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Keywords = power–law fluids

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18 pages, 1871 KB  
Article
Asymmetric Flow Dynamics in a Pneumatically Actuated Polydimethylsiloxane (PDMS) Micropump: Numerical Simulation and Experimental Validation
by Pei-Pei Hsu and Jr-Lung Lin
Micromachines 2026, 17(9), 1027; https://doi.org/10.3390/mi17091027 - 28 Aug 2026
Viewed by 55
Abstract
This study presents a comprehensive numerical and experimental investigation on a pneumatically actuated polydimethylsiloxane (PDMS) micropump integrated with passive check valves (PCVs). Advanced three-dimensional (3D) fluid–structure interaction (FSI) simulations were conducted to capture the nonlinear large deformation of the membrane and elucidate the [...] Read more.
This study presents a comprehensive numerical and experimental investigation on a pneumatically actuated polydimethylsiloxane (PDMS) micropump integrated with passive check valves (PCVs). Advanced three-dimensional (3D) fluid–structure interaction (FSI) simulations were conducted to capture the nonlinear large deformation of the membrane and elucidate the Newtonian flow dynamics. The maximum deformation calculated by the simulations was compared with the theoretical Timoshenko formula, demonstrating excellent agreement across the entire pressure range (3.0–100.0 kPa). The 3D FSI simulations revealed a considerable asymmetry in the flow dynamics between the suction and compression phases. Notably, at applied pressures exceeding 20.0 kPa, the discharge volume substantially outweighed the suction one. To characterize both the ideal and practical volumetric flow rates, curve-fitting analyses revealed that both the simulation and experimental data follow a consistent 1/3-power-law relationship with respect to the applied pressure. Experimentally, the micropump achieved a maximum volumetric flow rate of 2.6 mL/min at 70.0 kPa and 12.0 Hz. Furthermore, the micropump demonstrated a peak pumping efficiency of 56.95% at 35.0 kPa and 10.0 Hz relative to the ideal numerical baseline. By bridging idealized numerical bounds with experimental realities, this validated framework offers a robust predictive tool for optimizing flow asymmetry and pumping efficiency in advanced microfluidic systems. Full article
(This article belongs to the Special Issue MEMS/NEMS Devices and Applications, 4th Edition)
17 pages, 2692 KB  
Article
Quantum Dot-Hybridized Temperature- and Salt-Resistant Polyacrylamide for Enhanced Oil Recovery in High-Temperature and High-Salinity Reservoirs
by Hua Li, Jingjing He, Rui Jing, Song Wang, Aihui Li, Ting Chen, Daijun Du and Suhan Zhang
Polymers 2026, 18(17), 2084; https://doi.org/10.3390/polym18172084 - 28 Aug 2026
Viewed by 169
Abstract
Conventional partially hydrolyzed polyacrylamide (HPAM) suffers severe chain coiling, viscosity attenuation and precipitation under high-temperature and high-salinity reservoir brines, restricting its tertiary oil recovery efficiency. Herein, a novel carbon quantum dot hybrid terpolymer (QDHSTP) was synthesized via free-radical copolymerization, where silane-modified nitrogen-doped carbon [...] Read more.
Conventional partially hydrolyzed polyacrylamide (HPAM) suffers severe chain coiling, viscosity attenuation and precipitation under high-temperature and high-salinity reservoir brines, restricting its tertiary oil recovery efficiency. Herein, a novel carbon quantum dot hybrid terpolymer (QDHSTP) was synthesized via free-radical copolymerization, where silane-modified nitrogen-doped carbon quantum dots (FNCQDs) were covalently bonded to acrylamide (AM)/2-acrylamido-2-methylpropane sulfonic acid (AMPS)/diallyldimethylammonium chloride (DMDAAC) backbones. FTIR, 1H NMR and thermogravimetric analysis (TGA) verified successful grafting of FNCQDs, while SEM revealed a continuous three-dimensional entangled network constructed by polymer chains. Steady and oscillatory rheology systematically characterized the solution viscoelasticity: QDHSTP solutions followed the power-law shear-thinning model, with flow behavior index n decreasing from 0.698 to 0.676 and consistency factor k rising from 80.91 to 131.13 mPa·sn as concentration increased from 2000 to 3000 mg/L. All samples behaved as viscosity-dominated viscoelastic fluids, with elastic modulus exhibiting stronger frequency dependence. Benefiting from embedded FNCQDs, QDHSTP retained 79.74% and 76.06% of initial viscosity in 1.0 × 104 mg/L NaCl and CaCl2 brine, respectively, markedly better than that of the polymer without incorporated FNCQDs respectively, and maintained thickening capacity at 90 °C. Artificial sandstone core flooding demonstrated an incremental oil recovery of 29.8% over baseline waterflooding, attributed to mobility control and elastic residual oil stripping. This covalent nanohybrid strategy provides a facile route to construct thermo-salt tolerant polyacrylamides, offering a promising candidate polymer for harsh oil reservoir chemical flooding. Full article
(This article belongs to the Special Issue Application of Polymers in Enhanced Oil Recovery: 2nd Edition)
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17 pages, 485 KB  
Article
Thermal Convection of Power-Law Fluid in Bidispersive Porous Media with Throughflow
by Fatemah H. H. Al Mukahal, S. Suresh Kumar Raju, Gundlapally Shiva Kumar Reddy and Seepana Praveenkumar
Mathematics 2026, 14(17), 3073; https://doi.org/10.3390/math14173073 - 26 Aug 2026
Viewed by 168
Abstract
This study investigates the onset of thermal convection in a power-law fluid saturating a bidispersive porous medium using linear stability analysis. The eigenvalue problem is solved using the normal mode technique in conjunction with a numerical boundary value solver (bvp4c). The interaction parameter [...] Read more.
This study investigates the onset of thermal convection in a power-law fluid saturating a bidispersive porous medium using linear stability analysis. The eigenvalue problem is solved using the normal mode technique in conjunction with a numerical boundary value solver (bvp4c). The interaction parameter exhibits dual behavior depending on the rheology: it destabilizes the system in shear-thinning fluids while stabilizing it in Newtonian and shear-thickening regimes under certain conditions. The permeability ratio is found to have a consistently stabilizing effect, with higher values significantly delaying the onset of convection. Thermal transport parameters also play a crucial role, with increasing Peclet numbers generally enhancing stability, although non-monotonic behavior is observed in the shear-thinning regime due to competing effects of convective enhancement and thermal diffusion. For low values of the Peclet numbers, shear-thickening fluids exhibit the lowest critical Rayleigh number (least stable) and shear-thinning fluids the highest one (most stable). In contrast, for high Peclet numbers, shear-thickening fluids remain the least stable, while Newtonian fluids exhibit maximum stability. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Chaos Theory, 2nd Edition)
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25 pages, 28602 KB  
Article
Research on Hydrodynamic Performance of a 30 kW Rim-Driven Thruster and Its Coupling Mechanism with an AUV
by Xia Yang, Kunkun Li, Xiong Deng, Dingfeng Yu, Yiyun Peng, Yan Luo and Yanyang Wu
J. Mar. Sci. Eng. 2026, 14(16), 1544; https://doi.org/10.3390/jmse14161544 - 20 Aug 2026
Viewed by 254
Abstract
With the continuous expansion of deep-sea resource exploration, marine environmental monitoring, and underwater operations, Autonomous Underwater Vehicles (AUVs) have been increasingly widely applied. Aiming at the demand for high-performance main propulsion systems of Autonomous Underwater Vehicles (AUVs), this paper conducts research on the [...] Read more.
With the continuous expansion of deep-sea resource exploration, marine environmental monitoring, and underwater operations, Autonomous Underwater Vehicles (AUVs) have been increasingly widely applied. Aiming at the demand for high-performance main propulsion systems of Autonomous Underwater Vehicles (AUVs), this paper conducts research on the structural design and hydrodynamic performance of a 30 kW rim-driven thruster (RDT) and its coupling mechanism with AUVs. By combining computational fluid dynamics (CFD) simulations and experimental methods, the influence of the advance coefficient on the open-water performance of the thruster is revealed. An integrated coupling simulation model of the AUV and RDT is established to analyze the performance attenuation law of the thruster and the characteristics of the coupled flow field under wake flow conditions, and to clarify the two-way interaction mechanism between the thruster and AUV. Towing tank tests were carried out at sailing speeds ranging from 1 to 4 kn, which verifies the reliability of the numerical simulation model and the matching performance between the thruster and AUV. The results show that the open-water efficiency of the thruster reaches a peak value of 0.536 at the advance coefficient J=0.8, which is close to the optimal efficiency range with good matching performance of the propulsion system Under wake flow conditions, the attenuation range of the thrust coefficient of the thruster is 12.45–16.53% with the increase in advance coefficient. The main reasons are the uneven inflow velocity and unstable flow field pressure distribution caused by the non-uniform wake flow at the AUV stern. At the ship speeds of 2 kn, 3 kn and 4 kn, the self-propulsion rotational speeds obtained from test fitting are in good agreement with the simulation results, with all relative errors less than 8%. This study provides a theoretical basis and technical reference for the engineering design of medium and high-power rim-driven thrusters as well as the matching optimization of AUV-thruster systems. Full article
(This article belongs to the Section Ocean Engineering)
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18 pages, 1016 KB  
Article
Annulus Back-Pressure Transfer Law During Managed-Pressure Cementing Process in Ultra-Deep Wells
by Ning Li, Jingtian Zhang, Lvchao Yang, Xiao Cai, Heng Yang, Qingfeng Guo and Jie Liang
Processes 2026, 14(16), 2611; https://doi.org/10.3390/pr14162611 - 17 Aug 2026
Viewed by 289
Abstract
The formation pressure system of ultra-deep wells is complex, and managed pressure cementing (MPC) is a commonly used technical means of safety control and cementing quality improvement. During the MPC process, pump switching operations can induce substantial annular back-pressure. The attenuation of annular [...] Read more.
The formation pressure system of ultra-deep wells is complex, and managed pressure cementing (MPC) is a commonly used technical means of safety control and cementing quality improvement. During the MPC process, pump switching operations can induce substantial annular back-pressure. The attenuation of annular back-pressure within the wellbore serves as a pivotal foundation for the precise determination of back-pressure compensation values in ultra-deep wells. Building upon the one-dimensional transient flow model of the wellbore, we developed a transient transmission model for annular back-pressure and solved it using the finite difference method. The computational results were validated against experimental data, thereby elucidating the attenuation pattern of annular pressure waves in ultra-deep wells. The findings reveal that the primary controlling factors for the attenuation of pressure waves encompass well depth, the elastic modulus of the wellbore rock, and the rheological model of the drilling fluid. As well depth increases, the pressure wave exhibits a linear decrease, with discontinuities occurring at the casing and open-hole sections. The rate of pressure wave attenuation accelerates within the open-hole interval. The lower the elastic modulus of the open-hole segment, the more rapid the attenuation rate of the pressure wave becomes. The attenuation laws of annular fluids with different rheological models are ranked as follows: Power-law model > Herschel–Bulkley model > Bingham model. Under the computed well conditions, the pressure of the power-law fluid decreases to 85% of its initial back-pressure value. This research provides theoretical underpinnings for the design and execution of on-site MPC operations. Full article
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21 pages, 442 KB  
Article
Fuzzy–Viscous Fluid Dynamics with Dynamic Interval-Valued Intuitionistic Fuzzy Sets
by Osama Ogilat and Abd Ulazeez Alkouri
Mathematics 2026, 14(16), 2895; https://doi.org/10.3390/math14162895 - 11 Aug 2026
Viewed by 333
Abstract
The rheological behaviour of complex fluids such as blood and polymer melts is governed by viscosities that are inherently subject to epistemic uncertainty arising from incomplete knowledge of evolving small scales rather than intrinsic randomness. Classical continuum models assume precisely known viscosity functions, [...] Read more.
The rheological behaviour of complex fluids such as blood and polymer melts is governed by viscosities that are inherently subject to epistemic uncertainty arising from incomplete knowledge of evolving small scales rather than intrinsic randomness. Classical continuum models assume precisely known viscosity functions, an assumption that is physically unjustifiable in such systems, while existing fuzzy approaches have failed to integrate rigorously with the full conservation laws of continuum mechanics. To address this gap, we introduce Fuzzy–Viscous Fluid Dynamics (FVFD), a novel framework in which dynamic viscosity is governed by Dynamic Interval-Valued Intuitionistic Fuzzy Sets (DIVIFS), with membership functions grounded in Coleman–Gurtin internal-variable thermodynamics and evolution equations derived from a Lyapunov dissipation postulate. Employing the parabolic comparison principle together with Galerkin–Leray–Hopf theory, we establish that intuitionistic ordering constraints are preserved over time and prove the existence of global weak solutions to the coupled fuzzy Navier–Stokes equations (FNSEs). An exact analytical solution for fuzzy Couette flow is derived, recovering the classical Newtonian limit and shown, via a structural argument, to be non-linear precisely because and only because FVFD departs from the purely local generalised-Newtonian closure shared by the Power-law, Carreau–Yasuda, and Cross models. Three governing dimensionless parameters, the Reynolds number (Re), Damköhler number (Da), and fuzzy number (Fz), are identified and justified to characterise distinct flow regimes. This framework provides a rigorous, physically grounded alternative to stochastic and data-driven methods for explicitly tracking epistemic uncertainty through interval-valued hesitancy parameters, enabling more accurate modelling of complex fluids whose internal aggregation states remain inaccessible to direct observation. Full article
(This article belongs to the Special Issue Advanced Computational Fluid Dynamics and Applications)
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31 pages, 8376 KB  
Article
Study on the Influence of Medium Temperature on the Performance of a Space Micropump
by Danyang Zhou, Jintao Liu, Lilei Miao, Zhen Qu, Kaiyun Gu and Zhanhai Zhang
Aerospace 2026, 13(8), 674; https://doi.org/10.3390/aerospace13080674 - 28 Jul 2026
Viewed by 286
Abstract
The present work examines how variations in working fluid temperature govern the hydrodynamic behavior of a space-rated micropump. Using perfluorotriethylamine as the operating medium, three-dimensional CFD simulations employing the SST k-ω turbulence closure were carried out across a broad thermal spectrum, and [...] Read more.
The present work examines how variations in working fluid temperature govern the hydrodynamic behavior of a space-rated micropump. Using perfluorotriethylamine as the operating medium, three-dimensional CFD simulations employing the SST k-ω turbulence closure were carried out across a broad thermal spectrum, and the resulting flow physics were interpreted through entropy generation analysis. Based on the entropy production theory, the influence laws of different inlet temperatures on the external characteristics, internal characteristics, and flow loss characteristics of the micropump were quantitatively analyzed. The results show that temperature mainly affects the micropump performance by changing the viscosity and density of the working fluid. At low temperatures, the fluid viscosity increases significantly, leading to increased flow resistance, intensified internal friction, reduced head and efficiency, and increased shaft power. As the temperature increases to 0 °C and above, the viscosity change tends to moderate, and the external characteristic parameters tend to stabilize. The internal characteristic analysis shows that under low-temperature conditions, the high-pressure region in the impeller area expands and the turbulent kinetic energy decreases, but the flow separation is to a certain extent suppressed. The region near the volute tongue and the impeller outer edge are the main areas of entropy production loss, and their entropy production rates increase significantly with decreasing temperature. Moreover, at low temperatures, the high entropy production regions expand from locally isolated distributions to continuous large-scale distributions. The impeller outer edge dominates total entropy production, driven by peak fluid linear velocity and intense shear interaction with the volute wall. The findings elucidate how working fluid temperature governs both the hydrodynamic performance and the irreversible loss characteristics of the micropump. These insights can directly inform the engineering design of thermal management loops intended for orbital applications under severe temperature swings. Full article
(This article belongs to the Section Astronautics & Space Science)
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22 pages, 8496 KB  
Article
Rheological Properties and Prediction Method for Oil-Based Drilling Fluids Under High-Temperature and High-Pressure Conditions
by Mingsheng Liu, Yaopu Xu, Qi Xia, Haizhu Wang, Qingfeng Guo, Haizhi Zhang, Chenxi Ye, Guoxin Zhang, Bin Wang and Yong Zheng
Processes 2026, 14(15), 2387; https://doi.org/10.3390/pr14152387 - 24 Jul 2026
Viewed by 427
Abstract
The rheology of high-temperature and high-pressure oil-based drilling fluids is critical for managed pressure drilling in deep and ultra-deep wells. This study investigates the rheological behavior of high-temperature and high-pressure oil-based drilling fluid from the Tarim Basin under conditions of 60–160 °C and [...] Read more.
The rheology of high-temperature and high-pressure oil-based drilling fluids is critical for managed pressure drilling in deep and ultra-deep wells. This study investigates the rheological behavior of high-temperature and high-pressure oil-based drilling fluid from the Tarim Basin under conditions of 60–160 °C and 60–140 MPa. Three oil-based drilling fluids with densities of 1.8, 2.0, and 2.2 g/cm3 were tested under 60 temperature–pressure–density conditions, and six rotational speeds were selected for each condition, resulting in 360 rheological data points for model evaluation and parameter prediction. Rheological models, including Bingham, Power law, Casson, and Herschel–Bulkley, were established and evaluated to identify the optimal model. An improved high-temperature and high-pressure rheological parameter prediction model was proposed. Unlike previous correlations mainly developed for Bingham rheological parameters, the proposed model directly predicts the three Herschel–Bulkley parameters and introduces a quadratic pressure term to describe the nonlinear pressure dependence under high-temperature and high-pressure conditions. The results indicate that the Herschel–Bulkley model best characterizes the fluid’s rheological properties, with an average relative error of 2.64% in shear stress prediction and superior regression accuracy compared to Landmark WellPlan software, achieving an average error of 2.049%. Density significantly affects yield stress and consistency coefficient, while temperature and pressure have minimal impact on the flow index. Rheological parameters exhibit opposite trends under varying densities. The improved Herschel–Bulkley model enables precise rheological parameter predictions within the tested range, with average prediction accuracies of 81.40% for yield stress, 97.90% for flow index, and 87.05% for consistency coefficient, meeting engineering requirements. These findings provide theoretical support for managed pressure drilling in deep and ultra-deep wells. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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25 pages, 1544 KB  
Article
Thermal Analysis of the Downstream Spreading of a Planar Power-Law Liquid Jet with Convective Free-Surface Cooling
by Avnish Bhowan Magan
Symmetry 2026, 18(7), 1238; https://doi.org/10.3390/sym18071238 - 22 Jul 2026
Viewed by 303
Abstract
The two-dimensional thermal liquid jet of a non-Newtonian power-law fluid is investigated under shear-rate-dependent thermal diffusivity, resulting in a one-way coupled nonlinear system governing momentum and thermal transport. Two physically distinct free-surface thermal boundary conditions are examined: adiabatic insulation and convective heat loss. [...] Read more.
The two-dimensional thermal liquid jet of a non-Newtonian power-law fluid is investigated under shear-rate-dependent thermal diffusivity, resulting in a one-way coupled nonlinear system governing momentum and thermal transport. Two physically distinct free-surface thermal boundary conditions are examined: adiabatic insulation and convective heat loss. Conservation laws and conserved quantities for the governing system are derived systematically using the multiplier method. By coupling an appropriate conserved vector with an admitted Lie point symmetry, the governing partial differential equations are reduced to a coupled system of ordinary differential equations. Closed-form parametric families of solutions are then obtained for the thermal field. The analysis reveals fundamentally different thermal transport mechanisms across rheological regimes: shear-thinning fluids enhance thermal redistribution and become increasingly sensitive to convective cooling as the Biot number increases, whereas shear-thickening fluids suppress internal thermal transport, promoting greater thermal retention within the jet core and reducing the influence of free-surface cooling. These findings clarify the interplay between rheology, nonlinear thermal diffusion and free-surface cooling and provide new analytical insight into downstream thermal transport in non-Newtonian liquid jets. Full article
(This article belongs to the Section F: Engineering and Materials)
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29 pages, 4896 KB  
Article
Physics-Guided CFD–ML Framework for Sustainable Classical Wire Coating with Power-Law Fluids
by Kriengkrai Nabudda, Pongthep Poungthong, Wirote Ritthong and P. V. Elumalai
Eng 2026, 7(7), 352; https://doi.org/10.3390/eng7070352 - 18 Jul 2026
Viewed by 665
Abstract
This study presents an integrated Computational Fluid Dynamics (CFD) and machine learning framework for analyzing and optimizing classical wire coating processes involving non-Newtonian power-law fluids. A two-dimensional axisymmetric CFD model was developed in ANSYS Fluent 2024R1 to investigate the effects of the power-law [...] Read more.
This study presents an integrated Computational Fluid Dynamics (CFD) and machine learning framework for analyzing and optimizing classical wire coating processes involving non-Newtonian power-law fluids. A two-dimensional axisymmetric CFD model was developed in ANSYS Fluent 2024R1 to investigate the effects of the power-law index (n = 0.3–1.0) on flow, pressure, temperature, and density fields under non-isothermal conditions. A Latin Hypercube Sampling-based Design of Experiments was coupled with surrogate modelling and Sobol sensitivity analysis to evaluate process performance and identify optimal operating conditions. The results showed that velocity distributions were highly dependent on fluid rheology, with shear-thinning fluids producing broader plug-like flow regions and more uniform velocity profiles. In contrast, pressure, temperature, and density fields exhibited limited sensitivity to variations in the power-law index. Optimization indicated that low power-law indices, moderate pressure gradients, and low-to-moderate wire speeds maximize coating thickness while minimizing material loss. Ridge Polynomial Regression achieved excellent predictive accuracy for all response variables (R2 > 0.995). Sensitivity analysis revealed that the initial die gap is the dominant factor governing coating thickness, whereas material loss is influenced by combined effects of die geometry, fluid rheology, and wire speed. The proposed framework provides an efficient tool for process optimization and material conservation in industrial wire coating applications. Full article
(This article belongs to the Section Materials Engineering)
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16 pages, 9746 KB  
Article
Simulation Study on Flow Field and Total Noise Characteristics of Segmented Ducted Fan for Small UAVs
by Xulin Wang and Jianwei Ma
Vehicles 2026, 8(7), 165; https://doi.org/10.3390/vehicles8070165 - 15 Jul 2026
Viewed by 387
Abstract
Small unmanned aerial vehicles (UAVs) are widely used in civil and military fields, and their noise problem has always been the industry’s focus. Compared with a traditional propeller fan, a ducted fan offers higher aerodynamic efficiency, lower aerodynamic noise, and greater safety. It [...] Read more.
Small unmanned aerial vehicles (UAVs) are widely used in civil and military fields, and their noise problem has always been the industry’s focus. Compared with a traditional propeller fan, a ducted fan offers higher aerodynamic efficiency, lower aerodynamic noise, and greater safety. It has become the key power component of small UAVs. However, due to the rigid restriction on tip clearance, the traditional integral ducted fan is prone to generating a tip leakage vortex, which produces high-intensity aerodynamic noise and significantly reduces propulsion efficiency. To address the above key problem restricting the quiet flight of small UAVs, this paper designs a segmented ducted fan (SDF). It preliminarily explores the influence of the segmented clearance on the fan’s flow field structure and acoustic radiation characteristics. Specifically, the k-ω SST (shear stress transport) turbulence model and the broadband noise source model were used to establish a computational fluid dynamics model, and the effects of fan speed (20,000–40,000 rpm) and duct spacing (0–20 mm) on its aeroacoustic characteristics were systematically studied. The results showed that the SDF’s acoustic power level maximum (APLmax) was significantly higher than that of the traditional integral structure, especially at high speed. At 40,000 rpm, increasing the duct spacing to 20 mm resulted in a sudden increase in APLmax to 194.5 dB, 61.3 dB higher than that of the integral type. Its essence was derived from the three-stage chain amplification mechanism: (1) strong tip leakage vortex induced by geometric clearance; (2) broadband noise caused by vortex impacting the duct wall; (3) resonant coupling of leakage vortex harmonic frequency and duct cavity standing wave. Based on this, a collaborative noise reduction path was proposed: compressing the spacing to ≤10 mm to suppress the intensity of leakage vortex, designing the periodicity of failure vortex combined with the serrated blade tip/inner wall rubber strip, and blocking the acoustic cavity resonance with non-uniform wall stiffness or 8–10 kHz Helmholtz resonator, providing a solution for the low-noise design of UAV propulsion system. Unfortunately, our study cannot currently resolve transient characteristics; only time-averaged velocity/pressure flow-field contours and total acoustic power distribution are obtained for qualitative analysis of macroscopic noise variation laws and flow-sound correlation. Full article
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27 pages, 11113 KB  
Article
Numerical Simulation and Field Testing of Coal Seam Drilling Hole Gas Discharge Characteristics Based on Fluid–Solid Interaction
by Chong Liu, Junfeng Wang, Zhifan Lu, Zhiyu Dong, Kaiwen Ren and Yu Bai
Processes 2026, 14(13), 2212; https://doi.org/10.3390/pr14132212 - 7 Jul 2026
Viewed by 396
Abstract
The effectiveness of gas discharge depends on the geological conditions and drilling parameters. Investigating gas seepage behavior near boreholes under fluid–solid coupling conditions can provide theoretical support for scientifically determining the effective discharge radius (EDR) and ensuring mining safety. In this study, taking [...] Read more.
The effectiveness of gas discharge depends on the geological conditions and drilling parameters. Investigating gas seepage behavior near boreholes under fluid–solid coupling conditions can provide theoretical support for scientifically determining the effective discharge radius (EDR) and ensuring mining safety. In this study, taking Xinyuan Coal Mine as the engineering background, a fluid–solid coupled model describing gas migration was developed. The effects of the discharge duration, borehole diameter, permeability, and borehole layout on the spatiotemporal evolution of gas around boreholes and EDR were investigated. The results indicate that gas pressure around the borehole continuously decreases with time, and the affected zone expands elliptically. The EDR exhibits a power-law relationship with time. Increasing the borehole diameter enlarges the EDR, with the effect being particularly significant in the initial stage of gas discharge. After 5 h of gas discharge, the EDR in high-permeability coal seams is approximately twice that in low-permeability coal seams. Compared to the triple-flower patterns, the square pattern produces a larger EDR at the same time. The EDR calculated based on the measured values of the drill cuttings volume S value and drill cuttings desorption gas volume K1 value shows a high degree of consistency with the simulation results. After 5 h of gas discharge using the square pattern, the gas volume fraction at the upper corner of the working face dropped to the safe level of 6%, enabling mining to resume. Full article
(This article belongs to the Topic Advances in Coal Mine Disaster Prevention Technology)
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18 pages, 383 KB  
Article
Viscous Current Induced by Kelvin Force in Ordinary Fluids with Magnetic Susceptibility Contrasts
by Mutabe Aljaghtham, Kannan Premnath and Radi A. Alsulami
Mathematics 2026, 14(13), 2426; https://doi.org/10.3390/math14132426 - 6 Jul 2026
Viewed by 325
Abstract
The magnetic susceptibilities of various electrically insulating ordinary fluids depend on their local states, such as their density and temperature. When such fluids, which can be characterized as either paramagnetic or diamagnetic and occur commonly in nature, are subjected to magnetic field gradients, [...] Read more.
The magnetic susceptibilities of various electrically insulating ordinary fluids depend on their local states, such as their density and temperature. When such fluids, which can be characterized as either paramagnetic or diamagnetic and occur commonly in nature, are subjected to magnetic field gradients, it induces an effective body force—the Kelvin force. This force, which depends on the susceptibility and the gradient of the square of the magnetic field strength, can become one of the effective mechanisms for modulating the flow and transport, particularly where terrestrial gravity becomes negligible, such as in free space or under microgravity conditions. For the first time, we developed a theoretical model demonstrating that a viscous current can be generated due to the contrasts between the magnetic susceptibilities of the intruding and ambient fluids in the presence of gradients in magnetic fields, analogous to the viscous gravity current in terrestrial situations. We derived similarity solutions for the two-dimensional and axisymmetric currents arising from a balance between the Kelvin buoyancy and viscous forces with a prescribed power law for the magnetic field strength. These determine the shape and various spreading relationships of the viscous current. For a prescribed time variation in the source flux, it is shown that a family of scaling laws exists for the spreading rate and the thickness of the current, which depend on the steepness of the magnetic field gradient. Unlike gravity, since the driving horizontal buoyancy arising from the Kelvin force is externally specified, it potentially offers a mechanism to control the characteristic shape and the rate of motion of the viscous current. Full article
(This article belongs to the Special Issue Mathematical Fluid Dynamics: Theory, Analysis and Emerging Trends)
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38 pages, 3680 KB  
Article
A Multi-Scale Dynamical Model for Extreme Atmospheric Events: Coupling Navier–Stokes Transport with Multiplicative Chaos Cascades
by Manuel L. Esquível and Nadezhda P. Krasii
Axioms 2026, 15(7), 494; https://doi.org/10.3390/axioms15070494 - 1 Jul 2026
Viewed by 359
Abstract
We developed a multi-scale stochastic model for atmospheric events capable of generating extreme precipitation leading to flooding. The framework combines a deterministic continuum-mechanical backbone based on an augmented Navier–Stokes system with a probabilistic multiplicative cascade representing unresolved sub-grid intermittency. The cascade is conditioned [...] Read more.
We developed a multi-scale stochastic model for atmospheric events capable of generating extreme precipitation leading to flooding. The framework combines a deterministic continuum-mechanical backbone based on an augmented Navier–Stokes system with a probabilistic multiplicative cascade representing unresolved sub-grid intermittency. The cascade is conditioned dynamically through optimal transport constraints and shown to approximate a stochastic continuity equation in measure space. Extreme rainfall statistics were derived using Gaussian multiplicative chaos theory, yielding power-law tail behaviour governed by a physically parametrised intermittency coefficient. The model provides a principled bridge between fluid mechanics, stochastic geometry, and statistical risk estimation. Full article
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27 pages, 583 KB  
Article
Nonlinear Convection of a Power-Law Fluid-Saturated Reactive Porous Layer
by Gundlapally Shiva Kumar Reddy, S. Suresh Kumar Raju, Hasan Mulki and Basma Souayeh
Axioms 2026, 15(7), 487; https://doi.org/10.3390/axioms15070487 - 29 Jun 2026
Cited by 1 | Viewed by 337
Abstract
The present study examines the thermal stability characteristics of a power-law fluid confined within a porous layer under the influence of a chemical reaction. In the linear regime, the Galerkin technique is utilized to obtain closed-form solutions for the Rayleigh number associated with [...] Read more.
The present study examines the thermal stability characteristics of a power-law fluid confined within a porous layer under the influence of a chemical reaction. In the linear regime, the Galerkin technique is utilized to obtain closed-form solutions for the Rayleigh number associated with both stationary and oscillatory instability modes. The validity of the principle of exchange of stabilities is confirmed, demonstrating that convection sets in solely through stationary disturbances. Furthermore, to investigate the mechanisms of heat and mass transfer, the Landau equation is derived. The results indicate that the Damkohler, Lewis, and Peclet numbers contribute to an enhancement of heat and mass transport, whereas the solutal Rayleigh number tends to suppress these transport processes. Full article
(This article belongs to the Special Issue Recent Progress in Computational Fluid Dynamics)
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