of this document is to provide recommendations of best practices with regards to material selection, mechanical test method development, and design practices, lessons learned along the way, current research trends, and ongoing challenges with regards to AM polymers in marine environments. In particular, this report focuses on several key aspects: Material and process selection, Environmental conditioning and subsequent degradation quantification through mechanical characterization, Composite reinforcements on AM polymer substrates, Adhesion of instrumentation for mechanical characterization and loads measurements, Protective coatings for preventing biofouling and water ingress, Other MRE case studies where AM has proved particularly useful. Ultimately, we hope that the test methods that have been developed, data generated, and lessons learned from this research will be valuable to the MRE community (researchers and developers alike), as well as other industries, and can be used as a reference point as the respective MRE and AM industries continue to grow and mature.

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Review of recent WEC-Sim (v6.1) advanced features

WEC-Sim (Wave Energy Converter SIMulator) is an opensource software for modeling the motions, loads and power generation of wave energy converters. WEC-Sim performs simulations in the time domain using hydrodynamic coefficients calculated by boundary element method (BEM) frequency-domain potential flow solvers such as WAMIT, NEMOH, Capytaine, or Ansys AQWA. WEC-Sim development is ongoing, including various features, applications, and example cases used to demonstrate potential use-cases to meet the needs of the growing marine energy industry. Through input from a broad user base and an extensive team of developers and collaborators, new features of WEC-Sim are developed to expand the software’s use cases and improve overall functionality. Three new WEC-Sim features highlighted in this paper include updating WEC-Sim to be compatible with MoorDyn Version 2, incorporation of second order excitation loads (quadratic transfer functions) and allowing for dynamically changing hydrodynamics.

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Evaluation of a Wave Powered Water Pump Performance by Ocean Field Testing and WEC-Sim Modeling

This submission from AMEC (the Atlantic Marine Energy Center) includes data from an ocean field deployment of a wave powered water pump in March 2023. The wave pump is an upweller device, designed to enhance macroalgal aquaculture. The wave pump device was deployed off the coast of Isles of Shoals Appledore Island in Maine, USA. The data were collected using a custom-built DAQ module comprised of Arduino Unos. GPS time stamp accompanies the data. The data are volumetric flow rate from the wave pump, and relative motion of the device between float and spar buoys. Flow rate is measured by flow meter, and relative motion is measured by lidar. Calibration data for the lidar and flow meter sensors are included. This data set also includes synchronous Sofar Spotter buoy data from a mooring approximately 300 feet away from the wave pump mooring. Video data from the deployment are included from both on-board the device sporadically throughout the deployment, and from a webcam for a short duration of the deployment. Hydrophone data were also taken co-currently, and are available by contacting Martin Wosnik at the University of New Hampshire. The Matlab code used to process the field data is incorporated. A biological assessment is included which aided the NEPA consultation process, prior to conducting the field deployment. A WEC-Sim numerical model of the wave pump, and a re-design effort are part of this work. Code used to validate the WEC-Sim model from the field data are also included.

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Post Access Report: Initial testing of wave energy powered UV-C LED anti-biofouling system

In the experiment entitled “Initial Testing of Wave Energy Powered UV-C LED Anti-Biofouling System,” a UV-C LED was used to treat platinum-coated titanium coupons emulating CTD electrode material. An additional control set of coupons were exposed to seawater without the LED treatment. The experimental setup was deployed in seawater tanks at PNNL-Sequim’s Marine and Coastal Research Laboratory (MCRL) for the duration of six months. Tank seawater temperature data were collected for the duration of the experimental campaign. At two-month intervals triplicate sets of coupons were removed from both treatment and control test chambers and weighed to characterize biomass accumulation. After weighing, the coupons were photographed in initial condition, with a stain applied to highlight biofouling growth, and after rinsing off excess stain. These photographs were analyzed using PNNL’s Biofouling Growth Index (BGI) software and with a calculation of percentage dark pixels after conversion to grayscale. Additionally, at the final 6-month datapoint triplicate sets of control and test coupons were sent to PNNL-Richland’s Environmental Molecular Sciences Laboratory (EMSL) for scanning electron microscopy. All data organization and collection methods are described in further detail in the document “TEAMER_3newable_Data_Guide.pdf.” Biomass accumulation increased over time on both sets of coupons, and percent area biofouled demonstrated a similar trend. Analysis of the collected data resulted in the findings that treatment method has an impact on biofouling growth, though to a much less significant extent than time does. Additionally, qualitative findings included the presence of advanced life forms such as worms in the control test chamber, but not in the treated test chamber.

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Innovating Distributed Embedded Energy Prize (InDEEP): A Lessons Learned Report

The U.S. Department of Energy's Water Power Technologies Office (WPTO) launched the Innovating Distributed Embedded Energy Prize (InDEEP) in March 2023 to accelerate innovation in Distributed Embedded Energy Conversion Technologies (DEEC-Tec) for ocean wave energy. Administered by the National Laboratory of the Rockies (NLR) with technical support from Sandia National Laboratories (SNL), InDEEP focused on the development of small, distributed, and embeddable energy converters (DEECs) and their integration into scalable DEEC-Tec metamaterials for marine renewable energy applications. Spanning three phases over two years, InDEEP awarded approximately $2.3 million to teams from academia, industry, and startups. Phase I emphasized conceptual design. Phase II moved into the prototyping of individual DEECs. Phase III required integration into functional DEEC-Tec metamaterial prototypes. Across 60 submissions, teams explored a wide range of energy conversion mechanisms - including piezoelectric, variable-capacitance, ionic, and inductive methods. Note, the prize did not include the design nor demonstration of ocean wave energy conversion systems. Rather, the prize only required participants to design and demonstrate individual DEECs and corresponding DEEC-Tec metamaterials. This prize utilized a mix of novel and proven techniques to attract participants from outside marine energy, including an engagement leaderboard, robust recruitment, technical expert mentorship, and a suite of technical trainings. Key insights from the competition emphasized that DEEC-Tec metamaterials must be intentionally designed to produce beneficial emergent behaviors - advantages that go beyond simply combining multiple DEEC units. Top-performing teams showed that thoughtful design of system architecture, coordinated deformation, and systems adaptabilities could unlock meaningful performance gains both at the DEEC system level and DEEC-Tec metamaterial system level. A critical realization was that many DEEC-Tec metamaterials could benefit from being designed to accept lower-frequency energy inputs and shift those into higher-frequencies per each DEEC making up the respective DEEC-Tec metamaterial. Other important takeaways included the need for rigorous and quantitative performance testing, effective integration of power conditioning electronics, and the pivotal role of material science in enabling innovative, adaptive DEEC-Tec-based energy conversion designs. InDEEP also helped establish a growing DEEC-Tec community of practitioners, attracting participants from beyond traditional marine energy sectors. Through a strong support infrastructure, InDEEP fostered early-stage innovation and laid a foundation for future DEEC-Tec-based ocean wave energy conversion solutions - positioning DEEC-Tec as a promising pathway toward scalable, resilient ocean wave energy conversion. Through focused R&D of individual DEECs and their integration into DEEC-Tec metamaterials, alongside a growing, multidisciplinary community catalyzed by InDEEP, there is a strong opportunity to drive a disruptive shift in ocean wave energy conversion design and development. This convergence of novel architectures, emergent behaviors, and collaborative innovation positions DEEC-Tec as a transformative approach, moving the field from rigid, centralized energy conversion-based designs to resilient, modular systems highly adaptable for real-world ocean wave energy conversion applications.

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Physics-constrained Gaussian process model for prediction of hydrodynamic interactions between wave energy converters in an array

To improve the efficiency of wave farms and achieve maximum power generation, the layout of wave energy converters (WECs) in an array needs to be carefully designed so that the hydrodynamic interactions can be positively exploited. For this, the hydrodynamic characteristics of the WEC array in different layouts need to be calculated. However, such calculations using numerical models usually entail significant computational cost, especially for large arrays of WECs. To address the computational challenge, a physics-constrained Gaussian process (GP) model is proposed to replace the original expensive numerical model and predict the hydrodynamic characteristics of the WECs for any array layout. By exploring the relationship between the WEC array (i.e., the input) and different hydrodynamic characteristics (i.e., the output), here we summarize a set of physical constraints/features, including invariance, symmetry, and additivity. This prior knowledge about the input-output relationship is then directly embedded in the constructed GP model through the design of physics-constrained kernels. In particular, a double-sum invariant kernel is first developed to incorporate the invariance and symmetry features, and then an additive kernel is developed to incorporate the additive feature of the problem. The invariant kernel and the additive kernel are then integrated to construct the physics-constrained GP model. Compared to the standard GP model, the proposed physics-constrained GP models require less training data to achieve the desired accuracy in predicting the hydrodynamic characteristics and are also less vulnerable to the curse of dimensionality (i.e., good scalability for large arrays) due to the use of an additive kernel. The efficiency, accuracy, and scalability of the proposed approach are demonstrated through an application to predict the hydrodynamic characteristics for WEC arrays of different sizes and layouts.

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