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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 235 records · Page 13

Li-Ion Battery Thermal Characterization for Thermal Management Design

Battery design efforts often prioritize enhancing the energy density of the active materials and their utilization. However, optimizing thermal management systems at both the cell and pack levels is also key to achieving mission-relevant battery design. Battery thermal management systems, responsible for managing the thermal profile of battery cells, are crucial for balancing the trade-offs between battery performance and lifetime. Designing such systems requires accounting for the multitude of heat sources within battery cells and packs. This paper provides a summary of heat generation characterizations observed in several commercial Li-ion battery cells using isothermal battery calorimetry. The primary focus is on assessing the impact of temperatures, C-rates, and formation cycles. Moreover, a module-level characterization demonstrated the significant additional heat generated by module interconnects. Characterizing heat signatures at each level helps inform manufacturing at the design, production, and characterization phases that might otherwise go unaccounted for at the full pack level. Further testing of a 5 kWh battery pack revealed that a considerable temperature non-uniformity may arise due to inefficient cooling arrangements. To mitigate this type of challenge, a combined thermal characterization and multi-domain modeling approach is proposed, offering a solution without the need for constructing a costly module prototype.

25 ENERGY STORAGE↗

Training self-learning circuits for power-efficient solutions

As the size and ubiquity of artificial intelligence and computational machine learning models grow, the energy required to train and use them is rapidly becoming economically and environmentally unsustainable. Recent laboratory prototypes of self-learning electronic circuits, such as “physical learning machines,” open the door to analog hardware that directly employs physics to learn desired functions from examples at a low energy cost. In this work, we show that this hardware platform allows for an even further reduction in energy consumption by using good initial conditions and a new learning algorithm. Using analytical calculations, simulations, and experiments, we show that a trade-off emerges when learning dynamics attempt to minimize both the error and the power consumption of the solution—greater power reductions can be achieved at the cost of decreasing solution accuracy. Finally, we demonstrate a practical procedure to weigh the relative importance of error and power minimization, improving the power efficiency given a specific tolerance to error.

Stern, Menachem (ORCID:0000000302158082)↗

Development and application of hybrid AIMD/cDFT simulations for atomic-to-mesoscale chemistry

Many important chemical processes involve reactivity and dynamics in complex solutions. Gaining a fundamental understanding of these reaction mechanisms is a challenging goal that requires advanced computational and experimental approaches. However, important techniques such as molecular simulation have limitations in terms of scales of time, length, and system complexity. Furthermore, among the currently available solvation models, there are very few designed to describe the interaction between the molecular scale and the mesoscale. To help address this challenge, here, we establish a novel hybrid approach that couples first-principles plane-wave density functional theory with classical density functional theory (cDFT). In this approach, a region of interest described by ab initio molecular dynamics (AIMD) interacts with the surrounding medium described using cDFT to arrive at a self-consistent ground state. cDFT is a robust but efficient mesoscopic approach to accurate thermodynamics of bulk electrolyte solutions over a wide concentration range (up to 2M concentrations). Benchmarking against commonly used continuum models of solvation, such as SMD, as well as experiments, demonstrates that our hybrid AIMD–cDFT method is able to produce reasonable solvation energies for a variety of molecules and ions. With this model, we also examined the solvent effects on a prototype S N 2 reaction of the nucleophilic attack of a chloride ion on methyl chloride in the solution. The resulting reaction pathway profile and the solution phase barrier agree well with experiment, showing that our AIMD/cDFT hybrid approach can provide insight into the specific role of the solvent on the reaction coordinate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Performance Assessment of a Dual-purpose HP-TES for a Typical Year Comparing Different Climate Zones

Complete electrification of heating and cooling systems in the United States would overload the existing electrical grid. To this end, recent research efforts have focused on energy storage as one way to reduce ever-increasing peak electricity demands. One such technology is heat pump integrated thermal-energy storage (HP-TES) systems, which can enable load-shifting and reduce demand during peak hours. In this work, a Modelica model of a 4-Ton, dual-mode (heating and cooling) HP-TES system using a room-temperature phase-change material (PCM) integrated through a secondary hydronic loop was developed and simulated for a typical meteorological year in Riverside, CA (ASHRAE Climate Zone 2B), and Chicago, IL (ASHRAE Climate Zone 5A), for a DOE small office prototype building. The COP improvement and demand reduction were analyzed during the time-of-use peak hours along with the required recharge cycle energy demand. A typical summer in Riverside, CA resulted in model-predicted peak COP increases of 50 – 100% compared to the baseline heat pump, especially at higher outdoor temperatures, coupled with maximum peak energy reductions of 22%. During shoulder and winter season simulations, heating energy savings were higher as outdoor temperatures dropped below the PCM phase change temperature. For Chicago, IL, backup heating was necessary to meet the required system capacity for very cold ambient conditions, resulting in winter peak energy savings between 16 – 60% when accounting for backup heating requirements. The recharge energy was found to be mostly below the baseline HP energy during the peak. With improved component selections and controls, the recharge energy may be reduced. The outcomes from the simulations can provide first-order estimates for potential peak energy savings, challenges, and required controls in any location before conducting any field testing.

25 ENERGY STORAGE↗

Tandem Photovoltaics Core Program Final Technical Report

The Tandem Photovoltaics Core Program was a multi-year initiative aimed at advancing hybrid tandem solar cell technologies to enhance solar module efficiency beyond the limits of single junction devices. This project focused on the development, testing, and scaling of prototype photovoltaic devices, with the goal of achieving commercial relevance and driving industry adoption. The work was divided into three tasks: 1) Comparative Analysis of Tandem Technologies: This task focused on quantifying energy yield under real-world conditions and assessing economic viability of tandems relative to silicon-based modules. The project's modeling framework incorporated performance data, cost of materials, and manufacturing process impacts to optimize tandem designs 2) Tandem Integration and Prototyping: In this task, we developed innovative tandem designs by combining metal halide perovskite (MHP) top cells and silicon (Si) bottom cells. The project focuses on both mechanical integration and direct deposition techniques to enable compatibility with commercially relevant Si technologies, such as passivated contact or PERC cells. 3) Scale-up and Reliability: This task addressed the challenges of large-area fabrication by developing scalable deposition methods and robust interconnection schemes for tandems. The project looked at different accelerated testing such as thermal cycling, damp heat exposure, and potential induced degradation, to ensure long-term stability of devices in field conditions. Tandem solar cells can greatly increase module efficiency beyond conventional single junction (SJ) devices, which are approaching their theoretical limit. There are many ways to fabricate a tandem cell or module in terms of materials used, configuration, and terminal connection. This SETO core project focused critical factors in enabling tandems to enter the market, including hardware integration, technoeconomic analysis (TEA), and energy yield analysis. We focused on MHP/Si hybrid tandem solar cells and modules as a model system for their versatility in module design comparisons, providing valuable insights for other tandem options. While champion cells with areas <1cm2 are regularly demonstrated by groups around the world, it is significantly more challenging to translate these advances into modules, and fewer institutions and companies are working at the module level. This project addressed questions about module fabrication, testing, and reliability that are hard to answer without actually fabricating prototypes. We also performed analysis and road-mapping activities to understand the potential for a wider variety of tandems, including all-perovskite tandems fabricated in collaboration with the Perovskite PV core program. Detailed technical results from this project are described for each task in Section 7.

14 SOLAR ENERGY↗

Coal-derived conductive pavement for winter de-icing: prototype, modeling, and simulation

Existing pavement de-icing methods result in high installation and maintenance costs, traffic delays, excessive weariness and corrosion, and negative environmental and safety impacts. To overcome these challenges, this paper presents an innovative pathway to designing and constructing smart self-heating pavements using a low-cost coal-char bearing asphalt material. The conductive asphalt incorporates coal char, i.e., a key byproduct of the coal pyrolysis process, into the Stone Mastic Asphalt (SMA) mixture. This asphalt containing coal-derived solid carbon exhibits highly tailorable electrical conductivity, satisfactory mechanical and thermophysical properties, and superior cost-efficiency as compared to other conductive pavement materials. The de-icing performance was also demonstrated by laboratory experiments on a bench-scale prototype. Furthermore, an efficient thermal network model was developed and validated by experiments to investigate the transient thermal behavior and energy performance of the Ohmic heating pavement system. Furthermore, the whole-year energy simulation case studies were conducted on a bridge pavement with an annual energy use of 24.6–1444.8 kWh/m 2 , showcasing its potential in field applications across cool humid, cold humid, and subarctic/arctic climate zones.

42 ENGINEERING↗

Improved Air-Conditioning Demand Response of Connected Communities over Individually Optimized Buildings

Connected communities potentially offer much greater demand response capabilities over singular building energy management systems (BEMS) through an increase of connectivity. The potential increase in benefits from this next step in connectivity is still under investigation, especially when applied to existing buildings. This work utilizes EnergyPlus simulation results on eight different commercial prototype buildings to estimate the potential savings on peak demand and energy costs using a mixed-integer linear programming model. This model is used in two cases: a fully connected community and eight separate buildings with BEMS. The connected community is optimized using all zones as variables, while the individual buildings are optimized separately and then aggregated. These optimization problems are run for a range of individual zone flexibility values. The results indicate that a connected community offered 60.0% and 24.8% more peak demand savings for low and high flexibility scenarios, relative to individually optimized buildings. Energy cost optimization results show only marginally better savings of 2.9% and 6.1% for low and high flexibility, respectively.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Model America - Arizona extract from ORNL's AutoBEM v1.1

Oak Ridge National Laboratory (ORNL) has developed the Automatic Building Energy Modeling (AutoBEM) software suite to process multiple types of data, extract building-specific descriptors, generate building energy models, and simulate them on High Performance Computing (HPC) resources. For more information, see AutoBEM-related publications (bit.ly/AutoBEM).Two sets of sample data are provided for 2,555,152 buildings located within the boundary of Arizona in the United States:Data (846.3MB *.csv) - minimalist list of each building (rows) for the following fields (columns) • ID - unique building ID • Centroid - building center location in latitude/longitude (from Footprint2D) • Footprint2D - building polygon of 2D footprint (lat1/lon1_lat2/lon2_...) • State_abbr - state name • Area - estimate of total conditioned floor area (ft2) • Area2D - footprint area (ft2) • Height - building height (ft) • NumFloors - number of floors (above-grade) • WWR_surfaces - percent of each facade (pair of points from Footprint2D) covered by fenestration/windows (average 14.5% for residential, 40% for commercial buildings) • CZ - ASHRAE Climate Zone designation • BuildingType - DOE prototype building designation (IECC=residential) as implemented by OpenStudio-standards • Standard - building vintage • Sample Models (114GB*.zip by county) - OpenStudio and EnergyPlus building energy models named according to IDThis data is made free and openly available in hopes of stimulating any simulation-informed use case. Data is provided as-is with no warranties, express or implied, regarding fitness for a particular purpose. We wish to thank our sponsors which include Oak Ridge National Laboratory (ORNL), U.S. Dept. of Energy’s (DOE) Building Technologies Office (BTO), Office of Electricity (OE), and Biological and Environmental Research (BER).

54 ENVIRONMENTAL SCIENCES↗

Analysis of strategies to meet ASHRAE S241 infectious aerosol control targets by space type and region using EnergyPlus™ simulations

Professional organizations, such as ASHRAE, have recently proposed new voluntary standards for controlling infectious aerosols. Specifically, ASHRAE Standard 241 (S241) defines equivalent clean air targets for a range of space types that can be met through combinations of mitigation measures. This paper seeks to inform the selection of measures by space type and climate zone through building simulations that quantify the impacts of increased outdoor air ventilation; increasing filtration and/or adding germicidal ultraviolet (GUV) in the central heating, ventilation, and air-conditioning (HVAC) systems; or using portable air cleaners (PACs), upper room GUV, or whole room GUV approaches to increase equivalent clean air delivery. The measures are assessed individually and in practical combinations for their ability to meet S241 in four space types (offices, classrooms, dining areas, and healthcare waiting rooms) using prototype buildings modeled using EnergyPlus. The mitigation measures are compared holistically against baseline building operations using metrics for equivalent clean air, energy, and comfort. The results in this study show that single measures can meet S241 for offices with minimal impacts on energy and comfort, while either upper room GUV systems or combinations of measures such as MERV 13 HVAC filtration with PACs are needed to meet S241 for classrooms. The dining area and healthcare waiting room targets cannot be met in this study when assuming design occupancy and MS2 as the challenge agent, even when combining multiple measures together. This paper provides valuable considerations when designing measures to meet S241 for a range of spaces and scenarios.

GUV↗

Definition study for photovoltaic residential prototype system

A parametric sensitivity study and definition of the conceptual design is presented. A computer program containing the solar irradiance, solar array, and energy balance models was developed to determine the sensitivities of solar insolation and the corresponding solar array output at five sites selected for this study as well as the performance of several solar array/battery systems. A baseline electrical configuration was chosen, and three design options were recommended. The study indicates that the most sensitive parameters are the solar insolation and the inverter efficiency. The baseline PST selected is comprised of a 133 sg m solar array, 250 ampere hour battery, one to three inverters, and a full shunt regulator to limit the upper solar array voltage. A minicomputer controlled system is recommended to provide the overall control, display, and data acquisition requirements. Architectural renderings of two photovoltaic residential concepts, one above ground and the other underground, are presented. The institutional problems were defined in the areas of legal liabilities during and after installation of the PST, labor practices, building restrictions and architectural guides, and land use.

Imamura, M. S.↗

Multiabsorber Transition-Edge Sensors for X-Ray Astronomy

We are developing arrays of position-sensitive microcalorimeters for future x-ray astronomy applications. These position-sensitive devices commonly referred to as hydras consist of multiple x-ray absorbers, each with a different thermal coupling to a single-transition-edge sensor microcalorimeter. Their development is motivated by a desire to achieve very large pixel arrays with some modest compromise in performance. We report on the design, optimization, and first results from devices with small pitch pixels (<75 μm) being developed for a high-angular and energy resolution imaging spectrometer for Lynx. The Lynx x-ray space telescope is a flagship mission concept under study for the National Academy of Science 2020 decadal survey. Broadband full-width-half-maximum (FWHM) resolution measurements on a 9-pixel hydra have demonstrated ΔE(FWHM) = 2.23 ± 0.14 eV at Al-Kα, ΔE(FWHM) = 2.44 ± 0.29 eV at Mn-Kα, and ΔE(FWHM) = 3.39 ± 0.23 eV at Cu-Kα. Position discrimination is demonstrated to energies below <1 keV and the device performance is well-described by a finite-element model. Results from a prototype 20-pixel hydra with absorbers on a 50-μm pitch have shown ΔE(FWHM) = 3.38 ± 0.20 eV at Cr-Kα1. We are now optimizing designs specifically for Lynx and extending the number of absorbers up to 25/hydra. Numerical simulation suggests optimized designs could achieve ∼3 eV while being compatible with the bandwidth requirements of the state-of-the art multiplexed readout schemes, thus making a 100,000 pixel microcalorimeter instrument a realistic goal.

Smith, Stephen J.↗

Evaluation of Material Models within LS-DYNA(Registered TradeMark) for a Kevlar/Epoxy Composite Honeycomb

The performance of material models to simulate a novel composite honeycomb Deployable Energy Absorber (DEA) was evaluated using the nonlinear explicit dynamic finite element code LS-DYNA(Registered TradeMark). Prototypes of the DEA concept were manufactured using a Kevlar/Epoxy composite material in which the fibers are oriented at +/-45 degrees with respect to the loading axis. The development of the DEA has included laboratory tests at subcomponent and component levels such as three-point bend testing of single hexagonal cells, dynamic crush testing of single multi-cell components, and impact testing of a full-scale fuselage section fitted with a system of DEA components onto multi-terrain environments. Due to the thin nature of the cell walls, the DEA was modeled using shell elements. In an attempt to simulate the dynamic response of the DEA, it was first represented using *MAT_LAMINATED_COMPOSITE_FABRIC, or *MAT_58, in LS-DYNA. Values for each parameter within the material model were generated such that an in-plane isotropic configuration for the DEA material was assumed. Analytical predictions showed that the load-deflection behavior of a single-cell during three-point bending was within the range of test data, but predicted the DEA crush response to be very stiff. In addition, a *MAT_PIECEWISE_LINEAR_PLASTICITY, or *MAT_24, material model in LS-DYNA was developed, which represented the Kevlar/Epoxy composite as an isotropic elastic-plastic material with input from +/-45 degrees tensile coupon data. The predicted crush response matched that of the test and localized folding patterns of the DEA were captured under compression, but the model failed to predict the single-cell three-point bending response.

Polanco, Michael A.↗

An adaptive model-free robotic force control strategy for hydrodynamic real-time hybrid simulation of floating offshore wind turbines

Real-time hybrid simulation (RTHS) - a cyber-physical testing approach - promises to enhance the simulation fidelity of the model-scale experiments used to prototype floating offshore wind turbines (FOWTs). In hydrodynamic RTHS (hydro-RTHS), actuators emulate aerodynamic forces on model-scale FOWT specimens subjected to physical waves in a hydrodynamic laboratory. Robotic arms are promising candidates for actuation in hydro-RTHS due to their compact multi-degree-of-freedom (DOF) capabilities. Unlike classical RTHS for seismic applications, which typically relies on displacement control, hydro-RTHS requires 6-DOF force control on newly designed floating prototypes in a model-scale setting, which presents significant challenges, including modeling uncertainties, directional asymmetry, configuration drift, bandwidth limitations, and time-varying delays. To mitigate these constraints without extensive pre-test calibration, this study proposes an adaptive model-free robotic force control strategy that combines task-space explicit force control with a secondary joint-space pose-keeping task. The Adaptive Feedforward Compensator (AFC) is integrated into the force control loop to compensate for time-varying delay. Experimental testing was conducted using a Franka Emika Panda robotic arm with a 1:50 scale FOWT specimen under operational wind and wave conditions. Results demonstrate stable and consistent 6-DOF force tracking. Effective delay compensation was observed, with low-frequency delay reductions ranging from 71.4% to 91.8% and improvements in low-frequency surge force tracking of 25.0% to 52.1%. This study enhances robotic actuation performance in hydro-RTHS and introduces a force control strategy that supports reliable robotic operation in uncertain floating environments. Future work will explore disturbance-observer mechanisms to further enhance wave rejection capabilities under extreme wind and wave conditions.

17 WIND ENERGY↗

Nonadiabatic Dynamics Simulation of the Wavelength-Dependent Photochemistry of Azobenzene Excited to the nπ* and ππ* Excited States

Azobenzene is one of the most ubiquitous photoswitches in photochemistry and a prototypical model for photoisomerizing systems. Despite this, its wavelength-dependent photochemistry has puzzled researchers for decades. Upon excitation to the higher energy ππ* excited state instead of the dipole-forbidden nπ* state, the quantum yield of isomerization from trans- to cis-azobenzene is halved. The difficulties associated with unambiguously resolving this effect both experimentally and theoretically have contributed to lasting controversies regarding the photochemistry of azobenzene. Here, we systematically characterize the dynamic photoreaction pathways of azobenzene by performing first-principles simulations of the nonadiabatic dynamics following excitation to both the ππ* and the nπ* states. In this work, we demonstrate that ground-state recovery is mediated by two distinct S1 decay pathways: a reactive twisting pathway and an unreactive planar pathway. Increased preference for the unreactive pathway upon ππ* excitation largely accounts for the wavelength-dependent behavior observed in azobenzene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Digital Twin Framework for Liquid-cooled Supercomputers as Demonstrated at Exascale

We present ExaDigiT, an open-source framework for developing comprehensive digital twins of liquid-cooled supercomputers. It integrates three main modules: (1) a resource allocator and power simulator, (2) a transient thermo-fluidic cooling model, and (3) an augmented reality model of the supercomputer and central energy plant. The framework enables the study of "what-if" scenarios, system optimizations, and virtual prototyping of future systems. Using Frontier as a case study, we demonstrate the framework's capabilities by replaying six months of system telemetry for systematic verification and validation. Such a comprehensive analysis of a liquid-cooled exascale supercomputer is the first of its kind. ExaDigiT elucidates complex transient cooling system dynamics, runs synthetic or real workloads, and predicts energy losses due to rectification and voltage conversion. Throughout our paper, we present lessons learned to benefit HPC practitioners developing similar digital twins. We envision the digital twin will be a key enabler for sustainable, energy-efficient supercomputing.

Brewer, Wes↗

Noninteracting electrons in a prototypical one-dimensional sinusoidal potential

A prototypical model of a one-dimensional metallic monatomic solid containing noninteracting electrons is studied, where the argument of the cosine potential energy, periodic with the lattice, contains the first reciprocal lattice vector G 1 =2π/a, where a is the lattice constant. The time-independent Schrödinger equation can be written in reduced variables as a Mathieu equation for which numerically exact solutions for the band structure and wave functions are obtained. The band structure has band gaps that increase with increasing amplitude q of the cosine potential. In the extended-zone scheme, the energy gaps decrease with increasing index n of the Brillouin-zone boundary ka=nπ, where k is the crystal momentum of the electron. The wave functions of the band electron are derived for various combinations of k and q as complex combinations of the real Mathieu functions with even and odd parity, and the normalization factor is discussed. The wave functions at the bottoms and tops of the bands are found to be real or imaginary, respectively, corresponding to standing waves at these energies. Irrespective of the wave vector k within the first Brillouin zone, the electron probability density is found to be periodic with the lattice. The Fourier components of the wave functions are derived versus q, which reveal multiple reciprocal-lattice-vector components with variable amplitudes in the wave functions unless q = 0. The magnitudes of the Fourier components are found to decrease exponentially as a power of n for n~3 to 45 for ka = π/2 and q = 2, and a precise fit is obtained to the data. The probability densities and probability currents obtained from the wave functions are also discussed. The probability currents are found to be zero for crystal momenta at the tops and bottoms of the energy bands, because the wave functions for these crystal momenta are standing waves. To conlcude, the band structure is calculated from the central equation and compared to the numerically exact band structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Characteristics of products generated by selective sintering and stereolithography rapid prototyping processes

The trend in the modern global economy towards free market policies has motivated companies to use rapid prototyping technologies to not only reduce product development cycle time but also to maintain their competitive edge. A rapid prototyping technology is one which combines computer aided design with computer controlled tracking of focussed high energy source (eg. lasers, heat) on modern ceramic powders, metallic powders, plastics or photosensitive liquid resins in order to produce prototypes or models. At present, except for the process of shape melting, most rapid prototyping processes generate products that are only dimensionally similar to those of the desired end product. There is an urgent need, therefore, to enhance the understanding of the characteristics of these processes in order to realize their potential for production. Currently, the commercial market is dominated by four rapid prototyping processes, namely selective laser sintering, stereolithography, fused deposition modelling and laminated object manufacturing. This phase of the research has focussed on the selective laser sintering and stereolithography rapid prototyping processes. A theoretical model for these processes is under development. Different rapid prototyping sites supplied test specimens (based on ASTM 638-84, Type I) that have been measured and tested to provide a data base on surface finish, dimensional variation and ultimate tensile strength. Further plans call for developing and verifying the theoretical models by carefully designed experiments. This will be a joint effort between NASA and other prototyping centers to generate a larger database, thus encouraging more widespread usage by product designers.

Cariapa, Vikram↗

Modeling and simulation of transitional Rayleigh–Taylor flow with partially averaged Navier–Stokes equations

In this work, the partially averaged Navier–Stokes (PANS) equations are used to predict the variable-density Rayleigh–Taylor (RT) flow at Atwood number 0.5 and maximum Reynolds number 500. This is a prototypical problem of material mixing, featuring laminar, transitional, and turbulent flow, instabilities and coherent structures, density fluctuations, and production of turbulence kinetic energy by both shear and buoyancy mechanisms. These features pose numerous challenges to modeling and simulation, making the RT flow ideal to develop the validation space of the recently proposed PANS Besnard–Harlow–Rauenzahn-linear eddy viscosity model closure. The numerical simulations are conducted at different levels of physical resolution and test three approaches to set the parameters $f_\phi$ defining the range of physically resolved scales. The computations demonstrate the efficiency (accuracy vs cost) of the PANS model predicting the spatiotemporal development of the RT flow. Results comparable to large-eddy simulations and direct numerical simulations are obtained at significantly lower physical resolution without the limitations of the Reynolds-averaged Navier–Stokes equations in these transitional flows. The data also illustrate the importance of appropriate selection of the physical resolution and the resolved fraction of each dependent quantity $\phi$ of the turbulent closure, $f_\phi$. These two aspects determine the ability of the model to resolve the flow phenomena not amenable to modeling by the closure and, as such, the computations’ fidelity.

Navier Stokes equations↗