Fluids

27 pages, 14936 KB

Open AccessArticle

Experimentally Validated Discrete Phase Model for PM_2.5 and PM₁₀ with Numerical Transport Mapping

by Ren Paulo Estaquio, Ma Kevina Canlas, Neil Astrologo, Job Immanuel Encarnacion, Joshua Agar, Ken Bryan Fernandez, Julius Rhoan Lustro and Joseph Gerard Reyes

Fluids 2026, 11(4), 90; https://doi.org/10.3390/fluids11040090 (registering DOI) - 29 Mar 2026

Abstract

Indoor exposure to particulate matter (PM) depends on ventilation-driven transport, yet sensor placement in real rooms is often based on limited point data. This study develops and experimentally validates a transient CFD framework, using RANS airflow coupled with Lagrangian discrete phase tracking, to [...] Read more.

Indoor exposure to particulate matter (PM) depends on ventilation-driven transport, yet sensor placement in real rooms is often based on limited point data. This study develops and experimentally validates a transient CFD framework, using RANS airflow coupled with Lagrangian discrete phase tracking, to map PM_2.5 and PM₁₀ in a full-scale 2.0 × 3.0 × 2.5 m bedroom with a fixed, non-oscillating pedestal fan and an open window. Airflow was verified by grid independence and validated against 10-point velocity measurements (RMSE = 0.108 m·s⁻¹). Incense experiments (≈31 min burn) provided PM time series over the first 60 min at 16 locations on two heights; emission rate, burning time, and air-change rate (1.96–5.39 ACH) were calibrated so that accepted models achieved aggregate R² > 0.90. Spatial mapping on a 0.5 m grid shows that PM behavior is governed primarily by airflow-defined accumulation pockets rather than by source proximity alone. A near-source region consistently captured strong early-time peaks, whereas remote low-exchange pockets remained elevated during the decay phase. For PM_2.5, the most persistent hotspot is a ceiling-adjacent recirculation pocket, while for PM₁₀, gravitational settling shifted the dominant hotspots toward floor-layer, low-velocity regions. An exposure score combining normalized peak and time-averaged concentrations, interpreted together with particle-track persistence metrics, distinguished transiently traversed regions from true retention pockets. The results show that sensor placement should follow the monitoring objective: near-source regions are more responsive to peak events, ceiling pockets are more suitable for persistent PM_2.5 monitoring, and floor hotspots are more critical for PM₁₀. No single fixed sensor location adequately represents both particle sizes in the present bedroom and ventilation configuration. Full article

(This article belongs to the Special Issue CFD Applications in Environmental Engineering)

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22 pages, 2492 KB

Open AccessArticle

Sound Wave Propagation in Binary Gas Mixtures Flowing Through Microchannels According to a BGK-Type Kinetic Model for General Intermolecular Potentials and Maxwell Boundary Conditions

by Silvia Lorenzani

Fluids 2026, 11(4), 89; https://doi.org/10.3390/fluids11040089 (registering DOI) - 28 Mar 2026

Abstract

In this work, we assess the reliability of a new Bhatnagar–Gross–Krook (BGK)-type model of the linearized Boltzmann equation for binary gas mixtures by investigating the propagation of high-frequency sound waves in microchannels. In order to take into account the different gas–wall interaction properties [...] Read more.

In this work, we assess the reliability of a new Bhatnagar–Gross–Krook (BGK)-type model of the linearized Boltzmann equation for binary gas mixtures by investigating the propagation of high-frequency sound waves in microchannels. In order to take into account the different gas–wall interaction properties experienced by the mixture components, we solve the kinetic equations assuming Maxwell boundary conditions, with different accommodation coefficients for the two species. Unlike other BGK models existing in the literature, the newly proposed model can describe general intermolecular forces. Therefore, in order to test this ability, we specialize our computations to mixtures with two components of very different masses (disparate-mass gas mixtures like He-Xe), since, in this case, the intermolecular forces play a more significant role compared to mixtures with species of similar masses. Then, we compare the results with those obtained by the McCormack model, which has been shown to correctly reproduce many experimental data. Full article

(This article belongs to the Special Issue 10th Anniversary of Fluids—Recent Advances in Fluid Mechanics)

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16 pages, 3935 KB

Open AccessArticle

Numerical Study of Shark-Skin Memetic Riblets on the Trailing Vortex and Boundary Layer Flow of the Wind Turbine Airfoil

by Xiaopei Yang, Renzhong Wang, Bin Zuo and Boyan Jiang

Fluids 2026, 11(4), 88; https://doi.org/10.3390/fluids11040088 - 27 Mar 2026

Abstract

Shark skin grooves, known to reduce hydrodynamic drag, have inspired riblet structures for flow control. This study investigates their application to airfoils, where flow separation at high angles of attack (AOA) compromises aerodynamic stability and wind turbine performance. Numerical simulations were conducted using [...] Read more.

Shark skin grooves, known to reduce hydrodynamic drag, have inspired riblet structures for flow control. This study investigates their application to airfoils, where flow separation at high angles of attack (AOA) compromises aerodynamic stability and wind turbine performance. Numerical simulations were conducted using the SST k–ω model in ANSYS Fluent to analyze riblets placed on the suction surface (SS) of an airfoil. The riblets—oriented perpendicular to the flow—have a fixed height and width of 1 mm, with total lengths varying from 0.1, 0.2, 0.5, and 0.7 of the chord length. The influence of riblet geometry on trailing-edge (TE) vortex shedding and drag reduction under stall conditions is examined in detail. The results indicate that appropriately sized riblets suppress secondary vortex formation and extend the 2S vortex-shedding regime. Conversely, poorly dimensioned riblets can advance Hopf bifurcation in the wake. Analysis of the transient boundary layer structure reveals that the suppression of vortex shedding is primarily due to riblets attenuating fluid pulsation and Reynolds stresses caused by turbulent bursts. Full article

(This article belongs to the Special Issue Vortex Dynamics)

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14 pages, 6039 KB

Open AccessArticle

Flow Mechanism Analysis of Engine Valve Deviation Under Braking Conditions

by Wenchao Mo, Zhancheng Dou, Qiang Sun and Zhihang Chen

Fluids 2026, 11(4), 87; https://doi.org/10.3390/fluids11040087 - 27 Mar 2026

Abstract

The valve serves as the actuating component within the valve mechanism. Under braking conditions, the valve is prone to swaying, which significantly compromises the reliability and service life of the engine. Hence, this paper focuses on researching the deviation characteristics of engine valves. [...] Read more.

The valve serves as the actuating component within the valve mechanism. Under braking conditions, the valve is prone to swaying, which significantly compromises the reliability and service life of the engine. Hence, this paper focuses on researching the deviation characteristics of engine valves. Through a three-dimensional numerical simulation, we analyze the flow field around the valve in the instantaneous states. Our research has revealed that the flow surrounding the valve exhibits a complex multi-vortex structure. Specifically, we observed the evolution pattern of the asymmetric multi-vortex flow along the valve axis within three distinct zones: the asymmetry increase zone, the symmetric development zone, and the asymmetry re-increase zone. The asymmetry increase zone and the asymmetry re-increase zone are located in the curved section and the cylindrical body of the valve, respectively. These zones are the primary contributors to the lateral force acting on the valve, which in turn induces deviation. Based on these analysis results, further research must be conducted on the dynamic characteristics of the flow during valve movement and on optimizing the valve structure through flow control strategies. Full article

(This article belongs to the Special Issue Industrial CFD and Fluid Modelling in Engineering, 3rd Edition)

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15 pages, 1838 KB

Open AccessArticle

Rational Design of High-Performance Viscosifying Polymers in Confined Systems via a Machine-Learning-Accelerated Multiscale Framework for Enhanced Hydrocarbon Recovery

by Arturo Alvarez-Cruz, Estela Mayoral-Villa, Alfonso Ramón García-Márquez and Jaime Klapp

Fluids 2026, 11(4), 86; https://doi.org/10.3390/fluids11040086 - 26 Mar 2026

Abstract

Rational design of high-performance viscosifying polymers is critical for enhancing supercritical CO₂ flooding efficiency in enhanced oil recovery (EOR). Traditional experimental and simulation approaches are limited in exploring the vast design space of polymer architecture, flexibility, and intermolecular interactions. This work presents [...] Read more.

Rational design of high-performance viscosifying polymers is critical for enhancing supercritical CO₂ flooding efficiency in enhanced oil recovery (EOR). Traditional experimental and simulation approaches are limited in exploring the vast design space of polymer architecture, flexibility, and intermolecular interactions. This work presents an integrated machine learning (ML) and mesoscopic simulation framework using Dissipative Particle Dynamics (DPD) to accelerate the development of tailored polymeric thickeners. We systematically investigate synergistic effects of linear and branched polymer blends on solvent viscosity under Poiseuille flow, representative of flow in micro-fractures and pore throats. Key molecular descriptors are varied to generate a comprehensive rheological database. This data trains a deep neural network (DNN) surrogate model linking molecular parameters to macroscopic viscosity. The DNN is coupled with gradient ascent optimization for inverse design, enabling rapid virtual screening of thousands of formulations. A focused case study demonstrates that the star-like architectures with associative cores and semi-flexible backbones outperform linear analogs for supercritical CO₂ viscosity enhancement. The optimal candidate—a four-arm star polymer with linear side chains—was validated by DPD simulation. This multiscale “simulation-to-surrogate” methodology bridges molecular design with continuum-scale flow behavior, offering a transformative tool for formulating cost-effective, efficient, and sustainable next-generation EOR chemicals. Full article

(This article belongs to the Special Issue Pipe Flow: Research and Applications, 2nd Edition)

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15 pages, 2377 KB

Open AccessArticle

Optimization of Airflow Field and Experimental Verification for Wheat Cleaning Device Based on CFD-DEM

by Chunyan Zhang, Junrong He, Sai Yang, Yinhu Qiao, Lele Zhou and Leifeng Dai

Fluids 2026, 11(4), 85; https://doi.org/10.3390/fluids11040085 - 26 Mar 2026

Abstract

To address the issues of high impurity rates and grain loss during the wheat cleaning process, a coupled Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) approach was employed to investigate the internal airflow field and the fluid–solid coupling process of the [...] Read more.

To address the issues of high impurity rates and grain loss during the wheat cleaning process, a coupled Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) approach was employed to investigate the internal airflow field and the fluid–solid coupling process of the wheat cleaning device. The numerical simulation of the three-dimensional internal flow field is carried out in the high-Reynolds-number turbulent region, and the transient double precision solver based on the pressure–velocity coupling algorithm is used. The effects of the air inlet velocity and angle on the airflow field distribution and air separation efficiency were analyzed through CFD simulation. Based on this, the structure of the cleaning device was optimized, and the movement characteristics of materials under various wind forces were compared through CFD-DEM coupling simulation. The results showed that the optimal air separation parameters were an air inlet velocity of 10 m/s and an air inlet angle of 20 degrees. Under these conditions, the airflow distribution in the air separation box was uniform, and the impurity separation efficiency reached the highest level. After optimizing the equipment by installing a high-pressure fan, the number of impurities in the wheat collection box under windy conditions was 265, a reduction of 53.8% compared to 573 under windless conditions. Finally, through repeated experiments on the entire machine, it was verified that the impurity rate of the optimized device was 1.722% and the loss rate was 0.622%, which were 0.23% and 0.12% lower than those of the existing equipment, respectively, consistent with the simulation results. This study provides theoretical basis and technical support for the optimization design of wheat cleaning equipment. Full article

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29 pages, 9179 KB

Open AccessArticle

Quantitative Sensitivity Analysis of Key Parameters in Impellers of Vane-Type Mixed-Flow Pumps Under High Gas Content Conditions

by Minghao Zhou, Guangtai Shi, Yuanbo Shi and Peng Li

Fluids 2026, 11(4), 84; https://doi.org/10.3390/fluids11040084 - 25 Mar 2026

Abstract

Gas–liquid multiphase pumps are essential for deep-sea oil and gas production; however, their performance is severely limited under high gas volume fraction (GVF > 30%) conditions due to inefficient energy transfer and flow instability. In this study, a hybrid sensitivity analysis framework combining [...] Read more.

Gas–liquid multiphase pumps are essential for deep-sea oil and gas production; however, their performance is severely limited under high gas volume fraction (GVF > 30%) conditions due to inefficient energy transfer and flow instability. In this study, a hybrid sensitivity analysis framework combining the Morris screening method and Sobol global sensitivity analysis is developed to quantitatively investigate the effects of impeller geometric parameters on pump performance at a GVF of 80%. Euler–Euler two-phase CFD simulations coupled with Python-based automated sampling are employed. The results show that the impeller outer diameter, axial length, and blade wrap angle are the three most influential parameters. The impeller outer diameter contributes 35.7% to the pressure rise, while an axial length exceeding 44 mm induces axial backflow and reduces efficiency by 8.2%. A critical wrap angle of 114° is identified for gas–liquid energy distribution, beyond which large-scale gas vortices intensify flow instability. Based on these findings, a hierarchical optimization strategy is proposed, resulting in a 6.8% improvement in efficiency and a 12.3% increase in pressure rise. Full article

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23 pages, 28834 KB

Open AccessArticle

Patient-Specific Computational Hemodynamic Modeling of the Right Pulmonary Artery Using CardioMEMS Data: Validation, Simplification, and Sensitivity Analysis

by Angélica Casero, Laura G. Sánchez, Felicia Alfano, Pedro Navas, Juan F. Oteo, Carlos Arellano-Serrano and Manuel Gómez-Bueno

Fluids 2026, 11(3), 83; https://doi.org/10.3390/fluids11030083 - 19 Mar 2026

Abstract

This study investigates the application of computational hemodynamic modeling, involving both FSI and CFD models, using SimVascular to simulate blood flow in the right pulmonary artery for patient-specific cardiovascular assessment. The artery’s three-dimensional geometry was reconstructed from a computed tomography (CT) image, and [...] Read more.

This study investigates the application of computational hemodynamic modeling, involving both FSI and CFD models, using SimVascular to simulate blood flow in the right pulmonary artery for patient-specific cardiovascular assessment. The artery’s three-dimensional geometry was reconstructed from a computed tomography (CT) image, and pressure measurements from a CardioMEMS™ device were used as clinical ground truth for validation. To represent the arterial hemodynamics, we initially formulated a fluid–structure interaction (FSI) approach to capture wall mechanics. However, given the high computational cost of fully patient-specific FSI simulations for routine clinical decision-making, we evaluated the validity of key simplifications by assuming rigid vessel walls coupled with a three-element Windkessel (3WK) model and applying a half-sine inflow waveform derived from the patient’s cardiac output. These simplifications yielded results with minimal error: the rigid-wall assumption introduced a 1.1% deviation, while the idealized waveform resulted in a 0.56 mmHg offset. Crucially, while wall rigidity was acceptable, we found that arterial compliance in the boundary conditions is non-negotiable; reducing the model to a pure resistance approach resulted in non-physiological pressures (130 mmHg). A subsequent parametric analysis examined how varying resistance (R) and compliance (C) distinctively alter the pressure waveform morphology. The results underscore the potential of combining remote monitoring data with validated computational simulations to deepen the understanding of cardiovascular dynamics and enhance diagnostic and therapeutic approaches for cardiovascular diseases. Full article

(This article belongs to the Special Issue Advances in Hemodynamics and Related Biological Flows, 2nd Edition)

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16 pages, 2026 KB

Open AccessArticle

Deposition Mechanisms of Suspended Sediment in an Estuarine Artificial Lake: A Case Study of the Jiaojiang Estuary

by Lele Wang, Xiaoran Wei, Yu Han, Shichang Huang, Huamin Zhou, Maoming Sun, Wenlong Cheng and Yun Chen

Fluids 2026, 11(3), 82; https://doi.org/10.3390/fluids11030082 - 17 Mar 2026

Abstract

Artificial seawater lakes constructed in estuarine environments are highly susceptible to the intrusion of water containing high concentrations of suspended sediment, which can degrade water quality and threaten ecosystem stability. To clarify the settling mechanisms and sedimentation efficiency under high-turbidity conditions, this study [...] Read more.

Artificial seawater lakes constructed in estuarine environments are highly susceptible to the intrusion of water containing high concentrations of suspended sediment, which can degrade water quality and threaten ecosystem stability. To clarify the settling mechanisms and sedimentation efficiency under high-turbidity conditions, this study investigated the Baishawan Artificial Lake in the Jiaojiang Estuary, eastern China, through field observations, controlled still-water sedimentation experiments, and a multi-particle size sedimentation efficiency model. Field measurements revealed significant spatiotemporal variability in suspended sediment concentration (SSC), with higher SSC during spring tides than neap tides and a spatial gradient decreasing from the near-estuary zone to the artificial lake and offshore waters. Grain-size analysis showed that suspended sediment was dominated by clay and silt (>98%). Laboratory experiments indicated a two-stage settling process characterized by rapid initial sedimentation followed by gradual stabilization; under high concentration (1.32 kg/m³), SSC decreased by about 85% within 40 min due to concentration-enhanced flocculation, whereas under low-concentration conditions (0.24 kg/m³) approximately 14 h were required to reach the target concentration of 0.01 kg/m³. Model validation demonstrated that the multi-component sedimentation model effectively reproduced the temporal attenuation of SSC. Model application further suggested that when the initial SSC was 0.70 kg/m³ and the water depth was 5.7 m, the sedimentation tank could reduce the SSC to 0.01 kg/m³ within about 16–17 h, with an estimated annual sedimentation volume of ~65,000 m³ and a recommended dredging interval of five years. These results provide quantitative guidance for sedimentation tank operation and sediment management in estuarine artificial lakes and other high-turbidity coastal environments. Full article

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26 pages, 5753 KB

Open AccessArticle

Machine Learning for Fluid-Agnostic Laminar Heat Transfer Predictions Under Supercritical Conditions

by Luke Holtshouser, Gautham Krishnamoorthy and Krishnamoorthy Viswanathan

Fluids 2026, 11(3), 81; https://doi.org/10.3390/fluids11030081 - 16 Mar 2026

Abstract

Machine learning was employed to make fluid agnostic laminar heat transfer prediction in supercritical conditions, encompassing three fluids (sCO₂, sH₂O, sC₁₀H₂₂) representing a wide range of operating conditions. High-fidelity training data, consisting of both non-dimensional [...] Read more.

Machine learning was employed to make fluid agnostic laminar heat transfer prediction in supercritical conditions, encompassing three fluids (sCO₂, sH₂O, sC₁₀H₂₂) representing a wide range of operating conditions. High-fidelity training data, consisting of both non-dimensional and dimensional (operating parameter) as inputs and Nu and T_wall as outputs, were generated from grid-converged, steady-state, computational fluid dynamic (CFD) simulations. The Random Forest (RF) algorithm outperformed the artificial neural networks (ANNs) across all scenarios on the small multi-fluid dataset (~1600 data points) employed during the training process. When using non-dimensional parameters as inputs, Nu prediction fidelities were better than T_wall predictions for both ML algorithms across both horizontal and vertical configurations. The RF model trained on data from a specific flow configuration (horizontal/vertical) could predict T_wall within an accuracy of +/−1% with dimensional, operational parameters as inputs while being agnostic to the working fluid. Furthermore, by including the gravity vector as an additional variable during the training process, the RF model could predict T_wall accurately in a mixed, multi-fluid dataset containing data from both horizontal and vertical configurations. Full article

(This article belongs to the Special Issue 10th Anniversary of Fluids—Recent Advances in Fluid Mechanics)

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18 pages, 7585 KB

Open AccessArticle

Design and Characterization of a Bench-Top Ludwieg Tube for Aerodynamic Measurements via Simultaneous Quantification of Mach Number and Velocity

by Boris S. Leonov, Richard Q. Binzley, Nathan G. Phillips, Roman Rosser, Farhan Siddiqui, Arthur Dogariu and Richard B. Miles

Fluids 2026, 11(3), 80; https://doi.org/10.3390/fluids11030080 - 15 Mar 2026

Abstract

This article presents the design and detailed characterization of a new supersonic wind tunnel at the Aerospace Laboratory for Lasers, ElectroMagnetics, and Optics of Texas A&M University, tailored for optical diagnostic development and sub-scale fundamental compressible fluid dynamics research. A Ludwieg tube tunnel [...] Read more.

This article presents the design and detailed characterization of a new supersonic wind tunnel at the Aerospace Laboratory for Lasers, ElectroMagnetics, and Optics of Texas A&M University, tailored for optical diagnostic development and sub-scale fundamental compressible fluid dynamics research. A Ludwieg tube tunnel architecture was selected due to its robustness, versatility, and low operational costs. The tunnel consists of a 50-foot-long driver tube constructed from modular Tri-Clamp spools, a Mach 4 nozzle with 3 in. exit diameter configured as a free jet, and a fast-acting valve with 14 ms opening time for high-duty-cycle operation. Such construction proved to be a robust, compact, and affordable solution for academic applications. Characterization methods consisted of simultaneous high-speed dot-schlieren, total and static pressure measurements, and femtosecond laser electronic excitation tagging. Average flow velocity for the first steady-state test time was measured via FLEET at (668.0 ± 5.7) m/s. The Mach number was calculated based on the angles of the attached oblique shocks formed near the 30° cone model. Calculated Mach number was repeatable from run to run and had small oscillations near the average value of 3.96 ± 0.03. Based on the simultaneously measured velocity and Mach number, the static temperature was calculated to be between (68.6 ± 0.3) K and (66.3 ± 0.3) K throughout the 400 ms test time, completely defining the thermodynamic state of the generated freestream flow. Full article

(This article belongs to the Special Issue High-Speed Processes in Continuous Media)

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27 pages, 5611 KB

Open AccessArticle

A Compact-Stencil Wetting Boundary Condition for Three-Dimensional Curved Surfaces in a Phase-Field Lattice Boltzmann Method

by Makoto Sugimoto, Masayuki Kaneda, Kazuhiko Suga and Masaya Shigeta

Fluids 2026, 11(3), 79; https://doi.org/10.3390/fluids11030079 - 14 Mar 2026

Abstract

Accurate numerical reproduction of contact line dynamics on three-dimensional curved solid surfaces remains a challenging issue in multiphase flow simulations. In this study, a wetting boundary condition applicable to curved surfaces is developed within a three-dimensional phase-field lattice Boltzmann framework. The proposed method [...] Read more.

Accurate numerical reproduction of contact line dynamics on three-dimensional curved solid surfaces remains a challenging issue in multiphase flow simulations. In this study, a wetting boundary condition applicable to curved surfaces is developed within a three-dimensional phase-field lattice Boltzmann framework. The proposed method extends an existing curved-surface wetting model and focuses on improving the evaluation of interface normals and order-parameter gradients on Cartesian lattices, while preserving the compact computational stencils and efficiency inherent to the lattice Boltzmann method. Three-dimensional simulations of liquid spreading on a concave spherical surface and droplet spreading on a convex solid sphere are performed over a wide range of prescribed contact angles. The results show that the proposed method eliminates nonphysical behaviors observed with conventional staircase-based boundary conditions, such as droplet sliding along the solid surface and droplet detachment into the surrounding gas phase. In the convex spherical surface cases, the droplet height converges stably to equilibrium through damped oscillations, and the equilibrium droplet shapes show good agreement with theoretical predictions derived from geometric considerations under zero-gravity conditions over a broad range of contact angles. These results demonstrate that the proposed wetting boundary condition can accurately reproduce wetting phenomena on three-dimensional curved solid surfaces. Full article

(This article belongs to the Special Issue 10th Anniversary of Fluids—Recent Advances in Fluid Mechanics)

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35 pages, 18152 KB

Open AccessArticle

Empirical Energy Dissipation Model for Variable-Slope Three-Section Stepped Spillways Validated Through Dimensional Analysis and CFD Simulation

by Luis Antonio Yataco-Pastor, Ana Cristina Ybaceta-Valdivia, Yoisdel Castillo Alvarez, Reinier Jiménez Borges, Luis Angel Iturralde Carrera, José R. García-Martínez and Juvenal Rodríguez-Reséndiz

Fluids 2026, 11(3), 78; https://doi.org/10.3390/fluids11030078 - 13 Mar 2026

Abstract

Energy dissipation in stepped weirs depends on the complex interaction between geometry, flow regime, and surface aeration. The research proposes a dimensionless empirical model (RE3T) to predict the overall energy dissipation in three-section stepped weirs with variable slopes. The formulation integrates dimensional analysis [...] Read more.

Energy dissipation in stepped weirs depends on the complex interaction between geometry, flow regime, and surface aeration. The research proposes a dimensionless empirical model (RE3T) to predict the overall energy dissipation in three-section stepped weirs with variable slopes. The formulation integrates dimensional analysis based on the Vaschy–Buckingham theorem, controlled physical experimentation, and three-dimensional numerical simulations using CFD employing the RANS–SST turbulence model implemented in ANSYS CFX. Eighteen numerical simulations were performed covering seven geometric configurations and four hydraulic inlet conditions, covering slug, transitional, and skimming flow regimes. The CFD model was previously validated by comparison with a physical scale model, obtaining a discrepancy of only 0.38% in relative energy dissipation. The validated dataset was then used to calibrate an empirical multiplicative correlation composed of eight dimensionless groups associated with sectional slopes, number of steps, overall geometric ratio, and upstream Froude number. The proposed model achieved a coefficient of determination R² = 0.81, with relative errors generally less than 1% and a maximum deviation of 2.34%. The statistical indicators (RMSE, MAE, and bias) confirm the absence of significant systematic trends within the defined domain of validity. The results show that the Froude number and the slopes of the sections are the variables with the greatest influence on overall dissipation. The RE3T formulation is a physically consistent and computationally efficient predictive tool for the design and analysis of stepped weirs with variable slopes, extending the scope of traditional correlations developed for uniform slopes. Full article

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18 pages, 11977 KB

Open AccessArticle

Sediment Erosion of a Centrifugal Pump During Startup and Shutdown Processes Considering of Transient Flow in Pump Station

by Weiguo Zhao, Yahui Fan and Honggang Fan

Fluids 2026, 11(3), 77; https://doi.org/10.3390/fluids11030077 - 13 Mar 2026

Abstract

This study employed the Euler–Lagrange method and the Oka erosion model to numerically simulate sediment erosion in a centrifugal pump during the startup and shutdown processes. With a sediment particle size of 0.25 mm and a concentration of 0.135 kg/m³, the [...] Read more.

This study employed the Euler–Lagrange method and the Oka erosion model to numerically simulate sediment erosion in a centrifugal pump during the startup and shutdown processes. With a sediment particle size of 0.25 mm and a concentration of 0.135 kg/m³, the erosion distribution characteristics were analyzed considering the transient flow in the pump station. The results reveal that the impeller suffers the most severe erosion, and the erosion area is affected by the flow rate. At high flow rates, because of inertial and centrifugal forces, erosion concentrates near the shroud at the blade outlet. At low flow rates, vortices generated within the impeller passages cause particles to impact the mid-section of the blades, resulting in erosion in that area. In the inlet section, erosion primarily occurs on the outer wall surface with a relatively low severity at high flow rates, while vortices that occur at the outlet under low flow rates intensify localized erosion. Furthermore, owing to the hysteresis effect of the flow, the erosion during the startup process is more severe than during the shutdown process. In the fixed guide vane zone, at high flow rates, erosion is mainly concentrated in the leading edge and near the covers. At low flow rates, vortices generated between the fixed guide vanes lead to particle impacts on the vane surfaces near the inlet, causing severe localized erosion in this area. In the volute, erosion exhibits a spiral distribution pattern at high flow rates. When the flow rate changes rapidly, the flow field around the tongue region becomes unstable, inducing local erosion there. Full article

(This article belongs to the Special Issue Multiphase Flow and Fluid Machinery)

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23 pages, 1449 KB

Open AccessArticle

Parametrization of Subgrid Scales in Long-Term Simulations of the Shallow-Water Equations Using Machine Learning and Convex Limiting

by Md Amran Hossan Mojamder, Zhihang Xu, Min Wang and Ilya Timofeyev

Fluids 2026, 11(3), 76; https://doi.org/10.3390/fluids11030076 - 12 Mar 2026

Abstract

We present a method for parametrizing sub-grid processes in the shallow water equations. We define coarse variables and local spatial averages and use a feed-forward neural network to learn sub-grid fluxes. Our method results in a local parametrization that uses a four-point computational [...] Read more.

We present a method for parametrizing sub-grid processes in the shallow water equations. We define coarse variables and local spatial averages and use a feed-forward neural network to learn sub-grid fluxes. Our method results in a local parametrization that uses a four-point computational stencil, which has several advantages over globally coupled parametrizations. We demonstrate numerically that our method improves energy balance in long-term turbulent simulations and also accurately reproduces individual solutions. The long-term simulations refer to numerical studies where a fluid flow is simulated over a duration long enough to reach a statistical steady state. The neural network parametrization can be easily combined with flux limiting to reduce oscillations near shocks. More importantly, our method provides reliable parametrizations, even in dynamical regimes that are not included in the training data. Full article

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18 pages, 5534 KB

Open AccessArticle

Vortex Formation in Axial Stirring Systems Under the Influence of Baffle Geometry and Number

by Laura Lenters, Mathias Ulbricht and Heyko Jürgen Schultz

Fluids 2026, 11(3), 75; https://doi.org/10.3390/fluids11030075 - 11 Mar 2026

Abstract

In stirred tank reactors, especially without using baffles, the liquid surface can deform, which in stirring technology is referred to a vortex. These vortices can be advantageous for some mixing tasks, such as obtaining emulsions, they can also impair a consistent product quality. [...] Read more.

In stirred tank reactors, especially without using baffles, the liquid surface can deform, which in stirring technology is referred to a vortex. These vortices can be advantageous for some mixing tasks, such as obtaining emulsions, they can also impair a consistent product quality. Therefore, it is important for the production and process industry, to know whether a vortex occurs or not. Prediction is only possible with an outdated dimensionless baffle index and research on vortex formation with baffles is limited. In this study, two industrially important axial stirring systems—Propeller and Pitched-blade turbine—with different baffle geometries (rectangular, cylindrical, triangular) and numbers are assessed in regard to power input, vortex characteristics (depth, width, volume) and baffle state prediction. Power is recorded using strain gauges, while vortices are evaluated using an optical image evaluation method. The final vortex result is made dimensionless, accessible to the industry to enable improved predictions about the size of the vortices on an industrial scale in order to make the stirred tanks more economical and sustainable. Furthermore, an initial improvement of the baffle index for the investigated stirrers is given, because the original index incorrectly predicts the baffle state in 12.5% of cases. Full article

(This article belongs to the Special Issue Vortex Definition and Identification)

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15 pages, 3306 KB

Open AccessArticle

A Numerical Study of Frost Formation from Humid Air on Horizontal Cold Plate Surfaces Under Natural Convection

by Zhengsheng Yang, Fan Shi, Jiawang Li and Shukun Liu

Fluids 2026, 11(3), 74; https://doi.org/10.3390/fluids11030074 - 10 Mar 2026

Abstract

Based on a previously proposed dimensionless phase-change-driven frosting model, this study numerically investigates frost formation on a horizontal cold plate under natural convection using a Eulerian multiphase framework coupled with species transport. The model is validated against experimental data, showing errors within 5–18%; [...] Read more.

Based on a previously proposed dimensionless phase-change-driven frosting model, this study numerically investigates frost formation on a horizontal cold plate under natural convection using a Eulerian multiphase framework coupled with species transport. The model is validated against experimental data, showing errors within 5–18%; the maximum deviation of 17.07% occurs at

T_{w}

= −25 °C, possibly due to increased experimental uncertainty at very low temperatures. Results demonstrate that lower cold plate temperatures lead to greater frost thickness and higher ice volume fraction. A key physical insight is that under natural convection, local convective circulation causes enhanced frosting at the plate edges, resulting in spatial non-uniformity in both thickness and density. The study covers cold plate temperatures from −10 °C to −25 °C at relative humidity of 60%. The frost growth rate and density at both ends of the cold plate exceed those in the central region, and this difference intensifies with decreasing temperature. Within the frost layer, humid air velocity is nearly zero, while maximum velocity occurs near the sides due to natural convection. The simulation results show good agreement with experimental data, confirming the model’s reliability for natural convection scenarios. Full article

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26 pages, 2306 KB

Open AccessArticle

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

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

Ω_{p} (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 =

Ω_{p} / ω_{c} ≪ 1

. 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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19 pages, 3695 KB

Open AccessArticle

Low Reynolds Number Settling of Bent Rods in Quiescent Fluid

by Amirhossein Hamidi, Daniel Daramsing, Mark D. Gordon and Ronald E. Hanson

Fluids 2026, 11(3), 72; https://doi.org/10.3390/fluids11030072 - 9 Mar 2026

Abstract

This study experimentally investigates the settling behavior of bent (V-shaped and curved) and straight rods in a quiescent fluid at low and finite Reynolds numbers (

Re < 3

). The impact of the rod morphology on the terminal settling velocity and drag [...] Read more.

This study experimentally investigates the settling behavior of bent (V-shaped and curved) and straight rods in a quiescent fluid at low and finite Reynolds numbers (

Re < 3

). The impact of the rod morphology on the terminal settling velocity and drag coefficient was examined, with a particular focus on V-shaped rods compared to straight rods of the same dimensions (diameter and length) and curved rods of the same dimensions and projected area. The results show that V-shaped rods consistently settle faster than straight rods, with velocity differences influenced by the bend angle. This velocity difference reaches a maximum of 57% for a V-shaped rod with a diameter of 0.50 mm, an aspect ratio of 90, and a bend angle of 45 degrees. When compared to curved rods, V-shaped rods exhibit slightly higher terminal velocities, with a maximum difference of 4% in this study, attributed to differences in mean inclination angles. Furthermore, the drag coefficient trends reflect the interplay between the settling velocity and projected area changes with the rod geometry. A new semi-empirical model with an RMS error of 7.1% was also developed to predict the drag coefficients and terminal velocities of straight and bent rods within the ranges studied. These findings and the model presented underscore the significance of the fibre shape in accurately predicting settling dynamics, with implications for atmospheric transport modeling and industrial applications involving fibrous particles. Full article

(This article belongs to the Section Flow of Multi-Phase Fluids and Granular Materials)

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