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Keywords = inlet hydraulic efficiency

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28 pages, 12949 KB  
Article
Thermo-Hydraulic and Thermodynamic Analysis of Rotational–Perforated Static Mixer
by Hongrui Wei, Xuefang Gao, Dewu Wang, Yan Liu, Ruojin Wang, Zixuan Guo, Lei Wang, Meng Tang and Shaofeng Zhang
Processes 2026, 14(13), 2060; https://doi.org/10.3390/pr14132060 - 25 Jun 2026
Viewed by 172
Abstract
To clarify the thermo-hydraulic performance and thermodynamic characteristics of rotational–perforated static mixer (RPSM) for laminar heat transfer enhancement in circular tubes, a three-dimensional steady laminar flow model was developed for inlet Reynolds numbers from 200 to 1000. The heat transfer enhancement, resistance increase, [...] Read more.
To clarify the thermo-hydraulic performance and thermodynamic characteristics of rotational–perforated static mixer (RPSM) for laminar heat transfer enhancement in circular tubes, a three-dimensional steady laminar flow model was developed for inlet Reynolds numbers from 200 to 1000. The heat transfer enhancement, resistance increase, and irreversible losses of RPSM with two installation modes and Kenics were comparatively analyzed. The results show that RPSM (forward) exhibits the strongest practical heat transfer performance. Its convective heat transfer coefficient is on average 39.8% higher than that of Kenics, while its thermal effectiveness and number of transfer units are increased by 21.3% and 32.8%, respectively. However, the heat transfer enhancement of RPSM is accompanied by a significant increase in flow resistance. The Z-factors of RPSM (forward) and RPSM (backward) are approximately 3.4 and 6.2 times that of Kenics, respectively. Second law analysis shows that the Bejan numbers of all configurations are close to unity, indicating that total entropy generation is mainly dominated by heat transfer entropy generation. Although RPSM (forward) has a higher exergy destruction rate, its second law efficiency is on average 20.1% higher than that of Kenics. Flow–heat transfer coupling visualization shows that RPSM (forward) can maintain relatively continuous swirling and secondary flow structures, thereby promoting radial energy transport and temperature field uniformity. In contrast, RPSM (backward) induces stronger local recirculation and pressure loss, resulting in higher pumping power demand. Overall, for the specific RPSM geometry and Reynolds number range investigated in this study, RPSM (forward) shows advantages in heat transfer capacity and thermal exergy utilization, but these advantages are accompanied by a substantial flow resistance penalty. Therefore, further structural optimization should focus on retaining radial transport while reducing local pressure loss. Full article
(This article belongs to the Section Chemical Processes and Systems)
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23 pages, 2895 KB  
Article
A Hybrid Modelling and Simulation Framework for Energy-Efficient Operation of Heated Crude Oil Pipelines Under Small-Batch and Multi-Condition Operation
by Yi Guo, Chun Li, Yang Lv, Liuxiao Li, Yangfan Lu and Kai Wen
Modelling 2026, 7(3), 115; https://doi.org/10.3390/modelling7030115 - 12 Jun 2026
Viewed by 198
Abstract
Heated crude oil pipelines transporting high-pour-point, high-viscosity, and high-wax-content crude oil are increasingly operated under small-batch and multi-condition scenarios. Under such conditions, fixed-parameter models and experience-based operating strategies may fail to accurately describe the evolving thermo-hydraulic state, resulting in inaccurate temperature-safety assessment and [...] Read more.
Heated crude oil pipelines transporting high-pour-point, high-viscosity, and high-wax-content crude oil are increasingly operated under small-batch and multi-condition scenarios. Under such conditions, fixed-parameter models and experience-based operating strategies may fail to accurately describe the evolving thermo-hydraulic state, resulting in inaccurate temperature-safety assessment and conservative energy use. To address this problem, this study develops a hybrid modelling and simulation framework for the energy-efficient operation of heated crude oil pipelines. The framework integrates operating-state perception, online parameter inversion, transient thermo-hydraulic simulation, data assimilation, and rolling optimization. First, an online parameter inversion method based on inverse problem solving is established to dynamically identify the overall heat-transfer coefficient and friction correction factor from Supervisory Control and Data Acquisition (SCADA) measurements. Second, a transient thermo-hydraulic simulation and data-assimilation model is constructed to predict pressure, temperature, and safety margins under changing boundary conditions. Third, a constraint-aware rolling optimization strategy is introduced to coordinate heating and pumping operations while satisfying temperature and pressure constraints. The proposed framework is validated using a practical crude oil pipeline. Under a representative low-flow-rate condition, online parameter inversion corrects the overestimation of the thermo-hydraulic state by the fixed-parameter model: the total temperature drop along the pipeline is revised from 33.12 °C to 35.65 °C, and the minimum station-inlet oil temperature is revised from 24.77 °C to 21.61 °C. After optimization is introduced, the total operating energy consumption decreases from 11,715.65 kW to 11,287.43 kW, corresponding to a reduction of 3.66%, while all temperature and pressure constraints remain satisfied. Under time-varying boundary conditions, the rolling optimization strategy further adjusts heating-furnace operation according to variations in inlet flow rate, inlet oil temperature, and ambient temperature, thereby reducing cumulative heating energy consumption while maintaining safe operation. The results demonstrate that the proposed framework provides an implementable modelling and simulation approach for online state assessment, transient prediction, and energy-efficient operation of heated crude oil pipelines under variable operating conditions. Full article
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26 pages, 11903 KB  
Article
Topology Optimization of Liquid-Cooled Heat Sinks for High-Power-Density IGBT Modules
by Jinlie Li, Tianyu Ma, Xianjin Yin, Feng Wang, Zhuangzhuang Li, Zhenyu Zhang and Zhaolei Zheng
Appl. Sci. 2026, 16(12), 5887; https://doi.org/10.3390/app16125887 - 11 Jun 2026
Viewed by 218
Abstract
High-power-density insulated gate bipolar transistor (IGBT) modules in new energy vehicles require efficient heat dissipation and good temperature uniformity. This study proposes a tri-objective topology optimization method for a liquid-cooled heat sink using average temperature, temperature variance, and flow dissipation as the objective [...] Read more.
High-power-density insulated gate bipolar transistor (IGBT) modules in new energy vehicles require efficient heat dissipation and good temperature uniformity. This study proposes a tri-objective topology optimization method for a liquid-cooled heat sink using average temperature, temperature variance, and flow dissipation as the objective functions. A two-dimensional model was established in COMSOL to investigate the effects of the fluid volume fraction, inlet pressure, and optimization-weight distribution on the optimized topology and thermo-hydraulic performance. The results show that a fluid volume fraction of 0.4 and an inlet pressure of 15 Pa provide the best overall performance. Compared with the bi-objective design, introducing temperature variance as a third objective reduces temperature variance by 50.23%, with only a 1.08% increase in average temperature. Three-dimensional simulations further verify the optimized design. Compared with a conventional pin-fin heat sink, the topology-optimized structure reduces the average temperature by 10.43% and the temperature variance by 44.37%, while increasing the flow dissipation by 49.57%. These results show that tri-objective topology optimization is an effective method for improving the thermal management of high-power-density IGBT modules. Full article
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29 pages, 8060 KB  
Article
Numerical Investigation of a Concentration Divider for Ultrasound Calibration Using Constructal Design
by Kamille V. Machado, Vinicius R. Pepe, Fernanda Haeberle, António F. Miguel, Flávia S. F. Zinani and Luiz A. O. Rocha
Processes 2026, 14(11), 1837; https://doi.org/10.3390/pr14111837 - 5 Jun 2026
Viewed by 198
Abstract
This study applies the Constructal Design method to the geometric optimization of a branched symmetric concentration divider for calibrating ultrasound devices used to monitor tumor response with dynamic contrast. Accurate calibration ensures image quality and diagnostic reliability. The geometry consists of a three-dimensional, [...] Read more.
This study applies the Constructal Design method to the geometric optimization of a branched symmetric concentration divider for calibrating ultrasound devices used to monitor tumor response with dynamic contrast. Accurate calibration ensures image quality and diagnostic reliability. The geometry consists of a three-dimensional, tree-shaped flow network with two inlets and three outlets, where inlet 1 carries water containing contrast particles, while inlet 2 carries only water. Laminar flow simulations are performed using Computational Fluid Dynamics (CFD) with Ansys Fluent, assuming no-slip wall conditions and zero-pressure outlets. The analysis investigates the effects of the inlet velocity ratio, the diameter ratio, and the vertical positions of the central outlet and inlet tubes, while keeping the total volume and inlet diameter constant. Additionally, velocity, pressure, particle distributions, flow partition ratio, and hydraulic resistance are evaluated. Results show nearly linear concentration responses among the outlets (100%, 50%, and 0%) when the device approaches geometric symmetry with equal inlet velocities, demonstrating efficient control of flow splitting. Although the diameter ratio imposes a trade-off with hydraulic resistance, geometric symmetry combined with Constructal Design promotes improved flow uniformity and enhanced performance, with potential applications in microfluidic mixers that require precise intermediate concentrations. Full article
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20 pages, 5593 KB  
Article
Parametric Study of Sinusoidal Rib Turbulators for Heat Transfer Enhancement in Turbine Blade Internal Cooling Channels
by Lei Xia, Zhi-Gang Ruan, Wen Wang and Li-Hong Zhou
Processes 2026, 14(11), 1835; https://doi.org/10.3390/pr14111835 - 5 Jun 2026
Viewed by 210
Abstract
Higher turbine inlet temperatures improve cycle efficiency but intensify blade thermal loading, so internal passages rely on turbulators that raise convection within coolant pressure budgets. Streamwise sinusoidal ribs introduce curvature and spanwise phasing beyond straight transverse bars, yet reconciled multi-row thermal–hydraulic data for [...] Read more.
Higher turbine inlet temperatures improve cycle efficiency but intensify blade thermal loading, so internal passages rely on turbulators that raise convection within coolant pressure budgets. Streamwise sinusoidal ribs introduce curvature and spanwise phasing beyond straight transverse bars, yet reconciled multi-row thermal–hydraulic data for such layouts in high-aspect-ratio blade-cooling analogues remain scarce. Steady three-dimensional computational fluid dynamics (CFD) of turbulent airflow in a 4:1 rectangular channel with uniform heat flux on one ribbed wall are applied to compare nine parametric sinusoidal-rib layouts and one transverse baseline at bulk Reynolds numbers from 20,000 to 90,000. The normalized Nusselt number (Nu/Nu0), Fanning friction factor (f/f0), and composite thermal–hydraulic performance indices quantify the trade-off. Several layouts outperform the transverse baseline; a streamwise-increasing rib-height schedule achieves the highest pressure-drop-weighted index, whereas a large-amplitude uniform waviness gives the best heat-transfer-dominated index. The parametric matrix indicates when streamwise waviness merits further study in ribbed passage design. Full article
(This article belongs to the Section Chemical Processes and Systems)
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26 pages, 7439 KB  
Article
Hydraulic Characterization of a Direct-Acting Pressure-Reducing Valve Using CFD and Experimental Validation
by Gonzalo López-Villacís, Pablo Valle-Velasco, Martha Sevilla-Abarca, Diana Peralta-Zurita and Segundo Espín-Lagos
Fluids 2026, 11(6), 139; https://doi.org/10.3390/fluids11060139 - 2 Jun 2026
Viewed by 282
Abstract
This study presents the hydraulic characterization of a direct-acting pressure-reducing valve (PRV) using a combined experimental and numerical approach. An experimental test bench was implemented to measure inlet, control port, and outlet pressures over a flow rate range from 0 to 4.0 m [...] Read more.
This study presents the hydraulic characterization of a direct-acting pressure-reducing valve (PRV) using a combined experimental and numerical approach. An experimental test bench was implemented to measure inlet, control port, and outlet pressures over a flow rate range from 0 to 4.0 m3/h, under a constant inlet pressure of 8 bar and a set pressure of 3 bar. In parallel, a three-dimensional steady-state CFD model was developed using a sequential force balance analysis between hydraulic and spring restoring forces. The results show good agreement between numerical predictions and experimental data, with a maximum error below 10% in outlet pressure. The pressure drop exhibited a nonlinear increasing trend with flow rate, reaching values close to 1.8 bar at 4.0 m3/h. The flow coefficient Kv remained within a range of 2.2–3.0, while the pressure regulation coefficient S remained below 0.05, indicating stable regulation performance. Additional simulations at 25 bar provided improved agreement with manufacturer data, suggesting that catalog curves may be based on nominal pressure conditions. The proposed methodology demonstrates that steady-state CFD coupled with force balance analysis is an effective and computationally efficient approach for predicting the hydraulic behavior of direct-acting PRVs. Full article
(This article belongs to the Section Mathematical and Computational Fluid Mechanics)
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29 pages, 6516 KB  
Article
Numerical and Experimental Investigation of Hydraulic Optimization and Internal Flow Mechanisms in a Low-Specific-Speed Pump as Turbine
by Yin Luo and Bo Jiang
Water 2026, 18(11), 1343; https://doi.org/10.3390/w18111343 - 1 Jun 2026
Viewed by 294
Abstract
Pump-as-turbine (PAT) units have been widely used for energy recovery in water-supply networks, petrochemical systems, and small hydropower applications; however, their turbine-mode performance is often limited because most commercial pumps are originally designed for pumping conditions. To improve the hydraulic performance of a [...] Read more.
Pump-as-turbine (PAT) units have been widely used for energy recovery in water-supply networks, petrochemical systems, and small hydropower applications; however, their turbine-mode performance is often limited because most commercial pumps are originally designed for pumping conditions. To improve the hydraulic performance of a low-specific-speed PAT, this study developed a surrogate-assisted multi-objective optimization framework combining three-dimensional computational fluid dynamics (CFD), design of experiments, a Kriging surrogate model, and a multi-objective genetic algorithm. Five key impeller geometric parameters, including blade inlet angles, blade wrap angles, and impeller outlet diameter, were selected as design variables, and turbine-mode efficiency was maximized under a head constraint of H ≥ 24 m at the rated condition of 1450 r/min. The results showed that the optimized design increased efficiency from 72.34% to 84.42% while satisfying the head requirement. Comparative analyses of pressure and velocity fields in the impeller and volute further revealed that the performance improvement was mainly associated with enhanced flow-field uniformity and reduced local hydraulic losses. A dedicated PAT test rig was finally established to experimentally validate the optimized design. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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29 pages, 12637 KB  
Article
A CFD–GPR–NSGA-II Framework for Thermal–Hydraulic Optimization of Mini-Channel Liquid Cooling Plates in Electric Vehicle Battery Thermal Management Systems
by Nguyen Thanh Cong, Nguyen Thi Hong Ngoc, Nguyen Minh Chau, Do Van Quan, Vu Duc Binh, Nguyen Manh Quang, Le Dinh Dat, Dinh Van Nghiep and Le Van Quynh
Energies 2026, 19(11), 2621; https://doi.org/10.3390/en19112621 - 29 May 2026
Viewed by 614
Abstract
Liquid-cooled battery thermal management systems are essential for maintaining thermal safety, temperature uniformity, and hydraulic efficiency in electric vehicle battery modules. However, improving heat dissipation often increases pressure drop and pumping demand, making the thermal–hydraulic trade-off a key challenge in cooling plate design. [...] Read more.
Liquid-cooled battery thermal management systems are essential for maintaining thermal safety, temperature uniformity, and hydraulic efficiency in electric vehicle battery modules. However, improving heat dissipation often increases pressure drop and pumping demand, making the thermal–hydraulic trade-off a key challenge in cooling plate design. This study develops a CFD–GPR–NSGA-II-based multi-objective optimization framework for a mini-channel liquid cooling plate applied to a cylindrical 18650 lithium-ion battery module under a 4C discharge condition. The mini-channel thickness, wall thickness, and coolant inlet velocity are selected as design variables, while the maximum battery temperature, temperature difference, and pressure drop are used as objective functions. Sixty design samples are generated using Latin hypercube sampling and evaluated through CFD simulations. Gaussian process regression models are then constructed to approximate the nonlinear relationships between the design variables and the thermal–hydraulic responses, and the trained surrogate models are coupled with NSGA-II to identify Pareto-optimal solutions. The selected compromise design is finally verified using a full CFD simulation. Compared with the initial configuration, the CFD-verified optimized design reduces the maximum temperature, temperature difference, and pressure drop by 0.569 K, 0.557 K, and 338.612 Pa, respectively. Although the reduction in peak temperature is moderate, the optimized design improves temperature uniformity by 10.06% and reduces pressure drop by 43.25%, demonstrating a balanced improvement in thermal and hydraulic performance. A heat-load robustness check further confirms that the optimized design maintains a predictable thermal response under different heat generation levels. These results indicate that the proposed CFD–GPR–NSGA-II framework provides an effective and computationally efficient approach for designing mini-channel liquid cooling plates for electric vehicle battery thermal management. Full article
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29 pages, 879 KB  
Article
A Unified Methodology for Direct and Inverse Problems in Steady-State Thermal–Hydraulic Networks
by Mirco Ganz, Frank Tillenkamp and Christian Ghiaus
Energies 2026, 19(11), 2587; https://doi.org/10.3390/en19112587 - 27 May 2026
Viewed by 318
Abstract
Steady-state thermal–hydraulic network models are widely used for the analysis, design, and operation of energy systems. While direct problems with prescribed boundary conditions can often be solved efficiently, inverse problems such as set-point tracking and parameter identification are commonly addressed through repeated solution [...] Read more.
Steady-state thermal–hydraulic network models are widely used for the analysis, design, and operation of energy systems. While direct problems with prescribed boundary conditions can often be solved efficiently, inverse problems such as set-point tracking and parameter identification are commonly addressed through repeated solution of the corresponding direct problem. For large-scale networks with strong nonlinear couplings, such nested strategies can become computationally expensive and numerically burdensome. This paper presents a unified methodology for the solution of direct and inverse steady-state thermal–hydraulic problems within a single modeling workflow. In contrast to classical nested approaches, inverse problems are formulated in a simultaneous analysis and design framework, in which system states and selected system inputs are treated as unknowns simultaneously. The methodology combines externally causal component representations with acausal network balance relations in order to expose the structural dependencies of the assembled system and enable graph-based tearing reduction. Component-local evaluations, including possible component-internal nonlinear calculations, are encapsulated within the component models, while the nonlinear network closure problem is restricted to a reduced set of tearing variables.. Direct problems are solved by nonlinear root finding on the tearing-reduced residual system, whereas inverse problems are posed as tearing-reduced residual-constrained nonlinear programs with equality, inequality, and bound constraints. The methodology is demonstrated on a vapor-compression refrigeration cycle, where compressor speed and expansion valve opening are adjusted to satisfy prescribed cooling-load and superheat targets under varying condenser inlet temperatures. Implemented in Python, the proposed methodology supports transparent and reproducible modeling and provides a practical basis for simulation, set-point tracking, and constrained optimization of coupled thermal–hydraulic networks. Full article
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29 pages, 23263 KB  
Article
Hydraulic Characteristics of Large-Scale Vertical Mixed-Pump Device Under Pump as Turbine (PAT) Mode Applying Chaos Theory
by Can Luo, Kangzhu Jing, Wei Zhang, Ruimin Cai, Li Cheng, Chenzhi Xia, Bowen Zhang and Baojun Zhao
Machines 2026, 14(5), 556; https://doi.org/10.3390/machines14050556 - 15 May 2026
Viewed by 320
Abstract
As an important option for energy storage projects, pumping stations can also generate electricity when the upstream has surplus water and the pump system operates as a turbine (PAT mode). When it switches from pump mode to PAT mode, the pump operation state [...] Read more.
As an important option for energy storage projects, pumping stations can also generate electricity when the upstream has surplus water and the pump system operates as a turbine (PAT mode). When it switches from pump mode to PAT mode, the pump operation state changes significantly. This study adopts a numerical simulation to investigate the flow characteristics, time-frequency domain performance and chaotic features of pressure pulsation in a vertical mixed-flow pump device when it operates in different PAT modes. The results show that, when the pump operates in PAT mode, the flow in the straight passage remains smooth, but it deteriorates in the elbow-shaped draft tube, such as developing a spiral stream in the straight section, a disordered stream in the elbow section, and vortexes and flow separation at the beginning of the diffuser section, but it gradually becomes smooth after passing through the diffuser section. Under low-head PAT conditions, circumferential circulation cross flow occurs at the impeller inlet, reducing energy conversion efficiency. Under all PAT conditions, the flow on the blade surface near the hub is stable, but obvious vortexes happen near the shroud. As the head increases, the small-scale vortexes disappear on the mid-blade surface, and the flow becomes smoother on the blade surface near the shroud of the impeller. Except at the impeller outlet, pressure pulsation of the monitoring probes exhibits clear periodicity, with dominant frequencies corresponding to the rotational frequency, and its amplitudes decreasing from shroud to hub. Pressure pulsation under all PAT conditions is chaotic, and phase trajectories exhibit ring-shaped structures consisting of the ring circle and the ring surface. Differences in the circle spacing, size, and spatial position of the ring circle phase locus and ring surface phase locus are observed, and these variations are closely related to the PAT conditions. A correlative relationship exists between the chaotic correlation dimension and flow performance, which is of great significance for the condition monitoring and fault diagnosis of pump units. These findings not only enrich the theoretical research on the PAT mode of pumps, but also provide a reference for similar engineering applications and offer new insights into condition monitoring of hydraulic machinery. Full article
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25 pages, 6334 KB  
Article
Effects of Hydraulic Diameters on CO2 Absorption in Flat-Plate Membrane Contactors with Inserted S-Ribbed Carbon Fiber Turbulence Promoters
by Chii-Dong Ho, Ping-Cheng Hsieh, Thiam Leng Chew and Jyun-Jhe Li
Membranes 2026, 16(5), 162; https://doi.org/10.3390/membranes16050162 - 30 Apr 2026
Viewed by 497
Abstract
One-dimensional mass transfer resistance-in-series framework was developed theoretically and validated experimentally using a flat-plate polytetrafluoroethylene/polypropylene (PTFE/PP) membrane module to predict CO2 absorption fluxes and concentration distributions. The decline in CO2 absorption efficiency along the membrane module is primarily attributed to increased [...] Read more.
One-dimensional mass transfer resistance-in-series framework was developed theoretically and validated experimentally using a flat-plate polytetrafluoroethylene/polypropylene (PTFE/PP) membrane module to predict CO2 absorption fluxes and concentration distributions. The decline in CO2 absorption efficiency along the membrane module is primarily attributed to increased concentration polarization resistance and a reduced driving force concentration gradient. To alleviate these limitations, carbon fiber promoters were strategically embedded to suppress concentration polarization, reduce the mass transfer resistances, and enhance turbulence intensity. In the present study, device performance was further improved by implementing properly ascending or descending hydraulic equivalent widths along the absorbent feed channel. Under the descending configuration, an absorption flux enhancement of up to 44.94% was achieved relative to an empty-channel module (i.e., without S-ribbed carbon fiber inserts). Theoretical formulations were established to predict absorption fluxes under varying monoethanolamine (MEA) volumetric flow rates, CO2/N2 mixture flow rates, and inlet CO2 feed concentrations. The model predictions showed good agreement with experimental results obtained using MEA solutions under both ascending and descending hydraulic width operations, demonstrating effective mitigation of polarization effects and enhanced absorption flux along the absorbent feed channel. An economic assessment of the S-ribbed carbon fiber module was conducted by evaluating the trade-off between absorption flux enhancement and incremental power consumption. The results indicate that the proposed design provides a practical and economically viable approach for improving the performance of membrane-based CO2 capture technologies. In addition, an enhanced Sherwood number correlation, expressed in a simplified form, was developed and employed to estimate the mass transfer coefficients of CO2 membrane absorption modules incorporating S-ribbed carbon fiber promoters. Full article
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30 pages, 4983 KB  
Article
A Predictive Model for Separation Efficiency in Gas–Liquid Cyclone Separators
by Dongjing Chen, Jin Zhang, Ruiqi Lv, Ying Li and Xiangdong Kong
Processes 2026, 14(7), 1157; https://doi.org/10.3390/pr14071157 - 3 Apr 2026
Viewed by 568
Abstract
Entrained gas in hydraulic oil undermines system stability. A rapid engineering method for predicting the separation efficiency of gas–liquid cyclone separators is still lacking. This study proposes an engineering-oriented predictive framework by combining the split ratio, the characteristic scale of the locus of [...] Read more.
Entrained gas in hydraulic oil undermines system stability. A rapid engineering method for predicting the separation efficiency of gas–liquid cyclone separators is still lacking. This study proposes an engineering-oriented predictive framework by combining the split ratio, the characteristic scale of the locus of zero vertical velocity envelope, and the axial residence time. A relative migration index, derived from maximum tangential velocity and axial residence time, is coupled with a relative overflow-pipe insertion indicator to characterize the interaction between swirl intensity and effective separation space. The separation-capability transition is described using a coupled logistic mapping. Model coefficients are identified via Eulerian–Eulerian simulations on a calibration set. The model was evaluated on isolated simulation validation sets with varying geometries and inlet gas volume fractions, yielding an R2 of 0.762 and a root mean square error (RMSE) of 0.07. Particle Image Velocimetry validation tests on one representative prototype geometry gave RMSE values of 0.061 for simulation versus test and 0.108 for prediction versus test. The framework captures the macroscopic trend of separation efficiency within the investigated range, with the caveat that part of the model coefficients and intermediate inputs remain conditioned by simulation-derived quantities. Full article
(This article belongs to the Section Separation Processes)
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20 pages, 5855 KB  
Article
Internal Flow, Vibration, and Noise Characteristics of a Magnetic Pump at Different Rotational Speeds
by Fei Zhao, Bin Xia and Fanyu Kong
Water 2026, 18(7), 784; https://doi.org/10.3390/w18070784 - 26 Mar 2026
Viewed by 512
Abstract
A high-speed magnetic pump rated at 7800 r/min was studied. A numerical model was established, and a hydraulic, vibration, and noise testing system was set up to conduct flow simulations, noise, and vibration experiments at different speeds. The results show that increasing speed [...] Read more.
A high-speed magnetic pump rated at 7800 r/min was studied. A numerical model was established, and a hydraulic, vibration, and noise testing system was set up to conduct flow simulations, noise, and vibration experiments at different speeds. The results show that increasing speed leads to a higher pressure difference between the pump chamber and the cooling circuit. Meanwhile, the turbulent kinetic energy at the impeller outlet increases. Despite an increase in energy loss, the loss ratio decreases, and overall efficiency improves. The internal flow noise collected by the outlet hydrophone mainly comes from Rotor–Stator Interference (RSI), and it can sensitively capture changes in rotational speed. The dominant frequency of the outlet noise agrees well with the blade frequency calculated from the set speed, with a maximum deviation of 0.26%. As the speed increases, the overall sound pressure level (OASPL) at the inlet and outlet and the Root Mean Square (RMS) acceleration values at the outlet and pump body generally increase, while the acceleration at the motor base shows a decreasing trend. The conclusions are helpful for the design and optimization of rotary machinery such as high-speed magnetic pumps. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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16 pages, 3831 KB  
Article
Study on the Flow Characteristics and Energy Dissipation of Side Inlet/Outlet Structures
by Hai-Yan Lv, Ming-Jiang Liu, Qiang Long, Wang-Ru Wei and Jun Deng
Water 2026, 18(6), 678; https://doi.org/10.3390/w18060678 - 13 Mar 2026
Viewed by 505
Abstract
As a critical hydraulic component of pumped storage power stations, the side inlet/outlet directly affects unit efficiency, flow stability, and system safety. This study investigates the side inlet/outlet of a pumped storage power station using three-dimensional numerical simulations, focusing on the influence of [...] Read more.
As a critical hydraulic component of pumped storage power stations, the side inlet/outlet directly affects unit efficiency, flow stability, and system safety. This study investigates the side inlet/outlet of a pumped storage power station using three-dimensional numerical simulations, focusing on the influence of the diffuser length L on hydraulic performance, and further analyzes the underlying mechanisms of energy loss based on entropy production theory. The results indicate that, with increasing diffuser length L, the flow rates in individual channels gradually deviate from the design values, leading to an aggravated imbalance in flow distribution. In contrast, the velocity non-uniformity coefficient CV at the trash rack decreases, accompanied by a pronounced attenuation of recirculation and local flow separation, resulting in a more uniform and stable flow field. Moreover, increasing L improves the streamwise velocity uniformity within each channel, while the extent and intensity of the top recirculation zone are reduced, suppressing local flow separation. Quantitative analysis shows that when L increases from 65 m to 85 m, the total turbulent dissipation entropy production rate in the diffuser section increases linearly from 2732.32 W/K to 2842.32 W/K, whereas the direct dissipation entropy production rate increases from 0.41 W/K to 0.59 W/K. This indicates that turbulent dissipation entropy production plays a dominant role in the overall energy loss. Shorter diffusers tend to induce high-intensity local dissipation, whereas longer diffusers reduce local peak dissipation but increase the overall entropy production within the diffuser, reflecting a trade-off between local optimization and global energy loss. This study reveals the sensitivity and governing effects of diffuser length on the hydraulic characteristics of side inlet/outlets, providing a reference for geometry optimization and engineering design of similar hydraulic components. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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35 pages, 18152 KB  
Article
Empirical Energy Dissipation Model for Variable-Slope Three-Section Stepped Spillways Validated Through Dimensional Analysis and CFD Simulation
by Luis Antonio Yataco-Pastor, Ana Cristina Ybaceta-Valdivia, Yoisdel Castillo Alvarez, Reinier Jiménez Borges, Luis Angel Iturralde Carrera, José R. García-Martínez and Juvenal Rodríguez-Reséndiz
Fluids 2026, 11(3), 78; https://doi.org/10.3390/fluids11030078 - 13 Mar 2026
Viewed by 937
Abstract
Energy dissipation in stepped weirs depends on the complex interaction between geometry, flow regime, and surface aeration. The research proposes a dimensionless empirical model (RE3T) to predict the overall energy dissipation in three-section stepped weirs with variable slopes. The formulation integrates dimensional analysis [...] Read more.
Energy dissipation in stepped weirs depends on the complex interaction between geometry, flow regime, and surface aeration. The research proposes a dimensionless empirical model (RE3T) to predict the overall energy dissipation in three-section stepped weirs with variable slopes. The formulation integrates dimensional analysis based on the Vaschy–Buckingham theorem, controlled physical experimentation, and three-dimensional numerical simulations using CFD employing the RANS–SST turbulence model implemented in ANSYS CFX. Eighteen numerical simulations were performed covering seven geometric configurations and four hydraulic inlet conditions, covering slug, transitional, and skimming flow regimes. The CFD model was previously validated by comparison with a physical scale model, obtaining a discrepancy of only 0.38% in relative energy dissipation. The validated dataset was then used to calibrate an empirical multiplicative correlation composed of eight dimensionless groups associated with sectional slopes, number of steps, overall geometric ratio, and upstream Froude number. The proposed model achieved a coefficient of determination R2 = 0.81, with relative errors generally less than 1% and a maximum deviation of 2.34%. The statistical indicators (RMSE, MAE, and bias) confirm the absence of significant systematic trends within the defined domain of validity. The results show that the Froude number and the slopes of the sections are the variables with the greatest influence on overall dissipation. The RE3T formulation is a physically consistent and computationally efficient predictive tool for the design and analysis of stepped weirs with variable slopes, extending the scope of traditional correlations developed for uniform slopes. Full article
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