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19 pages, 2702 KB  
Article
Experimental and CFD Investigation of Bubble Dynamics in Geldart Group B Fluidized Beds: A Comparative 2D and 3D Analysis
by Zhu Yang, Germán Mazza, Maarten Vanierschot, Renaud Ansart and Yimin Deng
Appl. Sci. 2026, 16(13), 6372; https://doi.org/10.3390/app16136372 (registering DOI) - 25 Jun 2026
Abstract
Gas–solid bubbling fluidized beds involving Geldart Group B particles are fundamental to numerous industrial thermochemical processes, where bubble dynamics dictate the efficiency of heat and mass transfer. However, accurately predicting these complex hydrodynamic behaviors remains a challenge due to the non-linear coupling of [...] Read more.
Gas–solid bubbling fluidized beds involving Geldart Group B particles are fundamental to numerous industrial thermochemical processes, where bubble dynamics dictate the efficiency of heat and mass transfer. However, accurately predicting these complex hydrodynamic behaviors remains a challenge due to the non-linear coupling of phase interactions. This study presents a comprehensive validation of 2D and 3D Eulerian–Eulerian Two-Fluid Models (TFM) against an extensive experimental dataset. A ‘core-flow’ consistency principle is adopted, demonstrating that the 3D cylindrical simulation provides a physically equivalent representation of the central bubbling dynamics in the rectangular experimental bed. A key innovation of this work is a novel post-processing framework that bridges raw CFD datasets and quantitative bubbling metrics. Unlike traditional threshold-based segmentation or localized probe measurements, which are often limited by spatial resolution and noise sensitivity, the integrated use of Autodesk 3DS Max for volumetric reconstruction and customized MATLAB (R2024a) algorithms allows for the seamless processing of heterogeneous 2D and 3D data. This methodology significantly enhances the capability to track complex bubble coalescence and breakup events while improving batch-processing efficiency, providing a high-fidelity alternative for analyzing gas–-solid flow patterns in complex geometries. The results show that both experimental data and 2D simulations align with Werther’s correlation, yielding Mean Relative Errors (MRE) of 8.2% and 10.5%, respectively. In contrast, the 3D simulation tracks Darton’s prediction closely with a lower MRE of 7.4%, demonstrating superior concordance in volumetric bubble growth. The core innovation lies in the definition of a clear dimensional choice framework: 2D simulations are computationally sufficient and accurate for predicting macro-scale bubble heights and frequencies under pseudo-2D or narrow-bed constraints. However, 3D simulations are strictly necessary when evaluating unconstrained radial expansion, core-flow dynamics, and precise volumetric bubble diameters (dv) where full multi-directional degrees of freedom dictate hydrodynamics. Full article
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20 pages, 2581 KB  
Review
Advances in Protection Technologies and Materials for Deep Unconventional Oil and Gas Reservoirs
by Wenjie Su, Zhenjiang You, Xiaofeng Chang, Xifeng Hu, Wenmin Xie, Yijun Fan, Bochao Zhao, Zhenzhen Qiang, Hengji Zhang and Jiafeng Jin
Processes 2026, 14(12), 2024; https://doi.org/10.3390/pr14122024 (registering DOI) - 22 Jun 2026
Viewed by 138
Abstract
Deep unconventional oil and gas reservoirs are critical to hydrocarbon exploration and development in China. However, their complex geological and petrophysical features, including high temperature, high pressure, high salinity, multiple pressure systems, and intricate pore–fracture structures, make them highly susceptible to formation damage [...] Read more.
Deep unconventional oil and gas reservoirs are critical to hydrocarbon exploration and development in China. However, their complex geological and petrophysical features, including high temperature, high pressure, high salinity, multiple pressure systems, and intricate pore–fracture structures, make them highly susceptible to formation damage during drilling, completion, stimulation, and production. Effective reservoir protection is therefore essential for minimizing damage and improving development efficiency. This paper systematically reviews recent advances in reservoir protection for deep unconventional reservoirs, with a focus on evaluation methods and protective materials. Laboratory evaluation methods, including permeability recovery, nuclear magnetic resonance, pressure decay, and spontaneous imbibition, together with field-based approaches such as well testing and production decline analysis, are summarized and assessed for their applicability to complex damage characterization. Major damage mechanisms, including liquid-phase trapping, solid invasion, sensitivity damage, stress sensitivity, and wettability alteration, are analyzed with emphasis on working fluid–reservoir interactions under multi-field coupling conditions. Recent progress in protective materials is also reviewed, covering polymer-based materials such as gel sealing agents, delayed-swelling hydrogels, water-/oil-soluble temporary plugging agents, and film-forming polymers, as well as ultrafine CaCO3 and fiber-based materials. In addition, related protection technologies, including temporary plugging, film-forming fluid-loss control, underbalanced drilling, and low-damage completion fluids, are discussed. Existing models developed for conventional sandstone reservoirs are insufficient for deep unconventional systems. Future research should prioritize integrated evaluation and protection methods tailored to deep tight, shale, and fractured–vuggy carbonate reservoirs. This review provides a basis for understanding complex damage mechanisms, developing functional protective materials, and advancing integrated reservoir protection technologies for the efficient development of deep unconventional resources. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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36 pages, 8329 KB  
Article
Computational Flow Analysis of a Passive Control Windmill Sail Rotor with Field Measurement Verification
by Constantinos Condaxakis and Georgios V. Kozyrakis
Sustainability 2026, 18(12), 6294; https://doi.org/10.3390/su18126294 (registering DOI) - 18 Jun 2026
Viewed by 114
Abstract
This study presents a computational and experimental aerodynamic characterisation of a full-scale 5.5 m diameter, six-sail horizontal-axis windmill of the traditional Cretan Lasithi type, equipped with flexible woven polyester sails that act as a passive load-control mechanism. Seventeen operating points spanning wind speeds [...] Read more.
This study presents a computational and experimental aerodynamic characterisation of a full-scale 5.5 m diameter, six-sail horizontal-axis windmill of the traditional Cretan Lasithi type, equipped with flexible woven polyester sails that act as a passive load-control mechanism. Seventeen operating points spanning wind speeds of 2.3–18.3 m/s were simulated in OpenFOAM using a transient sliding-mesh Arbitrary Mesh Interface formulation with the k–ω SST turbulence closure on a 2.3 million cell grid, selected on the basis of a four-level grid convergence study. CFD simulations identify three distinct aerodynamic regimes: a drag-dominated high-TSR regime (λ > 2.1), a mixed lift–drag working range with peak loading near λ ≈ 1.4–1.5, and a deep-stall regime in which boundary-layer separation propagates from root to tip as λ falls below 1.0. Field measurements conducted at the Energy Systems Synthesis Lab of the Hellenic Mediterranean University in compliance with IEC 61400-12-1:2005(E) confirm that rotor speed stabilises passively at 55–58 RPM above 13 m/s without any active control mechanism; CFD predictions agree with measured power output within 8–12% across the 2–13 m/s attached-flow envelope. The combined evidence indicates that passive overspeed self-regulation is driven by aeroelastic sail deformation, reducing effective disc solidity at high wind speeds, a mechanism that rigid-geometry CFD correctly identifies in trend but cannot quantify in magnitude. The primary limitation of the present work is the rigid-sail assumption of the CFD model, which requires a two-way coupled fluid–structure interaction extension as a future step. Full article
(This article belongs to the Section Energy Sustainability)
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28 pages, 15060 KB  
Article
Hydrochemical Characteristics and Water–Rock Interaction of Typical Geothermal Reservoirs in Northern China: A Case Study from Tianjin Geothermal Field
by Qiuxia Zhang, Zhaolong Feng, Donglin Liu, Shengtao Li, Xiaofeng Jia, Jian Song and Yahui Yao
Energies 2026, 19(12), 2894; https://doi.org/10.3390/en19122894 - 18 Jun 2026
Viewed by 125
Abstract
Tianjin, nestled on the North China Plain, possesses abundant geothermal resources with tremendous potential for development and utilization. This study employs hydrogeochemical and isotopic analysis techniques to thoroughly explore the geochemical characteristics and circulation patterns of geothermal fluids in Tianjin, shedding light on [...] Read more.
Tianjin, nestled on the North China Plain, possesses abundant geothermal resources with tremendous potential for development and utilization. This study employs hydrogeochemical and isotopic analysis techniques to thoroughly explore the geochemical characteristics and circulation patterns of geothermal fluids in Tianjin, shedding light on the mechanisms underlying the formation and evolution of deep geothermal fluids. The findings reveal that atmospheric precipitation serves as the primary recharge source for the region’s geothermal fluids, with the calculated recharge heights coinciding with those of the Jixian mountainous area. This precipitation infiltrates through permeable layers and the deep, large faults surrounding the southern plain, entering relatively enclosed or semi-enclosed geothermal reservoirs. As they circulate, the geothermal fluids undergo intricate interactions with the surrounding rocks, including processes such as leaching, adsorption, carbonate reprecipitation, cation exchange, and decarbonation. The fluids circulate at depths ranging from 1.6 to 3.5 km, with temperatures spanning from 67 to 133 °C. Along the flow path, the anionic composition of the geothermal fluids shifts from HCO3 dominance in the north to a coexistence of Cl and SO42−, ultimately dominated by Cl in the south, accompanied by an increase in total dissolved solids (TDS). The results indicate that Tianjin geothermal fluids are mainly recharged by meteoric water and evolve along their flow paths through dissolution of evaporitic and carbonate minerals, cation exchange, and carbonate precipitation. Hydrochemical and Sr-isotope differences suggest generally limited vertical connectivity among the studied reservoirs, although local hydraulic interaction may occur near conductive faults. These results provide constraints on the hydrogeochemical evolution and management of geothermal resources in the Tianjin sedimentary basin. Full article
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22 pages, 10819 KB  
Article
Elastic Boundary Control in Acoustic Waveguides for High-Fidelity Physical-Layer Telemetry in Downhole Sensor Networks
by Hao Geng, Yingjian Xie, Zhihao Wang, Hu Han and Dong Yang
Sensors 2026, 26(12), 3826; https://doi.org/10.3390/s26123826 - 16 Jun 2026
Viewed by 216
Abstract
In the development of deep shale gas horizontal wells, precise geo-steering relies heavily on downhole sensor networks to acquire extensive formation and engineering parameters. Coiled tubing (CT) provides a promising acoustic waveguide for downhole sensing systems, but conventional acoustic sources rely on gravity-induced [...] Read more.
In the development of deep shale gas horizontal wells, precise geo-steering relies heavily on downhole sensor networks to acquire extensive formation and engineering parameters. Coiled tubing (CT) provides a promising acoustic waveguide for downhole sensing systems, but conventional acoustic sources rely on gravity-induced interfacial preload. Under highly deviated or horizontal well conditions, the loss of the axial gravity component may induce contact–nonlinearity instability, resulting in waveform distortion and spectral pollution. To address this limitation, a constant-stiffness preloading method based on elastic compliance control is proposed, together with a modal reconstruction strategy achieved by removing high-density tungsten blocks. A fluid–solid coupled dynamic model incorporating contact nonlinearity is established to reveal the dynamic separation mechanism of the acoustic source interface under varying gravity-vector conditions. Wave spring assemblies are then used to reconstruct the mechanical boundary and physically suppress time-domain clipping. Full-scale ground circulation experiments on a 1500 ft CT string show that the proposed method decouples acoustic-source performance from wellbore trajectory. Waveform asymmetry is reduced from 18.4% to 2.1%, and total harmonic distortion decreases from 12.5% to 1.8%. In addition, the first-order longitudinal natural frequency is shifted from 420 Hz to 2850 Hz, avoiding low-frequency pump noise and achieving a 12 dB SNR improvement. This physical-layer gain provides an optimized signal baseline for receiver-end demodulation algorithms. Ultimately, this study provides a robust physical-layer solution for acoustic telemetry in complex deep-earth environments, advancing the reliability of data interaction in downhole sensing systems. Full article
(This article belongs to the Section Industrial Sensors)
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18 pages, 6801 KB  
Article
Numerical Simulation of Horizontal Well Steering Fracturing Based on the Cohesive Zone Model
by Jian Shi, Peng Song, Jinsheng Zhao, Jun Yang, Jin Wang, Wantao Liu, Qiang Liu, Chen Yang and Mingyong Xu
Processes 2026, 14(12), 1951; https://doi.org/10.3390/pr14121951 - 15 Jun 2026
Viewed by 149
Abstract
Horizontal-well steering fracturing is an important completion strategy for unconventional reservoirs, where fracture growth is jointly controlled by wellbore azimuth, natural fractures, and inter-cluster stress interference. In this study, a two-dimensional fluid-solid-coupled hydraulic-fracturing model with embedded cohesive elements was developed to simulate fracture [...] Read more.
Horizontal-well steering fracturing is an important completion strategy for unconventional reservoirs, where fracture growth is jointly controlled by wellbore azimuth, natural fractures, and inter-cluster stress interference. In this study, a two-dimensional fluid-solid-coupled hydraulic-fracturing model with embedded cohesive elements was developed to simulate fracture initiation and growth at steering angles of 0°, 30°, 45°, 60°, and 90°. The Blanton, Warpinski-Teufel, and Blanton-Gao hydraulic-fracture/natural-fracture interaction criteria were used as mechanical benchmarks to interpret simulated capture, deflection, and penetration regimes. The simulations indicate that natural fractures preferentially guide fracture propagation: hydraulic fractures tend to be captured by, or propagate along, natural fractures at approach angles ≤30°, whereas penetration is more likely at approach angles ≥60°. In the single-stage single-cluster model, the 90° case produces the largest simulated fracture length and the highest failed-cohesive-element count. In the single-stage multi-cluster model with 3 m cluster spacing, the 30–45° interval shows more favorable fracture extension and interface activation than the 90° case because inter-cluster stress-shadow effects suppress fracture-network development at large steering angles. The resulting steering-angle window should be interpreted as a comparative result for the fixed mesh, deterministic natural-fracture realization, and baseline cluster-spacing configuration adopted here. These results provide a mechanistic basis for steering-fracturing design in hard-rock reservoirs while clarifying the applicability limits of the two-dimensional plane-strain approximation. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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41 pages, 3301 KB  
Review
Lattice-Based Volumetric Heat Sinks for Forced-Convection Cooling of Power Electronics: A Critical Review
by Ebelechukwu Okeke, Mehdi Khatamifar and Wenxian Lin
Energies 2026, 19(12), 2834; https://doi.org/10.3390/en19122834 - 14 Jun 2026
Viewed by 171
Abstract
Lattice-based heat sinks have attracted increasing attention as volumetric thermal management architectures for forced-convection cooling of high-power electronic systems. In contrast to conventional plate-fin, pin-fin, and straight-channel configurations, lattice geometries promote three-dimensional flow–solid interaction through interconnected ligament networks that modify boundary-layer development, wake [...] Read more.
Lattice-based heat sinks have attracted increasing attention as volumetric thermal management architectures for forced-convection cooling of high-power electronic systems. In contrast to conventional plate-fin, pin-fin, and straight-channel configurations, lattice geometries promote three-dimensional flow–solid interaction through interconnected ligament networks that modify boundary-layer development, wake formation, and internal heat-spreading pathways. This review synthesizes recent experimental and numerical studies to examine the thermo-fluid mechanisms governing lattice performance, with emphasis on the coupled influence of porosity, ligament dimensions, topology, orientation, and channel confinement on heat-transfer enhancement and hydraulic resistance. The analysis indicates that while lattice structures can increase average Nusselt number and improve temperature uniformity, these gains are intrinsically linked to pressure-drop penalties associated with flow tortuosity and form drag, resulting in regime-dependent thermal-hydraulic behavior. Apparent discrepancies reported across the literature are frequently attributable to differences in geometric definition, Reynolds-number normalization, and boundary-condition specification rather than to inconsistencies in physical mechanisms. By consolidating geometric scaling, performance metrics, manufacturing considerations, and system-level constraints, this review clarifies the conditions under which lattice heat sinks may provide net benefit relative to conventional cooling technologies and identifies key research directions required to support application-relevant design and evaluation. Full article
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30 pages, 5698 KB  
Review
Research Progress on Bionic Functional Surfaces for Friction Reduction, Wear Resistance, and Anti-Adhesion in Agricultural Machinery
by Honglei Zhang, Tiantian Jing, Jun Zhang, Dong Lv and Zhong Tang
Lubricants 2026, 14(6), 238; https://doi.org/10.3390/lubricants14060238 - 12 Jun 2026
Viewed by 303
Abstract
This review explicitly focuses on agricultural attachments and executing components that interact directly with soil and crops, rather than the tractor vehicle itself. Operating within complex and variable farmland media environments, the key components of agricultural machinery have long been constrained by bottlenecks [...] Read more.
This review explicitly focuses on agricultural attachments and executing components that interact directly with soil and crops, rather than the tractor vehicle itself. Operating within complex and variable farmland media environments, the key components of agricultural machinery have long been constrained by bottlenecks such as high-energy draught resistance, severe solid–liquid interfacial adhesion, and intense abrasive wear. Bionic functional surfaces, based on the coupling of micro-geometric morphology and surface-interface physical chemistry, provide a scientific approach to overcoming traditional tribological limitations by reconstructing the contact mechanics and fluid dynamics boundaries at the interface. This paper presents a comprehensive review of the latest research progress regarding bionic functional surfaces in the fields of friction reduction, wear resistance, and anti-adhesion in agricultural machinery. The article systematically categorises typical biological prototypes, such as soil-burrowing animals, aquatic organisms, and plant leaves, alongside their multidimensional feature extraction methods. It provides an in-depth analysis of core interaction mechanisms, ranging from static air cushion effects and dynamic wetting evolution to active electro-osmotic soil detachment, interfacial stress redistribution, and microscopic wear debris capture. Furthermore, it evaluates the efficacy of cross-scale coupled numerical simulation technologies in resolving interfacial interactions. At the engineering application level, this review extensively discusses the field performance of bionic structures in typical operational scenarios, including draught reduction in tillage and land preparation, blockage prevention in seed-metering channels, and low-damage harvesting in agricultural machinery. Finally, countermeasures are proposed to address the fatigue degradation of bionic surfaces under alternating field loads and the barriers to the large-scale fabrication of large-sized components. The paper further highlights the development trend towards the deep integration of bionic tribology with digital twins and intelligent wear-state perception technologies, aiming to provide systematic underlying theoretical and technical references for the research and development of the next generation of intelligent agricultural equipment characterised by low energy consumption and a prolonged service life. Full article
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23 pages, 11014 KB  
Article
Research on Multi-Field Coupling Response and Alignment Control of Super-Long-Span Steel Box Girder Synchronous Lifting
by Hongyu Xu, Xiaotong Sun, Xiaofeng Liu and Wenjie Li
Eng 2026, 7(6), 290; https://doi.org/10.3390/eng7060290 - 11 Jun 2026
Viewed by 196
Abstract
To investigate the posture control of super-long-span heavy steel box girders during synchronous lifting, this study takes the integral lifting project of the 82 m-span steel box girder of Xiaotun Bridge on the Fuyi Expressway as a case study. A fluid–solid–thermal three-field coupled [...] Read more.
To investigate the posture control of super-long-span heavy steel box girders during synchronous lifting, this study takes the integral lifting project of the 82 m-span steel box girder of Xiaotun Bridge on the Fuyi Expressway as a case study. A fluid–solid–thermal three-field coupled numerical model was established using Midas NFX 2024 R1 (a general-purpose finite element analysis software for multi-physics and fluid–structure interaction simulations) to explore the alignment and end-displacement characteristics of the steel box girder throughout the lifting process. The results show that under combined thermal and wind loads, girder deflection presents a daily cyclic pattern: temperature rise induces upward arching, while wind-induced vibration generates a mid-span instantaneous amplitude of ±25.0 mm, with a maximum coupled deflection of 31.78 mm. Girder end-displacement increases significantly at lifting heights of 5–25 m and peaks at 25 m. With further height increase and shortened sling length, sway frequency rises while maximum displacement gradually declines. When the plane tilt ratio exceeds 0.17% or the overall unbalanced displacement at lifting points exceeds 12 mm, local stress exceeds 95% of the allowable value, implying potential instability risks. For construction safety, a synchronous intelligent hydraulic lifting system based on the “displacement synchronization and load balancing” strategy was applied. Supported by real-time sensor feedback and adjustment, the system achieves millimeter-level lifting precision and welding positioning accuracy. This study provides a reference for similar synchronous lifting practices of large-span steel box girders. Full article
(This article belongs to the Section Chemical, Civil and Environmental Engineering)
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20 pages, 41743 KB  
Article
Hydrochemical Tracing for Solute Sources and Enrichment Mechanisms in Inland Lake Waters of the Qiangtang Plateau, Northern Tibet, China
by Yuanqing Liu, Dongguang Wen, Le Zhou, Lin Lv, Xuejun Ma, Jianhua Feng, Yanwei Guo, Jian Cao and Tao Lv
Minerals 2026, 16(6), 599; https://doi.org/10.3390/min16060599 - 3 Jun 2026
Viewed by 186
Abstract
To elucidate the solute sources, migration and enrichment mechanisms of water bodies in the endorheic lake region of the Qiangtang Plateau on the Tibetan Plateau and clarify the hydrogeochemical cycling patterns in alpine arid environments, this study focuses on two core scientific objectives: [...] Read more.
To elucidate the solute sources, migration and enrichment mechanisms of water bodies in the endorheic lake region of the Qiangtang Plateau on the Tibetan Plateau and clarify the hydrogeochemical cycling patterns in alpine arid environments, this study focuses on two core scientific objectives: quantitative identification of the multi-source contributions of aquatic solutes, and revelation of the key processes governing the enrichment of strategic elements including lithium (Li) and boron (B). To achieve these goals, we conducted systematic hydrogeological field investigations and collected 28 multi-type water samples, covering springs, rivers, thermal springs, freshwater lakes, salt lake brines, atmospheric precipitation, and glacial meltwater. The physicochemical properties, major ions, and trace elements of all samples were comprehensively analyzed. On this basis, the hydrogeochemical characteristics, evolutionary processes, and solute origins of regional waters were systematically explored. Combined with PHREEQC numerical simulation, principal component analysis (PCA), and Pearson correlation analysis, the dominant controlling factors of water geochemistry were quantified, and a conceptual hydrogeochemical evolution model was established. The results reveal a clear hydrogeochemical evolutionary gradient across the study area: water bodies evolve from low-salinity HCO3-Ca recharge end-members and transitional HCO3·SO4-Ca(Mg) type water to highly mineralized Cl-Na (SO4·Cl-Na) salt lake brines, accompanied by synchronous enrichment of Li, B, arsenic (As), and other characteristic elements. Solute accumulation in regional waters is governed by the ternary coupling effects of evaporative concentration, rock weathering and leaching, and deep geothermal fluid input, while cation exchange and mineral dissolution–precipitation reactions further modulate ionic composition and ratios. Elements including As, Li, B, and chloride (Cl) exhibit conservative migration behaviors in non-hydrothermal waters, whereas thermal springs possess unique geochemical signatures driven by deep fluid recharge. PCA results indicate that evaporative concentration serves as the primary controlling factor with a contribution rate of 55.39%; rock weathering provides the basic solute load (17.09%); and the coupled processes of deep fluid mixing and carbonate precipitation regulate elemental fractionation (14.21%). These findings systematically clarify the hydrogeochemical evolution laws and multi-source coupling mechanisms of inland lake waters in the Qiangtang Plateau. Furthermore, this study establishes a conceptual framework of “multi-source recharge–water–rock interaction–evaporative concentration”, advances the understanding of alpine hydrological cycling under climate change, and provides a solid scientific foundation for hydrological cycle research and green exploration of strategic mineral resources in endorheic salt lake regions. Full article
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56 pages, 794 KB  
Article
Prime-Enforced Helical Symmetry Constraints in Thermodynamic Emergence of Electromagnetism: Engineering Tunable Self-Organized Superconducting Shells via the Radial Helical Gear Condenser in Hybrid Layered Composites
by Muhamad Fouad
Symmetry 2026, 18(6), 959; https://doi.org/10.3390/sym18060959 - 2 Jun 2026
Viewed by 254
Abstract
The Zeta-Minimizer Theorem (ZMT) provides a complete deductive unification of statistical mechanics, number theory, helical geometry, thermodynamics, and electromagnetism from three primitive axioms alone. Starting with the non-proper Archimedean conical helix and the explicit covariant fugacity Hessian, the universal grand-partition function Z(s) is [...] Read more.
The Zeta-Minimizer Theorem (ZMT) provides a complete deductive unification of statistical mechanics, number theory, helical geometry, thermodynamics, and electromagnetism from three primitive axioms alone. Starting with the non-proper Archimedean conical helix and the explicit covariant fugacity Hessian, the universal grand-partition function Z(s) is constructed via the integer-gear rule. This functorially invariant object yields gear occupations, Lyapunov exponents, and interaction parameters that govern all subsequent results. Interface matching and marginal stability λ_2,19 (x_2) = 0 trigger superconductivity at solid–fluid boundaries, while the categorical invariance of Z(s) produces exact magnetic and electric equilibrium curves. The Variational Reaction Rate Theorem then projects the framework onto dynamics, yielding Maxwell’s equations, demystified electrical units as helical torque quantities, and a complete classification of electronic phases. Phonons, Cooper pairing, the superconducting gap, and the full BCS correspondence follow without additional postulates. The same marginal-stability condition reproduces the Casimir effect, the Quantum Hall effect, and the entire 115-year experimental history of superconductivity. Generalization of interface matching to arbitrary solid–liquid pairs and introduction of Variational Anchor Cancellation (VAC) self-organizes a shielded superconducting layer. Finally, the first-principles engineering blueprint of the Radial Helical Gear Condenser (RHGC) delivers a modular, self-regulating device that engineers superconductivity at ambient or near-ambient temperature using only a radial pressure gradient and existing pipeline technology. All predictions are zero-parameter and fully deducible from the three axioms. Full article
(This article belongs to the Section Physics)
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15 pages, 4501 KB  
Article
SPH-Based Lagrangian Coherent Structures for Characterising Fluid Deformation and Particle Effects in Non-Newtonian Particle-Laden Pipe Flows
by Kun Li, Xue Lian, Hanqiao Che, Jiansheng Bai and Bin Liu
Processes 2026, 14(11), 1798; https://doi.org/10.3390/pr14111798 - 30 May 2026
Viewed by 372
Abstract
Particle-laden pipe flows are ubiquitous in food, chemical and pharmaceutical processes, where solid particles significantly alter fluid deformation and mixing. Understanding these transport mechanisms is critical for process optimisation. A Lagrangian analysis framework based on a SPH-DEM simulation is proposed to compute finite-time [...] Read more.
Particle-laden pipe flows are ubiquitous in food, chemical and pharmaceutical processes, where solid particles significantly alter fluid deformation and mixing. Understanding these transport mechanisms is critical for process optimisation. A Lagrangian analysis framework based on a SPH-DEM simulation is proposed to compute finite-time Lyapunov exponent (FTLE) fields and extract Lagrangian coherent structures (LCSs) for non-Newtonian particle-laden pipe flows. The method directly exploits the inherently Lagrangian particle trajectories and computes the FTLE fields using the SPH interpolation scheme, avoiding the costly numerical integration required by conventional Eulerian approaches. Subsequently, LCSs are extracted via a ridge detection algorithm and the combined FTLE is introduced to quantify mixing intensity. The framework is validated against the Kármán vortex street benchmark, showing good agreement with experiment and numerical results. Then the validated framework is applied to non-Newtonian particle-laden pipe flows for a wide range (0 vol.%~30 vol.%) of particle loading. Results reveal a critical concentration range of 20 vol.%~30 vol.%, where the cross-sectionally average combined FTLE increases with concentration up to 20 vol.%, indicating enhanced mixing, but decreases beyond 30 vol.% as particle–particle interactions suppress near-wall fluid deformation. These findings provide a robust Lagrangian tool and new quantitative insights for optimising mixing and transport in industrial particulate flows, such as in food processing pipelines and chemical reactors. Full article
(This article belongs to the Section Particle Processes)
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19 pages, 1850 KB  
Article
Hydrodynamic Synchronization of Two Oscillators in a Newtonian Fluid
by Tomé A. F. da Silva, Brendon O. Pontes, Elias S. Lima and Rodrigo C. V. Coelho
Fluids 2026, 11(6), 133; https://doi.org/10.3390/fluids11060133 - 29 May 2026
Viewed by 258
Abstract
Particles moving in a fluid interact through the flow field they generate, which can lead to complex nonlinear dynamics. One important example is the synchronization of oscillatory motion in biological systems, such as the coordinated beating of cilia or flagella. In this work, [...] Read more.
Particles moving in a fluid interact through the flow field they generate, which can lead to complex nonlinear dynamics. One important example is the synchronization of oscillatory motion in biological systems, such as the coordinated beating of cilia or flagella. In this work, we investigate the synchronization of two oscillators interacting through a Newtonian fluid using numerical simulations based on the lattice Boltzmann method. The oscillators are modeled as solid particles undergoing periodic motion, while hydrodynamic interactions are resolved explicitly through the surrounding flow. We analyze how synchronization depends on key physical parameters, including the fluid viscosity, the distance between the oscillators, the natural oscillation frequency, and the initial phase difference. The results are compared with predictions from the Kuramoto model in order to relate the hydrodynamic interaction to an effective phase coupling. We find that the coupling strength required for synchronization increases with both the oscillation frequency and the fluid viscosity, while it decreases with the distance between the oscillators. These results provide insight into the mechanisms underlying fluid-mediated synchronization and help bridge microscopic hydrodynamic models with reduced phase-oscillator descriptions. Full article
(This article belongs to the Special Issue 10th Anniversary of Fluids—Recent Advances in Fluid Mechanics)
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22 pages, 4612 KB  
Article
Hydrodynamic Characteristics of Seepage Beneath Underwater Structures Under Complex Geological and Geometric Boundaries
by Meng Zhu, Jun Hu, Yanan Zhang and Enjin Zhao
J. Mar. Sci. Eng. 2026, 14(11), 1008; https://doi.org/10.3390/jmse14111008 - 29 May 2026
Viewed by 279
Abstract
The spatiotemporal evolution of seepage fields and the associated hydrodynamic risk of subsequent internal erosion pose a critical threat to the structural integrity of marine and hydraulic infrastructure. To quantify these complex fluid–solid interactions, this study develops a high-fidelity numerical model—coupling the Navier–Stokes [...] Read more.
The spatiotemporal evolution of seepage fields and the associated hydrodynamic risk of subsequent internal erosion pose a critical threat to the structural integrity of marine and hydraulic infrastructure. To quantify these complex fluid–solid interactions, this study develops a high-fidelity numerical model—coupling the Navier–Stokes equations with the Darcy–Forchheimer resistance model and the Volume of Fluid (VOF) method—to investigate transient hydrodynamics within porous foundations under complex geometric and geological boundary conditions. Parametric analyses reveal that spatial porosity distribution fundamentally dictates the system’s seepage capacity; notably, relocating a highly permeable stratum to the shallow sub-surface eliminates upper hydraulic bottlenecks and significantly escalates total volumetric discharge. Furthermore, the study systematically evaluates the hydrodynamic efficacy of multi-dimensional seepage control structures. Results demonstrate that while increasing the vertical depth of a cutoff wall is highly efficient in restricting bulk volumetric flux, it inadvertently induces intense localized streamline convergence and flow acceleration at the structural tip. Conversely, lateral expansion of the wall base, though yielding only a moderate reduction in total seepage, successfully diffuses this concentrated flow and substantially attenuates peak pore fluid velocities. Ultimately, a combined design paradigm is proposed for practical coastal engineering applications: prioritizing vertical penetration to optimize bulk seepage reduction, concurrently integrated with moderate lateral base expansion to redistribute concentrated hydrodynamic shear stresses, thereby minimizing the hydrodynamic potential for localized piping and ensuring long-term stability against seepage-induced degradation. Full article
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30 pages, 18433 KB  
Article
An Adaptive Coupling of Edge-Based Smoothed FEM and SPH with a Bidirectional Element-Particle Transformation Algorithm for Laser Powder Bed Fusion
by Ming Suo and Ting Long
Materials 2026, 19(11), 2264; https://doi.org/10.3390/ma19112264 - 27 May 2026
Viewed by 309
Abstract
Laser powder bed fusion (LPBF) poses significant simulation challenges due to its highly nonlinear thermo-fluid-solid coupling. To address this, we propose an adaptive framework coupling the edge-based smoothed finite element method (ES-FEM) and smoothed particle hydrodynamics (SPH) via a bidirectional element-particle transformation algorithm. [...] Read more.
Laser powder bed fusion (LPBF) poses significant simulation challenges due to its highly nonlinear thermo-fluid-solid coupling. To address this, we propose an adaptive framework coupling the edge-based smoothed finite element method (ES-FEM) and smoothed particle hydrodynamics (SPH) via a bidirectional element-particle transformation algorithm. This integration leverages ES-FEM for modeling solid thermo-mechanical responses and SPH for resolving melt pool dynamics, enabling fully coupled simulation of temperature, fluid flow, and stress within a unified model. The framework comprises three key components: a nodal mass normalization scheme ensuring conservation during transformations, a ghost particle algorithm for solid-fluid heat transfer and interaction, and a bidirectional finite-element-to-particle conversion mechanism. This work represents the first implementation of bidirectional coupling between mesh-free Lagrangian SPH and Lagrangian FEM. The validation against benchmark cases confirms the framework’s accuracy in capturing transient thermal, hydrodynamic, and mechanical behavior. It successfully reproduces key LPBF phenomena, including melt pool morphology, Marangoni flows, and residual stress evolution, demonstrating its suitability for high-fidelity LPBF process simulation. It should be noted that the current ES-FEM-SPH framework has not taken into account the recoil pressure, evaporation, and the interaction between the powder and the molten pool. The powder is regarded as a rigid body. Future work will focus on incorporating these neglected physical factors to further improve the predictive capability of the proposed framework. Full article
(This article belongs to the Section Metals and Alloys)
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