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Keywords = Lagrangian analysis

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21 pages, 10271 KB  
Article
Kinetic Uncertainty in Hydrogen Jet Flames Using Lagrangian Particle Statistics
by Shuzhi Zhang, Vansh Sharma and Venkat Raman
Hydrogen 2026, 7(2), 56; https://doi.org/10.3390/hydrogen7020056 (registering DOI) - 22 Apr 2026
Abstract
Hydrogen-enriched fuel injection in staged gas-turbine combustors is commonly achieved through jet-in-crossflow (JICF) configurations, where flame stabilization is governed by a local balance between flow-induced strain/mixing and chemical reaction rates. This work investigates turbulent reacting JICF relevant to staged combustion conditions using high-fidelity [...] Read more.
Hydrogen-enriched fuel injection in staged gas-turbine combustors is commonly achieved through jet-in-crossflow (JICF) configurations, where flame stabilization is governed by a local balance between flow-induced strain/mixing and chemical reaction rates. This work investigates turbulent reacting JICF relevant to staged combustion conditions using high-fidelity simulations with adaptive mesh refinement (AMR) and differential-diffusion effects together with Lagrangian particle statistics. Chemistry model uncertainties are incorporated by using a projection method that maps uncertainty estimates from detailed mechanisms into the model used in this work. Results show that the macroscopic flame topology remains in a stable two-branch regime (lee-stabilized and lifted) and is primarily controlled by the jet momentum–flux ratio J. Visualization of the normalized scalar dissipation rate reveals that the flame front resides on the low-dissipation side of intense mixing layers, occupying an intermediate region between over-strained and under-mixed regions. While hydrogen content does not significantly change the global stabilization mode for the cases studied, uncertainty analysis reveals composition-dependent differences that are not apparent in the mean behavior alone. In particular, visualization in Eulerian (χ, T) state-space analysis and particle statistics conditioned on the stoichiometric surface demonstrate that higher-hydrogen cases observe a lower scalar dissipation rate and exhibit substantially reduced variability in OH production under kinetic-parameter perturbations, whereas lower-hydrogen blends experience higher dissipation and amplified chemical sensitivity. These findings highlight that, even in globally similar JICF regimes, the hydrogen content can modify the local response of the flame to kinetic-parameter uncertainty, motivating uncertainty-aware interpretation and design for hydrogen-fueled staging systems. Full article
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20 pages, 1246 KB  
Article
Comparative Performance of Gaussian Plume and Backward Lagrangian Stochastic Models for Near-Field Methane Emission Estimation Using a Single Controlled Release Experiment
by Aashish Upreti, Kira B. Shonkwiler, Stuart N. Riddick and Daniel J. Zimmerle
Atmosphere 2026, 17(4), 417; https://doi.org/10.3390/atmos17040417 - 20 Apr 2026
Abstract
Methane (CH4) is a major component of natural gas and a potent greenhouse gas. Increasing atmospheric methane concentrations are attributed to emissive anthropogenic activities by an average of 13 ppb per yr since 2020 and are linked to a changing global [...] Read more.
Methane (CH4) is a major component of natural gas and a potent greenhouse gas. Increasing atmospheric methane concentrations are attributed to emissive anthropogenic activities by an average of 13 ppb per yr since 2020 and are linked to a changing global climate. Mitigating CH4 emissions from oil and gas production sites has recently become a target to reduce overall greenhouse gas emissions; however, monitoring the efficacy of mitigation strategies depends on accurate quantification of CH4 emissions at the facility-level. Near-field quantification of methane (CH4) emissions from oil and gas (O&G) facilities remains challenging due to the effects of atmospheric variability and sensor configuration on atmospheric dispersion models. This study evaluates the performance of two atmospheric dispersion models, the Gaussian plume (GP) and backward Lagrangian stochastic (bLS), by comparing calculated CH4 emissions to controlled single-point emissions between 0.4 and 5.2 kg CH4 h−1. Emissions were calculated by both models using 121 individual sets of measurements comprising five-minute averaged downwind methane mixing ratios and matching meteorological data. The comparison shows that the bLS approach achieved a higher proportion of emission estimates within a factor of two (FAC2) of the known emission rates compared to the GP approach. The emissions calculated by the bLS model also had a lower multiplicative error and reduced bias relative to GP. Other error-based metrics further confirmed the bLS model performed better, as it yielded lower RMSE and MAE than GP. Statistical analysis of the emission data shows that the lateral and vertical alignment of the source and the sensor plays a critical role in emission estimations, as measurements made closer to the plume centerline and at a distance between 40 and 80 m downwind yielded the best FAC2 agreement. High wind meander degraded the ability of both approaches to generate representative emissions, particularly with the GP approach, as it violates the modeling approach’s assumption of steady-state emissions. Data suggest emissions calculated by the bLS model are comprehensively in better agreement, but the computational demands of the modeling approach and integration into fenceline systems limit real-time applicability. While these results provide insight into model performance under controlled near-field conditions, their applicability to more complex or heterogeneous oil and gas production environments (e.g., the regions Marcellus or Unita Basins) remains limited and uncertain. Full article
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38 pages, 13650 KB  
Article
Nonlinear Motion Analysis of Floating Bodies in Waves Using the MPS Method
by Xianglong Fu, Di Ren, Jun Soo Park, Xiangxi Han, Junlong Su, Zhanbin Meng and Kunpeng Chen
Water 2026, 18(8), 893; https://doi.org/10.3390/w18080893 - 8 Apr 2026
Viewed by 268
Abstract
This paper develops a two-dimensional fully Lagrangian meshless fluid–structure interaction solver by integrating the Moving Particle Semi-implicit (MPS) method with continuum mechanics to investigate the nonlinear interaction between waves and floating bodies. The stability and accuracy of the proposed model are validated through [...] Read more.
This paper develops a two-dimensional fully Lagrangian meshless fluid–structure interaction solver by integrating the Moving Particle Semi-implicit (MPS) method with continuum mechanics to investigate the nonlinear interaction between waves and floating bodies. The stability and accuracy of the proposed model are validated through several benchmark cases. Furthermore, the solver is employed to analyze the dynamic response of a flat plate floating body in waves. The numerically generated waves exhibit a minimum error of approximately −0.5% and a period consistent with theoretical values, maintaining a smooth and continuous free surface. Due to the inherent limitations of the two-dimensional wave-floating body simulation, the Root Mean Square Error (RMSE) of the interaction results ranges from 5.4% to 15.2%. These findings indicate that the proposed method provides a valuable reference for the design and analysis of floating structures in ocean engineering. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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26 pages, 4937 KB  
Article
Modelling the Effect of Vertical Alternating Current Electric Field on the Evaporation of Sessile Droplets
by Yuhang Li and Yanguang Shan
Processes 2026, 14(7), 1066; https://doi.org/10.3390/pr14071066 - 26 Mar 2026
Viewed by 316
Abstract
We developed an arbitrary Lagrangian–Eulerian (ALE)-based multiphysics model for evaporation from a contact-line-pinned sessile drop of neat water subject to a vertically oriented sinusoidal alternating current (AC) electric field applied across parallel-plate electrodes. The framework fully couples electrostatics, incompressible flow, heat transfer with [...] Read more.
We developed an arbitrary Lagrangian–Eulerian (ALE)-based multiphysics model for evaporation from a contact-line-pinned sessile drop of neat water subject to a vertically oriented sinusoidal alternating current (AC) electric field applied across parallel-plate electrodes. The framework fully couples electrostatics, incompressible flow, heat transfer with evaporative cooling, and transient vapour transport in air, and includes an instantaneous, voltage-controlled electrowetting contact-angle response under constant-contact-radius conditions. Validation against published data shows that the model captures both pinned-droplet evaporation and electrically induced deformation. Because Maxwell traction scales with the squared electric-field magnitude, droplet height and contact angle exhibit a robust 2:1 frequency-doubled response, producing two peak–trough events per voltage period. The resulting periodic deformation drives oscillatory interfacial shear and internal recirculation, yielding a synchronous double-peaked evaporative-flux waveform. Gas-side analysis quantifies a time-varying diffusion-layer thickness via a characteristic diffusion length; two thinning events per period coincide with flux maxima, indicating that AC enhancement is dominated by periodic compression of the vapour boundary layer and reduced gas-side mass-transfer resistance. Increasing voltage amplitude (0–60 kV) strongly accelerates volume loss, while frequency has a secondary effect: the cycle-averaged flux rises from 1 to 10 Hz but decreases slightly at 20 Hz due to phase lag and weaker boundary-layer modulation. Full article
(This article belongs to the Section Energy Systems)
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26 pages, 2306 KB  
Article
A Reduced-Order Burgers-Type Vortex Model with Shear-Driven Gyroscopic Precession
by Waleed Mouhali
Fluids 2026, 11(3), 73; https://doi.org/10.3390/fluids11030073 - 10 Mar 2026
Viewed by 323
Abstract
Slow lateral wandering and trochoidal-like motion are commonly observed in intense atmospheric vortices, yet most reduced-order vortex models assume a fixed axis or represent centre motion as purely advective. In this work, we propose a minimal reduced-order framework in which slow gyroscopic precession [...] Read more.
Slow lateral wandering and trochoidal-like motion are commonly observed in intense atmospheric vortices, yet most reduced-order vortex models assume a fixed axis or represent centre motion as purely advective. In this work, we propose a minimal reduced-order framework in which slow gyroscopic precession is introduced as an explicit degree of freedom superimposed on a rapidly rotating vortex core. The vortex is represented by a Burgers–Rott-type velocity field with time-dependent stretching rate and circulation, while the vortex centre undergoes a slow precessional motion governed by a time-dependent rate Ωp(t). The evolution of the vortex parameters is coupled to environmental variability through simple relaxation laws driven by standard large-scale diagnostics, including convective available potential energy, vertical shear, and background vorticity. A tracker-only analysis of tropical cyclone best-track data is used to constrain the appropriate dynamical regime at the track scale, indicating that observed centre wandering typically occurs in a slow-precession limit P = Ωp/ωc1. Numerical demonstrations in cyclone-like configurations show that, despite the smallness of the precession number, cumulative lateral displacement and enhanced Lagrangian dispersion can develop over the vortex lifetime. The proposed framework is intended as a proof-of-concept reduced-order model that isolates the role of weak, environmentally forced precession in modulating vortex wandering and transport, and complements more detailed numerical and observational studies. Full article
(This article belongs to the Special Issue Vortex Definition and Identification)
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20 pages, 2567 KB  
Article
A Computational Algorithm for Optimal Resource Allocation in Nonlinear Multi-Module Systems with Bilateral Constraints
by Kamshat Tussupova, Gulbanu Mirzakhmedova, Diana Rakhimova and Zhansaya Duisenbekkyzy
Computers 2026, 15(3), 179; https://doi.org/10.3390/computers15030179 - 9 Mar 2026
Viewed by 417
Abstract
This study addresses the problem of optimal resource allocation in nonlinear multi-module dynamic systems arising in complex computational and techno-economic processes, where numerical stability and strict enforcement of structural constraints are critical. The objective is to develop a computationally efficient optimal control algorithm [...] Read more.
This study addresses the problem of optimal resource allocation in nonlinear multi-module dynamic systems arising in complex computational and techno-economic processes, where numerical stability and strict enforcement of structural constraints are critical. The objective is to develop a computationally efficient optimal control algorithm capable of handling bilateral control constraints and external balance conditions without resorting to large-scale nonlinear programming or boundary-value shooting. The proposed method is based on a modified Lagrangian formulation, in which bilateral Karush–Kuhn–Tucker (KKT) conditions are analytically embedded into the optimality system. The resulting computational scheme consists of a coupled system of matrix and vector differential equations solved through a non-iterative backward–forward integration procedure. Numerical experiments conducted on a nonlinear model with Cobb–Douglas-type operators demonstrate the stable convergence of the trajectories toward a stationary regime, strict satisfaction of bilateral constraints, and consistent enforcement of balance relations throughout the planning horizon. Empirical scalability analysis indicates approximately cubic computational complexity with respect to the state dimension, while sensitivity tests confirm the numerical robustness across different integration tolerances and ODE solvers. These results demonstrate that the proposed structure-preserving framework provides a computationally stable and practically implementable approach to constrained optimal control in nonlinear multi-module systems. Full article
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14 pages, 3902 KB  
Article
Near-Surface Responses Under Wind Forcing: Lagrangian ADCP Observations
by Jun Myoung Choi and Young Ho Kim
J. Mar. Sci. Eng. 2026, 14(5), 492; https://doi.org/10.3390/jmse14050492 - 4 Mar 2026
Viewed by 290
Abstract
Wind-driven shear and vertical mixing in the upper meter of the ocean strongly regulate near-surface circulation and buoyant tracer transport, yet direct field observations immediately beneath the air–sea interface remain scarce. We present Lagrangian observations, equipped with an upward-looking Acoustic Doppler Current Profiler [...] Read more.
Wind-driven shear and vertical mixing in the upper meter of the ocean strongly regulate near-surface circulation and buoyant tracer transport, yet direct field observations immediately beneath the air–sea interface remain scarce. We present Lagrangian observations, equipped with an upward-looking Acoustic Doppler Current Profiler (ADCP), collected during 5–7 April 2022 in the Jeju Strait under wind stresses of 0.0006–0.19 Pa. Near-surface shear and turbulence metrics were resolved within the top surface layer (TSL), and a response-time analysis showed that upper-layer shear responded most promptly to wind variability, whereas deeper-layer shear and sea-state metrics adjusted more slowly. Wave-period variability exhibited the weakest coupling, indicating additional nonlocal influences. Reynolds-stress estimates showed that the along-wind momentum flux was predominantly negative, indicating net downward transfer of downwind momentum, while cross-direction fluxes were smaller on average and frequently reversed sign, consistent with intermittent lateral transfers associated with evolving wave–current interactions. Using an eddy-viscosity framework, we derived stress-based exponential-saturation parameterizations for depth-averaged shear and vertical diffusivity, with the diffusivity magnitude treated as sensitive to the assumed turbulent Prandtl number. The relationships are intended for event-scale conditions within the observed forcing range and provide field-constrained, implementation-ready formulations for near-surface transport and mixing models. Full article
(This article belongs to the Section Physical Oceanography)
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15 pages, 14508 KB  
Article
Aircraft Ditching by Simulation: A Contribution to Support Virtual Analysis Using a Meshfree Pointset Method
by Christian Leon Muñoz, Dieter Kohlgrüber and Michael Petsch
Aerospace 2026, 13(3), 226; https://doi.org/10.3390/aerospace13030226 - 28 Feb 2026
Viewed by 350
Abstract
The investigation of the emergency situation of an aircraft landing on water is mandatory for the certification of novel aircraft. In this context, computer-aided methods are becoming more relevant to support physical testing and to extend the analysis to further impact conditions. In [...] Read more.
The investigation of the emergency situation of an aircraft landing on water is mandatory for the certification of novel aircraft. In this context, computer-aided methods are becoming more relevant to support physical testing and to extend the analysis to further impact conditions. In this work, the meshless Lagrangian Finite Pointset Method was integrated into an aircraft pre-design process chain and used for the simulation of the interaction between the water and the structure during ditching. To assess the applicability of the method, results from simulations were compared with experimental data from water impact tests of curved panels and scaled models. In addition, the method was implemented in ditching simulations using a generic mid-range aircraft model. Results are analyzed in terms of accuracy, flexibility, and performance. Full article
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22 pages, 3099 KB  
Article
A New Hyperbolic PID-Type Control Scheme for a Direct-Drive Pendulum
by Javier Blanco Rico, Fernando Reyes-Cortes and Basil Mohammed Al-Hadithi
Electronics 2026, 15(5), 942; https://doi.org/10.3390/electronics15050942 - 25 Feb 2026
Viewed by 438
Abstract
This paper addresses the position control problem for a Lagrangian pendulum. Using a strict Lyapunov function, a rigorous analysis is presented to prove that the closed-loop system equilibrium point composed of the pendulum dynamics and a classical linear PID control is globally asymptotically [...] Read more.
This paper addresses the position control problem for a Lagrangian pendulum. Using a strict Lyapunov function, a rigorous analysis is presented to prove that the closed-loop system equilibrium point composed of the pendulum dynamics and a classical linear PID control is globally asymptotically stable. Motivated by these results, the theoretical proposal is extended to analyze a novel hyperbolic PID-type control scheme; reformulating the Lyapunov function, global asymptotic stability of the equilibrium point for the corresponding closed-loop equation is demonstrated. The proposed hyperbolic scheme is a rational function with bounded control action composed of a suitable combination of hyperbolic sine and cosine functions. The hyperbolic structure is used in the proportional, integral, and derivative terms of the control algorithm to drive the position error and joint velocity to zero. Experimental results of both a linear PID and a novel hyperbolic PID-type controller on a direct-drive pendulum are presented to illustrate the effectiveness and performance of the proposed control algorithm. Full article
(This article belongs to the Special Issue Robust Control of Dynamic Systems)
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19 pages, 2646 KB  
Article
Study on Mechanism of Soil Displacement Effect in Large-Diameter PHC Pipe Piles
by Chenghu Yin, Jianqing Bu and Chuanyi Sui
Appl. Sci. 2026, 16(5), 2197; https://doi.org/10.3390/app16052197 - 25 Feb 2026
Viewed by 260
Abstract
In order to investigate the soil displacement effects and penetration resistance mechanisms of large-diameter PHC pipe piles (1200 mm) in complex railway geology, a tripartite framework combining field tests, theoretical analysis, and numerical simulations was established based on the Xiong’an–BDA Express Line project. [...] Read more.
In order to investigate the soil displacement effects and penetration resistance mechanisms of large-diameter PHC pipe piles (1200 mm) in complex railway geology, a tripartite framework combining field tests, theoretical analysis, and numerical simulations was established based on the Xiong’an–BDA Express Line project. A coupled discrete–continuum analysis using the Coupled Eulerian–Lagrangian (CEL) method was conducted to model the large-deformation process of pile driving in soft clay and stratified layers. The results indicate that the installation process induces a “squeezing effect” that critically enhances pile–soil interfacial friction. The theoretical analysis incorporating the extended Lade–Duncan yield criterion significantly improved prediction accuracy, reducing the relative error of side friction from 22% (using the Mohr–Coulomb model) to 5%. Furthermore, the CEL simulation demonstrated high reliability in predicting deep-depth friction and pile tip resistance, effectively capturing the stress redistribution in complex strata. Therefore, the combined application of pre-drilling and large-diameter piles is recommended for deformation-sensitive infrastructure, and the proposed validated framework offers practical guidance for design optimization and parameter selection in similar geological conditions. Full article
(This article belongs to the Special Issue Recent Advances in Pile Foundation Engineering)
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33 pages, 12130 KB  
Article
Optimal Operation Strategy for Regional CCHP Systems Considering Thermal Transmission Delay and Adaptive Temporal Discretization
by Shunchun Yao, Shunzhe Zhao, Jiehui Zheng, Youcai Liang, Qing Wang and Pingxin Wang
Appl. Sci. 2026, 16(4), 1711; https://doi.org/10.3390/app16041711 - 9 Feb 2026
Viewed by 341
Abstract
With the increasing integration of regional energy systems, the dynamic coupling characteristics of cooling, heating, and power flows have become significantly pronounced. However, traditional scheduling models often utilize steady-state assumptions that neglect the thermal transmission delay of the pipeline network, leading to spatiotemporal [...] Read more.
With the increasing integration of regional energy systems, the dynamic coupling characteristics of cooling, heating, and power flows have become significantly pronounced. However, traditional scheduling models often utilize steady-state assumptions that neglect the thermal transmission delay of the pipeline network, leading to spatiotemporal mismatches between energy supply and load demand. To address this issue, this paper proposes an optimal operation strategy for regional Combined Cooling, Heating, and Power (CCHP) systems that explicitly integrates thermal inertia. First, a Pipeline Fluid Micro-element Discretization Method (PFMDM) is developed based on the Lagrangian specification to accurately characterize the dynamic flow and thermal decay processes without the heavy computational burden of partial differential equations. In addition, the accuracy of PFMDM is directly benchmarked against a high-fidelity transient PDE solver (finite-volume TVD–MUSCL scheme) over a wide range of pipe lengths, flow velocities, and thermal loss coefficients, where the outlet-temperature RMSE remains below 0.2 °C. This model quantitatively reveals the “Virtual Energy Storage” (VES) mechanism of the pipeline network. Second, to overcome the “curse of dimensionality” in dynamic scheduling, a Load-Gradient-Based Adaptive Temporal Discretization (LG-ATD) method is proposed. This method maintains a fine-grained baseline for electrical settlement while dynamically aggregating thermal/cooling steps based on load fluctuations. Simulation results demonstrate that the proposed strategy corrects the significant physical deviations of the traditional steady-state model. The analysis reveals that the steady-state model underestimates the required heating and cooling supply capacities by up to 26.66% and 39.15%, respectively, due to the neglect of transmission losses and delays. By leveraging the VES mechanism, the proposed method enables a fuel-shift in the energy-supply structure, substantially decreasing the electricity purchasing cost (by 75.2% in the tested case). This reduction reflects a reallocation from grid purchases to on-site gas-fired cogeneration to maintain physical feasibility under delay and loss effects, and therefore, it is accompanied by an increase in natural gas consumption and a higher total operating cost. Furthermore, the LG-ATD method significantly alleviates the computational burden by substantially compressing the presolved model size and reducing the overall solving time by more than 80%, thereby effectively mitigating the curse of dimensionality for practical engineering applications. Full article
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12 pages, 2744 KB  
Article
Incorporating Radioactive Decay Chains Within Lagrangian Marine Radionuclide Transport Models for Assessing the Consequences of Nuclear Accidents
by Carmen Cortés and Raúl Periáñez
J. Mar. Sci. Eng. 2026, 14(4), 328; https://doi.org/10.3390/jmse14040328 - 8 Feb 2026
Viewed by 357
Abstract
Lagrangian particle-tracking models are increasingly used to simulate radionuclide transport in marine environments, especially for assessing the consequences of accidental releases. However, existing models generally neglect radioactive decay chains, limiting their ability to reproduce the complete behavior of radionuclides and their progeny. To [...] Read more.
Lagrangian particle-tracking models are increasingly used to simulate radionuclide transport in marine environments, especially for assessing the consequences of accidental releases. However, existing models generally neglect radioactive decay chains, limiting their ability to reproduce the complete behavior of radionuclides and their progeny. To the authors’ knowledge, this work presents the first implementation of radioactive decay chains within a fully three-dimensional Lagrangian marine radionuclide transport model, explicitly coupling stochastic particle tracking with decay kinetics and dynamic sediment–water interactions, enabling a realistic simulation of parent–daughter transformations in the ocean. The approach is tested for the chain in the Western Mediterranean Sea, following a hypothetical nuclear accident. Results confirm that the stochastic treatment accurately reproduces analytical decay solutions and can be seamlessly incorporated into operational-scale transport simulations. The framework can be extended to other radionuclide series and marine domains, providing a versatile and computationally efficient tool for emergency response, environmental impact assessment, and safety analysis in nuclear engineering applications. Full article
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27 pages, 4986 KB  
Article
DI-WOA: Symmetry-Aware Dual-Improved Whale Optimization for Monetized Cloud Compute Scheduling with Dual-Rollback Constraint Handling
by Yuanzhe Kuang, Zhen Zhang and Hanshen Li
Symmetry 2026, 18(2), 303; https://doi.org/10.3390/sym18020303 - 6 Feb 2026
Viewed by 319
Abstract
With the continuous growth in the scale of engineering simulation and intelligent manufacturing workflows, more and more problem-solving tasks are migrating to cloud computing platforms to obtain elastic computing power. However, a core operational challenge for cloud platforms lies in the difficulty of [...] Read more.
With the continuous growth in the scale of engineering simulation and intelligent manufacturing workflows, more and more problem-solving tasks are migrating to cloud computing platforms to obtain elastic computing power. However, a core operational challenge for cloud platforms lies in the difficulty of stably obtaining high-quality scheduling solutions that are both efficient and free of symmetric redundancy, due to the coupling of multiple constraints, partial resource interchangeability, inconsistent multi-objective evaluation scales, and heterogeneous resource fluctuations. To address this, this paper proposes a Dual-Improved Whale Optimization Algorithm (DI-WOA) accompanied by a modeling framework featuring discrete–continuous divide-and-conquer modeling, a unified monetization mechanism of the objective function, and separation of soft/hard constraints; its iterative trajectory follows an augmented Lagrangian dual-rollback mechanism, while being rooted in a three-layer “discrete gene–real-valued encoding–decoder” structure. Scalability experiments show that as the number of tasks J increases, the DI-WOA ranks optimal or sub-optimal at most scale points, indicating its effectiveness in reducing unified billing costs even under intensified task coupling and resource contention. Ablation experiment results demonstrate that the complete DI-WOA achieves final objective values (OBJ) 8.33%, 5.45%, and 13.31% lower than the baseline, the variant without dual update (w/o dual), and the variant without perturbation (w/o perturb), respectively, significantly enhancing convergence performance and final solution quality on this scheduling model. In robustness experiments, the DI-WOA exhibits the lowest or second-lowest OBJ and soft constraint violation, indicating higher controllability under perturbations. In multi-workload generalization experiments, the DI-WOA achieves the optimal or sub-optimal mean OBJ across all scenarios with H = 3/4, leading the sub-optimal algorithm by up to 13.85%, demonstrating good adaptability to workload variations. A comprehensive analysis of the experimental results reveals that the DI-WOA holds practical significance for stably solving high-quality scheduling problems that are efficient and free of symmetric redundancy in complex and diverse environments. Full article
(This article belongs to the Section Computer)
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30 pages, 6352 KB  
Review
Research Progress on Numerical Simulation Methods for Metallurgical Fluidization
by Langfeng Fan, Mingzhuang Xie, Hongliang Zhao, Rongbin Li, Zhenglin Zhang and Fengqin Liu
Processes 2026, 14(3), 555; https://doi.org/10.3390/pr14030555 - 5 Feb 2026
Viewed by 734
Abstract
Numerical simulation has become a powerful and versatile toolkit for investigating gas–solid flow behavior in metallurgical fluidization processes. This review summarizes recent advances in the application of computational fluid dynamics (CFD)-based approaches, particularly the Eulerian–Eulerian and Eulerian–Lagrangian methods, within the field of metallurgical [...] Read more.
Numerical simulation has become a powerful and versatile toolkit for investigating gas–solid flow behavior in metallurgical fluidization processes. This review summarizes recent advances in the application of computational fluid dynamics (CFD)-based approaches, particularly the Eulerian–Eulerian and Eulerian–Lagrangian methods, within the field of metallurgical fluidization. It covers model development, particle and bubble dynamics, reactor flow field analysis, and structural optimization. The study demonstrates that numerical simulation plays a crucial role in elucidating fluidization mechanisms, optimizing process parameters, and guiding reactor design. For example, numerical simulation provides key quantitative insights, such as the enhancement of iron ore reduction rates by up to 40% with increased gas velocity and the optimization of reactor cone angles to 5–10° for improved stability, in the design of hydrogen-based iron oxide reduction reactors. However, this review identifies that current research is predominantly focused on iron ore reduction, while numerical studies on fluidized-bed smelting of non-ferrous metals, such as zinc, copper, and aluminum, remain relatively limited. Future efforts should aim to broaden the application of numerical simulation in non-ferrous metallurgy, develop efficient multi-scale coupled computational methods, and integrate artificial intelligence technologies to advance metallurgical fluidization toward greater efficiency, energy savings, and intelligent operation. Full article
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23 pages, 5044 KB  
Article
Flow Prediction and Simulation Analysis of Thermoplastic Composites PA6 Hot Moulding Resin
by Qingyu Li, Zhixu Dong, Shibo Mu, Xingwei Sun, Jianlong Zhao, Heran Yang, Yin Liu, Fuyan Yao, Xiaoming Fu, Weifeng Zhang, Dongxu Bao and Yaping Zhao
Appl. Sci. 2026, 16(3), 1243; https://doi.org/10.3390/app16031243 - 26 Jan 2026
Viewed by 399
Abstract
This study characterised the hot-press forming process of long carbon fibre PA6 materials using laminates prepared from UD-CA708A prepregs manufactured by Nanjing Special Plastic Composites Materials Co., Ltd. In order to investigate the resin flow behaviour during the hot compression moulding process, a [...] Read more.
This study characterised the hot-press forming process of long carbon fibre PA6 materials using laminates prepared from UD-CA708A prepregs manufactured by Nanjing Special Plastic Composites Materials Co., Ltd. In order to investigate the resin flow behaviour during the hot compression moulding process, a unified model integrating the material forming and resin flow sequences was established by Lagrangian and Eulerian discretization methods. Simultaneous measurements by rotational and torsional rheometers revealed that in-plane fibre flow dominated, and the long carbon fibre PA6 material showed anisotropic behaviour. The anisotropic viscosity tensor principal model was used to characterise this anisotropy, the parameters of which were determined experimentally by the rheometer. Based on these findings, a unified modelling approach for material forming and resin flow was developed and applied to simulation analysis. The validity of the anisotropic viscosity intrinsic model and the unified simulation framework is verified by integrating the rheological analysis, in-mold analysis, and evaluation of the microstructure and mechanical properties of the moulded specimens, which provides a technical framework and a strategy for the application of the model in complex geometries. Full article
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