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21 pages, 9882 KB  
Article
Non-Darcian Flow Characterization in Three-Dimensional Rough-Walled Fractures Using Forchheimer and Izbash Equations
by Jingjing Long, Yinbin Zhu, Xin He, Anbang Pan, Yongqiang Lu and Wenmin Yao
Water 2026, 18(18), 2324; https://doi.org/10.3390/w18182324 (registering DOI) - 17 Sep 2026
Abstract
This study numerically investigated the applicability of the Forchheimer and Izbash equations for describing non-Darcian flow in three-dimensional (3D) rough-walled rock fractures. High-precision flow simulations were conducted on 52 synthetic 3D rough-walled fractures with varied apertures and surface roughness, generated from 56 combinations [...] Read more.
This study numerically investigated the applicability of the Forchheimer and Izbash equations for describing non-Darcian flow in three-dimensional (3D) rough-walled rock fractures. High-precision flow simulations were conducted on 52 synthetic 3D rough-walled fractures with varied apertures and surface roughness, generated from 56 combinations after excluding four cases with surface contact, under different hydraulic gradients. The simulation results captured transverse flow, back flow, and non-uniform streamlines on horizontal planes, which cannot be observed in conventional two-dimensional (2D) fracture models. The total eddy volume ratio negatively correlated with the aperture and positively correlated with roughness, and the 3D fractures exhibited a much smaller eddy volume ratio than the 2D fractures. Both equations provided excellent fits to the simulated data, with coefficients of determination R2 > 0.996. Notably, the Forchheimer coefficients showed strong and monotonic correlations with the aperture and roughness and are therefore predictable and characterizable, whereas the Izbash coefficients showed weak and non-monotonic correlations. Since non-negligible prediction errors occurred at low Reynolds numbers when the equations were fitted over the entire flow range, a piecewise fitting strategy was proposed, which reduced the prediction errors of both equations to within 5% across the full range and quantitatively divided the flow into the Darcy, weak inertial, and strong inertial regimes. Double-parameter equations relating the critical Reynolds numbers to the aperture and roughness were then established, allowing the flow regime to be predicted directly from the geometric parameters without additional simulation. These findings facilitate reasonable flow regime division and accurate full-range flow characterization in rock fractures. Full article
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31 pages, 2488 KB  
Article
XGBoost-Based Prediction of Velocity Distribution in an Open-Channel Bend and Multilevel SHAP Interpretation of Hydrodynamic Mechanisms
by Cheng Yang, Yang Shao, Hefang Jing and Suiju Lv
Water 2026, 18(18), 2322; https://doi.org/10.3390/w18182322 - 16 Sep 2026
Abstract
Velocity distributions in curved open-channel flows exhibit strong three-dimensionality and nonlinear behavior, posing challenges to both accurate prediction and physical interpretation. Using measured velocity data from nine discharge–water-depth combinations in a laboratory 180° open-channel bend, this study developed an integrated eXtreme Gradient Boosting [...] Read more.
Velocity distributions in curved open-channel flows exhibit strong three-dimensionality and nonlinear behavior, posing challenges to both accurate prediction and physical interpretation. Using measured velocity data from nine discharge–water-depth combinations in a laboratory 180° open-channel bend, this study developed an integrated eXtreme Gradient Boosting (XGBoost)–SHapley Additive exPlanations (SHAP) framework, with multiple linear regression (MLR), random forest (RF), and a back-propagation neural network (BPNN) used for comparison. Leave-one-condition-out cross-validation was used to evaluate the predictive accuracy and stability of the four models. A stratified sampling strategy was then adopted to construct the training dataset, allowing information from all flow regimes to contribute to robust parameter calibration; the two data-partitioning strategies yielded broadly comparable predictive performance. Using models trained with stratified sampling, multidimensional model evaluation was further conducted using global statistical metrics, segment-wise predictive performance, held-out extreme-condition tests, and measured–predicted agreement, among other criteria, with XGBoost consistently showing the best performance. Multilevel SHAP analyses quantified global feature importance, pairwise interactions, streamwise variations in feature contributions, SHAP–PDP dependence relationships, and condition-specific attribution. The SHAP results indicate a two-level attribution structure in the model: hydraulic variables jointly define the global velocity baseline, and their contribution signs can switch between positive and negative. Spatial variables characterize cross-sectional velocity redistribution. Strong discharge–depth interaction is associated with width-to-depth-ratio-dependent adjustment of the bend flow field. The proposed framework establishes a complete experiment-driven prediction–mechanism interpretation workflow for sharply curved open-channel flow and provides new quantitative insight into model-represented multifactor hydrodynamic interactions in open-channel bends. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
18 pages, 1112 KB  
Article
Regularities of the Structure Formation Process in Complex Food Systems During Mixing
by Igor Stadnyk, Volodymyr Piddubnyi, Liudmyla Kiurcheva, Vitaliy Pidlisnyj, Zbigniew Kowalczyk, Maciej Kuboń and Taras Hutsol
Sustainability 2026, 18(18), 9508; https://doi.org/10.3390/su18189508 - 16 Sep 2026
Abstract
An integrated information–energy framework is proposed for assessing boundary kinematic interactions and viscoelastic structure formation during wheat dough mixing in a novel polyhedral chamber. The approach couples spatial boundary velocity fields with non-equilibrium viscous energy dissipation evaluated via thixotropic hysteresis loops. Experimental viscometric [...] Read more.
An integrated information–energy framework is proposed for assessing boundary kinematic interactions and viscoelastic structure formation during wheat dough mixing in a novel polyhedral chamber. The approach couples spatial boundary velocity fields with non-equilibrium viscous energy dissipation evaluated via thixotropic hysteresis loops. Experimental viscometric measurements conducted at T = 28 °C demonstrated that progressive structural homogenization reduces specific power input from 5143.7 → 4510.2 W/m3, representing a 12.3% energy reduction under investigated operating regimes. Evaluation of thixotropic energy dissipation established an optimal gluten network structuralization time at τ = 3.6 min, which shortens the mixing cycle by 14% compared to conventional processing without inducing overmixing degradation. A generalized Maxwell constitutive model with a distributed relaxation spectrum was calibrated against experimental flow curves, demonstrating high predictive accuracy (R2 > 0.92, agreement exceeding 90%). The proposed framework establishes a quantitative bridge between boundary shear kinematics, macromolecular gluten preservation, and processing energy efficiency, providing a physically sound foundation for designing high-performance mixing equipment. Full article
(This article belongs to the Section Sustainable Food)
42 pages, 4908 KB  
Review
Water Balance Approach for Evapotranspiration Dynamics: A Comprehensive Review
by Mahesh Lal Maskey, Bibash Dhakal, Anitha Madapakula, Arjun Thapa and Gafar (Lanre) Agunbiade
Hydrometeorology 2026, 1(1), 7; https://doi.org/10.3390/hydrometeorology1010007 - 16 Sep 2026
Abstract
Evapotranspiration (ET) is a major component of the water and energy cycle, influencing hydrologic processes, agricultural management, groundwater recharge, and land surface–atmosphere interactions. Water balance methods for estimating ET are widely used because of their direct connection to the conservation of mass and [...] Read more.
Evapotranspiration (ET) is a major component of the water and energy cycle, influencing hydrologic processes, agricultural management, groundwater recharge, and land surface–atmosphere interactions. Water balance methods for estimating ET are widely used because of their direct connection to the conservation of mass and their applicability across scales. This review examines the theoretical basis and recent developments in water balance approaches for estimating ET across different hydroclimatic regimes. It summarizes classic soil water balance methods, physically based hydrologic models, remote-sensing approaches, and integrated machine learning techniques. Major themes include uncertainty in precipitation, runoff, and storage estimates; groundwater flow; water balance closure; spatial heterogeneity; and the integration of Moderate Resolution Imaging Spectroradiometer (MODIS), Landsat, and ground-based observations. More recently, hybrid physics-based and machine learning approaches have advanced ET estimation by combining process-based understanding with data-driven methods. Advances in computational hydrology, data assimilation, and Earth observation datasets are improving applications related to irrigation management, drought assessment, climate adaptation, and water-resource planning. Challenges remain in quantifying uncertainty, assessing model transferability, and representing groundwater and storage dynamics under changing hydroclimatic conditions. Overall, the review highlights the continued importance of water balance approaches for understanding ET dynamics and supporting sustainable water-resource management. Full article
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40 pages, 716 KB  
Article
Hydraulic Performance of Variable-Tread Stepped Spillways: Froude Number Reduction and Energy Redistribution at the Stilling-Basin Inlet
by Luis Antonio Yataco Pastor, Yoisdel Castillo Alvarez, Reinier Jiménez Borges, Marcos Aviles, Omar Rodríguez-Abreo, Luis Angel Iturralde Carrera, Carlos Alberto González-Gutiérrez and Juvenal Rodríguez-Reséndiz
Hydrology 2026, 13(9), 250; https://doi.org/10.3390/hydrology13090250 (registering DOI) - 15 Sep 2026
Abstract
Transverse modification of step geometry has been repeatedly proposed as a means of increasing energy dissipation in stepped spillways, with numerically reported gains ranging from 5.6% to 34.7% for labyrinth configurations, in unresolved contradiction with air–water experimental evidence that detects no measurable difference. [...] Read more.
Transverse modification of step geometry has been repeatedly proposed as a means of increasing energy dissipation in stepped spillways, with numerically reported gains ranging from 5.6% to 34.7% for labyrinth configurations, in unresolved contradiction with air–water experimental evidence that detects no measurable difference. The objective of this study is threefold: to verify whether the transverse alternation of the tread length increases the net energy dissipation of the coupled chute–stilling basin system, to quantify its effect on the kinematic and energetic state of the flow delivered to the terminal energy dissipator, and to delimit its domain of applicability. That premise is subjected to verification through 38 three-dimensional Reynolds-averaged Navier–Stokes (RANS) simulations (kω shear-stress transport (SST) closure, homogeneous volume-of-fluid (VOF) formulation) performed in ANSYS CFX 2025 R2, comparing a three-section stepped spillway with a uniform rectilinear footprint against a configuration with transverse LL/2 alternation, under 19 geometric–hydraulic combinations spanning the nappe, transition, and skimming flow regimes (0.57dc/h2.93). The model was verified through a mesh-convergence analysis of the uniform configuration (grid convergence index, GCI =0.66%, on the approach depth) and validated against a physical scale model (0.38% discrepancy, exceeding the propagated experimental uncertainty); a three-level mesh study of the variable-tread configuration shows that its toe-flow response develops as the transverse tread strips become resolved and is not yet mesh-independent at the finest level, which is stated as a limitation of the quantitative results. Because the homogeneous multiphase formulation does not include an air-entrainment submodel, all results correspond to the modeled non-aerated flow conditions. The results do not support the hypothesis of a net dissipative gain: the global energy balance of the two topologies is equivalent within the numerical resolution of the study (bias +0.13 pp; root-mean-square error (RMSE) 0.26 pp), of the order of the discretization uncertainty of the study itself. The actual effect is a redistribution of the dissipative partition that conditions the flow delivered to the energy dissipator: the toe Froude number is reduced in all 19 paired cases (16.5–88.4%; mean: 34.1%). In nine scenarios the hydraulic jump is conditioned without being suppressed (Fr1 from 3.95–4.57 to 1.19–3.71), the energy delivered to the stilling basin drops by 18.3–57.9%, and the residual energy decreases by up to 14.98%; under subcritical toe flow, the same thickening increases the delivered energy by 12.3–19.4% and penalizes the residual energy by up to 18.08%; in two intermediate-discharge scenarios the jump is suppressed, yielding no benefit whatsoever. The transition is expressed through a critical threshold, nominally (dc/h)crit1.48 within the observed separation interval 1.44<dc/h<1.53: the thirteen resolvable scenarios preserve the predicted sign separation without exception. The variable footprint is not a dissipation intensifier but a chute–dissipator coupling element, applicable only to high relative discharges. Full article
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29 pages, 6499 KB  
Article
Computational Fluid Dynamics Simulations of Water Mist Penetration Through a Hot Air Jet
by Rana Uzair Zahid and Tarek Beji
Fluids 2026, 11(9), 234; https://doi.org/10.3390/fluids11090234 - 15 Sep 2026
Abstract
Water-based suppression systems are widely employed in fire safety engineering, yet the accurate CFD modelling of their interaction with fire-driven flows remains a significant challenge. This study evaluates the impact of drag force modelling and grid mesh resolution on interaction boundary height predictions [...] Read more.
Water-based suppression systems are widely employed in fire safety engineering, yet the accurate CFD modelling of their interaction with fire-driven flows remains a significant challenge. This study evaluates the impact of drag force modelling and grid mesh resolution on interaction boundary height predictions between a hot air jet at experimental velocities of 3.3, 4.2, and 5.3 ms−1 and a full-cone 30° water spray nozzle operating at 0.084 LPM using the Fire Dynamics Simulator (FDS 6.9.1), employing the Very Large Eddy Simulation (VLES) turbulence simulation mode with the Deardorff subgrid-scale and WALE near-wall turbulence models. Gas phase and water spray simulations were independently validated against the experimental measurements of Zhou, with the water spray study establishing that representative Lagrangian particles must be on the order of 105 to avoid spurious zero readings in far-field measurements. Interaction phase modelling was conducted using mesh cell sizes of 4 mm and 2 mm with a localized drag reduction approach, confirmed to operate within the LES regime through an a posteriori turbulence resolution assessment. The results demonstrate that improved drag physics combined with refined grid resolution yields meaningful improvements in the predicted interaction boundary height, highlighting the importance of addressing both aspects concurrently for reliable multi-phase flow predictions in FDS. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics of Multiphase Systems)
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27 pages, 4991 KB  
Article
Hydrate Secondary Formation and Blockage Prediction Model in Wellbore During Depressurization-Based Hydrate Production
by Kexin Zhang, Yufa He, Geng Zhang, Yunjian Zhou, Chao Ma and Cheng Lu
Processes 2026, 14(18), 2926; https://doi.org/10.3390/pr14182926 - 15 Sep 2026
Abstract
During depressurization-based natural gas hydrate production, low-temperature and high-pressure wellbore conditions can induce secondary hydrate formation and deposition, risking flow channel blockage and production safety compromise. This study develops a predictive kinetic model for secondary hydrate formation and blockage in annular and mist [...] Read more.
During depressurization-based natural gas hydrate production, low-temperature and high-pressure wellbore conditions can induce secondary hydrate formation and deposition, risking flow channel blockage and production safety compromise. This study develops a predictive kinetic model for secondary hydrate formation and blockage in annular and mist flows, the flow patterns most susceptible to hydrate hazards. The model integrates multiphase flow, heat and mass transfer, hydrate phase change, and particle transport and deposition, coupling conservation equations with hydrate phase equilibrium and flow regime transition criteria to quantitatively predict the hydrate formation rate, deposition rate, and wall blockage severity. Validation against published experimental loop data shows that model-predicted pressure drop increases fall within 5.3% of measurements. Simulations based on a production well in the South China Sea’s Shenhu area provide quantitative predictions of three key operational controls: enlarging the tubing diameter compresses the hydrate stability zone; increasing the gas–liquid ratio suppresses hydrate formation by limiting free water; and the liquid production rate exerts stronger control over formation and deposition than the gas rate. The model serves as a practical quantitative tool for wellbore blockage risk assessment and operational decision support during hydrate trial production. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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26 pages, 1098 KB  
Review
Environmental Air Sampling of Respiratory Viruses in School Settings: A Scoping Review
by Angeliki Chatziantoniou and Apostolos Vantarakis
Aerobiology 2026, 4(3), 18; https://doi.org/10.3390/aerobiology4030018 - 14 Sep 2026
Viewed by 81
Abstract
Background/Objectives: Schools are recognised sites of exposure to respiratory viruses for students and staff, representing a recognised public health concern. Environmental air sampling has been developed as a non-invasive surveillance approach that can detect circulating respiratory viruses, including those shed by asymptomatic persons, [...] Read more.
Background/Objectives: Schools are recognised sites of exposure to respiratory viruses for students and staff, representing a recognised public health concern. Environmental air sampling has been developed as a non-invasive surveillance approach that can detect circulating respiratory viruses, including those shed by asymptomatic persons, without the need for individual testing. However, the methodological and operational evidence base for this approach within educational settings remains nascent. This scoping review systematically maps the extant literature, characterising targeted respiratory viruses, sampling and analytical methodologies, assessed environmental covariates, and critical knowledge gaps. Methods: Adhering to the PRISMA-ScR guidelines, a systematic search of PubMed, Web of Science, and ScienceDirect was executed without temporal restrictions. Results: Eleven studies met the inclusion criteria. Viral RNA detection frequencies exhibited substantial heterogeneity (0–98.5%), primarily attributable to the study design parameters, single-target assays yielding lower positivity versus broad-spectrum multiplex panels, compounded by the stringency of concurrent infection-control interventions. In the singular investigation reporting comprehensive viral ranking, rhinovirus predominated, followed by respiratory syncytial virus (RSV-A/B), and influenza A/B. SARS-CoV-2 detection was profoundly influenced by the pandemic phase dynamics. Critically, all positive detections signified nucleic acid presence, with zero studies confirming viable virions via infectivity assays, representing a fundamental interpretive limitation. Conclusions: Airborne respiratory viral RNA from infected school occupants is unequivocally detectable, positioning environmental sampling as a promising adjunct to clinical surveillance for syndromic characterisation. Nevertheless, translating this approach into a robust, real-time operational infection-control instrument necessitates rigorous methodological harmonisation, alongside comprehensive assessments of viral infectivity, economic viability, and pragmatic feasibility to bridge prevailing translational gaps. Beyond mapping the primary studies, this review additionally benchmarks school-based sampling against practice in hospitals, universities, and other congregate settings, evaluates surface sampling as a complementary environmental modality, and analyses the dilution-limited regime that governs airborne viral detection in ventilated classrooms, which defines the performance envelope that next-generation high-flow, low-loss samplers must meet. Full article
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30 pages, 24263 KB  
Article
Multi-Material Joints of Biocompatible Ti15Ta, Ti10Ta2Nb2Zr, and Ti13Nb13Zr5Cu Titanium Alloys Fabricated by Laser Powder Bed Fusion for Functionally Graded Orthopedic Implants
by Igor Polozov, Victoria Nefyodova and Anton Zolotarev
Metals 2026, 16(9), 1015; https://doi.org/10.3390/met16091015 - 12 Sep 2026
Viewed by 191
Abstract
In this work, multi-material joints of three biocompatible low-modulus titanium alloys—Ti15Ta, Ti10Ta2Nb2Zr, and Ti13Nb13Zr5Cu—were produced and systematically investigated by laser powder bed fusion (LPBF) for the development of functionally graded orthopedic implants. Three pairwise joints were examined (Ti10Ta2Nb2Zr/Ti15Ta, Ti15Ta/Ti13Nb13Zr5Cu, and Ti13Nb13Zr5Cu/Ti10Ta2Nb2Zr). The process [...] Read more.
In this work, multi-material joints of three biocompatible low-modulus titanium alloys—Ti15Ta, Ti10Ta2Nb2Zr, and Ti13Nb13Zr5Cu—were produced and systematically investigated by laser powder bed fusion (LPBF) for the development of functionally graded orthopedic implants. Three pairwise joints were examined (Ti10Ta2Nb2Zr/Ti15Ta, Ti15Ta/Ti13Nb13Zr5Cu, and Ti13Nb13Zr5Cu/Ti10Ta2Nb2Zr). The process parameters governing the formation of the transition zones were optimized: all nine combinations of alloy pair and regime yielded a relative density of 99.35–99.73% with no macroscopic defects; one-way ANOVA showed that the baseline parameters of the second alloy provided a relative density equal to or significantly higher than that obtained with an increased energy input. EDS mapping and point analysis indicated that the transition zone (10–90% width ≈ 250–320 µm) forms through the intermixing of the melts within a common melt pool; after annealing at 900 °C for 1 h, the interface becomes blurred owing to interdiffusion, and the microstructure evolves into a uniform lamellar (α + β) structure. In the as-built condition, the Ti10Ta2Nb2Zr/Ti15Ta joint exhibited σUTS = 598 ± 9 MPa, δ = 14.2 ± 1.9%, and E = 96 ± 3 GPa, with fracture occurring in the Ti15Ta region. The joints involving Ti13Nb13Zr5Cu are limited by the inherent brittleness of this alloy, which is removed for the Ti15Ta/Ti13Nb13Zr5Cu pair by annealing. The elastic modulus of the dense joints (94–101 GPa) remains well above that of cortical bone, so that a clinically relevant reduction in stiffness has to be provided by a porous architecture rather than by the alloy composition alone. In vitro testing of the monolithic alloys (osteoblasts and gingival fibroblasts, MTT with n = 6 and flow cytometry) revealed no cytotoxic effect in terms of membrane integrity; the metabolic activity of gingival fibroblasts on Ti10Ta2Nb2Zr remained below the 70% level, whereas among the monolithic alloys the most stable osteoblast activity and the most pronounced recovery of fibroblast activity were observed on Ti13Nb13Zr5Cu. The biological response of the transition zones themselves has not yet been evaluated. These results provide a processing and materials-science basis for the further development of functionally graded implants. Full article
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32 pages, 8277 KB  
Article
Discharge Validation of Cylindrical Feed Pellets in Conical Hoppers Using Discrete Element Method
by Kunyaphorn Santhisan and Kwanchai Kraitong
Eng 2026, 7(9), 469; https://doi.org/10.3390/eng7090469 - 11 Sep 2026
Viewed by 175
Abstract
Prolonged storage of pelleted feed causes arching above the outlet of conical silos, yet how far the wall material governs the discharge stability of non-spherical pellets remains unresolved. An experimentally calibrated Discrete Element Method (DEM) framework was established in Ansys Rocky for the [...] Read more.
Prolonged storage of pelleted feed causes arching above the outlet of conical silos, yet how far the wall material governs the discharge stability of non-spherical pellets remains unresolved. An experimentally calibrated Discrete Element Method (DEM) framework was established in Ansys Rocky for the gravity discharge of cylindrical feed pellets (2 mm × 5 mm, aspect ratio 2.5) from 1:10 scaled steel and fiberglass conical silos at an outlet-to-particle-size ratio of approximately 18, after 4 h of consolidation. Of the hopper half-angles tested (10°, 20°, 30° and 45°), only 10° sustained gravity discharge; the others blocked completely in both wall materials. Parameters calibrated from consolidated-load direct shear tests reproduced the cumulative discharged mass to a MAPE of 2.5% (R2 = 0.99, steel) and 3.9% (R2 = 0.963, fiberglass), whereas the instantaneous flow rate remained stochastic. Both silos discharged in pulses, at 0.94 and 0.79 kg/s, with coefficients of variation of 25% and 28%. Mass flow indices of 0.211 and 0.278 place both in the funnel-flow regime, and measured peak wall pressures near the outlet reached ≈2000 Pa (steel) against ≈1650 Pa (fiberglass). Reducing wall friction from 0.83 to 0.74, therefore, did not improve stability: for elongated pellets at a low outlet-to-particle-size ratio, surface smoothness alone is no remedy, and outlet sizing, interlocking and wall load management must be addressed together. Full article
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17 pages, 7666 KB  
Article
Influence of Relative Spatial Layout of Fire and Openings on Neutral Plane Characteristics and Distribution Mechanisms of Mass and Heat Release for Spill Plumes in Compartment Fires
by Mingming He, Zelin Sun, Xin Ma, Hao Huang, Chao Ding, Yufei Dai and Zheng Wang
Fire 2026, 9(9), 391; https://doi.org/10.3390/fire9090391 - 9 Sep 2026
Viewed by 263
Abstract
This paper presents a numerical investigation into full-scale double-opening compartment fires. It aims to reveal the underlying mechanisms by which the relative spatial layout of the fire source and openings influences neutral plane characteristics, flow field dynamics, and the allocation of spill plume [...] Read more.
This paper presents a numerical investigation into full-scale double-opening compartment fires. It aims to reveal the underlying mechanisms by which the relative spatial layout of the fire source and openings influences neutral plane characteristics, flow field dynamics, and the allocation of spill plume heat release. The findings indicate that asymmetric boundary constraints in corner-door configurations cause the neutral plane to deform into an “S-shape.” The average neutral plane height decreases significantly as the total heat release rate increases. Moreover, the closer the fire source is located to the door, the more pronounced the descent of the neutral plane becomes. Furthermore, complex internal vortices and momentum losses induced by asymmetric layouts cause classical mass flow rate prediction formulas to overestimate actual values. By introducing a spatial structural factor to calibrate the discharge coefficient, the theoretical calculations of the inflow mass flow rates achieve a high degree of agreement with the simulation results, reducing the relative error to approximately 15%. The results also demonstrate that variations in door and window positions have limited influence on the overall spill-plume mass flow rate. However, different opening configurations modify the spatial aerodynamic characteristics of the flow field, thereby affecting the spatial distribution of external heat release. The incoming airflow from a centrally positioned door directs the fuel gases toward the window, whereas the wall-bounded vortex induced by a corner door entrains fuel to spill out from the door. Once the fire scale exceeds the critical indoor heat release rate, the compartment enters a ventilation-limited regime. This results in increased outward transport of unburned gases and an abrupt rise in the external heat release rate. Full article
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31 pages, 5594 KB  
Article
Simulation of Dripping Faucet Chaos Based on Physics-Informed Neural Networks
by Jingmin Liang, Qiyue Ma, Yixiang Deng, Chao Gao, Chenyang Zhao, Fenglong Wang, Chengbo Duan, Chunlong Xu and Zhen Wang
Fluids 2026, 11(9), 226; https://doi.org/10.3390/fluids11090226 - 9 Sep 2026
Viewed by 133
Abstract
Dripping faucets exhibit chaotic dynamics with order–chaos transitions and multi-field coupling. This study built a physics-informed neural network (PINN) model using high-speed camera and numerical simulation data. The model incorporates physical constraints and employs multi-dimensional verification to simulate chaos and ensure consistency with [...] Read more.
Dripping faucets exhibit chaotic dynamics with order–chaos transitions and multi-field coupling. This study built a physics-informed neural network (PINN) model using high-speed camera and numerical simulation data. The model incorporates physical constraints and employs multi-dimensional verification to simulate chaos and ensure consistency with the real system. Strategies including yargeted preprocessing, feature extraction, and physics enhancement alleviate the scarcity and poor quality of chaotic data. The PINN with an adapted network structure significantly improves prediction accuracy and generalization, boosting computational efficiency by over 100 times. More precisely, the inference speedup relative to FEM reached ~3800× under comparable resolution; this refers to prediction (inference) time, not training time. Long short-term memory (LSTM) performed best in predicting chaotic regions, achieving a 0.92 correlation between predicted and actual maximum Lyapunov exponents. A multi-step prediction strategy, physics-constrained loss function, and comprehensive verification framework ensure long-term prediction accuracy and physical consistency. Out-of-distribution validation on unseen fluids (diethylene glycol, glycerol–diethylene glycol) and extrapolated flow rates confirmed that the PINN retained 87–91% accuracy under OOD conditions, versus 71–78% for the LSTM baseline. A systematic sensitivity analysis further demonstrated that the loss-function weighting coefficients occupied a robust near-optimal plateau. The model comparison is fully quantitative, with all metrics reported alongside 95% bootstrap confidence intervals and a small-data learning curve demonstrating the PINN’s advantage in data-scarce regimes. Deep learning-based chaos identification and Lyapunov exponent estimation accurately capture the system’s chaotic characteristics. Computational optimization, hybrid precision training, distributed strategies, and model compression enhanced the simulation efficiency and indicate the feasibility of deployment. This study demonstrates that machine learning can effectively reveal the nonlinear dynamic behavior of dripping faucet systems, offering a novel approach for complex fluid dynamics and related applications. Full article
(This article belongs to the Section Mathematical and Computational Fluid Mechanics)
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65 pages, 2162 KB  
Article
Temporal-Window-Aware Physics-Informed Edge IDS for Multi-Class IoV Misbehavior Detection Under Ideal and Realistic BSM Observability
by Abdelhabib Bourouis, Ahlem Nasri, Sofiane Zaidi, Liamine Bekhouche and Carlos T. Calafate
Vehicles 2026, 8(9), 215; https://doi.org/10.3390/vehicles8090215 - 9 Sep 2026
Viewed by 207
Abstract
The Internet of Vehicles (IoV) relies on Basic Safety Messages (BSMs) for cooperative awareness, yet these broadcasts remain vulnerable to falsification, replay, flooding, Sybil-based, and motion-manipulation attacks. This paper proposes a temporal-window-aware physics-informed edge-oriented Intrusion Detection System (IDS) for 20-class IoV misbehavior detection [...] Read more.
The Internet of Vehicles (IoV) relies on Basic Safety Messages (BSMs) for cooperative awareness, yet these broadcasts remain vulnerable to falsification, replay, flooding, Sybil-based, and motion-manipulation attacks. This paper proposes a temporal-window-aware physics-informed edge-oriented Intrusion Detection System (IDS) for 20-class IoV misbehavior detection under two simulation-based BSM observability regimes: ideal noise-free kinematics and realistic noise-inclusive observables reconstructed using the sensor-error components supplied separately by VeReMi Extension. Accordingly, “realistic” denotes a noise-inclusive simulation condition rather than real-world validation. From VeReMi Extension streams, the framework derives a compact 20-feature representation capturing kinematics, timing, replay cues, pseudonym dynamics, position-consistency residuals, zero-pattern behavior, and long-horizon motion indicators. These features are normalized with a training-only robust scaler, organized into sender-specific temporal windows, and classified using a lightweight three-layer stacked Long Short-Term Memory (LSTM) with residual temporal pooling. Four implementation variants are evaluated: dense Keras, default-optimized TensorFlow Lite, pruning-only Keras, and pruning-plus-compression TensorFlow Lite. Temporal sensitivity identifies T=40 as the best robustness–latency compromise under the realistic noise-inclusive regime. At T=40, the final pruned-and-compressed TensorFlow Lite model achieves 99.60% accuracy and 99.09% macro-F1 under ideal observability, and 99.38% accuracy and 98.67% macro-F1 under realistic noise-inclusive observability, with an 88.38 KB footprint and 0.1283 ms controlled-runtime latency. Large-scale Central Processing Unit (CPU) benchmarks on 150,000 noise-inclusive test sequences provide a platform-dependent runtime reference, with the pruned TensorFlow Lite model reaching 99.14% accuracy, 98.18% macro-F1, and 3.544 ms average latency on a multi-core Intel Xeon CPU. To complement this high-throughput evaluation, edge-deployment potential is profiled using the official C++ TensorFlow Lite benchmark tool. When evaluated using a single CPU thread without batching, the final artifact achieves an unbatched per-sequence latency of 1.356 ms, corresponding to less than 1.4% of the standard 100 ms BSM generation interval. An architecture-width ablation identifies the 64/32/32 recurrent stack as the performance–resource knee point: expanding it to 128/64/64 improves validation macro-F1 by only 0.0019 percentage points while increasing TensorFlow Lite footprint and latency by factors of 2.46 and 2.32, respectively. A training-time architecture-preserving feature-family ablation confirms that engineered descriptors are essential: raw kinematics alone reduce noise-inclusive macro-F1 from 98.67% to 67.49%, with pseudonym dynamics and position-consistency cues producing the largest individual degradations. Full article
(This article belongs to the Section Safety and Security in Vehicles)
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17 pages, 18102 KB  
Article
Active Droplet Formation in a Microfluidic Cross-Junction Using Stacked Piezoelectric Actuators
by He Yang, Baokai Huang, Wen Wang, Zhanfeng Chen and Keqing Lu
Micromachines 2026, 17(9), 1069; https://doi.org/10.3390/mi17091069 - 9 Sep 2026
Viewed by 208
Abstract
On-demand droplet formation is of crucial importance to the engineering applications of droplet microfluidics. This work presents an experimental investigation on active control of droplet formation using stacked piezoelectric actuators. Two stacked piezoelectric actuators are placed adjacent to the continuous phase channel, producing [...] Read more.
On-demand droplet formation is of crucial importance to the engineering applications of droplet microfluidics. This work presents an experimental investigation on active control of droplet formation using stacked piezoelectric actuators. Two stacked piezoelectric actuators are placed adjacent to the continuous phase channel, producing periodic excitations on the continuous phase flow. It is found that droplet formation greatly depends on the excitation frequency and voltage. Droplet formation synchronizes piezoelectric excitation at a small excitation frequency, i.e., droplet formation frequency equals excitation frequency and its subharmonics. Beyond a critical value of the excitation frequency, a neglected effect of excitation frequency on droplet generation is observed. The droplet generation frequency could be increased up to ~2.6 times that without excitation. The droplet generation frequency exhibits a stepwise increase with rising excitation voltage. When the droplet formation frequency equals the excitation frequency, droplet formation undergoes filling, necking, and pinching-off. When the droplet formation frequency is half of the excitation frequency, additional refilling and re-necking stages are observed. The regime diagram of the droplet formation frequency in the synchronization mode is presented. The scaling of the generated droplet length is deduced. Since periodic excitations are employed on the continuous phase flow, the proposed active control method could minimize the detrimental impact on biochemical reagents within droplets. Full article
(This article belongs to the Special Issue Microfluidics in Biomedical Research, 2nd Edition)
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19 pages, 6747 KB  
Article
Fluid–Structure Interaction Simulation of a Supersonic Reefed Parachute Cluster During the Inflation Process
by Zhenxin Ye, Sheng Gu, Shengping Gong and Siyu Zhang
Aerospace 2026, 13(9), 818; https://doi.org/10.3390/aerospace13090818 - 9 Sep 2026
Viewed by 189
Abstract
To investigate the multi-stage inflation mechanism of a supersonic reefed parachute cluster, an ALE-based fluid–structure interaction method is applied. The canopy permeability is modeled using the Ergun equation, and the virtual structure contact method is employed to handle contact issues induced by large [...] Read more.
To investigate the multi-stage inflation mechanism of a supersonic reefed parachute cluster, an ALE-based fluid–structure interaction method is applied. The canopy permeability is modeled using the Ergun equation, and the virtual structure contact method is employed to handle contact issues induced by large canopy deformation. A flow-domain time-step updating strategy is employed to perform finite-mass inflation simulation. The accuracy of the adopted method is validated by wind-tunnel test data. Full-stage simulations from supersonic to subsonic regimes are conducted to investigate the canopy deformation, flow-field structure, system attitude, and aerodynamic response of the parachute cluster–payload system. The results demonstrate that the parachute cluster maintains stable overall attitudes throughout multi-stage inflation, with axial translation dominating and lateral interference remaining negligible. A steady bow shock with strong inter-canopy shock interaction is formed in the first supersonic stage, followed by prominent vortex shedding in the second transonic stage, and full wake isolation with optimal deceleration efficiency achieved in the third subsonic stage. Quantitative comparison with a single-parachute system reveals stage-dependent interference: higher peak load and stronger oscillations in the supersonic stage, and approximately twice the load in the transonic/subsonic stages. The findings can provide critical theoretical guidance and technical support for engineering implementation of supersonic reefed parachute cluster deceleration systems. Full article
(This article belongs to the Section Aeronautics)
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