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Keywords = turbulent diffusion

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25 pages, 8138 KB  
Article
Design Methodology for Fishtailed Pipe Diffusers and Its Application to a High-Pressure Ratio Centrifugal Compressor
by Junnan Liu, Dingxi Wang and Xiuquan Huang
Aerospace 2025, 12(8), 746; https://doi.org/10.3390/aerospace12080746 - 21 Aug 2025
Viewed by 123
Abstract
A high-performance diffuser is crucial for a high-pressure ratio centrifugal compressor to achieve high efficiency. Pipe diffusers have been proven effective in enhancing the performance of such compressors. However, detailed design methodologies for pipe diffusers are scarcely covered in the existing literature. Thus, [...] Read more.
A high-performance diffuser is crucial for a high-pressure ratio centrifugal compressor to achieve high efficiency. Pipe diffusers have been proven effective in enhancing the performance of such compressors. However, detailed design methodologies for pipe diffusers are scarcely covered in the existing literature. Thus, this paper provides a comprehensive design methodology specifically for fishtailed pipe diffusers. This methodology begins by defining the throat and outlet areas using gas-dynamic functions and then establishes the centerline by choosing the angle distributions. Finally, various cross-sectional profiles are defined along the centerline, completing the diffuser’s design. To demonstrate the proposed methodology, a fishtailed pipe diffuser is designed to contrast with the original diffuser of the National Aeronautics and Space Administration’s High-Efficiency Centrifugal Compressor (NASA HECC). Numerical analysis shows that the fishtailed pipe diffuser increases the compressor’s total pressure ratio and isentropic efficiency over its whole operating range. At the design operating point, the isentropic efficiency and the total pressure ratio are increased by 2.4 percentage points and 2.7%, respectively. This demonstrates the effectiveness of the proposed design methodology for fishtailed pipe diffusers. Full article
(This article belongs to the Special Issue Progress in Turbomachinery Technology for Propulsion (2nd Edition))
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22 pages, 10891 KB  
Article
DNS Study of Freely Propagating Turbulent Lean-Premixed Flames with Low-Temperature Chemistry in the Broken Reaction Zone Regime
by Yi Zhang, Yinhu Kang, Xiaomei Huang, Pengyuan Zhang and Xiaolin Tang
Energies 2025, 18(16), 4357; https://doi.org/10.3390/en18164357 - 15 Aug 2025
Viewed by 295
Abstract
The novel engines nowadays with high efficiency are operated under the superpressure, supercritical, and supersonic extreme conditions that are situated in the broken reaction zone regime. In this article, the propagation and heat/radical diffusion physics of a high-pressure dimethyl ether (DME)/air turbulent lean-premixed [...] Read more.
The novel engines nowadays with high efficiency are operated under the superpressure, supercritical, and supersonic extreme conditions that are situated in the broken reaction zone regime. In this article, the propagation and heat/radical diffusion physics of a high-pressure dimethyl ether (DME)/air turbulent lean-premixed flame are investigated numerically by direct numerical simulation (DNS). A wide range of statistical and diagnostic methods, including Lagrangian fluid tracking, Joint Probability Density Distribution (JPDF), and chemical explosive mode analysis (CEMA), are applied to reveal the local combustion modes and dynamics evolution, as well as the roles of heat/mass transport and cool/hot flame interaction in the turbulent combustion, which would be beneficial to the design of novel engines with high performances. It is found that the three-staged combustion, including cool-flame, warm-flame, and hot-flame fronts, is a unique behavior of DME flame under the elevated-pressure, lean-premixed condition. In the broken reaction zone regime, the reaction zone thickness increases remarkably, and the heat release rate (HRR) and fuel consumption rate in the cool-flame zone are increased by 16% and 19%, respectively. The diffusion effect not only enhances flame propagation, but also suppresses the local HRR or fuel consumption. The strong turbulence interplaying with diffusive transports is the underlying physics for the enhancements in cool- and hot-flame fronts. The dominating diffusive sub-processes are revealed by the aid of the diffusion index. Full article
(This article belongs to the Section I2: Energy and Combustion Science)
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19 pages, 17392 KB  
Article
Reducing Gas Accumulation in Horizontal Diffusers Under Two-Phase Flow Using Upstream Cross-Flow Steps
by Michael Mansour, Nicola Zanini, Mena Shenouda, Michele Pinelli, Alessio Suman and Dominique Thévenin
Int. J. Turbomach. Propuls. Power 2025, 10(3), 20; https://doi.org/10.3390/ijtpp10030020 - 7 Aug 2025
Viewed by 206
Abstract
In gas–liquid two-phase flows, diverging channels such as diffusers often develop low-pressure separation zones where gas can accumulate, hindering pressure recovery and reducing system performance. This issue is particularly critical in centrifugal pumps, where it leads to efficiency losses. Unlike pumps, diffusers without [...] Read more.
In gas–liquid two-phase flows, diverging channels such as diffusers often develop low-pressure separation zones where gas can accumulate, hindering pressure recovery and reducing system performance. This issue is particularly critical in centrifugal pumps, where it leads to efficiency losses. Unlike pumps, diffusers without rotating components allow for more precise experimental studies. This research investigates a passive control method using upstream cross-flow steps to reduce gas accumulation in a horizontal diverging channel. Thin metallic sheets with toothed geometries of 2 mm, 5 mm, and 8 mm heights were installed upstream to interact with the flow. These features aim to enhance turbulence, break up larger gas pockets, and promote vertical bubble dispersion, all while minimizing additional flow separation. The diffuser was intentionally designed with an expanding angle to encourage flow separation and gas accumulation. The experiments covered various two-phase flow conditions (liquid Reynolds number 59,530–78,330; gas Reynolds number 3–9.25), and high-speed imaging captured detailed phase interactions. The results show that the steps significantly reduce gas accumulation, especially at higher water flow rates. These findings support the development of more accurate computational models and offer insights for optimizing centrifugal pump designs by minimizing gas buildup in separated flow regions. Full article
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30 pages, 8037 KB  
Review
A Review of Multiscale Interaction Mechanisms of Wind–Leaf–Droplet Systems in Orchard Spraying
by Yunfei Wang, Zhenlei Zhang, Ruohan Shi, Shiqun Dai, Weidong Jia, Mingxiong Ou, Xiang Dong and Mingde Yan
Sensors 2025, 25(15), 4729; https://doi.org/10.3390/s25154729 - 31 Jul 2025
Viewed by 363
Abstract
The multiscale interactive system composed of wind, leaves, and droplets serves as a critical dynamic unit in precision orchard spraying. Its coupling mechanisms fundamentally influence pesticide transport pathways, deposition patterns, and drift behavior within crop canopies, forming the foundational basis for achieving intelligent [...] Read more.
The multiscale interactive system composed of wind, leaves, and droplets serves as a critical dynamic unit in precision orchard spraying. Its coupling mechanisms fundamentally influence pesticide transport pathways, deposition patterns, and drift behavior within crop canopies, forming the foundational basis for achieving intelligent and site-specific spraying operations. This review systematically examines the synergistic dynamics across three hierarchical scales: Droplet–leaf surface wetting and adhesion at the microscale; leaf cluster motion responses at the mesoscale; and the modulation of airflow and spray plume diffusion by canopy architecture at the macroscale. Key variables affecting spray performance—such as wind speed and turbulence structure, leaf biomechanical properties, droplet size and electrostatic characteristics, and spatial canopy heterogeneity—are identified and analyzed. Furthermore, current advances in multiscale modeling approaches and their corresponding experimental validation techniques are critically evaluated, along with their practical boundaries of applicability. Results indicate that while substantial progress has been made at individual scales, significant bottlenecks remain in the integration of cross-scale models, real-time acquisition of critical parameters, and the establishment of high-fidelity experimental platforms. Future research should prioritize the development of unified coupling frameworks, the integration of physics-based and data-driven modeling strategies, and the deployment of multimodal sensing technologies for real-time intelligent spray decision-making. These efforts are expected to provide both theoretical foundations and technological support for advancing precision and intelligent orchard spraying systems. Full article
(This article belongs to the Special Issue Application of Sensors Technologies in Agricultural Engineering)
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21 pages, 6272 KB  
Article
Numerical Study of Gas Dynamics and Condensate Removal in Energy-Efficient Recirculation Modes in Train Cabins
by Ivan Panfilov, Alexey N. Beskopylny, Besarion Meskhi and Sergei F. Podust
Fluids 2025, 10(8), 197; https://doi.org/10.3390/fluids10080197 - 29 Jul 2025
Viewed by 243
Abstract
Maintaining the required relative humidity values in the vehicle cabin is an important HVAC task, along with considerations related to the temperature, velocity, air pressure and noise. Deviation from the optimal values worsens the psycho-physiological state of the driver and affects the energy [...] Read more.
Maintaining the required relative humidity values in the vehicle cabin is an important HVAC task, along with considerations related to the temperature, velocity, air pressure and noise. Deviation from the optimal values worsens the psycho-physiological state of the driver and affects the energy efficiency of the train. In this study, a model of liquid film formation on and removal from various cabin surfaces was constructed using the fundamental Navier–Stokes hydrodynamic equations. A special transport model based on the liquid vapor diffusion equation was used to simulate the air environment inside the cabin. The evaporation and condensation of surface films were simulated using the Euler film model, which directly considers liquid–gas and gas–liquid transitions. Numerical results were obtained using the RANS equations and a turbulence model by means of the finite volume method in Ansys CFD. Conjugate fields of temperature, velocity and moisture concentration were constructed for various time intervals, and the dependence values for the film thicknesses on various surfaces relative to time were determined. The verification was conducted in comparison with the experimental data, based on the protocol for measuring the microclimate indicators in workplaces, as applied to the train cabin: the average ranges encompassed temperature changes from 11% to 18%, and relative humidity ranges from 16% to 26%. Comparison with the results of other studies, without considering the phase transition and condensation, shows that, for the warm mode, the average air temperature in the cabin with condensation is 12.5% lower than without condensation, which is related to the process of liquid evaporation from the heated walls. The difference in temperature values for the model with and without condensation ranged from −12.5% to +4.9%. We demonstrate that, with an effective mode of removing condensate film from the window surface, including recirculation modes, the energy consumption of the climate control system improves significantly, but this requires a more accurate consideration of thermodynamic parameters and relative humidity. Thus, considering the moisture condensation model reveals that this variable can significantly affect other parameters of the microclimate in cabins: in particular, the temperature. This means that it should be considered in the numerical modeling, along with the basic heat transfer equations. Full article
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20 pages, 8538 KB  
Article
Compressor Diffuser Design Impact on a Microjet Working Line—An Experimental and Numerical Case Study
by Valeriu Drăgan, Bogdan Gherman, Oana Dumitrescu, Cornel Mihai Tărăbîc and Cristian Olariu
Aerospace 2025, 12(8), 667; https://doi.org/10.3390/aerospace12080667 - 26 Jul 2025
Viewed by 334
Abstract
This study examines the performance of two diffuser configurations—a trumpet-shaped and a semi-diagonal design—for application in micro gas turbine engines, aiming to assess their suitability in terms of efficiency and operational flexibility. Both diffusers were initially evaluated using steady-state CFD simulations with the [...] Read more.
This study examines the performance of two diffuser configurations—a trumpet-shaped and a semi-diagonal design—for application in micro gas turbine engines, aiming to assess their suitability in terms of efficiency and operational flexibility. Both diffusers were initially evaluated using steady-state CFD simulations with the k-omega SST turbulence model, followed by experimental testing on an actual engine across the start-up sequence from idle to 70% of nominal speed. Performance was mapped over four constant-speed lines for each configuration. Results showed that the trumpet-shaped diffuser offered a greater choke margin but suffered from increased aerodynamic losses, whereas the semi-diagonal diffuser demonstrated higher efficiency but required closer alignment with the target operating point. The k-omega SST model showed strong predictive accuracy, with 5.13% agreement across all instrumented parameters for all investigated speed lines. These findings suggest that while the trumpet diffuser provides better stability, the semi-diagonal design is more efficient when properly targeted. Future work will focus on extending the analysis to higher speed ranges and transient regimes using harmonic balance CFD methods and enhanced data acquisition techniques. Full article
(This article belongs to the Section Aeronautics)
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16 pages, 2159 KB  
Article
A New Depth-Averaged Eulerian SPH Model for Passive Pollutant Transport in Open Channel Flows
by Kao-Hua Chang, Kai-Hsin Shih and Yung-Chieh Wang
Water 2025, 17(15), 2205; https://doi.org/10.3390/w17152205 - 24 Jul 2025
Cited by 1 | Viewed by 358
Abstract
Various nature-based solutions (NbS)—such as constructed wetlands, drainage ditches, and vegetated buffer strips—have recently demonstrated strong potential for mitigating pollutant transport in open channels and river systems. Numerical modeling is a widely adopted and effective approach for assessing the performance of these interventions. [...] Read more.
Various nature-based solutions (NbS)—such as constructed wetlands, drainage ditches, and vegetated buffer strips—have recently demonstrated strong potential for mitigating pollutant transport in open channels and river systems. Numerical modeling is a widely adopted and effective approach for assessing the performance of these interventions. This study presents the first development of a two-dimensional (2D) meshless advection–diffusion model based on an Eulerian smoothed particle hydrodynamics (SPH) framework, specifically designed to simulate passive pollutant transport in open channel flows. The proposed model marks a pioneering application of the ESPH technique to environmental pollutant transport problems. It couples the 2D depth-averaged shallow water equations with an advection–diffusion equation to represent both fluid motion and pollutant concentration dynamics. A uniform particle arrangement ensures that each fluid particle interacts symmetrically with eight neighboring particles for flux computation. To represent the pollutant transport process, the dispersion coefficient is defined as the sum of molecular and turbulent diffusion components. The turbulent diffusion coefficient is calculated using a prescribed turbulent Schmidt number and the eddy viscosity obtained from a Smagorinsky-type mixing-length turbulence model. Three analytical case studies, including one-dimensional transcritical open channel flow, 2D isotropic and anisotropic diffusion in still water, and advection–diffusion in a 2D uniform flow, are employed to verify the model’s accuracy and convergence. The model demonstrates first-order convergence, with relative root mean square errors (RRMSEs) of approximately 0.2% for water depth and velocity, and 0.1–0.5% for concentration. Additionally, the model is applied to a laboratory experiment involving 2D pollutant dispersion in a 90° junction channel. The simulated results show good agreement with measured velocity and concentration distributions. These findings indicate that the developed model is a reliable and effective tool for evaluating the performance of NbS in mitigating pollutant transport in open channels and river systems. Full article
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19 pages, 5629 KB  
Article
A Numerical Investigation of the Flame Characteristics of a CH4/NH3 Blend Under Different Swirl Intensity and Diffusion Models
by Ahmed Adam, Ayman Elbaz, Reo Kai and Hiroaki Watanabe
Energies 2025, 18(15), 3921; https://doi.org/10.3390/en18153921 - 23 Jul 2025
Viewed by 251
Abstract
This study investigates the effects of diffusion modeling and swirl intensity on flow fields and NO emissions in CH4/NH3 non-premixed swirling flames using large eddy simulations (LESs). Simulations are performed for a 50/50 ammonia–methane blend at three global equivalence ratios [...] Read more.
This study investigates the effects of diffusion modeling and swirl intensity on flow fields and NO emissions in CH4/NH3 non-premixed swirling flames using large eddy simulations (LESs). Simulations are performed for a 50/50 ammonia–methane blend at three global equivalence ratios of 0.77, 0.54, and 0.46 and two swirl numbers of 8 and 12, comparing the unity Lewis number (ULN) and mixture-averaged diffusion (MAD) models against the experimental data includes OH-PLIF and ON-PLIF reported in a prior study by the KAUST group. Both models produce similar flow fields, but the MAD model alters the flame structure and species distributions due to differential diffusion (DD) and limitations in its Flamelet library. Notably, the MAD library lacks unstable flame branch solutions, leading to extensive interpolation between extinction and stable branches. This results in overpredicted progress variable source terms and reactive scalars, both within and beyond the flame zone. The ULN model better reproduces experimental OH profiles and localizes NO formation near the flame front, whereas the MAD model predicts broader NO distributions due to nitrogen species diffusion. Higher swirl intensities shorten the flame and shift NO production upstream. While a low equivalence ratio provides enough air for good mixing, lower ammonia and higher NO contents in exhaust gases, respectively. Full article
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26 pages, 7439 KB  
Review
A Review of Marine Dual-Fuel Engine New Combustion Technology: Turbulent Jet-Controlled Premixed-Diffusion Multi-Mode Combustion
by Jianlin Cao, Zebang Liu, Hao Shi, Dongsheng Dong, Shuping Kang and Lingxu Bu
Energies 2025, 18(15), 3903; https://doi.org/10.3390/en18153903 - 22 Jul 2025
Viewed by 540
Abstract
Driven by stringent emission regulations, advanced combustion modes utilizing turbulent jet ignition technology are pivotal for enhancing the performance of marine low-speed natural gas dual-fuel engines. This review focuses on three novel combustion modes, yielding key conclusions: (1) Compared to the conventional DJCDC [...] Read more.
Driven by stringent emission regulations, advanced combustion modes utilizing turbulent jet ignition technology are pivotal for enhancing the performance of marine low-speed natural gas dual-fuel engines. This review focuses on three novel combustion modes, yielding key conclusions: (1) Compared to the conventional DJCDC mode, the TJCDC mode exhibits a significantly higher swirl ratio and turbulence kinetic energy in the main chamber during initial combustion. This promotes natural gas jet development and combustion acceleration, leading to shorter ignition delay, reduced combustion duration, and a combustion center (CA50) positioned closer to the Top Dead Center (TDC), alongside higher peak cylinder pressure and a faster early heat release rate. Energetically, while TJCDC incurs higher heat transfer losses, it benefits from lower exhaust energy and irreversible exergy loss, indicating greater potential for useful work extraction, albeit with slightly higher indicated specific NOx emissions. (2) In the high-compression ratio TJCPC mode, the Liquid Pressurized Natural Gas (LPNG) injection parameters critically impact performance. Delaying the start of injection (SOI) or extending the injection duration degrades premixing uniformity and increases unburned methane (CH4) slip, with the duration effects showing a load dependency. Optimizing both the injection timing and duration is, therefore, essential for emission control. (3) Increasing the excess air ratio delays the combustion phasing in TJCPC (longer ignition delay, extended combustion duration, and retarded CA50). However, this shift positions the heat release more optimally relative to the TDC, resulting in significantly improved indicated thermal efficiency. This work provides a theoretical foundation for optimizing high-efficiency, low-emission combustion strategies in marine dual-fuel engines. Full article
(This article belongs to the Special Issue Towards Cleaner and More Efficient Combustion)
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23 pages, 9064 KB  
Article
A Computational Thermo-Fluid Dynamics Simulation of Slot Jet Impingement Using a Generalized Two-Equation Turbulence Model
by Antonio Mezzacapo, Rossella D’Addio and Giuliano De Stefano
Energies 2025, 18(14), 3862; https://doi.org/10.3390/en18143862 - 20 Jul 2025
Viewed by 1354
Abstract
In this study, a computational thermo-fluid dynamics simulation of a wide-slot jet impingement heating process is performed. The present configuration consists of a turbulent incompressible air jet impinging orthogonally on an isothermal cold plate at a Reynolds number of around 11,000. The two-dimensional [...] Read more.
In this study, a computational thermo-fluid dynamics simulation of a wide-slot jet impingement heating process is performed. The present configuration consists of a turbulent incompressible air jet impinging orthogonally on an isothermal cold plate at a Reynolds number of around 11,000. The two-dimensional mean turbulent flow field is numerically predicted by solving Reynolds-averaged Navier–Stokes (RANS) equations, where the two-equation eddy viscosity k-ω model is utilized for turbulence closure. As the commonly used shear stress transport variant overpredicts heat transfer at the plate due to excessive turbulent diffusion, the recently developed generalized k-ω (GEKO) model is considered for the present analysis, where the primary model coefficients are suitably tuned. Through a comparative analysis of the various solutions against one another, in addition to reference experimental and numerical data, the effectiveness of the generalized procedure in predicting both the jet flow characteristics and the heat transfer at the plate is thoroughly evaluated, while determining the optimal set of model parameters. By improving accuracy within the RANS framework, the importance of model adaptability and parameter tuning for this specific fluid engineering application is demonstrated. This study offers valuable insights for improving predictive capability in turbulent jet simulations with broad engineering implications, particularly for industrial heating or cooling systems relying on wide-slot jet impingement. Full article
(This article belongs to the Special Issue Computational Fluids Dynamics in Energy Conversion and Heat Transfer)
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14 pages, 4131 KB  
Article
An Experimental and Modelling Study on the Effect of Vegetation-Influenced Water Velocity on Cadmium Accumulation in Corbicula fluminea
by Nan Geng, Guojin Sun, Lin Zhang and Hui Wang
Sustainability 2025, 17(14), 6570; https://doi.org/10.3390/su17146570 - 18 Jul 2025
Viewed by 293
Abstract
Cadmium (Cd) accumulation by benthic organisms poses a significant threat to aquatic environmental safety. Both vegetation and water velocity in rivers could influence this process, yet their coupled interaction mechanisms remain unclear. This study used laboratory flume experiments to simulate four scenarios: static [...] Read more.
Cadmium (Cd) accumulation by benthic organisms poses a significant threat to aquatic environmental safety. Both vegetation and water velocity in rivers could influence this process, yet their coupled interaction mechanisms remain unclear. This study used laboratory flume experiments to simulate four scenarios: static water (C0), pure water velocity (C+H), vegetation-water velocity (V+H), and coexistence of vegetation-water velocity-Corbicula fluminea (C. fluminea) (C+V+H). The dynamics of Cd release from sediment to overlying water and its bioaccumulation within C. fluminea were investigated. A mathematical model coupling Cd release, diffusion, and C. fluminea bioaccumulation was developed based on the lattice Boltzmann method (LBM). The results showed that compared to the non-vegetation group (C+H), the presence of vegetation (V+H, C+V+H) initially reduced sediment resuspension and Cd release. However, the turbulence induced by vegetation significantly increased the Cd diffusion coefficient and equilibrium concentration in the water. Consequently, Cd accumulation in C. fluminea within the vegetation-water velocity group (C+V+H) was significantly higher than in the pure water velocity group (C+H). The established LBM model exhibited good simulation accuracy (for overlying water Cd concentration: R2 = 0.8201–0.942; for C. fluminea Cd concentration: R2 = 0.7604–0.8191) and successfully reproduced the processes of Cd release and bioaccumulation under varying vegetation-water velocity conditions. This study elucidates the mechanism by which vegetation promotes Cd accumulation in C. fluminea by altering water velocity structure and diffusion characteristics, providing crucial theoretical parameters for multi-media migration and transformation models of heavy metals in complex water velocity environments and for early warning systems concerning Cd accumulation risks in riverine organisms. Full article
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10 pages, 332 KB  
Article
An Empirical Theoretical Model for the Turbulent Diffusion Coefficient in Urban Atmospheric Dispersion
by George Efthimiou
Urban Sci. 2025, 9(7), 281; https://doi.org/10.3390/urbansci9070281 - 18 Jul 2025
Viewed by 834
Abstract
Turbulent diffusion plays a critical role in atmospheric pollutant dispersion, particularly in complex environments such as urban areas. This study proposes a novel theoretical approach to enhance the calculation of the turbulent diffusion coefficient in pollutant dispersion models. We propose a new expression [...] Read more.
Turbulent diffusion plays a critical role in atmospheric pollutant dispersion, particularly in complex environments such as urban areas. This study proposes a novel theoretical approach to enhance the calculation of the turbulent diffusion coefficient in pollutant dispersion models. We propose a new expression for the turbulent diffusion coefficient (KC), which incorporates both hydrodynamic and turbulence-related time scales. This formulation links the turbulent diffusion coefficient to pollutant travel time and turbulence intensity, offering more accurate predictions of pollutant concentration distributions. By addressing the limitations of existing empirical models, this approach improves the parameterization of turbulence and reduces uncertainties in predicting maximum individual exposure under various atmospheric conditions. The study presents a theoretical model designed to advance the current understanding of atmospheric dispersion modeling. Experimental validation, while recommended, is beyond the scope of this work and is suggested as a direction for future empirical research to confirm the practical utility of the model. This theoretical formulation could be integrated into urban air quality management frameworks, providing improved estimations of pollutant peaks in complex environments. Full article
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32 pages, 735 KB  
Article
Dynamic Balance: A Thermodynamic Principle for the Emergence of the Golden Ratio in Open Non-Equilibrium Steady States
by Alejandro Ruiz
Entropy 2025, 27(7), 745; https://doi.org/10.3390/e27070745 - 11 Jul 2025
Viewed by 686
Abstract
We develop a symmetry-based variational theory that shows the coarse-grained balance of work inflow to heat outflow in a driven, dissipative system relaxed to the golden ratio. Two order-2 Möbius transformations—a self-dual flip and a self-similar shift—generate a discrete non-abelian subgroup of [...] Read more.
We develop a symmetry-based variational theory that shows the coarse-grained balance of work inflow to heat outflow in a driven, dissipative system relaxed to the golden ratio. Two order-2 Möbius transformations—a self-dual flip and a self-similar shift—generate a discrete non-abelian subgroup of PGL(2,Q(5)). Requiring any smooth, strictly convex Lyapunov functional to be invariant under both maps enforces a single non-equilibrium fixed point: the golden mean. We confirm this result by (i) a gradient-flow partial-differential equation, (ii) a birth–death Markov chain whose continuum limit is Fokker–Planck, (iii) a Martin–Siggia–Rose field theory, and (iv) exact Ward identities that protect the fixed point against noise. Microscopic kinetics merely set the approach rate; three parameter-free invariants emerge: a 62%:38% split between entropy production and useful power, an RG-invariant diffusion coefficient linking relaxation time and correlation length Dα=ξz/τ, and a ϑ=45 eigen-angle that maps to the golden logarithmic spiral. The same dual symmetry underlies scaling laws in rotating turbulence, plant phyllotaxis, cortical avalanches, quantum critical metals, and even de-Sitter cosmology, providing a falsifiable, unifying principle for pattern formation far from equilibrium. Full article
(This article belongs to the Section Entropy and Biology)
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12 pages, 9217 KB  
Article
Nonlinearity in Turbulent Diffusion as a Possible Cause of Stellar Flares
by Elena Popova
Astronomy 2025, 4(3), 12; https://doi.org/10.3390/astronomy4030012 - 7 Jul 2025
Viewed by 298
Abstract
Extremely powerful flares releasing energy well above 1032 erg are rare compared to the typical manifestations of solar activity, which are already being routinely monitored by the existing Space Weather network—with some level of predictability. However, much less is known about the [...] Read more.
Extremely powerful flares releasing energy well above 1032 erg are rare compared to the typical manifestations of solar activity, which are already being routinely monitored by the existing Space Weather network—with some level of predictability. However, much less is known about the mechanisms behind such rare events (like the well-documented Carrington event of 1859) or about hypothetical superflares that could exceed current energy estimates by several orders of magnitude. We propose a model based on the nonlinear suppression of turbulent diffusion with increasing magnetic field, which ultimately leads to the random occurrence of regions with a magnetic field amplitude significantly exceeding the magnetic field amplitude in a regular cycle. This is similar to the mechanism of a local “explosion of an overheated boiler”. Such regions can be correlated with flares. In our model, flares have different powers. Full article
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32 pages, 3446 KB  
Article
Finite Element Method for Time-Fractional Navier–Stokes Equations with Nonlinear Damping
by Shahid Hussain, Xinlong Feng, Arafat Hussain and Ahmed Bakhet
Fractal Fract. 2025, 9(7), 445; https://doi.org/10.3390/fractalfract9070445 - 4 Jul 2025
Viewed by 562
Abstract
We propose a hybrid numerical framework for solving time-fractional Navier–Stokes equations with nonlinear damping. The method combines the finite difference L1 scheme for time discretization of the Caputo derivative (0<α<1) with mixed finite element methods (P1b–P1 and [...] Read more.
We propose a hybrid numerical framework for solving time-fractional Navier–Stokes equations with nonlinear damping. The method combines the finite difference L1 scheme for time discretization of the Caputo derivative (0<α<1) with mixed finite element methods (P1b–P1 and P2P1) for spatial discretization of velocity and pressure. This approach addresses the key challenges of fractional models, including nonlocality and memory effects, while maintaining stability in the presence of the nonlinear damping term γ|u|r2u, for r2. We prove unconditional stability for both semi-discrete and fully discrete schemes and derive optimal error estimates for the velocity and pressure components. Numerical experiments validate the theoretical results. Convergence tests using exact solutions, along with benchmark problems such as backward-facing channel flow and lid-driven cavity flow, confirm the accuracy and reliability of the method. The computed velocity contours and streamlines show close agreement with analytical expectations. This scheme is particularly effective for capturing anomalous diffusion in Newtonian and turbulent flows, and it offers a strong foundation for future extensions to viscoelastic and biological fluid models. Full article
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