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At least 469 records · Page 26

An Analysis Framework for Distribution Network DER Integration Analysis in India: Distributed Solar in Tamil Nadu

This report is part of a two-part series that represents a year-long collaboration with the Tamil Nadu Generation and Distribution Corporation Limited (TANGEDCO) on power sector planning. The first report in this series, the Pathways for Tamil Nadu’s Electric Power Sector 2017-2030 report outlines NREL’s work with TANGEDCO's electricity sector planning department to develop a model of the State’s power system and evaluate multiple scenarios of system growth given resource constraints, costs of technologies, and power sector policies. This second report in this series focuses on the rapidly transforming distribution network in the State. The report outlines a framework developed by NREL with TANGEDCO's distribution utility to quickly and accurately analyze the impacts of integrating renewable energy, specifically rooftop solar PV onto Tamil Nadu's distribution system. Together these studies help to prepare Tamil Nadu for a rapidly transforming power system.

14 SOLAR ENERGY↗

Energy Resilient Recovery in Puerto Rico: Hurricane Maria Recovery Support

This report covers microgrids as a special application of distributed energy resources (DERs) in Puerto Rico. This is one of a series of reports describing the U.S. Department of Energy (DOE) multi-laboratory efforts undertaken. To ensure the sustainable, long-term recovery of Puerto Rico's electric power grid from hurricanes Maria and Irma and to build capacity to manage future potential natural disasters in the most secure and resilient way, DOE convened experts from multiple national laboratories to develop a comprehensive set of data, models, analytic tools, and studies, considering inputs from a wide variety of stakeholder groups, to support technically sound recommendations for Puerto Rico's energy investment decisions. In Phase 1 of the multi-laboratory effort to support Puerto Rico's recovery, the National Renewable Energy Laboratory (NREL) provided the utility company Puerto Rico Electric Power Authority (PREPA) recommendations for a new framework of interconnection standards to accelerate the integration of utility-scale, transmission-connected, renewable electrical generation and energy storage that ensure cross-technology compatibility and enable high deployment levels without compromising grid reliability, safety, or security (https://www.nrel.gov/docs/fy19osti/73848.pdf). In Phase 2, NREL published a report focused on the interconnection of distributed energy resources (DERs) to the electric distribution system in Puerto Rico (https://www.nrel.gov/docs/fy21osti/77127.pdf). This report familiarized the reader with Puerto Rico's distribution infrastructure and operational practices and procedures that are relevant to DER interconnection. The report also provided considerations for streamlining the interconnection process given the expected increase in deployments resulting from Puerto Rico's renewable portfolio standard goal of 100% renewables by 2050. Accordingly, the report identifies considerations and concerns associated with the increase in intermittent generation, strategies for DER interconnection best practices, and the potential use of the latest technological solutions identified in the latest revision of the Institute of Electrical and Electronics Engineers 1547-2018 interconnection standard. Additionally, the report identified ways to improve the physical resiliency of installed DERs. This task describes how distributed energy systems may participate in and contribute to improving the resiliency of Puerto Rico's energy infrastructure in the future. This report presents an analysis of the Puerto Rico grid to illustrate the possible different microgrid and minigrid scenarios. The capability to form sustained microgrids and minigrids has the potential to provide a high level of resiliency during disturbances on the grid. DERs, on the other hand, have the capability to aid in the microgrid operation by providing grid support as well as grid-forming functionality. Other tasks in Phase 3 include voltage regulation in distribution networks using DERs and transmission-and-distribution co-simulation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A Variable-Resolution Stretched-Grid General Circulation Model and Data Assimilation System with Multiple Areas of Interest: Studying the Anomalous Regional Climate Events of 1998

The new stretched-grid design with multiple (four) areas of interest, one at each global quadrant, is implemented into both a stretched-grid GCM (general circulation model) and a stretched-grid data assimilation system (DAS). The four areas of interest include: the U.S./Northern Mexico, the El Nino area/Central South America, India/China, and the Eastern Indian Ocean/Australia. Both the stretched-grid GCM and DAS annual (November 1997 through December 1998) integrations are performed with 50 km regional resolution. The efficient regional down-scaling to mesoscales is obtained for each of the four areas of interest while the consistent interactions between regional and global scales and the high quality of global circulation, are preserved. This is the advantage of the stretched-grid approach. The global variable resolution DAS incorporating the stretched-grid GCM has been developed and tested as an efficient tool for producing regional analyses and diagnostics with enhanced mesoscale resolution. The anomalous regional climate events of 1998 that occurred over the U.S., Mexico, South America, China, India, African Sahel, and Australia are investigated in both simulation and data assimilation modes. Tree assimilated products are also used, along with gauge precipitation data, for validating the simulation results. The obtained results show that the stretched-grid GCM and DAS are capable of producing realistic high quality simulated and assimilated products at mesoscale resolution for regional climate studies and applications.

Fox-Rabinovitz, Michael S.↗

OR-AGENT framework – Architecting electrified heavy-duty drayage applications

The widespread adoption of zero-emission vehicles in heavy-duty (HD) commercial freight transportation faces considerable technoeconomic challenges. For heavy-duty trucks, ensuring high uptime, cost parity with diesel, and safety standards is especially critical as these vehicles operate over long distances with heavy loads, where any downtime or off-nominal behaviors significantly impacts logistics, productivity, and the total cost of ownership. Unlike traditional diesel refueling, BEV charging infrastructure must be co-optimized with vehicle deployment, operational demands, and grid capacity to ensure cost-effective and reliable freight operations. However, the lack of a standardized ownership and service model has led to a fragmented approach—where commercial vehicle operators may invest in, own, and maintain both vehicle/batteries and charging/energy infrastructure. This disconnect may exclude energy service providers from the equation, forcing fleet operators to explore ‘behind-the-fence’ energy solutions that increase capital investment, operational downtime, overhead costs, and, in some cases, net carbon emissions. To address these issues, this study introduces OR-AGENT (Optimal Regional Architecture Generation for Efficient National Transport), a comprehensive modeling framework that integrates powertrain architectures, charging infrastructures, and energy backbone systems into a cohesive strategy. In this paper, OR-AGENT is applied to develop an interconnected systems architecture for energy efficiency and resiliency enhancement of heavy-duty drayage vehicles at the Port of Savannah, GA. This framework showcases an interconnected systems approach to electrifying heavy-duty drayage vehicles at the Port of Savannah, GA. The study assessed BEVs with 400–1200 kWh battery capacities, accounting for seasonal variations in weather and freight routing. A diverse charging mix (150 kW–1250 kW) was evaluated alongside grid capacity constraints, cost, and carbon intensity analysis, leading to the development of a strategic microgrid/Distributed Energy Resources (DER) deployment architecture to ensure a reliable and sustainable transition. However, the findings also highlight the need for alternative zero-emission solutions for remaining trips, such as larger batteries, electrified roadways, hydrogen powertrains, or net-zero emission fuels. In conclusion, the findings are incorporated into a Total Cost of Ownership (TCO) model to identify optimal architectures for an interconnected electrified ecosystem.

Commercial vehicles↗

Design and Operation of Energy Systems with Large Amounts of Variable Generation: IEA Wind TCP Task 25 (Final Summary Report)

This report summarizes findings on wind integration from the 17 countries or sponsors participating in the International Energy Agency Wind Technology Collaboration Program (IEA Wind TCP) Task 25 from 2006-2020. Both real experience and studies are reported. Many wind integration studies incorporate solar energy, and most of the results discussed here are valid for other variable renewables in addition to wind. The national case studies address several impacts of wind power on electric power systems. In this report, they are grouped under long-term planning issues and short-term operational impacts. Long-term planning issues include grid planning and capacity adequacy. Short-term operational impacts include reliability, stability, reserves, and maximizing the value of wind in operational timescales (balancing related issues). The first section presents the variability and uncertainty of power system-wide wind power, and the last section presents recent studies toward 100% shares of renewables. The appendix provides a summary of ongoing research in the national projects contributing to Task 25 for 2021-2024. The design and operation of power and energy systems is an evolving field. As ambitious targets toward net-zero carbon energy systems are announced globally, many scenarios are being made regarding how to reach these future decarbonized energy systems, most of them involving large amounts of variable renewables, mainly wind and solar energy. The secure operation of power systems is increasingly challenging, and the impacts of variable renewables, new electrification loads together with increased distribution system resources will lead to somewhat different challenges for different systems. Tools and methods to study future power and energy systems also need to evolve, and both short-term operational aspects (such as power system stability) and long-term aspects (such as resource adequacy) will probably see new paradigms of operation and design. The experience of operating and planning systems with large amounts of variable generation is accumulating, and research to tackle the challenges of inverter-based, nonsynchronous generation is on the way. Energy transition and digitalization also bring new flexibility opportunities, both short and long term.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Airport Ground Support Equipment Analysis

Ground support equipment (GSE) plays a critical role in providing services to aircraft at arrival and departure gates, ensuring smooth and efficient airport operations. As the airline industry seeks to reduce costs and expand energy options, electric GSE (eGSE) is emerging as a promising solution. This project examines the integration of eGSE into airport operations, addressing key considerations such as vehicle deployment, charging infrastructure, and grid impacts. We developed a flexible, bottom-up modeling framework to evaluate energy demands and infrastructure requirements across more than 300 U.S. airports, providing actionable insights to support electrification planning and implementation. The study focuses on eight major types of GSE with commercially available electric counterparts: aircraft tractors, ground power units, baggage tractors, belt loaders, cargo loaders, catering trucks, lavatory trucks, and water trucks. Project results include annual charging load profiles, total energy consumption, and the charger and fleet requirements for each airport.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Numerical solutions of Navier-Stokes equations for a Butler wing

The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for the Mach number 3.5 and Reynolds number of 2,000,000. The simulation is done by integrating the viscous Navier-Stokes equations. These equations govern the unsteady, viscous, compressible and heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. O-type and H-type grids have been used for this study, and results are compared. The governing equations are solved by the McCormack time-split method, and the results are compared with other theoretical and experimental results. The codes are written in FORTRAN, vectorized and currently run on the CDC Vector Processing System (VPS-32) computer.

Abolhassani, Jamshid S.↗

Large-eddy simulation of a backward facing step flow using a least-squares spectral element method

We report preliminary results obtained from the large eddy simulation of a backward facing step at a Reynolds number of 5100. The numerical platform is based on a high order Legendre spectral element spatial discretization and a least squares time integration scheme. A non-reflective outflow boundary condition is in place to minimize the effect of downstream influence. Smagorinsky model with Van Driest near wall damping is used for sub-grid scale modeling. Comparisons of mean velocity profiles and wall pressure show good agreement with benchmark data. More studies are needed to evaluate the sensitivity of this method on numerical parameters before it is applied to complex engineering problems.

Chan, Daniel C.↗

An Application of the Quadrature-Free Discontinuous Galerkin Method

The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.

Lockard, David P.↗

Conceptual Design Study of a Thermal Energy Storage System Using Granular Solids for Coal-fired Boilers

<span style="font-size: 12pt;">Presentation for the 2020 International Pittsburgh Coal Conference held virtually from September 8-11, 2020.</span><span style="font-size: 12pt;">Abstract: As electricity from various renewable energy sources is increasingly supplied to the power grid, the grid’s stability will be challenged. Proposed grid-stability solutions will need to address variability of sources, such as solar and wind energy, in order to alleviate problems such as overgeneration and ramping. In regions where increases in solar energy are prominent, such as California, the net power demand curve often referred to as “the Duck Curve,” has caused problems for energy dispatchers, due to over-generation and fast ramping demands. In this project, we investigated a conceptual design for a Thermal Energy Storage System (TESS) integrated into a coal-fired power plant to support grid-scale storage. Implementing a TESS into power plants can allow for an increase in renewable sources, increase grid resilience, and allow conventional coal-fired plants to operate more efficiently. For this project, a TESS using granular solids as the energy-storage media is integrated into a conventional coal-fired power plant. The purpose of the TESS is to store energy from the flue gas during low demand periods and transfer the energy to steam during peak demand periods. The storage allows the stabilization of combustion and related boiler components at low loads and provides the opportunity to avoid some shutdowns. This study uses thermodynamic properties of several candidate thermal storage materials to estimate the size of storage system required for several operating scenarios. </span>

Huckaby, E. David↗

EMT data generation

The integration of inverter-based resources (IBRs) in power systems is accelerating, bringing with it significant benefits such as reduced greenhouse gas emissions, improved grid resilience, and increased energy independence. Despite these advantages, the widespread adoption of IBRs introduces several challenges, including issues related to grid stability, increased operational complexity, and the need for updated regulatory frameworks. To address these challenges, IEEE released Standard 2800 in 2022, which sets forth the necessary interconnection capabilities and performance criteria for IBRs connected to transmission and sub-transmission systems. This standard outlines the performance requirements to ensure the reliable integration of IBRs into the bulk power system. Furthermore, in 2023, the North American Electric Reliability Corporation (NERC) published a reliability guideline for electromagnetic transient (EMT) modeling of BPS-connected IBRs. This guideline provides recommendations for developing EMT model requirements, performing model quality checks, and implementing verification practices specifically for EMT models representing BPS-connected inverter-based resources in reliability studies conducted by transmission planners and planning coordinators. These standards and guidelines have a profound impact on EMT studies for transmission networks, influencing system stability analyses, grid recovery and resynchronization processes, fault ride-through evaluations, protection and coordination strategies, advanced control methodologies, and the inclusion of IBRs in transient models of transmission networks. As a result, the generation of EMT data is crucial for conducting various transient-based studies to understand the impact of IBRs. EMT data generation use cases serve as the basis for scenarios in event detection and identification use cases, providing comprehensive details about EMT data generation for transmission grids with inverter-based resources. These use cases supply sufficient training and validation datasets for subsequent EMT analysis algorithms.

Xia, Qianxue↗

Integrated energy-water-land nexus planning in the Colorado River Basin (Argentina)

Integrated energy-water-land (EWL) planning promotes synergies and avoids conflicts in ways that sector-specific planning approaches cannot. Many important decisions that influence emerging EWL nexus issues are implemented at regional (e.g., large river basin, electricity grid) and sub-regional (e.g., small river basin, irrigation district) scales. However, actual implementation of integrated planning at these scales has been limited. Simply collecting and visualizing data and interconnections across multiple sectors and sub-regions in a single modeling platform is a unique endeavor in many regions. This study introduces and applies a novel approach to linking together multiple sub-regions in a single platform to characterize and visualize EWL resource use, EWL system linkages within and among sub-regions, and the EWL nexus implications of future policies and investments. This integrated planning methodology is applied in the water-stressed Colorado River Basin in Argentina, which is facing increasing demands for agricultural and fossil fuel commodities. Guided by stakeholders, this study seeks to inform basin planning activities by characterizing and visualizing (1) the basin’s current state of EWL resources, (2) the linkages between sectors within and among basin sub-regions, and (3) the EWL nexus implications of planned future agricultural development activities. Results show that water scarcity, driven in part by human demands that have historically reached 60% of total surface water supply, poses a substantial constraint to economic development in the basin. The Colorado basin has the potential to serve as a testbed for crafting novel and generalizable sub-regional EWL planning approaches capable of informing the EWL planning dialogue globally.

54 ENVIRONMENTAL SCIENCES↗

Integrating an Ensemble Reward System into an Off-Policy Reinforcement Learning Algorithm for the Economic Dispatch of Small Modular Reactor-Based Energy Systems

Nuclear Integrated Energy Systems (NIES) have emerged as a comprehensive solution for navigating the changing energy landscape. They combine nuclear power plants with renewable energy sources, storage systems, and smart grid technologies to optimize energy production, distribution, and consumption across sectors, improving efficiency, reliability, and sustainability while addressing challenges associated with variability. The integration of Small Modular Reactors (SMRs) in NIES offers significant benefits over traditional nuclear facilities, although transferring involves overcoming legal and operational barriers, particularly in economic dispatch. This study proposes a novel off-policy Reinforcement Learning (RL) approach with an ensemble reward system to optimize economic dispatch for nuclear-powered generation companies equipped with an SMR, demonstrating superior accuracy and efficiency when compared to conventional methods and emphasizing RL’s potential to improve NIES profitability and sustainability. Finally, the research attempts to demonstrate the viability of implementing the proposed integrated RL approach in spot energy markets to maximize profits for nuclear-driven generation companies, establishing NIES’ profitability over competitors that rely on fossil fuel-based generation units to meet baseload requirements.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Numerical solutions of Navier-Stokes equations for a Butler wing

The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and Reynolds number of 2,000,000. The simulation is done by integrating the viscous Navier-Stokes equations. These equations govern the unsteady, viscous, compressible and heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. The O-type and H-type grids have been used for this study, and results are compared. The governing equations are solved by the MacCormack time-split method, and the results are compared with other theoretical and experimental results. The codes are written in FORTRAN, vectorized and currently run on the CDC Vector Processing System (VPS-32) computer.

Abolhassani, Jamshid S.↗

Design of Phase-Change Thermal Storage Device in a Heat Pump for Building Electric Peak Load Shaving: Preprint

Replacing carbon-intensive fossil fuel heating systems with electric heat pumps powered by renewables is a promising approach to decarbonize the building sector. However, one of the technical barriers of this approach is the large scale of heat demand, which will put excessive stress on the electricity grid. Integrating thermal energy storage (TES) into the heating systems can help alleviate this problem, by shifting thermal load and thus shaving peaks in the building electric load. Therefore, it is critical to understand how to design a thermal storage device in a heat pump for peak load shaving. In this study, we developed a numerical model for a cascaded vapor compression heat pump system integrating a phase change thermal storage device. This novel system can control the net thermal charging and discharging rate of the TES independently from the building's thermal load, which allows for precise control of electric power use. In the current study, we controlled the system to shave building electric peak load during a cold winter morning, and to charge TES during the relatively warm afternoon while still providing space heating. We used the model to evaluate the system performance with and without peak shaving. We also investigated the effect of PCM transition Tt on the peak reduction and electric energy saving potentials. The results show that peak shaving scheme effectively reduces the peak electric power consumption during a predefined discharge time window. When comparing to the no shaving case, for PCM Tt = 10 degrees C, the peak electric load reduction is 23.5%. When comparing to an air-source heat pump with back up electric heater, as Tt increases from 0 to 20 degrees C, the peak reduction increases from 46.1% to 50.9%. Integrating PCM Tt = 10 degrees C with peak shaving leads to the 45.5% of electric energy saving, which is the highest among the three transition temperatures.

electric energy saving↗

Powered By: Transmission Planning

Presented as part of the NREL Grid Planning and Analysis Center's (GPAC) "Powered By" Series, this iteration focuses not on a specific tool but instead on a domain of expertise/capability being built out at NREL: transmission planning. Various sets of tools are integrated together in this presentation to present a combination of transmission focus areas, case studies, tools and future directions of transmission research.

capacity expansion↗

Integrated Modeling Report for CO 2 Storage with Enhanced Oil Recovery in Northern Michigan

The Midwest Regional Carbon Sequestration Partnership (MRCSP) was founded in 2003 as part of the U.S. Department of Energy’s (DOE’s) Regional Carbon Sequestration Partnership initiative. Since its founding, MRCSP has made significant strides toward making CCUS a viable option for states in the region. The public/private consortium, funded through the DOE Regional Carbon Sequestration Initiative, brings together nearly 40 industry partners and 10 states. Battelle, as the project lead, oversees research, development and operations and coordinates activities among the partners. The incremental, phased approach has built a valuable knowledge base for the industry and paved the way for commercial-scale adoption of CCUS technologies. From 2008 to 2020, MRCSP Phase III focused on the development of large-scale injection projects. This report is part of a series of reports prepared under the Midwestern Regional Carbon Sequestration Partnership (MRCSP) Phase III (Development Phase). These reports summarize and detail the findings of the work conducted under the Phase III project. MRCSP has been investigating various reservoir characterization and modeling technologies related to Carbon Capture, Utilization, and Storage (CCUS) in conjunction with carbon dioxide enhanced oil recovery (CO 2 -EOR) operations in multiple Silurian-age (Niagaran), oil-bearing, carbonate pinnacle reefs in northern Michigan, USA. This report provides a comprehensive discussion of reservoir modeling studies that were conducted for tracking oil production, forecasting CO 2 plume migration, and estimating associated storage in a number of reefs that were at different stages of their CO 2 -EOR life cycle. The modeling process for simulating oil production, CO 2 injection, and associated storage in these reefs entails two phases. The first phase, geologic framework modeling, integrates all pertinent geological and geophysical data (from logs, cores and seismic surveys) about reservoir structure, geometry, rock types, and property distributions (porosity, permeability, water saturation) into a 3-D distributed grid-based static earth model (SEM). The second phase, dynamic reservoir modeling, uses the SEM as a platform to simulate the movement of oil, gas, water, and CO 2 within the reservoir during primary hydrocarbon production, as well as during subsequent phases such as CO 2 -injection assisted EOR, plume migration, and associated storage. In addition, an assessment of coupled process effects is also carried out, where the impacts of geochemical and geo-mechanical processed induced by CO 2 injection are studied.

01 COAL, LIGNITE, AND PEAT↗

Computations of Boiling in Microgravity

The absence (or reduction) of gravity, can lead to major changes in boiling heat transfer. On Earth, convection has a major effect on the heat distribution ahead of an evaporation front, and buoyancy determines the motion of the growing bubbles. In microgravity, convection and buoyancy are absent or greatly reduced and the dynamics of the growing vapor bubbles can change in a fundamental way. In particular, the lack of redistribution of heat can lead to a large superheat and explosive growth of bubbles once they form. While considerable efforts have been devoted to examining boiling experimentally, including the effect of microgravity, theoretical and computational work have been limited. Here, the growth of boiling bubbles is studied by direct numerical simulations where the flow field is fully resolved and the effects of inertia, viscosity, surface deformation, heat conduction and convection, as well as the phase change, are fully accounted for. Boiling involves both fluid flow and heat transfer and thus requires the solution of the Navier-Stokes and the energy equations. The numerical method is based on writing one set of governing transport equations which is valid in both the liquid and vapor phases. This local, single-field formulation incorporates the effect of the interface in the governing equations as source terms acting only at the interface. These sources account for surface tension and latent heat in the equations for conservation of momentum and energy as well as mass transfer across the interface due to phase change. The single-field formulation naturally incorporates the correct mass, momentum and energy balances across the interface. Integration of the conservation equations across the interface directly yields the jump conditions derived in the local instant formulation for two-phase systems. In the numerical implementation, the conservation equations for the whole computational domain (both vapor and liquid) are solved using a stationary grid and the phase boundary is followed by a moving unstructured two-dimensional grid. While two-dimensional simulations have been used for preliminary studies and to examine the resolution requirement, the focus is on fully three-dimensional simulations. The numerical methodology, including the parallelization and grid refinement strategy is discussed, and preliminary results shown. For buoyancy driven flow, the heat transfer is in good agreement with experimental correlations. The changes when gravity is turned off and/or fluid shear is added are discussed, as well as the difference between simulations of a layer freely releasing bubbles versus simulations using only one wavelength initial perturbation. Figure 1 shows the early stages of the formation of a three-dimensional bubble from a thin vapor layer. The boundary conditions are periodic in the x and y direction, the bottom is a hot and the top allows a free outflow. The jagged edge of the surface close to the bottom of the computational domain is due to some of the surface elements being on the other side of the domain and some elements not plotted by our plotting routine. In the second figure, we show the temperature distribution through two perpendicular planes.

Tryggvason, G.↗