Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “energy analysis at scale”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 595 records · Page 33

PERFORMANCE ANALYSIS OF AN ENGINEERING SCALE HYDROTHERMAL LIQUEFACTION SYSTEM

This work evaluates the Modular Hydrothermal Liquefaction System (MHTLS), an engineering-scale, integrated continuous HTL plant operated at the Pacific Northwest National Laboratory (PNNL), for converting realistic wet wastes into energy-dense biocrudes. The production campaigns discussed here processed algae, sewage sludges, lignocellulosic blends, Industrial food waste, and engineered food-waste slurries at 350?°C and around 200?bar, with nominal feed rates of ~12?L?h?¹. We report biocrude yields and composition, establish mass and elemental (C, N) balances, and quantify energy performance via heater duties, heat-exchanger behavior, and system-level efficiencies. Biocrudes contained 76–80?wt?% C (dry, ash-free) with HHVs of 38-41?MJ?kg?¹, substantially higher than feed materials HHVs of 16.6–26.1?MJ?kg?¹ and approaching petroleum fuels. Dry, ash-free biocrude yields of 32–53?wt?% corresponded to 43–71?wt?% carbon yields, with 18–40?wt?% of feed carbon routed to the aqueous phase. Thermal efficiencies were 50-65%, and total energy efficiencies, including reactor heat input, were 35-55%. A counter-current tube-in-tube heat exchanger delivered U values of 200–450?W?m?²?K?¹, with fouling-induced declines impacting heat recovery and heater duty. The analysis highlights three priorities for the process intensification of HTL: robust, fouling-resistant heat recovery, hydrodynamically suitable reactor and heat-exchanger designs, simplified and predictable solids management, and biocrude-water separation.

Biocrude production↗

Secondary electron emission for reticulated carbon foam surfaces using direct measurements and spectroscopic analysis

This study investigates secondary electron emission (SEE) characteristics of reticulated foams using direct measurements and analytical modeling. Total SEE was quantified, revealing suppression of up to 44% in carbon foam structures compared to planar graphite surfaces. An optimal geometric configuration was identified and supported by analytical models. SEE angular dependence experiments showed diverse behaviors: fiber-like behavior and directional dependence for pore and ligaments on the mm scale, with fuzz-like characteristics when the foam features are between 10–100 µm. Electron energy analyzer measurements showed that carbon foams preferentially suppress inelastic backscattered electrons (BSEs) more so than true secondary electrons (SEs). The analysis indicated a larger fraction of low-energy SE generation in foams compared to flat surfaces due to increased emission from curved fiber ligaments and tertiary SEs from high-energy BSEs. These findings have implications for design and optimization of materials with tailored electron emission properties for applications like plasma-facing components, spacecraft materials, and accelerator surfaces.

Auger↗

NORTH DAKOTA CARBONSAFE PHASE III: SITE CHARACTERIZATION AND PERMITTING OF GEOLOGIC STORAGE OF CARBON DIOXIDE

The Energy & Environmental Research Center (EERC), in partnership with Minnkota Power Cooperative Inc. (Minnkota), SLB, and Computer Modelling Group Ltd. (CMG), supported wide-scale deployment of carbon capture and storage (CCS) as part of the U.S. Department of Energy (DOE) National Energy Technology Laboratory Carbon Storage Assurance Facility Enterprise (CarbonSAFE) Initiative Phase III. This phase included the acquisition, analysis, and development of information to fully characterize two storage complexes to demonstrate viable storage resources for commercial volumes of CO2 (defined by DOE as a minimum of 50 million tonnes [MMt] of CO2 within a 30-year period) (National Energy Technology Laboratory, 2024). Phase III also involved the preparation, submission, and approval of North Dakota underground injection control (UIC) Class VI storage facility permits (SFPs)—required precursors to applications for Class VI injection well permits. The presumed viability of commercial-scale CCS, situated adjacent to Minnkota’s Milton R. Young Station (MRYS), is validated by Minnkota’s continued pursuit of Project Tundra—an initiative to build the world’s largest lignite-based CCS project in central North Dakota (www.projecttundrand.com). Project Tundra comprises two scopes of work, Tundra Capture (installation of postcombustion CO2 capture at MRYS) and Tundra SGS (secure geologic storage). The efforts of North Dakota CarbonSAFE Phase III, Site Characterization and Permitting, supported Tundra SGS. Extensive site-specific characterization activities included a successful multimeasurement geophysical approach and drilling a stratigraphic test well (J-ROC 1, subsequently renamed Liberty-1) adjacent to MRYS. Core collection and analyses, downhole testing and fluid sampling, and geophysical logging were performed on J-ROC 1 and on a nearby stratigraphic test well (known as J-LOC 1), which was drilled, cored, and tested under a complementary project funded by the North Dakota Lignite Research Program. The injection tests performed on J-LOC 1 positively impacted the CarbonSAFE project, resulting in fewer proposed injection wells and significant construction, operations, and monitoring cost savings. The characterization data collected and analyses performed were integrated into geologic models, and successive numerical simulations were run to determine CO2 plume extent and subsurface pressure buildup associated with the planned CO2 injection rate of nearly 4 MMt per year. The latter doubles the CarbonSAFE Initiative goal with an estimated 100 MMt of CO2 stored in 20 years. Application of the U.S. Environmental Protection Agency’s (EPA’s) method for estimating the Class VI Rule area of review (AOR) to the overpressurized Broom Creek Formation inspired an alternative method of calculation, called risk-based AOR delineation. This peer-reviewed method was applied for the first time during the storage facility-permitting process. The two SFP applications submitted in 2021 successfully resulted in North Dakota Industrial Commission (NDIC) orders in 2022 authorizing the creation of the storage facility areas and amalgamation of pore space as well as establishing financial responsibility requirements. After approval of the SFPs, Minnkota filed in 2022 applications for permits to reenter the J-ROC 1 well and to drill two new wells—all with the intended purpose to become Class VI injection wells. To establish eligibility under the Internal Revenue Code for Section 45Q tax incentives, a monitoring, reporting, and verification (MRV) plan was prepared and submitted by Minnkota to EPA in 2022, resulting in the first such plan approved in North Dakota. Also in 2022, under the National Environmental Policy Act (NEPA), Minnkota prepared and submitted an environmental information volume (EIV) describing the proposed CCS project and associated potential environmental impacts. Based on the EIV, DOE determined that the proposed construction project required an environmental assessment, and Minnkota submitted the first draft in 2023 and a revised draft in 2024. Both submissions were followed by a public comment period. Subsequently, DOE issued a finding of no significant impact (FONSI) on September 13, 2024. A successful outreach program, strongly based in the production, presentation, and dissemination of informational material, fostered an environment to aid stakeholders in making informed decisions regarding the planned project. Opportunities for public input were provided at various steps along the way, including at county planning and zoning meetings, before and during the SFP administrative hearing, and during environmental assessment public comment periods. In addition, land/pore space owners and mineral owners had various points of contact, including granting access rights, securing pore space leasing, and mineral owner notifications. Based upon the successful storage facility permitting issued by NDIC, approval of the MRV plan by EPA, and receipt of a FONSI under the NEPA, Minnkota is continuing its pursuit of Project Tundra. In December 2023, the Office of Clean Energy Demonstrations under its Carbon Capture Demonstrations Projects Program announced funding for the capture system (Office of Clean Energy Demonstrations, 2023) and a proposal for CarbonSAFE Phase IV: Construction funding was submitted in March 2024 for the storage project. A go/no-go decision to proceed with construction and operations in the Broom Creek Formation is anticipated in 2024. References National Energy Technology Laboratory, CarbonSafe Initiative, https://netl.doe.gov/carbon-management/carbon-storage/carbonsafe (accessed August 2024). Office of Clean Energy Demonstrations, 2023, OCED selects three projects in CA, ND, and TX to reduce harmful carbon pollution, create new economic opportunities, and advance carbon reducing technologies, December, www.energy.gov/oced/articles/oced-selects-three-projects-ca-nd-and-tx-reduce-harmful-carbon-pollution-create-new (accessed August 2024).

Peck, Wesley↗

Electrothermal mineralization of per- and polyfluoroalkyl substances for soil remediation

Abstract Per- and polyfluoroalkyl substances (PFAS) are persistent and bioaccumulative pollutants that can easily accumulate in soil, posing a threat to environment and human health. Current PFAS degradation processes often suffer from low efficiency, high energy and water consumption, or lack of generality. Here, we develop a rapid electrothermal mineralization (REM) process to remediate PFAS-contaminated soil. With environmentally compatible biochar as the conductive additive, the soil temperature increases to >1000 °C within seconds by current pulse input, converting PFAS to calcium fluoride with inherent calcium compounds in soil. This process is applicable for remediating various PFAS contaminants in soil, with high removal efficiencies ( >99%) and mineralization ratios ( >90%). While retaining soil particle size, composition, water infiltration rate, and cation exchange capacity, REM facilitates an increase of exchangeable nutrient supply and arthropod survival in soil, rendering it superior to the time-consuming calcination approach that severely degrades soil properties. REM is scaled up to remediate soil at two kilograms per batch and promising for large-scale, on-site soil remediation. Life-cycle assessment and techno-economic analysis demonstrate REM as an environmentally friendly and economic process, with a significant reduction of energy consumption, greenhouse gas emission, water consumption, and operation cost, when compared to existing soil remediation practices.

Science & Technology - Other Topics↗

Multi-device analysis of energy loss duration and pellet penetration with implications for shattered pellet injection in ITER

A robust disruption mitigation system (DMS) requires accurate characterization of key disruption timescales, one of the most notable being the thermal quench (TQ). Recent modeling of shattered pellet injection (SPI) into ITER plasmas, using JOREK and INDEX, suggests long TQ durations (6–10 ms) and slow cold front propagation due to the large plasma size. If validated, these predictions would have an impact on the desired pellet parameters and mitigation strategies for the ITER DMS. To resolve these questions, a database of SPI experiments from several small-to-large sized devices (J-TEXT, KSTAR, AUG, DIII-D, and JET) has been compiled under the auspices of the International Tokamak Physics Activity MHD, disruptions, and control topical group. Analysis of the energy loss duration (proxy for the TQ duration) with machine size is presented for both mixed neon/deuterium (Ne/D) SPI and pure deuterium (D) SPI. Several metrics for the energy loss onset (e.g. soft x-ray signal drop, I p dip, and radiation flash) were considered as the conventional metric, electron cyclotron emission, is often cut-off during SPI. Several scalings with different onset metrics showed an increase in energy loss duration with machine size. The energy loss duration was additionally shown to be a function of the ratio between the number of SPI neon atoms injected and the stored energy. Analysis of the pellet shard position relative to the cold front found that in larger devices, pellets are typically found inboard of the q = 2 surface at the energy loss onset. Lastly, the delay between the pellet shards hitting the q = 2 surface and the energy loss onset was additionally found to increase with machine size. This suggests that the pellet shards in large devices will penetrate faster and further than the cooling front.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Driving Force Dependent Photoinduced Charge Transfer Dynamics in Polymer-Wrapped Semiconducting Single-Walled Carbon Nanotubes

Here, we investigate the thermodynamic driving-force dependences of photoinduced charge separation (CS) and subsequent charge transfer dynamics in single-walled carbon nanotube (SWNT)–perylenediimide (PDI) donor–acceptor (D–A) superstructures. Pump–probe spectroscopy reveals that [SWNT (•+)n ]-(PDI –• ) n CS states form on an ∼100 fs time scale following photoexcitation; these dynamics are invariant across an ∼400 mV driving force range, indicating that SWNT hole polaron formation time scales are determined by nanotube lattice and solvent relaxation. These CS states feature SWNT hole polarons adjacent to (geminate) and nearby (nongeminate) PDI radical anions. Analysis of the free energy dependence for charge recombination (CR) of [SWNT •+ ] geminate -(PDI –• ) CS states highlights an ∼2 meV value for D–A electronic coupling (HAB) and ∼0.93 eV for the total reorganization energy (λ T ). A corresponding driving force dependence of the CR dynamics for [SWNT •+ ] nongeminate -(PDI –• ) CS states indicates a diminished H AB value (∼0.6 meV) and a larger λ T (∼1.1 eV), consistent with larger transfer distances. SWNT excitons that persist following photoinduced CS drive photooxidation of PDI –• components of [SWNT (•+)n ]-(PDI –• ) n CS states ( 1 SWNT* + PDI •– → PDI + SWNT •– ); this reaction manifests a significantly reduced λ T value (∼0.67 eV) as the initially prepared SWNT reduced state bears the character of a conduction band injected electron ([SWNT •– ] CB ). This reaction thus gives rise to relaxed, nongeminate SWNT electron and hole polarons on the same nanotube; these polarons react on a 10 2 ps time scale independent of the electronic structure of these SWNT-PDI superstructures.

anions↗

First-Principles Modeling of the Repassivation of Corrosion Resistant Alloys: Part I. O and Cl Adsorption Energy

To understand the mechanism of repassivation, a key process that controls the performance of corrosion resistant alloys (CRAs), it is useful to obtain some fundamental parameters that describe the atomistic processes. Oxygen and chlorine adsorption energies were systematically calculated with density functional theory for Ni-22Cr alloys with seven different solute elements: Co, Cu, Fe, Mn, Mo, Ru and W. All elements other than Cu enhance both O and Cl adsorption to alloy surfaces. Cr has the strongest effect among these elements. Surface configurations that give stronger O adsorption also tend to give stronger Cl adsorption. While this makes it difficult to differentiate the effect of these solute elements on the oxidation/repassivation tendency of alloys, these fundamental properties provide the foundation for higher scale models that could be used to study the oxidation process during corrosion and potentially inform the design of CRAs. Bader charge analysis reveals a strong relationship between the adatom adsorption energy and the Bader charges of both O and Cl adatom. In conclusion, the work function of alloy surfaces is increased by O while decreased by Cl, suggesting that Cl adsorption can have an intrinsic negative impact on corrosion resistance by decreasing the barrier to electron transfer.

36 MATERIALS SCIENCE↗

Near-wall reconstruction of higher order moments and length scales using the POD

An analysis of the near-wall behavior of the proper orthogonal decomposition (POD) eigenfunctions derived from direct numerical simulation (DNS) of channel flow is performed. Consistent with previous studies, a low order multi-mode reconstruction of the kinetic energy and Reynolds shear stress suffices. A similar reconstruction of the isotropic dissipation rate is shown to be insufficient, however. An analysis is performed of the multi-mode composition of the dissipation rate in the near-wall region, and it is shown that a significant number of higher-order modes are required to achieve the correct asymptotic consistency in the near-wall region. In an attempt to avoid this problem, a length scale definition is proposed in terms of an integration of the correlation tensor which factors in the presence of the wall. The wall is accounted for by only integrating out to 2y(+) and not over the entire domain. Viscous and inviscid estimates for the dissipation were used in the near-wall and core regions respectively, in conjunction with this length scale representation to obtain an estimate of the dissipation throughout the domain. The resulting dissipation exhibits the proper behavior near the wall and in the inertial layer. A 1 POD mode estimate of the length scale is computed and found to agree quite well with the length scale obtained when the entire correlation tensor is used.

Glauser, Mark N.↗

U.S. Solar Photovoltaic System and Energy Storage Cost Benchmarks: Q1 2021

NREL has been modeling U.S. solar photovoltaic (PV) system costs since 2009. This year, our report benchmarks costs of U.S. PV for residential, commercial, and utility-scale systems, with and without storage, built in the first quarter of 2021 (Q1 2021). The methodology includes bottom-up accounting for all system and project-development costs incurred when installing residential, commercial, and utility-scale systems and it models the capital costs and levelized cost of energy for such systems.

14 SOLAR ENERGY↗

Development of Ionic Based Fluid to Improve Fluid Hydraulics in Enhanced Geothermal Systems

This research advances the field of geothermal energy by developing and evaluating novel fluid systems designed explicitly for high-temperature subsurface environments to enhance fracture flow distribution. The project integrates chemical synthesis, environmental assessment, rheological testing, microfluidic analysis, and reservoir-scale laboratory testing and analysis to identify optimal ionic and nonionic fluids for Enhanced Geothermal Systems (EGS).

15 GEOTHERMAL ENERGY↗

Modeled Results of Four Residential Energy Efficiency Measure Packages for Deriving Advanced Building Construction Research Targets

The Advanced Building Construction (ABC) Initiative from the U.S. Department of Energy Building Technologies Office is working to accelerate industrialized construction innovations for decarbonizing buildings. To inform performance and cost targets for research under the ABC Initiative, this analysis used the ResStock™ tool to evaluate the energy savings, utility bill impacts, and carbon emissions impacts of four simulated upgrade packages with specific target performance levels on a large sample of residential dwelling units (approximately 550,000) representative of the U.S. housing stock.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Sizing Small-Scale Renewable Energy Systems for the Navajo Nation and Rural Communities

The Navajo Nation consists of about 55,000 residential homes spread across 27,000 square miles of trust land in the Southwest region of the United States. The Navajo Tribal Utility Authority (NTUA) reports that approximately 15,000 homes on the reservation do not have electricity due to the high costs of connecting rural homes located miles from utility distribution lines. In order to get these rural homeowners access electricity, NTUA and other Native owned companies are examining small-scale renewable energy systems to provide power for necessary usage such as lighting and refrigeration. The goal of this study is to evaluate the current renewable deployment efforts and provide additional considerations for photovoltaic (PV) systems that will optimize performance and improve efficiency to reduce costs. There are three case studies presented in different locations on the Navajo Nation with varying solar resource and energy load requirements. For each location, an assessment is completed that includes environmental parameters of the site- specific landscape and a system performance analysis of an off-grid residential PV system. The technical process, repeated for each location, demonstrates how the variance and uniqueness of each household can impact the system requirements after optimizations are applied. Therefore, the household variabilities and difference in locations must be considered. The differing results of each case study suggests additional analysis is needed for designing small-scale PV systems that takes a home-land-family specific approach to allow for better efficiency and more flexibility for future solar innovations to be considered for overall cost reductions.

14 SOLAR ENERGY↗

High-Temperature Aquifer Thermal Energy Storage (HT-ATES) Projects in Germany and the Netherlands—Review and Lessons Learned

Aquifer thermal energy storage (ATES) is a concept that can help to address heating and cooling needs through the use of the subsurface as a seasonal thermal energy storage (STES) system. Over 2800 ATES systems have been deployed with storage temperatures typically below 25 °C and only a few with higher temperatures (>40 °C), which would increase the energy density and utility of the stored thermal fluids. Until now, only a few high-temperature aquifer thermal energy storage (HT-ATES) projects have been initiated and are still in operation. These HT-ATES projects have encountered a range of technical and non-technical challenges. This study reviews ten such projects: four in Germany and six in the Netherlands. The non-technical issues include public acceptance, a lack of regulatory framework for these systems, managing overlapping uses of the subsurface, managing changes with the providers and off-takers of thermal energy, and obtaining financing to implement these projects. Common technical issues include geological factors such as incomplete characterization of the subsurface and reservoir heterogeneity; geochemical issues such as mineral scaling, corrosion, and biofouling; lower than expected thermal recovery; and issues with system design and reliability. This review highlights benefits and challenges faced by HT-ATES projects with the goal to use the lessons learned to improve the siting, design, development, and operation of such systems. Recommendations include improved initial subsurface site characterization, use of coupled process models to optimize system design and predict system performance, cascaded uses of stored thermal energy to better utilize the stored heat, monitoring networks to provide feedback on system performance, and expanded system scale to allow for continued operation even when maintenance of some system components is required. Techno-economic modeling and risk analysis could be used to optimize such HT-ATES project design and identify key factors that will affect sustained economic viability. In addition, design flexibility is important for these systems to allow for changing conditions regarding the supply and demand of thermal energy. Adopting these findings should improve the performance and reduce the risks for future HT-ATES projects worldwide.

15 - GEOTHERMAL ENERGY↗

Three-wave coupling observed between a shear Alfvén wave and a kink-unstable magnetic flux rope

Results from a laboratory experiment are presented in which, for the first time, a shear Alfvén wave is launched using an antenna in a current-carrying plasma column that is tailored to be either stable or unstable to the kink oscillation. As the plasma is driven kink unstable, the frequency power spectrum of the Alfvén wave evolves from a single peak to a peak with multiple sidebands separated by integer multiples of the kink frequency. The main sidebands (one on either side of the launched wave peak in the power spectrum) are analyzed using azimuthal wavenumber matching, perpendicular and parallel wavenumber decomposition, and bispectral time series analysis. The dispersion relation and three-wave matching conditions are satisfied, given each sideband is a propagating Alfvén wave that results from the interaction of the pump Alfvén wave and the co-propagating component of a half-wavelength, standing kink mode. The interaction is shown to generate smaller perpendicular wavelength Alfvén waves that drive energy transport to scales that will approach the dissipation scale of k⊥ρs=1, with k⊥ being the perpendicular wavenumber and ρs being the ion gyroradius at the electron temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Quantifying agricultural productive use of energy load in Sub-Saharan Africa and its impact on microgrid configurations and costs

The use of advanced energy technologies for agricultural purposes—such as irrigation, refrigeration, crop processing, and egg incubation—has the potential to increase crop yield, reduce vulnerability to changing precipitation patterns, increase shelf life, strengthen income and employment opportunities in rural areas, and reduce emissions by displacing fossil fuel-based technologies. These productive uses of energy (PUE) in remote areas could potentially be powered by microgrids that additionally serve otherwise unelectrified communities, most of which are located in rural Sub-Saharan Africa. Here, in this paper, we use high-resolution geospatial data to estimate the end-use electricity demand for a range of agricultural PUE across Sub-Saharan Africa, and we share these data in an open-access mapping tool. Next, we use REopt®, a techno-economic optimization model of energy systems, to determine the cost and system sizing implications of incorporating agricultural PUE into microgrid designs in Kenya and Zambia. We estimate the upper bound of agricultural PUE demand for irrigation, milling, shelling, refrigeration, and egg incubation across Sub-Saharan to be 16.8 TWh/yr. We find that incorporating local agricultural PUE into microgrid system designs increases the required system sizing while having minimal impact on the levelized cost of energy of these systems. Our analysis is the first to demonstrate the PUE potential in the agricultural sector at a 10x10-kilometer resolution across Sub-Saharan Africa and to show, at scale, how site-specific PUE can impact the cost and sizing of microgrids that are otherwise deployed to serve local household and community load.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Engineering-Scale Testing of the Biphasic Solvent Based CO 2 Absorption Capture Technology at a Covanta Waste-to-Energy Facility

The original goals of this project were to advance the development and demonstration of the Biphasic CO 2 Absorption Process (BiCAP) technology for CO 2 capture from waste-to-energy (WTE) generation at a 2.5 tonne per day (TPD) engineering scale. This project has primarily focused on the basic design of the 2.5 TPD pilot system within the inside battery limits pertaining to CO 2 capture. The project also conducted a preliminary techno-economic analysis (TEA) for BiCAP at a scale of 100,000 tonne per year (TPY) of CO 2 capture and a preliminary life cycle analysis (LCA) with a primary focus on the environmental impacts related to global warming potential.

09 BIOMASS FUELS↗

Lattice physics calculations using the embedded self-shielding method in polaris, Part II: Benchmark assessment

Polaris is a 2D multigroup lattice physics capability in the SCALE code system used for the analysis of light water reactor fuel designs. In this work, verification and validation results of Polaris in SCALE 6.2 are presented. The SCALE/KENO continuous-energy Monte Carlo code is used as a reference to compare the results of more than 2,000 combinations of pressurized water reactor and boiling water reactor lattice designs and state points. Radiochemical assay measurements were also used to assess the accuracy of depletion calculations. Results show that Polaris, with ENDF/B-VII.1 cross section library, produces accurate lattice physics data for core simulators.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The mean logarithm emerges with self-similar energy balance.

The attached eddy hypothesis of Townsend (The Structure of Turbulent Shear Flow, 1956, Cambridge University Press) states that the logarithmic mean velocity admits self-similar energy-containing eddies which scale with the distance from the wall. Over the past decade, there has been a significant amount of evidence supporting the hypothesis, placing it to be the central platform for the statistical description of the general organisation of coherent structures in wall-bounded turbulent shear flows. Nevertheless, the most fundamental question, namely why the hypothesis has to be true, has remained unanswered over many decades. Under the assumption that the integral length scale is proportional to the distance from the wall y , in the present study we analytically demonstrate that the mean velocity is a logarithmic function of y if and only if the energy balance at the integral length scale is self-similar with respect to y , providing a theoretical basis for the attached eddy hypothesis. The analysis is subsequently verified with the data from a direct numerical simulation of incompressible channel flow at the friction Reynolds number Reτ≃5200 (Lee & Moser, J. Fluid Mech., vol. 774, 2015, pp. 395–415).

42 ENGINEERING↗