Generalization of boundary-layer momentum-integral equations to three-dimensional flows including those of rotating system
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FLOW, VISCOUS↗
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Results for “THREE-DIMENSIONAL BOUNDARY LAYER”
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Evaluating mesoscale model predictions of diurnal speedup events in the Altamont Pass Wind Resource Area of California
Mesoscale model predictions of wind, turbulence, and wind energy capacity factors are evaluated in the Altamont Pass Wind Resource Area of California (APWRA), where the diurnal regional sea breeze and associated terrain-driven speedup flows drive wind energy production during the summer months. Results from the Weather Research and Forecasting model version 4.4 using a novel three-dimensional planetary boundary layer (3D PBL) scheme, which treats both vertical and horizontal turbulent mixing, are compared to those using a well-established one-dimensional (1D) scheme that treats only vertical turbulent mixing. Each configuration is evaluated over a nearly 3-month-long period during the Hill Flow Study, and due to the recurring nature of the observed speedup flows, diurnal composite averaging is used to capture robust trends in model performance. Both model configurations showed similar overall skill. The general timing and direction of the speedup flows is captured, but their magnitude is overestimated within a typical wind turbine rotor layer. Both also fail to capture a persistent observed near-surface jet-like flow, likely due to the limited grid resolution that is typical of mesoscale models. However, the 3D PBL configuration shows several minor improvements over the 1D PBL configuration, including improved wind speed and turbulence kinetic energy profiles during the accelerating phase of the speedup events, as well as reduced positive wind speed bias at surface stations across the APWRA region. Using a mesoscale wind farm parameterization, modeled capacity factors are also compared to monthly data reported to the US Energy Information Administration (EIA) during the study period. Although the monthly trend in the data is captured, both model configurations overestimate capacity factors by roughly 7 %–11 %. Through model evaluation, this study provides confidence in the 3D PBL scheme for wind energy applications in complex terrain and provides guidance for future testing.
17 WIND ENERGY↗
Impact of atmospheric turbulence on performance and loads of wind turbines: knowledge gaps and research challenges
Wind energy harvesting from the atmosphere takes place in the atmospheric boundary layer. The boundary layer shear and buoyancy create three-dimensional turbulent eddies spanning a range of scales that form a continuous forward cascade of kinetic energy to the smallest scales of motion where energy is dissipated. Large-scale atmospheric circulations modulate the boundary layer turbulence, characterized by coherence and intermittency. As wind turbines grow in size and the integrated control of both turbines and wind farms spans greater distances, the relationship between the scales of atmospheric turbulence and the design and operation of wind energy facilities has entered new territory. The boundary layer turbulence impacts both wind turbine power production and turbine loads. Optimizing wind turbine and wind farm performance requires an understanding of how turbulence affects both wind turbine efficiency and reliability. While the characteristics of atmospheric boundary layer turbulence have been observed and studied in detail over the last few decades, there are still significant gaps in our understanding of the impact of turbulence on wind power resources and wind farm operations. This paper outlines the current state of turbulence research relevant to wind energy applications and points to gaps in our knowledge that need to be addressed to effectively utilize wind resources.
Kosović, Branko [Johns Hopkins Univ., Baltimore, M↗
A Visualization Study of Secondary Flows in Cascades
Flow-visualization techniques are employed to ascertain the streamline patterns of the nonpotential secondary flows in the boundary layers of cascades, and thereby to provide a basis for more extended analyses in turbomachines. The three-dimensional deflection of the end-wall boundary layer results in the formation of a vortex within each cascade passage. The size and tightness of the vortex generated depend upon the main-flow turning in the cascade passage. Once formed, a vortex resists turning in subsequent blade rows, with consequent unfavorable angles of attack and possible flow disturbances on the pressure surfaces of subsequent blade rows when the vortices impinge on these surfaces. Two major tip-clearance effects are observed, the formation of a tip-clearance vortex and the scraping effect of a blade with relative motion past the wall boundary layer. The flow patterns indicate methods for improving the blade tip-loading characteristics of compressors and of low- and high-speed turbulence.
Herzig, Howard Z↗
Aerodynamic Design of Axial-flow Compressors. Volume III
Chapters XI to XIII concern the unsteady compressor operation arising when compressor blade elements stall. The fields of compressor stall and surge are reviewed in Chapters XI and XII, respectively. The part-speed operating problem in high-pressure-ratio multistage axial-flow compressors is analyzed in Chapter XIII. Chapter XIV summarizes design methods and theories that extend beyond the simplified two-dimensional approach used previously in the report. Chapter XV extends this three-dimensional treatment by summarizing the literature on secondary flows and boundary layer effects. Charts for determining the effects of errors in design parameters and experimental measurements on compressor performance are given in Chapters XVI. Chapter XVII reviews existing literature on compressor and turbine matching techniques.
COMPRESSORS - PRESSURE RATIO↗
Flow of Gas Through Turbine Lattices
This report is concerned with fluid mechanics of two-dimensional cascades, particularly turbine cascades. Methods of solving the incompressible ideal flow in cascades are presented. The causes and the order of magnitude of the two-dimensional losses at subsonic velocities are discussed. Methods are presented for estimating the flow and losses at high subsonic velocities. Transonic and supersonic flows in lattices are then analyzed. Some three-dimensional features of the flow in turbines are noted.
BOUNDARY LAYER - AIRFOILS - CASCADES↗
Seismic response of vertical dry storage casks under three-dimensional earthquake motions
Ensuring the long-term seismic safety of dry storage casks (DSCs) is becoming increasingly critical as these systems evolve from temporary to de facto permanent repositories for spent nuclear fuels. Traditional seismic soil–structure interaction (SSI) assessment methods use one-dimensional deconvolution or simplified boundary conditions to model incident waves. Although computationally appealing, simplifying assumptions may alter the seismic risk by neglecting the full complexity of three-dimensional (3D) wave propagation effects. To address this challenge, this paper introduces a novel high-fidelity computational framework that leverages the Domain Reduction Method (DRM) with perfectly matched layers (PML) to accurately transfer complex, 3D seismic wavefields from regional-scale fault-rupture simulations into local-scale finite element models of DSCs. Using broadband, physics-based ground motions from a generic M w 7.0 strike-slip event, both single-cask and multi-cask configurations were investigated under near- and far-field conditions. Emphasis is placed on capturing complex SSI, spatial variability in the ground motion, and nonlinear phenomena such as cask rocking and sliding. Numerical results demonstrate that near-field conditions, where forward directivity and fling-step effects dominate, lead to significantly higher DSC rocking and sliding. Far-field cases, by contrast, generally exhibit modest responses. Incorporating SSI tends to amplify or alter DSC response spectra and introduce response variability, which underscores the need for site-specific evaluations and robust modeling approaches to ensure the seismic integrity of DSCs in interim spent fuel storage installations.
Das, Tonmoy↗
A twist grain boundary phase in aqueous solutions of the nucleic acid tetramer GTAC
At high concentration, long Watson/Crick (WC) double-helixed DNA forms columnar crystal or liquid crystal phases of linear, parallel duplex chains packed on periodic lattices. This can also be a structural motif of short NA oligomers such as the 5’-GTAC-3’ studied here, which makes four-base WC duplexes having hydrophobic blunt ends. End-to-end aggregation then assembles these duplexes into columns and columnar phases are stabilized, in spite of breaks in the double helix every four bases. But the new degrees of freedom introduced by such breaks also enable opportunities for a more diverse palette of self-assembly modes, producing striking self-assemblies of DNA that would not be achievable with contiguous polymers. These include recently reported three-dimensional (3D) periodic low-density nanoscale networks of GCCG, and the twist grain boundary (TGB) phase presented here. In the TGB, columns of GTAC pairs assemble into monolayer sheets in which the duplex columns are mutually parallel. However, unlike in the columnar crystals, these sheets stack in helical fashion into lamellar arrays in which the column axis of each layer is rotated through a 60° angle with respect to the columns in neighboring layers. This assembly of DNA is unique in that it the fills a 3D volume wherein the major grooves of columns in each layer mutually enter and interlock with the major grooves of columns in neighboring layers. This locking is optimized by small adjustments in structure enabled by the breaks in the duplex backbones.
DNA↗
Recent progress in atomic-scale controlled plasma processing
Atomic-scale control in plasma processing is becoming increasingly critical for fabricating of advanced semiconductor devices, particularly as the industry shifts toward three-dimensional (3D) architectures and high-aspect-ratio (HAR) structures. This review presents a comprehensive overview of recent developments in atomic-scale controlled plasma processes, organized along two key directions: the hierarchical structure of plasma–surface interactions and the generational evolution of atomic layer processing (ALP) technologies. We examined the gas phase, where molecular design enables selective generation of ions and radicals; the boundary layer, where transport phenomena govern species delivery into nanoscale features, and the surface, where temperature-dependent reactions and cyclic processing determine etching selectivity and precision. Building on this foundation, we outline five generations of ALP—from thermal atomic layer deposition to transport-aware, temporally and structurally decoupled processes—highlighting the increasing sophistication of process control. The review further explores the transition from empirical recipe development to science-based, data-driven methodologies. By integrating quantum-chemical modeling, advanced diagnostics, and machine learning, we demonstrated how predictive models can link plasma species composition to process outcomes, enabling autonomous and adaptive control strategies. Finally, this review discusses the broader societal implications of plasma process innovation through the E4 quartet: energy and resource efficiency, environmental sustainability, evolutionary advancement, and educational promotion. These principles guide the development of sustainable and intelligent atomic-scale manufacturing technologies that are not only technically advanced but also socially responsible.
Ishikawa, Kenji [Nagoya Univ. (Japan)] (ORCID:0000↗
Pyrochlore NaYbO2: A Potential Quantum Spin Liquid Candidate
The search for quantum spin liquids (QSL) and chemical doping in such materials to explore superconductivity have continuously attracted intense interest. Here, we report the discovery of a potential QSL candidate, pyrochlore-lattice β-NaYbO2. Colorless and transparent NaYbO2 single crystals, layered α-NaYbO2 (∼250 μm on edge) and octahedral β-NaYbO2 (∼50 μm on edge), were grown for the first time. Synchrotron X-ray single-crystal diffraction unambiguously determined that the newfound β-NaYbO2 belongs to the three-dimensional pyrochlore structure characterized by the R3̅m space group, corroborated by synchrotron X-ray and neutron powder diffraction and pair distribution function. Magnetic measurements revealed no long-range magnetic order or spin glass behavior down to 0.4 K with a low boundary spin frustration factor of 17.5, suggesting a potential QSL ground state. Under high magnetic fields, the potential QSL state was broken and spins order. Our findings reveal that NaYbO2 is a fertile playground for studying novel quantum states.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Boundary-layer Transition at High Reynolds Numbers as Obtained in Flight of a 20 Degree Cone-cylinder with Wall to Local Stream Temperature Ratios near 1.0
Boundary-layer transition data at low ratios of wall to local stream temperature have been obtained during the free flight of a highly polished cone-cylinder to a maximum Mach number of 5.02 A maximum transition Reynolds number of 32 x 10(exp 6) occurred at a distance of 25.84 inches from the cone apex. The temperature ratio at transition for a local Mach number of 4.0 was approximately 1.30 as compared with theoretical infinite stability solutions of 1.47 and 1.65 by Dunn and Lin (three-dimensional) and Van Driest (two-dimensional), respectively.
Rabb, Leaonard↗
The shape of convection in 2D and 3D global simulations of stellar interiors
Context. Theoretical descriptions of convective overshooting in stellar interiors often rely on a basic one-dimensional parameterization of the flow called the filling factor for convection. Several different definitions of the filling factor have been developed for this purpose, based on: (1) the percentage of the volume, (2) the mass flux, and (3) the convective flux that moves through the boundary. Aims. We examine these definitions of the filling factor with the goal of establishing their ability to explain differences between 2D and 3D global simulations of stellar interiors that include fully compressible hydrodynamics and realistic microphysics for stars. Methods. We study convection and overshooting in pairs of identical two-dimensional (2D) and three-dimensional (3D) global simulations of stars produced with MUSIC , a fully compressible, time-implicit hydrodynamics code. We examine pairs of simulations for (1) a 3 M ⊙ red giant star near the first dredge-up point, (2) a 1 M ⊙ pre-main-sequence star with a large convection zone, (3) the current sun, and (4) a 20 M ⊙ main-sequence star with a large convective core. Results. Our calculations of the filling factor based on the volume percentage and the mass flux indicate asymmetrical convection near the surface for each star with an outer convection zone. However, near the convective boundary, convective flows achieve inward-outward symmetry for each star that we study; for 2D and 3D simulations, these filling factors are indistinguishable. A filling factor based on the convective flux is contaminated by boundary-layer-like flows, making a theoretical interpretation difficult. We present two possible new alternatives to these frequently used definitions of a filling factor, which instead compare flows at two different radial points. The first alternative is the penetration parameter of Anders et al. (2022, ApJ, 926, 169). The second alternative is a new statistic that we call the plume interaction parameter. We demonstrate that both of these parameters captures systematic differences between 2D and 3D simulations around the convective boundary.
79 ASTRONOMY AND ASTROPHYSICS↗
Outflow Boundary Conditions for Turbine-Integrated Rotating Detonation Combustors
This study examines outflow boundary conditions (BCs) in computational fluid dynamics (CFD) simulations of a transition duct with and without guide vanes that converts supersonic flow exiting a rotating detonation combustor (RDC) to subsonic flow to drive a turbine. Since the flow exiting the transition duct has swirling shock waves with significant spatial and temporal variations in pressure, temperature, and Mach number, imposing proper BCs poses a challenge. To ensure all swirling shock waves exit the transition duct without creating non-physical reflected waves at its outlet, this study examined three outflow BCs: (1) the average pressure imposed at the duct’s outlet, (2) a nonreflecting BC (NRBC) with a specified average pressure imposed at the duct’s outlet, (3) the average pressure imposed at the outlet of an extension duct made up of a buffer layer and a sponge layer. This study is based on the three-dimensional, unsteady density-weighted-ensemble-averaged continuity, Navier–Stokes, and energy equations for a thermally perfect gas closed by the realizable k–ε model and “enhanced” wall functions. The results obtained show that imposing an average pressure at the transition duct’s outlet produces spurious waves that degrade the physical meaningfulness of the solution. When the NRBC was applied, swirling shock waves exited the duct’s outlet without creating spurious waves. However, its usage requires the gas to be thermally, as well as calorically, perfect, which this study shows could be a concern. By imposing the average pressure at the outlet of an extension duct, the gas does not need to be calorically perfect. The results obtained show the effects of the sponge layer’s length and coarsening ratio on damping nonuniformities in non-physical reflected waves to ensure the flow exiting the transition duct’s outlet can do so as if there are no boundaries present and has the desired average pressure—even though the BC is applied at the extension duct’s outlet.
gas turbines↗
The Role of Subcloud Mesoscale Convergence in Sculpting Convective Updraft Width and Depth
The initiation of deep moist convection is governed in part by the horizontal width of updrafts near cloud base, which limits the deleterious effects of entrainment-driven dilution on buoyant thermals ascending through the free troposphere. However, the factors controlling cloud-base updraft width, which in turn dictates cloud depth, are not well understood. We track the evolving three-dimensional structure of the mesoscale subcloud forcing for vertical motion and near-cloud thermodynamic ingredients within a high-resolution ensemble of simulations of seven realistic daytime orographic convection initiation events to determine their relative roles in controlling cloud width and depth. Statistical analysis of approximately 5000 cloudy updraft samples indicates that the most important contributors to the width of cloudy updrafts across the ensemble are the depth and magnitude of the subcloud mesoscale ascent. However, the depth achieved by clouds is more consistently predicted by the near-cloud ambient relative humidity within the lower to middle free troposphere and convective available potential energy. Therefore, although the width of cloudy updrafts may be partly set at low levels by the mesoscale vertical mass and moisture flux, the likelihood of deep moist convection is governed by the generation of positive buoyancy within cumulus thermals and entrainment-driven dilution that reduces it. The persistence of the low-level mesoscale vertical forcing locally consolidates and vertically transports boundary layer moisture, helping to reduce updraft dilution. However, these factors vary in relative impacts on cloudy updrafts across individual cases, indicating multiple pathways for deep convection initiation.
Convective storms↗
The "limiting line" in mixed subsonic and supersonic flow of compressible fluids
It is well known that the vorticity for any fluid element is constant if the fluid is non-viscous and the change of state of the fluid is isentropic. When a solid body is placed in a uniform stream, the flow far ahead of the body is irrotational. Then if the flow is further assumed to be isentropic, the vorticity will be zero over the whole filed of flow. In other words, the flow is irrotational. For such flow over a solid body, it is shown by Theodorsen that the solid body experiences no resistance. If the fluid has a small viscosity, its effect will be limited in the boundary layer over the solid body and the body will have a drag due to the skin friction. This type of essentially isentropic irrotational flow is generally observed for a streamlined body placed in a uniform stream, if the velocity of the stream is kept below the so-called "critical speed." At the critical speed or rather at a certain value of the ratio of the velocity of the undisturbed flow and the corresponding velocity of sound, shock waves appear. This phenomenon is called the "compressibility bubble." Along a shock wave, the change of state of the fluid is no longer isentropic, although still adiabatic. This results in an increase in entropy of the fluid and generally introduces vorticity in an originally irrotational flow. The increase in entropy of the fluid is, of course, the consequence of changing part of the mechanical energy into heat energy. In other words, the part of fluid affected by the shock wave has a reduced mechanical energy. Therefore, with the appearance of shock waves, the wake of the streamline body is very much widened, and the drag increases drastically. Furthermore, the accompanying change in the pressure distribution over the body changes the aerodynamic moment acting on it and in the case of an airfoil decreases the lift force. All these consequences of the breakdown of isentropic irrotational flow are generally undesirable in applied aerodynamics. Its occurrence should be delayed as much as possible by modifying the shape or contour of the body. However, such endeavor will be very much facilitated if the cause or the criterion for the breakdown can be found first.
MACH NUMBER↗
Additional considerations in analytical solution for time-dependent heat conduction in a three-dimensional multilayer sphere
This work presents an analytical method to solve the heat conduction equation in three dimensions for problems consisting of multilayer concentric spheres. The method can be used to treat time-varying heat conduction problems where the heat source that drives the transient is time-invariant. Equally applicable to all Poisson-type problems with concentric spherical geometry, the method consists of representing the solution as a summation of weighted eigenfunctions. The weights for each eigenfunction are computed algebraically. Previous work has already established the core constituents of the methodology. The current work augments the existing methods by including consideration of nonzero interface resistance between layers and explicit discussion on the boundary condition homogenization required to treat inhomogeneous problems. Also, two demonstration problems are presented. One demonstration problem is based on the method of manufactured solutions and therefore allows for comparison with exact expressions for the solution temperature distribution. The second, more complex, demonstration problem relies on the finite element method for comparisons. The expected convergence behavior is observed for both demonstration problems.
97 - MATHEMATICS AND COMPUTING↗
Bio-inspired alula-based winglet design for enhanced heat transfer in high temperature fin-and-tube heat exchangers
Fin-and-tube heat exchangers (FTHEs) are widely used for high-temperature flue-gas heat recovery, but their performance is often limited by wake regions and non-uniform fin-surface temperatures. This study proposes and numerically evaluates four bio-inspired longitudinal vortex generator (VG) configurations in a high-temperature FTHE with flue-gas inlet temperature ∼1230 K: double-delta, curved double-delta, alula, and a new curved-alula geometry. The reference fin is not hydraulically plain; it already incorporates leading-edge separation columns and convex protrusions, so the alula-type winglets are assessed as downstream add-ons acting on a strongly disturbed flow. In a second step, perforations (one, two and three circular holes) are introduced into the curved-alula VGs to further tailor the flow field. Three-dimensional simulations with the Shear Stress Transpor (SST) $k - ω$ model, temperature-dependent flue-gas properties and conjugate conduction are carried out for gas-side Reynolds numbers $Re_g ≈ 8.0$ x $10^2 - 3.6$ x $10^3$ (mass flow rates 0.5 – 2.5 g/s), and the designs are compared in terms of surface heat flux, Nusselt number, friction factor and hydrothermal performance factor (HTPF). For this already-promoted fin, the additional downstream winglets provide moderate, incremental hydrothermal gains. At the highest Reynolds number, the best non-perforated design (curved-alula) increases surface heat flux from 1630.9 to 1794.7 kW/m² (∼ 10 % gain) and the Nusselt number from 227.6 to 242.6 (∼ 7 % gain), while the friction factor rises from 0.26 to about 0.30, yielding HTPF values close to unity (∼ 0.9 – 1.0). Introducing circular perforations into the curved-alula winglets acts mainly as a wake-bleeding refinement: the three-hole configuration provides a heat flux of 1824.7 kW/m² and a pressure drop of 127.9 Pa, with HTPF in the range ∼ 1.03 – 1.14 and a small (∼ 1 – 3 %) improvement over the solid curved-alula design. Flow-field analysis shows that the perforated curved-alula VGs shrink tube-wake regions, thin the thermal boundary layer and homogenize the fin-surface temperature (outlet-gas temperature ∼ 510 – 520 K and fin-surface temperature ∼ 420 – 421 K for the three-hole case). An optimal flue-gas mass flow rate of ∼ 1 g/s ($Re_g ≈ 1.5$ x $10^3$) is identified, beyond which additional heat-transfer gains are offset by rapidly increasing pressure losses. Overall, the results highlight that initial fin geometry and VG placement are as important as VG shape: alula-based winglets are expected to yield larger relative gains on simpler flat-fin layouts or when positioned closer to the fin leading edge and tube
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
A North Sea in Situ Evaluation of the Fitch Wind Farm Parameterization Within the Mellor-Yamada-Nakanishi-Niino and 3D Planetary Boundary Layer Schemes
Wind resource assessments and wind power forecasts that account for wind farm wakes are sensitive to the choice of planetary boundary layer (PBL) scheme. This work compares the one-dimensional Mellor-Yamada-Nakanishi-Niino (MYNN) PBL scheme with a three-dimensional PBL (3DPBL) scheme, evaluating predictions made with both schemes against two sets of North Sea in situ observations of wind farm wakes. The optimal PBL scheme varies based on the observations (FINO1 tower vs. aircraft), the quantity of interest (wind speed vs. turbulence kinetic energy [TKE]), and the error metric (bias, centered root mean square error [cRMSE], R2, and earth mover's distance [EMD]). Whereas 3DPBL wind speeds outperform MYNN wind speeds with respect to the cRMSE at the FINO1 site located at a single point within the turbine rotor layer, 3DPBL TKE bias is larger than MYNN TKE bias when compared to aircraft observations taken 100 m above a wind farm. Wind speeds in the aircraft region are ambiguous with regard to which PBL scheme is optimal. Aircraft MYNN wind speeds outperform 3DPBL wind speeds with respect to R2 and cRMSE but underperform with respect to bias and EMD. Future evaluations across broader temporal and spatial scales may offer further insight into model differences.
17 WIND ENERGY↗