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Search Results (354)

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Keywords = phase velocity dispersion

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25 pages, 6772 KB  
Article
Effect of Dual-Hole Nozzle Injection Angle on Primary Breakup and Near-Nozzle Spray Dynamics of High-Pressure Diesel Jets: Volume-of-Fluid Numerical Investigation
by Souad Tahar, Fatma Zohra Saidoune, Faouzi Didi, Mounir Zirari, Hichem Ykrelef and Ebrahim E. Elsayed
Processes 2026, 14(15), 2405; https://doi.org/10.3390/pr14152405 - 26 Jul 2026
Viewed by 304
Abstract
Optimizing fuel injector geometry represents a critical pathway toward cleaner and more efficient diesel combustion. This study presents a comprehensive numerical investigation of the influence of the dual-hole nozzle injection angle on the primary atomization behavior and spray hydrodynamics of high-pressure diesel jets. [...] Read more.
Optimizing fuel injector geometry represents a critical pathway toward cleaner and more efficient diesel combustion. This study presents a comprehensive numerical investigation of the influence of the dual-hole nozzle injection angle on the primary atomization behavior and spray hydrodynamics of high-pressure diesel jets. The present analysis is deliberately restricted to cold-flow, near-nozzle primary breakup under isothermal conditions (293.15 K) so that the hydrodynamic and aerodynamic breakup mechanisms can be isolated in the immediate vicinity of the orifice before evaporation and combustion occur. Two-dimensional simulations are conducted using an Eulerian Volume-of-Fluid (VOF) framework with finite element discretization, three injection-angle configurations (0°, 5°, and 10°) under realistic engine conditions (injection pressure: 138 MPa; chamber pressure: 2.32 MPa; nozzle diameter: 100 µm). The numerical model was validated against the experimental and computational benchmark data of Ménard et al., showing reasonable qualitative agreement in jet morphology, although the 2D nature of the model leads to an exaggerated accumulation of liquid at the spray tip compared to the 3D reference. The validation therefore supports the qualitative trends and the relative angular comparison, but the absolute quantitative predictions remain subject to this 2D structural limitation. Results reveal that the injection angle exerts a decisive influence on the competition between axial momentum and radial dispersion. The neutral 0° configuration yields an overly concentrated jet with limited interfacial destabilization and poor air entrainment, whereas the 10° angle produces excessive radial spreading at the expense of axial penetration depth. By contrast, the 5° convergence angle provides the best trade-off among the three tested configurations under the studied conditions, promoting enhanced Rayleigh–Plateau instability growth, earlier ligament formation, and finer droplet generation—favorable to a more homogeneous air–fuel mixture. These findings provide quantitative guidance for dual-hole injector geometry design and demonstrate the suitability of high-fidelity VOF-based methods for resolving complex two-phase atomization phenomena relevant to low-emission diesel engine design. Quantitatively, the peak axial velocity is reached at the nozzle exit for all configurations; relative to the 0° baseline, the 5° convergence angle increases the fuel–air interfacial spreading by about 141% while retaining roughly 90% of its axial penetration at the monitoring positions P1–P3, whereas the 10° case loses about 26% of axial penetration for a comparable radial spread. Full article
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29 pages, 22307 KB  
Article
Transport Characteristics of Coal Fines and Anti-Deposition Structural Optimization in Standing Valves of Coalbed Methane Drainage Pumps
by Yicheng Wang, Wanzhong Li, Jianning Xu, Yapeng Li and Liaobo Li
Modelling 2026, 7(4), 149; https://doi.org/10.3390/modelling7040149 - 23 Jul 2026
Viewed by 206
Abstract
Stable drainage of coalbed methane wells is essential for reducing reservoir pressure and promoting methane desorption. However, coal fines carried by produced water tend to accumulate and deposit within the standing valves of drainage pumps. To address this common problem, this study investigates [...] Read more.
Stable drainage of coalbed methane wells is essential for reducing reservoir pressure and promoting methane desorption. However, coal fines carried by produced water tend to accumulate and deposit within the standing valves of drainage pumps. To address this common problem, this study investigates the transport characteristics of coal fines within the standing valve during the liquid-dominated water-pumping stage of the plunger upstroke, with the standing valve fully open. Theoretical calculations, numerical simulations, and settling experiments were conducted for three coal fines size fractions of 60–100, 100–200, and 200–400 mesh to validate the model’s predictive capability for coal fines motion. The results show that the RNG k–ε model has the lowest mean absolute relative error, at 14.50%. A solid–liquid two-phase flow model was employed to comparatively analyze five valve seat cone angles ranging from 105° to 165° and representative inlet velocities of 0.1–0.4 m/s. The results indicate that the mixture within the standing valve accelerates markedly while passing through the narrow clearance between the valve ball and the valve seat and then decelerates in the region above the valve ball. The region above the valve ball and the valve seat transition region are the primary locations of instantaneous coal fines enrichment. Increasing the inlet velocity generally enhances coal fines transport capacity and reduces the local maximum solid-phase volume fraction. Larger coal fines particles exhibit more pronounced inertial deviation and a higher degree of local enrichment, whereas smaller particles show stronger flow-following behavior and a more dispersed spatial distribution. The results further indicate that, within the investigated structural range, the 150° valve seat cone angle provides the best overall balance between coal fines transport capacity and hydraulic resistance. Ultimately, the findings provide a theoretical foundation and methodological reference for understanding the anti-clogging mechanisms of CBM pump standing valves, optimizing structural parameters, and guiding the blockage-resistant design of downhole flow components. Full article
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30 pages, 7065 KB  
Article
Energy-Efficient Hydrodynamic Treatment of High-Solid Water-Based Spent Drilling Fluids from Uranium Technological Wells: Experimental Validation, Response-Surface Modeling, and Process Stability
by Bakytzhan Kaliyev, Bulbul Mauletbekova, Garifolla Serali, Aidana Myrzabekova, Yerzhan Sarybayev, Doszhan Balgayev, Vladislav V. Kukartsev and Boris V. Malozyomov
Appl. Sci. 2026, 16(14), 7306; https://doi.org/10.3390/app16147306 - 21 Jul 2026
Viewed by 285
Abstract
Spent water-based drilling fluids generated during technological-well drilling for uranium production are high-solid, chemically heterogeneous suspensions whose treatment is constrained by water scarcity, waste-handling requirements, reagent demand and electrical-energy consumption. This study evaluated a recirculating flow-through disperser that converts pressure-driven flow into controlled [...] Read more.
Spent water-based drilling fluids generated during technological-well drilling for uranium production are high-solid, chemically heterogeneous suspensions whose treatment is constrained by water scarcity, waste-handling requirements, reagent demand and electrical-energy consumption. This study evaluated a recirculating flow-through disperser that converts pressure-driven flow into controlled nominal velocity gradients and localized contact zones. The laboratory-pilot dataset comprised five high-solid water-based spent-fluid samples, 120 hydrodynamic treatment runs, 216 particle-size-bin observations corresponding to 12 complete distributions, nine mechanical-mixing baseline tests and ten repeated-cycle runs. The investigated range covered nominal Camp–Stein-equivalent velocity gradients of 500–1500 s−1, treatment times of 60–180 s and flocculant dosages of 0–100 g/t dry solids. A 50 L batch was recirculated through a disperser with a cylindrical geometric envelope of approximately 4.75 L. The maximum separation efficiency was 94.20%. The recommended compromise condition (G = 1300 s−1, τ = 150 s and 50 g/t dry solids) achieved 92.15 ± 1.81% separation efficiency, residual aqueous-phase TSS of 125.2 ± 30.0 mg/L, water recovery of 83.84 ± 0.28%, sludge-volume reduction of 59.02 ± 2.11% and wall-plug specific energy consumption of 0.1227 ± 0.0062 kWh/m3. A separate ten-cycle series yielded 0.1245 ± 0.0065 kWh/m3, consistent with the triplicate compromise-mode result. Two-factor response-surface models reproduced the measured G–τ trends and provided prediction intervals for operating-window screening within the investigated fluid class. The findings support coupled energy–separation optimization, rather than selection of the maximum nominal mixing intensity. Full article
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31 pages, 22757 KB  
Article
Depth-Dependent Characterization of Vertical Cracks in Concrete Using Lamb Wave Active Sensing
by Nontawat Srisapan, Theophilus Asumah and Roohollah Askari
Sensors 2026, 26(14), 4563; https://doi.org/10.3390/s26144563 - 18 Jul 2026
Viewed by 339
Abstract
Vertical cracks in concrete present a major challenge for many conventional nondestructive testing methods (NDT) and structural health monitoring (SHM) methods. Elastic wave-based approaches offer strong interaction with crack faces and depth sensitivity; however, their effectiveness is often limited by the lack of [...] Read more.
Vertical cracks in concrete present a major challenge for many conventional nondestructive testing methods (NDT) and structural health monitoring (SHM) methods. Elastic wave-based approaches offer strong interaction with crack faces and depth sensitivity; however, their effectiveness is often limited by the lack of repeatable and tunable excitation sources. Repeatability is critical because scattered and attenuated signals require stacking to achieve adequate signal-to-noise ratios, while tunability is essential because key crack attributes are frequency-dependent and must be probed at appropriate wavelengths. In this study, we develop an active sensing system utilizing a linear impact actuator as a repeatable and tunable mechanical source for elastic-based NDT and apply it to a 0.24 m thick concrete slab containing three surface-breaking vertical cracks with depths of 6, 12, and 18 cm, respectively. The actuator is tuned by adjusting impact conditions to generate A0-dominated Lamb wave responses. For each crack, two linear arrays are deployed, one parallel and one perpendicular to the crack trace, to investigate directional anisotropy. Phase-velocity anisotropy is quantified using the A0 Lamb wave dispersion curves, while the effective quality factor is used as a complementary indicator of direction-dependent attenuation. Our results show that phase velocities are consistently higher for crack-parallel propagation than for crack-perpendicular propagation, and that the degree of anisotropy increases with crack depth. The quality factor decreases with increasing crack depth and exhibits anisotropic behavior, with systematically lower values for crack-perpendicular measurements compared to crack-parallel measurements. Overall, the results demonstrate that controllable and repeatable impact excitation establishes a reliable framework for elastic-wave-based characterization of idealized vertical cracks in concrete. Full article
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17 pages, 4567 KB  
Article
Experimental Study on Atomization Characteristics of Droplet Field in the Downstream Region of Hydraulic Nozzles Under Co-Flow Disturbance
by Zhirong Wu, Wen Li, Yongping Chen, Shiqiang Chen and Chunyu Liu
Processes 2026, 14(13), 2206; https://doi.org/10.3390/pr14132206 (registering DOI) - 6 Jul 2026
Viewed by 265
Abstract
Hydraulic nozzles are widely utilized for dust removal, cooling, and waste heat recovery in mining production. Nevertheless, the influence of co-flow disturbance on the atomization characteristics within the downstream region of droplet fields remains inadequately understood. In this study, three typical hydraulic nozzles [...] Read more.
Hydraulic nozzles are widely utilized for dust removal, cooling, and waste heat recovery in mining production. Nevertheless, the influence of co-flow disturbance on the atomization characteristics within the downstream region of droplet fields remains inadequately understood. In this study, three typical hydraulic nozzles were selected, and the atomization characteristics of the downstream region under different co-flow disturbance intensities were experimentally investigated. The results reveal that increasing co-flow disturbance velocity does not intensify the reduction in sauter mean diameter (SMD), but markedly reduces the dispersed phase fraction (DPF). Under four co-flow disturbance velocities (1.5, 3.0, 4.5, and 6.0 m/s), the relative reduction rates of mean SMD are 6.77%, 3.27%, 4.42% and 2.60%, while those of mean DPF are 13.86%, 35.85%, 52.88%, and 61.86% (e.g., hollow-cone nozzle), respectively. The variation in SMD is achieved through the redistribution of cumulative volume among CV1, CV2, CV3, and CV4. As the velocity increases from 0 to 3 m/s, the mean SMD of the three hydraulic nozzles exhibits a decreasing trend, which can be directly attributed to the continuous increase in the total cumulative volume of CV1 and CV2, and the continuous decrease in those of CV3 and CV4. For the hollow-cone and solid square-cone nozzles, the SMD first decreases and then increases, with the turning point occurring at 3.0 m/s, consistent with the variation trend of cumulative volume fractions. In contrast, for the solid-cone nozzle, the SMD continues to decrease at velocities exceeding 3.0 m/s. This work provides both a fundamental understanding of atomization characteristics in the downstream region of hydraulic nozzles under co-flow disturbance and practical guidance for velocity control in mine spray systems. Full article
(This article belongs to the Section Energy Systems)
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27 pages, 9650 KB  
Article
Freeze–Thaw Performance and Microstructural Stability of Alkali-Activated Slag Mortars Incorporating Mussel Shell Waste
by Merve Şahin Yön
Buildings 2026, 16(13), 2511; https://doi.org/10.3390/buildings16132511 - 24 Jun 2026
Viewed by 232
Abstract
This study investigates the use of mussel shells (MSs), a biogenic by-product of the food industry, as a partial replacement for ground granulated blast furnace slag (GBFS) in alkali-activated mortars. Given their high CaCO3 content, MSs represent a sustainable secondary raw material [...] Read more.
This study investigates the use of mussel shells (MSs), a biogenic by-product of the food industry, as a partial replacement for ground granulated blast furnace slag (GBFS) in alkali-activated mortars. Given their high CaCO3 content, MSs represent a sustainable secondary raw material that reduces both waste disposal burden and reliance on natural resources, while offering a low-carbon alternative to conventional cement-based binders. Alkali-activated mussel shell/slag mortars (AAMSs) were produced with MS replacement ratios of 0%, 5%, 10%, 15%, and 20% by mass of GBFS. Sodium hydroxide (NaOH) and sodium silicate (Na2SiO3) were used as alkaline activators. Fresh specimens were cured at 60 °C for 48 h. The experimental program included workability, compressive and flexural strength, water absorption, porosity, density, capillarity, ultrasonic pulse velocity (UPV), and freeze–thaw (F-T) resistance tests. Increasing MS content slightly reduced flowability and mechanical strength, while increasing water absorption, porosity, and capillarity. The M0 series achieved the highest 28-day compressive strength (54.06 MPa), while M15 exhibited the highest flexural strength (5.23 MPa). Following F-T cycling, the 5% and 10% MS series demonstrated the best compressive strength (30 MPa). The 10% MS exhibits a relatively balanced overall performance, providing the best balance between mechanical performance, F-T resistance, and microstructural stability, as confirmed by scanning electron microscopy (SEM)/energy-dispersive X-ray spectroscopy (EDS) analyses showing elevated Ca/Si ratios and the formation of Ca-rich crystalline phases. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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21 pages, 8102 KB  
Article
Optimization of Oxygen Pressure in HVOF Spraying for Enhanced Corrosion Resistance and Thermal Stability of Al-Cu-Fe Quasicrystalline Coatings
by Dilnoza Baltabayeva, Sherzod Kurbanbekov, Ali Coruh, Lyaila Bayatanova, Sattarbek Bekbayev, Berik Kaldar and Diyar Patchakhanov
Nanomaterials 2026, 16(13), 790; https://doi.org/10.3390/nano16130790 - 23 Jun 2026
Viewed by 493
Abstract
Al-Cu-Fe quasicrystalline coatings were deposited on AISI 321 stainless steel substrates by high-velocity oxy-fuel (HVOF) spraying at oxygen pressures of 3.0, 3.5, and 4.0 bar. The influence of oxygen pressure on the phase composition, microstructure, porosity, corrosion behavior, thermal stability, and microhardness of [...] Read more.
Al-Cu-Fe quasicrystalline coatings were deposited on AISI 321 stainless steel substrates by high-velocity oxy-fuel (HVOF) spraying at oxygen pressures of 3.0, 3.5, and 4.0 bar. The influence of oxygen pressure on the phase composition, microstructure, porosity, corrosion behavior, thermal stability, and microhardness of the coatings was investigated using X-ray diffraction (XRD), scanning electron microscopy coupled with energy-dispersive spectroscopy (SEM/EDS), ImageJ porosity analysis, electrochemical corrosion testing in 3.5 wt.% NaCl solution, simultaneous thermal analysis (TGA/DSC), and microhardness measurements. XRD analysis revealed the formation of quasicrystalline-related intermetallic phases together with Al, Fe3Al13, FeAl, Fe3O4, CuFe2O4, Cu2O, and CuO phases. The coating deposited at 3.5 bar exhibited the lowest porosity (5.37%), the most homogeneous microstructure, and the largest residual coating thickness after corrosion testing. SEM and EDS analyses indicated that corrosion preferentially initiated at pores, splat boundaries, and phase interfaces, while the coating produced at 3.5 bar demonstrated the most stable surface condition after exposure to a 3.5 wt.% NaCl solution. Thermal analysis showed that all coatings remained stable up to 900 °C. Sample (a) exhibited the lowest mass loss and the highest thermal stability, whereas sample (b) demonstrated the most favorable combination of structural integrity, phase ordering, coating density, corrosion-related performance, and thermal stability. Microhardness values of the coatings ranged from 754 to 778 HV, significantly exceeding that of the AISI 321 substrate. The results demonstrate that oxygen pressure is a critical parameter controlling the microstructure and functional properties of HVOF-sprayed Al-Cu-Fe coatings, with 3.5 bar providing the most balanced set of properties. Full article
(This article belongs to the Section Nanocomposite Materials)
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21 pages, 30993 KB  
Article
Microstructure and Mechanical–Tribological Properties of HVOF-Sprayed (WC-Co+Ni) Coatings on Ductile Cast Iron
by Marzanna Ksiazek, Lukasz Boron and Adam Tchorz
Materials 2026, 19(12), 2640; https://doi.org/10.3390/ma19122640 - 18 Jun 2026
Viewed by 323
Abstract
High Velocity Oxy-Fuel (HVOF) thermal spraying enables the deposition of dense coatings with low porosity, high hardness, and good fracture resistance. Tungsten carbide–cobalt (WC-Co) coatings are widely used in industrial and aerospace applications due to their excellent wear resistance; however, improving crack resistance [...] Read more.
High Velocity Oxy-Fuel (HVOF) thermal spraying enables the deposition of dense coatings with low porosity, high hardness, and good fracture resistance. Tungsten carbide–cobalt (WC-Co) coatings are widely used in industrial and aerospace applications due to their excellent wear resistance; however, improving crack resistance and coating–substrate adhesion remains a key challenge. In this study, WC-Co+Ni composite coatings were deposited on ductile cast iron, with emphasis on the role of Ni addition in controlling microstructure development under HVOF conditions. Microstructural characterization was performed using optical, scanning, and transmission electron microscopy (OM, SEM, TEM), while phase composition and chemical analysis were determined by X-ray diffraction (XRD) and energy-dispersive spectroscopy (EDS). The coatings exhibited a dense, low-porosity microstructure composed of fine WC and W2C carbides embedded in a Co–Ni binder, with locally nanocrystalline regions. XRD analysis confirmed WC and W2C as the dominant phases, with weak reflections corresponding to the η-phase (Co6W6C), indicating local decarburization. The addition of Ni increases the fraction of the transient liquid phase during particle flight, enhancing carbide dissolution and mass transport in the binder, which accelerates decarburization kinetics and promotes η-phase formation. Simultaneously, Ni modifies the binder into a more ductile Co–Ni matrix, reducing the detrimental effect of brittle η-phase on coating integrity. Mechanical and tribological testing (instrumented indentation and scratch testing) demonstrated improved crack resistance, wear resistance, and adhesion. The results show that Ni addition enables process-driven microstructural tailoring of HVOF-sprayed WC-Co coatings, leading to enhanced performance despite the presence of η-phase. Full article
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24 pages, 30661 KB  
Article
Controlling Effect of Heterogeneity in High-Permeability Reservoirs on Waterflood Sweep Characteristics and Remaining-Oil Distribution
by Deshuo Tao, Chunlei Yu, Lijie Liu, Xuan Lu, Dejun Wu and Haixiang Zhang
Processes 2026, 14(12), 1869; https://doi.org/10.3390/pr14121869 - 9 Jun 2026
Viewed by 224
Abstract
High-permeability reservoirs at the extra-high water-cut stage commonly exhibit preferential flow, limited sweep expansion, and complex remaining-oil occurrence. To clarify the pore-scale mechanisms controlling waterflood sweep and remaining-oil retention, this study integrates CT-assisted core flooding and microfluidic chip visualization using a high-permeability sandstone [...] Read more.
High-permeability reservoirs at the extra-high water-cut stage commonly exhibit preferential flow, limited sweep expansion, and complex remaining-oil occurrence. To clarify the pore-scale mechanisms controlling waterflood sweep and remaining-oil retention, this study integrates CT-assisted core flooding and microfluidic chip visualization using a high-permeability sandstone core from the Guantao Formation in the Bohai Bay Basin. The CT-assisted core flooding experiment was used to quantify the stage-wise evolution of pores swept by the water phase, while the microfluidic experiment was used to visualize displacement pathways, local bypassing, and remaining-oil morphology under controlled pore-network conditions. The results show that waterflood sweep exhibits clear stage-wise evolution. During the low water-cut stage, injected water preferentially advances through large pore channels, resulting in limited sweep efficiency. With increasing water cut, pores newly swept by the water phase gradually shift from large pores to medium and small pores, accompanied by increasing displacement pressure. Under the present experimental conditions, the lower radius limit of pores newly swept by the water phase is approximately 7.54 μm, corresponding to a capillary force of about 0.9 MPa. When the injected volume exceeds approximately 2.5 PV, the sweep efficiency approaches a plateau and increases only from 0.72 to 0.75 at 5.0 PV, indicating that approximately 25% of the pore space remains difficult to be effectively swept. Image-based classification indicates that remaining oil can be divided into six occurrence types: clustered, porous, columnar, dead-end, film-like, and granular. Clustered and porous are the dominant occurrence types, accounting for a combined 59.7% of the total remaining oil. Pore-structure heterogeneity controls the microscopic sweep boundary through the combined effects of intra-unit structural dispersion and cross-unit structural contrast, which together regulate capillary resistance, seepage resistance, preferential flow, local bypassing, and remaining-oil retention. Microfluidic observations further show that permeability contrast and displacement velocity affect pore-scale displacement pathways and remaining-oil morphology. These findings provide experimental evidence for understanding the lower sweep-radius limit and remaining-oil occurrence mechanisms in high-permeability heterogeneous reservoirs at the extra-high water-cut stage, while the chip-scale velocity effects should be interpreted as pore-scale mechanistic evidence and require further validation before field-scale application. Full article
(This article belongs to the Section Sustainable Processes)
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16 pages, 4460 KB  
Article
Nanofluid-Driven Heat Transfer Augmentation for Enhanced Geothermal Extraction in U-Shaped Wells
by Junhui Guo, Jingyi Wang, Shefeng Gu, Jing Li, Zheng Wang and Sijia Wang
Energies 2026, 19(11), 2706; https://doi.org/10.3390/en19112706 - 4 Jun 2026
Viewed by 347
Abstract
U-shaped well geothermal energy exploitation has become a key pathway for sustainable energy development, valued for its clean and stable attributes. However, constrained by the limited heat transfer capacity between the wellbore and traditional circulating water, the thermal extraction efficiency of the circulating [...] Read more.
U-shaped well geothermal energy exploitation has become a key pathway for sustainable energy development, valued for its clean and stable attributes. However, constrained by the limited heat transfer capacity between the wellbore and traditional circulating water, the thermal extraction efficiency of the circulating fluid in the U-shaped well remains difficult to breakthrough, severely hindering the large-scale application. This work conducts a study on the optimization of the thermal conductivity performance of circulating working fluids based on water-phase dispersed nanoparticles, aiming to explore efficient heat transfer methods for the circulating working fluids in geothermal reservoir U-shaped wells. The finite element simulation is employed to analyze the influence of Al2O3 nanoparticle concentration (0–5%) and injection rate (4000–9000 m3/d) on thermal conductivity performance and flow characteristics. The results demonstrate that the Al2O3-H2O nanofluid with a particle size of 10 nm and a concentration of 5% exhibits the optimal heat transfer performance. Under the optimization objective of maximizing net heat output with the pipe-velocity safety constraint satisfied, when the injection rate is 5000 m3/d, the heat extraction efficiency is improved by 21.31% compared with that of pure water. This work may provide theoretical data for efficient geothermal exploitation. Full article
(This article belongs to the Section H2: Geothermal)
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19 pages, 3282 KB  
Article
Exploring Bifurcation Analysis, Conservation Laws and Soliton Dynamics for the Dual-Mode Nonlinear Schrödinger Equation with Applications
by Muhammad Arshad, Naila Nasreen, Evren Hincal, Mohamed Hafez and Muhammad Farman
Math. Comput. Appl. 2026, 31(3), 97; https://doi.org/10.3390/mca31030097 - 2 Jun 2026
Viewed by 354
Abstract
This study examines the dynamical behavior of the dual-mode nonlinear Schrödinger equation (d-mNLSE), which describes the interaction, amplification, and attenuation of two coexisting wave modes in nonlinear media. The model incorporates key physical parameters including the nonlinearity coefficient, interaction phase velocity, and dispersion [...] Read more.
This study examines the dynamical behavior of the dual-mode nonlinear Schrödinger equation (d-mNLSE), which describes the interaction, amplification, and attenuation of two coexisting wave modes in nonlinear media. The model incorporates key physical parameters including the nonlinearity coefficient, interaction phase velocity, and dispersion parameter, which significantly influence the evolution of nonlinear waves. By applying the modified Sardar sub-equation method (mSS-EM), a wide spectrum of exact analytical solutions is derived. These solutions include mixed trigonometric waves, shock-type structures, singular solutions, complex dark–bright solitons, multi-peak solitons, periodic and mixed-periodic waves, as well as mixed hyperbolic structures. The analytical findings provide useful insight into nonlinear wave propagation phenomena arising in fluid mechanics, water wave dynamics, ocean engineering, and related physical systems. Moreover, the conservation laws of the d-mNLSE are established, which leads to the conserved quantities of impulse power, momentum, and energy and describes the invariant characteristics of the soliton solutions during their propagation. The bifurcation analysis of the reduced dynamical model is carried out to explore the qualitative characteristics of the obtained solutions. The equilibrium points of the considered model are calculated, and their stability properties are analyzed systematically. To demonstrate the physical characteristics of the obtained solutions, different kinds of two-dimensional, three-dimensional, and contour plots are plotted using symbolic computations software. These findings confirm that the analytical method used to obtain the soliton solutions can be used to obtain a variety of soliton solutions of nonlinear evolution equations that appear in applied sciences and engineering. Full article
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21 pages, 7182 KB  
Article
Improved Thermo-Hydraulic Stability and Boiling Heat Transfer Through a Novel Three-Layer Microchannel Heat Sink with 3/4 Open-Ring Pin Fin Arrays
by Guangyao Liu, Can Ji, Zhigang Liu, Peter D. Lund, Yeyao Liu, Fuqiang Xu, Shenglong Zhang, Cong Wang and Donghao Li
Materials 2026, 19(10), 2143; https://doi.org/10.3390/ma19102143 - 20 May 2026
Viewed by 338
Abstract
This study systematically investigated flow boiling characteristics within a novel three-layer microchannel heat sink with 3/4 open-ring pin fin arrays, designed for high-heat-flux thermal management of low-carbon metallurgical reactors. Two-phase flow regimes, pressure drop, and wall temperature responses were analyzed. To evaluate the [...] Read more.
This study systematically investigated flow boiling characteristics within a novel three-layer microchannel heat sink with 3/4 open-ring pin fin arrays, designed for high-heat-flux thermal management of low-carbon metallurgical reactors. Two-phase flow regimes, pressure drop, and wall temperature responses were analyzed. To evaluate the impact of functional surface material properties on thermo-hydraulic behavior, a hydrophilic nano-coating modification was applied to the inner copper channel walls for comparison. Increasing the flow rate triggered a transition from a vapor-dominated confined slug flow to a liquid-dominated dispersed bubble flow, which effectively improved the thermo-hydraulic stability. Hydrophilic surface modification resulted in an average pressure drop reduction of 33% and significantly diminished the sensitivity of flow resistance to velocity variations. Through hydrophilic treatment, the localized vapor film effect at high velocities was suppressed, and temperature field homogenization was promoted, yielding a maximum convective heat transfer coefficient of 7760 W/(m2·°C), i.e., 72.9% enhancement over the baseline heat sink. The underlying mechanism is attributed to the formation of a stable near-wall thin liquid film and the promotion of high-frequency nucleate boiling. These results will be of high relevance for developing efficient cooling solutions for power electronics, thereby supporting the advancement of low-carbon metallurgical reactors. Full article
(This article belongs to the Special Issue Advances in Low-Carbon and Zero-Carbon Metallurgical Technologies)
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26 pages, 5135 KB  
Article
Rayleigh Wave Propagation on the Partially Saturated Poro-Thermo-Viscoelastic Half-Space Based on Fractional Order Viscoelasticity
by Li Li and Wei Zhuang
Mathematics 2026, 14(10), 1751; https://doi.org/10.3390/math14101751 - 19 May 2026
Viewed by 298
Abstract
This paper probes into the propagation characteristics of Rayleigh waves in a partially saturated, porous, thermo-viscoelastic half-space, with full consideration of the fractional viscoelastic effect and thermal coupling effect. A fractional Zener model is introduced to depict the thermo-viscoelastic mechanical behavior of the [...] Read more.
This paper probes into the propagation characteristics of Rayleigh waves in a partially saturated, porous, thermo-viscoelastic half-space, with full consideration of the fractional viscoelastic effect and thermal coupling effect. A fractional Zener model is introduced to depict the thermo-viscoelastic mechanical behavior of the solid skeleton by constructing a complete set of governing equations that include mass balance, generalized Darcy’s law, momentum balance, and generalized heat conduction. Field equations are derived by means of Helmholtz vector decomposition, and the dispersion equation, and the phase velocity expression of Rayleigh waves are obtained by combining the traction-free and adiabatic boundary conditions of the medium. The impacts of key material properties, such as medium saturation, intrinsic permeability, medium viscoelasticity, and thermal expansion coefficient, on the dispersion feature of Rayleigh waves are discussed in detail. Numerical analysis results show that an increase in the thermal expansion coefficient will lead to a rise in Rayleigh wave phase velocity, in which the increase in P1 compressional wave velocity plays a dominant role among the velocities of various types of waves. Meanwhile, the attenuation coefficient of Rayleigh waves presents a decreasing trend and gradually tends to be stable with the growth of the thermal expansion coefficient. Similarly, the phase velocity of Rayleigh waves also increases with the rise in fractional order index, which is jointly dominated by the velocity enhancement of P1 waves and S waves. In addition, the attenuation coefficient of Rayleigh waves increases first and then decreases with the increase in fractional order index and reaches the peak value when the fractional order index is about 0.4. The research results reveal the influence of laws of thermal expansion characteristics and viscoelasticity on Rayleigh wave propagation and provide theoretical support for the analysis of wave propagation characteristics in porous media in relevant engineering applications. Full article
(This article belongs to the Special Issue Advances in Fractional Order Models and Applications)
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16 pages, 4362 KB  
Article
Application of Ambient Noise Tomography with the Modified Frequency-Bessel Transform in Coastal Sedimentary Exploration: A Case Study of the Paleo-Yellow River Estuary
by Yang Su, Yusen Wu, Yongtian Zhao, Pengfei Yu and Chao Zhang
Appl. Sci. 2026, 16(10), 4889; https://doi.org/10.3390/app16104889 - 14 May 2026
Viewed by 416
Abstract
Shallow shear-wave velocity structures provide useful constraints on sedimentary architecture in coastal abandoned-estuary settings, yet laterally continuous velocity information remains limited in the Paleo-Yellow River Estuary, Yancheng, Eastern China. In this study, vertical-component ambient noise recorded by a dense linear array of 102 [...] Read more.
Shallow shear-wave velocity structures provide useful constraints on sedimentary architecture in coastal abandoned-estuary settings, yet laterally continuous velocity information remains limited in the Paleo-Yellow River Estuary, Yancheng, Eastern China. In this study, vertical-component ambient noise recorded by a dense linear array of 102 short-period stations over 27 days was used to derive Rayleigh-wave phase-velocity dispersion curves by the modified frequency-Bessel (MFJ) method. Sequential 1D S-wave velocity models were inverted beneath moving subarrays and interpolated to construct a pseudo-2D velocity profile along the survey line. For comparison, the conventional spatial autocorrelation (SPAC) method was applied to the same dataset using the same subarray length, usable frequency band, and inversion-layer parameterization. The MFJ method produces clearer and more concentrated fundamental-mode dispersion energy and suppresses high-frequency crossed artefacts more effectively than SPAC, which improves the stability of dispersion picking. The resulting velocity model reveals a laterally heterogeneous shallow sedimentary system and outlines a U-shaped low-velocity zone that is spatially consistent with the mapped paleochannel boundary. These results indicate that MFJ-based ambient-noise imaging can provide useful complementary geophysical constraints for paleochannel mapping and shallow sedimentary characterization in coastal abandoned-estuary settings. Full article
(This article belongs to the Special Issue Exploration Geophysics and Seismic Surveying)
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Article
Effect of Mechanical Activation on Spinel Transformation and Chromium Reduction from Ferroalloy Waste Under SHS Conditions
by Sanat Tolendiuly, Nursultan Rakhym, Kaster Kamunur, Sharafkhan Assylkhan, Lyazzat Mussapyrova and Sandugash Tanirbergenova
Metals 2026, 16(5), 522; https://doi.org/10.3390/met16050522 - 12 May 2026
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Abstract
Chromium-containing ferroalloy wastes represent an important secondary resource; however, chromium is mainly bound in thermodynamically stable spinel phases, which complicates its reduction. Unlike previous studies focusing on pure oxide systems, this work demonstrates the enhanced destabilization and subsequent reduction of MgCr2O [...] Read more.
Chromium-containing ferroalloy wastes represent an important secondary resource; however, chromium is mainly bound in thermodynamically stable spinel phases, which complicates its reduction. Unlike previous studies focusing on pure oxide systems, this work demonstrates the enhanced destabilization and subsequent reduction of MgCr2O4 spinel in real ferroalloy wastes under SHS conditions, revealing a non-monotonic relationship between activation time and reduction efficiency. A critical activation threshold (~30 min) was identified, beyond which particle agglomeration suppresses reaction kinetics. Powder mixtures based on HShP and KEK wastes with Al–C–Si reducing agents were mechanically activated for 10–120 min and subsequently subjected to SHS at 950 °C. The combustion parameters, phase composition (XRD), microstructure (SEM), and elemental composition (EDS) were analyzed. The results show a pronounced non-monotonic dependence of combustion temperature and front velocity on activation time, with maximum values at ~30 min (1920 °C and 1.10 mm/s for HShP; 1765 °C and 0.98 mm/s for KEK). XRD analysis indicates that MgCr2O4 was not detected within the XRD detection limits and that the highest relative amount of metallic chromium phase (~8% for HShP and ~6.8% for KEK) was observed at the same activation time. SEM observations reveal the formation of a more dispersed and porous structure, while EDS indicates an increase in chromium content up to ~15 wt.% in local regions. At longer activation times, overgrinding and agglomeration reduce process efficiency. Mechanical activation enhances chromium reduction through improved mass transfer, with an optimal activation time of ~30 min. The chromium reduction efficiency was evaluated using a semi-quantitative approach based on XRD phase analysis and supported by EDS data, allowing comparative assessment of reduction efficiency rather than absolute extraction values. These results highlight the existence of a critical mechanochemical activation threshold governing the balance between enhanced reactivity and agglomeration effects. Full article
(This article belongs to the Section Powder Metallurgy)
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