Search Results (318)

Constructed wetlands (CWs) are widely used as an ecological technology for wastewater treatment. However, the accumulation of microplastics (MPs) in their substrates may impair long-term performance and threaten the operational sustainability of these nature-based treatment systems. To elucidate the transport behaviour of MPs in wetland substrates, this study developed a numerical model based on the lattice Boltzmann method (LBM) to simulate advection, hydrodynamic dispersion, and reversible first-order adsorption/desorption of MPs in saturated porous media. The model incorporates a salinity-dependent non-linear attachment rate coefficient, which captures the compression of the electrical double layer and the enhanced attachment efficiency with increasing salinity. Pore-scale flow is solved using the LBM with an Ergun-type drag term to represent the resistance of the porous matrix. The model was validated against experimental breakthrough curves from column studies using quartz sand and coastal wetland soils under five salinity levels (0–35 PSU) reported in the literature. Quantitative validation yielded coefficients of determination (R²) ranging from 0.782 to 0.960 (RMSE = 0.024–0.045) for calibration cases and 0.741 to 0.946 (RMSE = 0.027–0.048) for independent validation cases across both substrates, excluding the soil cases at 3.5 and 35 PSU. Here, both observed and simulated effluent concentrations were identically zero, resulting in the statistically forced R² = 1.000 and RMSE = 0, which are mathematical artefacts rather than indicators of predictive performance. The simulations reproduce the observed reduction in peak relative concentration by over 50% in sand and near-complete retention (C/C₀ ≈ 0) in soil at high salinities (3.5 and 35 PSU). Results demonstrate that the model successfully reproduces the differences in MP breakthrough behaviour across different substrate types and salinity levels. By linking salinity-enhanced retention to the risk of irreversible clogging and shortened wetland lifespan, the model provides a predictive tool for evaluating the sustainability of CWs under saline stress. This study offers a scientific basis for optimizing hydraulic management (e.g., flushing strategies) to mitigate microplastic pollution and enhance the long-term sustainability and resilience of constructed wetlands in coastal and saline environments. Full article

This study investigates the low-Reynolds-number rotation of two eccentric spheres within an incompressible fluid that accounts for both micro-rotational effects and the presence of a porous medium. The region between the spheres contains a rigid, stationary skeleton, and we model the resulting flow using the Brinkman-extended Darcy approach. We derive the governing field equations, which account for the resistance to rotation through specific fluid viscosity parameters, while also incorporating surface slip effects on the interior sphere. The system of equations is solved using a semi-analytical boundary collocation method, where the fluid motion is expressed through a series of mathematical expansions satisfied at discrete points along the spherical boundaries. Our numerical results demonstrate that the hydrodynamic torque exerted on the spheres is highly sensitive to the porous environment. Specifically, increasing the permeability of the medium from $0.001$ to $0.5$ results in a substantial torque increase of approximately $210\%$. Additionally, the fluid’s resistance to micro-rotation acts as a torque-enhancing factor, with a variation in viscosity parameters from $0.02$ to $0.45$ inducing a $5.25\%$ increase in torque under conditions of high eccentricity. These findings were validated against established benchmarks for standard fluids in non-porous media, showing excellent agreement. Full article

This study analyzes the combined effects of non-Newtonian rheology and electrostatics on the transient electroosmotic flow of Maxwell fluids in soft channels. The walls of the rigid channels are hydrophobic, ionically charged, and coated with a polyelectrolyte layer (PEL). This design is intended to regulate both the surface electric potential and the flow velocity. The mathematical model is based on modified Poisson–Boltzmann and momentum equations, which are solved numerically using a one-dimensional (1D) approach. The results indicate that high potentials, exceeding the Debye–Hückel limit, are achieved under conditions of thick polyelectrolyte layers, high surface charge density, and a higher concentration of fixed charges compared to the electrolyte ionic concentration. In this regime, steric effects increase the electric potential; however, this potential increase is limited by the formation of a Donnan potential. The hydrodynamic analysis demonstrates that the velocity magnitude is influenced not only by the wall potential but also by the spatial distribution of free charge density and electroosmotic force, which, in turn, are affected by steric effects. Additionally, changing the polarity and concentration of fixed charge in the PEL produces asymmetric flows, and while hydrodynamic slip enhances velocity, the drag parameter reduces it. Finally, the dimensionless parameters that control the time required to dampen the oscillatory flow induced by viscoelastic effects and reach steady-state are mainly the relaxation time, the drag parameter, the PEL thickness, and the electrokinetic parameter of the PEL, while the surface charge density and the external pressure gradient exert a comparatively minor influence. Full article

Small-scale vertical-axis wind turbines (VAWTs) are increasingly essential for the “blue economy,” providing autonomous power to remote coastal communities, offshore platforms, and marine industries. However, the design of efficient Darrieus-type rotors is complicated by complex unsteady aerodynamics, particularly the phenomenon of dynamic stall. This study aims to establish and validate a cost-effective yet accurate mathematical modeling approach for simulating unsteady turbulent flow around a Darrieus H-rotor to support practical engineering applications. The research methodology integrates computational fluid dynamics (CFD) with physical experiments in a hydrodynamic channel. The numerical model utilizes the unsteady Reynolds-averaged Navier–Stokes (URANS) equations closed with the Strain-Adaptive Linear Spalart–Allmaras (SALSA) turbulence model, chosen for its efficiency in capturing flow separation. The system of initial equations was being devised relatively to an arbitrary curvilinear coordinate system. The pressure and velocity fields have been coordinated using the artificial compressibility method adapted to calculate non-stationary problems. Experimental verification was conducted in the GT-400 hydrodynamic tube using a three-bladed H-rotor model, where flow structures were visualized via the colored jet method at tip speed ratios λ ranging from 2 to 5 and Reynolds number 1470. The findings reveal that dynamic stall occurs over a significant portion of the blade trajectory, characterized by vortex generation at the leading edge and subsequent advection along the chord. Qualitative comparison demonstrates a high degree of correlation between the calculated vortex dynamics and physical flow spectra. These results confirm that the URANS-SALSA approach provides a rational compromise between computational cost and physical accuracy. Full article

Sediment deposition in water diversion channels threatens the operational safety and water supply reliability of large-scale inter-basin water transfer projects. This study investigates the deposition patterns and sediment reduction strategies for the diversion channel of the Shigu Water Source Project, a key intake hub of the Central Yunnan Water Diversion Project on the Jinsha River. A one-dimensional total-load sediment mathematical model (HELIU-2) was used to simulate deposition volume, particle size distribution, and sediment concentration at the pumping station intake under eight design scenarios spanning high-, medium-, and low-sediment years. Results show that over 95% of the deposited sediment in front of the pumping station is finer than 0.05 mm. Dredging reduces the deposition thickness at the pump intake by 13–25% in high-sediment years, significantly enhancing sediment trapping efficiency and reducing both average and maximum sediment concentrations. Longer diversion channels increase total deposition by 9–13% but reduce intake sediment concentration by 2–5% and decrease local deposition thickness by 27–42%, especially in high-sediment years. These findings provide quantitative support for optimizing desilting basin layout, channel length design, and dredging schedules. The proposed modeling framework and mitigation strategies may provide a reference for other large-scale water diversion systems facing similar sedimentation challenges. Full article

Here, we consider a nonlinear hydrodynamic model with mixed dispersion–temporal evolution as the scalar version of the generalized shallow-water wave equation, which specifically provides a comprehensive and versatile framework for studying energy propagation in nonlinear fluids of constrained depth. This equation is acknowledged as an integrable model in the analysis of tidal wave dynamics and in simulations of weather variations, tsunami prediction, and irrigation flows. We also investigate a few of its singular and periodic solitary wave solutions by employing various Riccati-based ansatzes. These results highlight the necessity of studying various nonlinear wave phenomena, which may have potential applications in various domains of physics and applied mathematics. These results extend the variety of its solutions and also enrich the existing knowledge about its solutions with various profiles. To improve visual clarity and to facilitate structural understanding, the solution profiles are represented graphically using Maple software (version 2023.2) in 3D, 2D, and contour plots.We also discuss its invariance under infinitesimal transformations, which yields a one-dimensional Hamilton–Jacobi-like equation. Full article

Accurate prediction of contaminant transport and self-purification processes in rivers remains challenging because pollutant dispersion, biochemical reactions, and hydrodynamic conditions interact across multiple spatial scales. This study aims to develop and compare mathematical models for soluble contaminant transport and biodegradable organic matter removal in channels and rivers. Unsteady advection–diffusion–reaction equations were formulated for one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) transport scenarios and solved through numerical techniques based on the transformation of partial differential equations into systems of ordinary differential or algebraic equations. In parallel, the classical Streeter–Phelps model and an extended formulation incorporating turbulent diffusion were implemented to evaluate organic load degradation and oxygen deficit dynamics. Simulations were performed using a Matlab R2019a-based computational framework under representative hydraulic and reaction conditions obtained from literature data and empirical correlations. The results showed that, under specific conditions, the 3D model reproduced trends comparable to those predicted by the 2D model, while the latter approached the behavior of the 1D formulation. The Streeter–Phelps model predicted an organic load removal efficiency of 97.74%, a purification index of 1.9564, a critical time of 18.43 h, and a critical distance of 6.93 km. These findings provide a useful framework for river water-quality assessment and support future applications involving complex hydrodynamic and pollutant-loading scenarios. Full article

With the increasing complexity of operating conditions and the trend toward structural compactness in generators, the unbalanced electromagnetic force induced by air-gap eccentricity has become a critical factor affecting rotor dynamic behavior and operational reliability. To address the strong coupling and modeling challenges among the electromagnetic field, mechanical force field, and lubrication flow field under eccentric conditions, this study proposes a multi-physics coupled modeling approach that integrates electromagnetic, structural, and fluid dynamic interactions. Based on the spatial pose characteristics of the rotor under eccentric conditions, a three-dimensional mathematical model of the air-gap length is established, and an analytical expression for the lubricating oil film thickness distribution is derived. This framework enables the coupled solution of unbalanced electromagnetic force, hydrodynamic oil film supporting force, and rotor dynamic response. A 60 kW-rated diesel generator was selected as the research object for both numerical simulations and experimental investigations. The numerical results indicate that when the load power increases from 0 kW to 60 kW, the displacement amplitude of the rotor in the y-direction increases by approximately 155%, demonstrating a significant enhancement of transverse vibration intensity under increasing unbalanced electromagnetic excitation. Comparison between experimental and numerical results shows good agreement in both variation trends and amplitude levels, with a maximum relative error of 4.07%, thereby validating the accuracy and reliability of the proposed electromagnetic–structural–fluid coupled model for predicting rotor dynamic response in generators. Full article

This work presents a mathematical and numerical framework for the design and analysis of a remotely operated vehicle (ROV) intended for shallow-water reef exploration. The vehicle consists of an open-frame structure with a sealed pressure housing and a four-thruster propulsion system that enables omnidirectional maneuverability and stable low-speed operation. The hydrodynamic behavior of the ROV is modeled using the incompressible Reynolds-averaged Navier–Stokes equations, which are solved numerically to obtain the velocity and pressure fields around the vehicle. Thruster-induced flow is represented through a Multiple Reference Frame (MRF) formulation, allowing thrust generation and momentum exchange to be resolved directly from the governing equations without prescribing artificial source terms. The propulsion model is supported by experimental bollard-pull characterization of T200 thrusters, from which quadratic thrust laws were identified. A quantitative validation against published experimental data shows deviations within 6–9% and a root-mean-square error (RMSE) of approximately 1.6 N, confirming the accuracy of the proposed thrust model. The CFD-predicted axial force ($F_Z\approx -17.60\mathrm{N}$) was further shown to be consistent with the experimentally derived thrust law when evaluated at the corresponding equivalent operating condition. Structural response is evaluated through a one-way fluid–structure interaction (FSI) strategy, in which the hydrodynamic loads obtained from the CFD solution are transferred to a linear elastic structural model. The validity of the one-way coupling assumption is supported by explicit displacement-to-length ratios in the range $\delta /L\sim$ 10⁻⁵–10⁻³, confirming negligible geometric feedback on the flow field. The results show that the combined CFD–FSI formulation provides physically consistent predictions while remaining computationally efficient. The aluminum configuration exhibited a maximum von Mises stress of approximately 21.1 MPa, remaining safely within the elastic regime, whereas the ABS configuration reached a maximum displacement of 2.9 mm, indicating substantially higher structural compliance. Overall, the experimentally validated propulsion model, quantitatively supported CFD predictions, and asymptotically justified one-way FSI coupling constitute the main contributions of this study, providing a reproducible and physically consistent methodology for the analysis and optimization of reef-class ROVs. Full article

The trajectory tracking problem of underactuated unmanned surface vehicles (USVs) with unknown physical parameters arising from hydrodynamic effects is addressed using a robust control strategy based on a sliding-mode dynamic neural network identifier. To handle the unknown physical parameters, a dynamic neural network identifier with a novel structure is developed, enabling the construction of an equivalent mathematical model of the USV dynamics. To compensate for the underactuated nature of the system, a coordinate transformation is introduced. Using this transformation, together with the proposed identifier, a nonsingular sliding-mode controller is designed. Lyapunov-based analysis establishes finite-time convergence of the neural weight estimation errors to zero and convergence of the identification errors to a bounded neighborhood of zero. Furthermore, once the identification errors enter this bounded region, they asymptotically converge to zero. In addition, the closed-loop stability analysis guarantees finite-time convergence of the tracking errors. The effectiveness of the proposed identifier–controller framework is validated through simulation studies that incorporate explicit actuator saturation constraints and external disturbances to emulate realistic operating conditions. These results demonstrate the practical applicability of the proposed control strategy, as the commanded inputs remain within the physical limits of the propulsion system. Comparative results with a state-of-the-art model-based super-twisting controller show that the proposed approach achieves comparable tracking performance while eliminating the need for prior knowledge of the system’s dynamic parameters. Full article

Predicting the maneuverability of ships equipped with twin azimuth thrusters remains challenging due to their complex hydrodynamic interactions. This study develops an integrated framework that combines Computational Fluid Dynamics (CFD) with an enhanced Manoeuvring Mathematical Group (MMG) Model. Using the platform supply vessel Hai Yang Shi You 661 as a case study, all requisite hydrodynamic derivatives and propeller coefficients were efficiently obtained through CFD-based captive model tests, including oblique towing and Planar Motion Mechanism tests, conducted in STAR-CCM+ 2206. A core contribution of this work is the systematic evaluation of how hydrodynamic model fidelity affects prediction accuracy. Numerical turning circle simulations were executed with three models of increasing complexity: one with only linear derivatives, a second incorporating nonlinear higher-order terms, and a third, full model that additionally includes nonlinear velocity coupling terms. The results, rigorously validated against full-scale trial data, demonstrate that while the basic CFD-MMG approach is feasible, the inclusion of nonlinear coupling terms is critical for achieving accurate predictions in large-amplitude maneuvers. This enhancement reduced the maximum error in tactical diameter prediction from over 25% to approximately 11.8%. Consequently, this study provides a validated and cost-effective framework for maneuvering the prediction of azimuth-thruster vessels and offers clear, quantitative guidance on the necessary level of model complexity for practical engineering applications. Full article

To address the strongly nonlinear hydrodynamic coupling and complex maneuvering challenges encountered by large ships during berthing operations in restricted waters, this paper proposes a high-precision autonomous berthing control system incorporating four-quadrant propeller hydrodynamics. Based on an improved Mathematical Maneuvering Group (MMG) framework, a three-degree-of-freedom (3-DOF) dynamic model is established to accurately capture the transient thrust and torque mappings of the propeller over all four quadrants. A dynamic line-of-sight (LOS) guidance system with a nonlinearly decaying acceptance radius is tightly coupled with PD/PI controllers to coordinate and regulate the rudder angle and propeller rotational speed. The numerical solver was rigorously validated against turning-test data for the S-175 container ship, with the errors of the key parameters all controlled within 15%. Subsequently, under the environmental conditions of Yangshan Port, full-condition path-planning and berthing simulations were conducted for the novel B-573 container ship under steady-current disturbances. These simulations evaluated multiple flow directions, namely due south, due north, due west, and due east defined in the Earth-fixed coordinate system, as well as multiple intensity levels ranging from 0 to 1.5 m/s that were specifically tested under the due north current. Quantitative evaluation shows that, under the highly challenging current condition of 1.0 m/s, the dynamic corrective mechanism effectively drives the global mean absolute error (MAE) to converge to 85.50 m, representing a 62% statistical reduction relative to the transient peak value. In addition, a parameter sensitivity analysis based on the cumulative cross-track error confirms that, when subject to variations in the underlying hydrodynamic parameters, the proposed system can suppress fluctuations in trajectory error to a very low level, thereby demonstrating a certain degree of control robustness. During the terminal berthing stage, the vessel smoothly completed an extreme deceleration from an initial speed of 6.4 m/s to a full stop within 588 s, while constraining the maximum astern rotational speed to −2 rps and seamlessly passing through all four propeller quadrants. The results confirm that the proposed autopilot framework possesses a certain degree of engineering feasibility in complex maritime environments. Full article

Mathematical and numerical models for Packed Bed Thermal Energy Storage (PBTES) systems are essential to predict the different parameters that influence their thermodynamic behavior and then optimize their performance and efficiency. In this research paper, an industrial-scale sensible thermocline Packed Bed Thermal Energy Storage system (9.17 m high and 4.72 m in diameter) was modeled and simulated during the heat charging process, based on FEM, CFD one-dimensional, and two-phase analysis. The model rigorously couples the Local Thermal Non-Equilibrium (LTNE) energy formulation with Darcy–Forchheimer hydrodynamics. The developed model was verified and validated using experimental data from the literature. The model was in close agreement with the experiment, with a global mean relative error of 3.62%. The two-dimensional velocity and temperature fields were presented to describe flow and temperature distributions in the hybrid medium (free and porous). The effect of varying flow rates (8–15 kg/s), porosities (0.35–0.55), and particle diameters (5–20 cm) on the thermal behavior of the heat storage system, temperature fields for solid and fluid, thermocline behavior, and charge efficiency were evaluated and presented. The simulation results demonstrate that the system achieves a high charge efficiency of 92.3% at a nominal charging rate of 15 kg/s. Increasing mass flow rate accelerates charging but widens the thermocline thickness and thermal stratification. Furthermore, increasing the porosity from 0.35 to 0.55 reduced charging time, decreased the temperature difference between the HTF and the storage medium by 10 °C, and increased the final heat charging efficiency by 8%. On the contrary, an increase in particle size from 5 to 20 cm leads to a slower rise in temperature within the solid phase, creating an important LTNE lag of ≈34 °C, thereby reducing the final heat charge efficiency by 16%, and prolonging the time required to charge the tank. Full article

Pectins are structurally complex plant polysaccharides whose functional properties strongly depend on molecular structure that may vary depending on the source of origin. The present study aimed to characterize and compare the hydrodynamic properties of pectins obtained from red and blackcurrants in semidilute and concentrated aqueous solutions. Pectins were extracted and analyzed using light scattering methods and rheology at 25 °C, 30 °C, 35 °C and 40 °C. The methodology used enabled the determination of the hydrodynamic properties of the pectins with changing temperature and concentration, and mathematical modeling was performed using the Kohlrausch–Williams–Watts model. The obtained samples differed in molecular structure, and these differences were reflected in the chain behavior in aqueous solution. The results indicate that even closely related botanical sources may yield pectins with significantly different functional properties. Hydrodynamic studies revealed that relaxation phenomena occurred in a similar manner for redcurrant pectin in the concentrated region and for blackcurrant pectin in the semidilute region (similar diffusion coefficients). Under shear flow conditions, blackcurrant pectin solutions behaved like Newtonian fluids, whereas redcurrant pectin exhibited complex, non-Newtonian behavior. Redcurrant pectin solutions also exhibited lower apparent viscosity values at concentrations comparable to those of blackcurrant pectin. The ability to scale apparent viscosity values indicated a unchanging friction mechanism in viscous flow, characteristic of semidilute and concentrated regions. Full article

In this paper, considering the influence of high-temperature and high-pressure environments on the operating characteristics of rotary combined seals, a mathematical model of rotary composite seals is established based on the thermo-elastohydrodynamic lubrication theory. Furthermore, based on a static analysis of the composite seal and by using the deformation influence coefficient matrix method under the small deformation theory, the elastic deformation distribution of the composite seal under the action of oil film pressure is determined. Combined with the hydrodynamic lubrication equation, the energy equation for the temperature field, and the viscosity-temperature equation, the thermo-elastohydrodynamic lubrication model of the rotary composite seal is solved using the finite difference method, and the oil film thickness distribution and oil film pressure distribution during the operation of the composite seal are calculated. The results show that the sealing medium pressure has a significant effect on the sealing performance. In the axial direction, the oil film pressure first increases and then decreases, while remaining within a stable fluctuation range. Full article