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43 pages, 2643 KB  
Article
Toward a General Analytical Formulation for the Hydrodynamic Behavior of Tesla Valves
by Mauricio De la Cruz-Ávila, Mario Ivan Estrada-Delgado, Francisco Javier Castillo Guerrero and Rosanna Bonasia
Water 2026, 18(13), 1649; https://doi.org/10.3390/w18131649 - 7 Jul 2026
Viewed by 354
Abstract
Tesla valves are passive hydraulic devices capable of producing directional flow resistance without moving components, making them attractive for applications in microfluidics, thermal systems, and high-reliability hydraulic circuits. Despite extensive experimental and numerical studies, an analytical formulation capable of describing the hydrodynamic behavior [...] Read more.
Tesla valves are passive hydraulic devices capable of producing directional flow resistance without moving components, making them attractive for applications in microfluidics, thermal systems, and high-reliability hydraulic circuits. Despite extensive experimental and numerical studies, an analytical formulation capable of describing the hydrodynamic behavior of Tesla valves under varying operating and geometric conditions remains limited. In this work, a comprehensive analytical model is developed to describe the pressure losses, flow redistribution, and diodicity behavior of Tesla valves through a physics-based formulation derived from conservation laws, dimensional analysis, and inertial scaling principles. The proposed model incorporates the influence of Reynolds number, flow partition, geometric ratios, branch inclination angle, and number of diode stages within a unified nonlinear framework. A closed structural equation is obtained that relates hydraulic losses and directional asymmetry to the internal geometry of the valve. The formulation reveals the existence of geometric and energetic constraints governing rectification efficiency, including bounds associated with stage number, channel scaling, and angular momentum exchange. The results show that Tesla valve performance emerges from a delicate balance between inertial amplification and dissipative mechanisms, providing an analytical framework for the design and optimization of Tesla-type hydraulic systems across multiple scales. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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23 pages, 10195 KB  
Article
Comparative Thermodynamic Analysis of CO2 Refrigeration Cycles with Internal Heat Exchanger, Mechanical Subcooling, and Ejector Configurations
by Muhsin Kılıç and Orhan Mert Duraner
Appl. Sci. 2026, 16(13), 6503; https://doi.org/10.3390/app16136503 - 30 Jun 2026
Viewed by 371
Abstract
This study presents a comparative thermodynamic assessment of four widely used CO2 refrigeration configurations, namely, the basic cycle (BC), internal heat exchanger cycle (IHEX), mechanical subcooling cycle (MSC), and ejector cooling cycle (ECS), operating under both subcritical and transcritical conditions. The investigated [...] Read more.
This study presents a comparative thermodynamic assessment of four widely used CO2 refrigeration configurations, namely, the basic cycle (BC), internal heat exchanger cycle (IHEX), mechanical subcooling cycle (MSC), and ejector cooling cycle (ECS), operating under both subcritical and transcritical conditions. The investigated systems were analyzed using validated numerical models developed in the Engineering Equation Solver (EES) under evaporating temperatures ranging from −30 °C to +5 °C and gas cooler temperatures ranging from 30 °C to 50 °C. For each operating condition, the refrigeration cycles were thermodynamically optimized in order to maximize the coefficient of performance (COP). The results indicate that an increasing gas cooler temperature significantly reduces the COP of all investigated systems, whereas an increasing evaporating temperature improves cycle performance. Among the investigated configurations, the MSC system exhibited the highest thermodynamic performance improvement, particularly under severe transcritical operating conditions characterized by high gas cooler temperatures and low evaporating temperatures. The ECS configuration also provided considerable performance enhancement by reducing throttling-related thermodynamic losses and compressor pressure ratio. In contrast, the IHEX configuration yielded comparatively moderate but relatively stable performance improvement with lower system complexity. In addition to the thermodynamic comparison, a simplified engineering-oriented practical assessment framework based on a relative cost index (RCI) was introduced to comparatively evaluate implementation complexity, control requirements, maintenance considerations, and relative investment burden of the investigated systems. The results indicate that, although the MSC configuration provides the highest thermodynamic performance, it is also associated with the highest implementation complexity and relative investment requirement, whereas the IHEX configuration offers a simpler and lower-cost alternative with moderate performance enhancement. The present study provides engineering-oriented comparative guidance regarding the thermodynamic performance, practical applicability, and operational suitability of advanced CO2 refrigeration systems under varying climatic and operational conditions. Full article
(This article belongs to the Special Issue Advances in Thermal Engineering: From Fundamentals to Applications)
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46 pages, 1464 KB  
Article
Mathematical Modeling and Dynamical Analysis of a Nonlinear Coupled Stress-Mitigation System with Signed Threshold-Relative Policy Feedback and Physics-Informed Neural Network Simulation
by Khaled Aldwoah, Faez A. Alqarni, Osman Osman, L. M. Abdalgadir, Amel Touati and Waleed Adel
Mathematics 2026, 14(12), 2231; https://doi.org/10.3390/math14122231 - 22 Jun 2026
Viewed by 229
Abstract
This study develops and analyzes a four-state nonlinear policy–feedback dynamical system that couples a system stressor, an accumulated burden, a signed mitigation–response variable, and a signed policy-pressure variable. The proposed model represents governance response through a smooth threshold-centered feedback mechanism, in which the [...] Read more.
This study develops and analyzes a four-state nonlinear policy–feedback dynamical system that couples a system stressor, an accumulated burden, a signed mitigation–response variable, and a signed policy-pressure variable. The proposed model represents governance response through a smooth threshold-centered feedback mechanism, in which the policy-pressure dynamics depend continuously on the deviation of the stressor from a prescribed reference threshold. Unlike reduced-order formulations with purely exogenous interventions, the present framework generates endogenous interactions among stress accumulation, burden evolution, mitigation response, and policy adjustment. The qualitative analysis establishes local well-posedness in the admissible phase domain, conditional nonnegativity of the accumulated burden, and boundedness of trajectories on admissible intervals. An autonomous effective system is then derived to characterize quasi-stationary mean behavior of the periodically forced dynamics. For this effective system, local stability is investigated using Gershgorin estimates and Routh–Hurwitz criteria, leading to explicit analytical conditions for local asymptotic stability and a critical policy-responsiveness threshold associated with possible Hopf-type oscillatory transitions. The analysis highlights the stabilizing role of mitigation damping and cubic saturation in regulating the feedback loop. To approximate the nonlinear system, a Physics-Informed Neural Network (PINN) surrogate is constructed by embedding the governing equations into a differentiable residual loss while enforcing the initial conditions analytically. The accumulated burden is represented through an admissible neural-network ansatz to preserve the well-definedness of the logarithmic coupling term, while the mitigation–response and policy-pressure variables remain signed in accordance with the model formulation. Numerical validation against reference ode45 solutions across two governance regimes shows maximum absolute errors of order 103, indicating that the PINN provides a reliable differentiable surrogate for the coupled policy–feedback dynamics. The resulting framework offers a foundation for future inverse modeling, parameter estimation, and data-assimilation studies involving policy responsiveness, intervention thresholds, and burden- suppression effects. Full article
(This article belongs to the Section C2: Dynamical Systems)
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18 pages, 2539 KB  
Article
Multi-Damping Mechanism Analysis and Quality Factor Optimization of Micromachined Disk Resonator Gyroscopes
by Ruotong Qi and Zhirui Liao
Micromachines 2026, 17(6), 727; https://doi.org/10.3390/mi17060727 - 16 Jun 2026
Viewed by 293
Abstract
A high quality factor, denoted as the Q-factor, is crucial for micromachined disk resonator gyroscopes, commonly referred to as DRGs, to suppress thermomechanical noise and improve bias stability. However, the coupled energy dissipation mechanisms under low-pressure conditions impose significant limitations on further Q-factor [...] Read more.
A high quality factor, denoted as the Q-factor, is crucial for micromachined disk resonator gyroscopes, commonly referred to as DRGs, to suppress thermomechanical noise and improve bias stability. However, the coupled energy dissipation mechanisms under low-pressure conditions impose significant limitations on further Q-factor enhancement. This paper establishes a rigorous multiphysics damping analysis framework for DRGs and quantitatively investigates the contributions of air damping, thermoelastic damping, and anchor loss. A free-molecular squeeze-film damping model is derived based on kinetic gas theory and molecular energy transfer mechanisms, avoiding the continuous fluid assumption of the classical Reynolds equation, which fails in low-pressure regimes. Due to the highly symmetric ring structure and central anchor design, finite element method simulations reveal an extremely high anchor-loss-limited quality factor, Q_anchor, of approximately 1.85 × 1012, indicating negligible anchor-induced dissipation. Under an operating pressure of 0.1 Pa, air damping is validated as the absolute dominant energy dissipation mechanism with a gas quality factor, Q_air, of approximately 1.105 × 105, which is significantly lower than the thermoelastic damping quality factor, Q_TED, evaluated at 8.98 × 105. To break the classical trade-off between squeeze-film damping suppression and capacitive drive efficiency, a decoupled gap optimization strategy is proposed. By maintaining the drive electrode gap, gap_e, at 7.2 µm while increasing only the parasitic ring-to-suspended-mass gap, gap_m, to 12 µm, the squeeze-film-damping-limited Q-factor is improved by approximately 25% to 1.381 × 105 without degrading electromechanical coupling efficiency. In addition, the optimal anchor radius is determined to be approximately 160 µm. The proposed framework provides practical design guidance for high-Q DRGs and other MEMS resonant inertial sensors. Full article
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29 pages, 13320 KB  
Article
Modeling One-Dimensional Consolidation Problems Using Physics-Informed Neural Networks with Domain Decomposition
by Yang Chen, De’an Sun and Jie Zhou
Appl. Sci. 2026, 16(12), 6065; https://doi.org/10.3390/app16126065 - 15 Jun 2026
Viewed by 276
Abstract
Soil consolidation modeling is essential for estimating settlement and pore-water pressure dissipation, but analytical solutions are limited for layered soils with complex drainage and interface conditions. This study evaluates physics-informed neural networks (PINNs) for one-dimensional consolidation of saturated soils and extends them to [...] Read more.
Soil consolidation modeling is essential for estimating settlement and pore-water pressure dissipation, but analytical solutions are limited for layered soils with complex drainage and interface conditions. This study evaluates physics-informed neural networks (PINNs) for one-dimensional consolidation of saturated soils and extends them to a domain-decomposed XPINN framework for two-layered soils. Governing equations, boundary conditions, interface-continuity constraints, and synthetic measurement data are embedded in the loss function. Layer-wise locally adaptive activation functions (L-LAAF) and residual-based adaptive resampling (RAR) are used to improve training stability. For homogeneous soil, the PINN accurately reproduces the analytical solution, although conventional finite difference methods remain more efficient for simple single-query forward analysis. For heterogeneous soil, the full XPINN model achieves a relative L2 error of 0.0173 ± 0.0058, whereas removing RAR, L-LAAF, or domain decomposition increases the error to 0.0578 ± 0.0555, 0.1488 ± 0.0378, and 0.1673 ± 0.0104, respectively. In inverse tests using synthetic noisy measurements, denser and lower-noise observations improve the identification of unknown drainage coefficients. The framework provides a meshless and continuous representation for forward and inverse layered consolidation problems, but validation with laboratory or field data remains necessary. Full article
(This article belongs to the Section Civil Engineering)
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16 pages, 421 KB  
Article
Direct Measurement of Total Aerodynamic Resistance in Mine Roadways Using a Two-Point Flow-Based Method
by Bui Thanh Hoa, Klaudia Zwolińska-Glądys and Marek Borowski
Mining 2026, 6(2), 41; https://doi.org/10.3390/mining6020041 - 15 Jun 2026
Viewed by 270
Abstract
Accurate modeling of underground mine ventilation requires reliable estimates of roadway aerodynamic resistance. Conventional methods, based on geometric surveys or barometric pressure measurements, have notable limitations, including neglect of local losses, high time requirements, and sensitivity to environmental disturbances. This paper introduces a [...] Read more.
Accurate modeling of underground mine ventilation requires reliable estimates of roadway aerodynamic resistance. Conventional methods, based on geometric surveys or barometric pressure measurements, have notable limitations, including neglect of local losses, high time requirements, and sensitivity to environmental disturbances. This paper introduces a two-point flow-based method for determining roadway resistance directly from in situ measurements. Using basic instruments (anemometer, differential manometer, thermometer, and hygrometer), measurements are taken at two points along a straight airway. The pressure drop is calculated via the Bernoulli equation, allowing resistance to be determined without relying on geometric data or friction assumptions. This method captures both frictional and local losses inherently. Field testing in five roadway sections of a coal mine in Vietnam yielded resistance values 10–15 times higher than theoretical friction-only estimates, highlighting the importance of local losses. The equivalent cross-sectional areas back-calculated from the measured resistance using literature-based friction factors showed consistency with geometric survey data (typical deviation 3–6%), indicating internal coherence of the measurements. Full validation against independent barometric or CFD methods remains a subject of ongoing research. The method is simple, fast, minimally disruptive, and compatible with ventilation modeling tools. It provides a practical and accurate alternative for resistance estimation under real operating conditions. Full article
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37 pages, 3950 KB  
Article
A Physics-Regularized Neural Inversion Framework for Well-Test Parameter Identification in Long Horizontal Wells Intersecting Multiple Faults
by Changyong Li, Peng Xiao, Tao Cao, Zhaoxu Wang, Yiyao Li, Wenrui Lv, Zhenye Xu and Ren-Shi Nie
Processes 2026, 14(12), 1846; https://doi.org/10.3390/pr14121846 - 7 Jun 2026
Viewed by 237
Abstract
Long horizontal wells in high-permeability fault-block reservoirs may intersect multiple faults, leading to complex pressure-transient responses, strong parameter coupling in conventional well-test interpretation, inefficient manual history matching, and pronounced non-uniqueness in fault-property identification. To address these challenges, this study proposes a physics-regularized neural [...] Read more.
Long horizontal wells in high-permeability fault-block reservoirs may intersect multiple faults, leading to complex pressure-transient responses, strong parameter coupling in conventional well-test interpretation, inefficient manual history matching, and pronounced non-uniqueness in fault-property identification. To address these challenges, this study proposes a physics-regularized neural inversion framework based on a PINN parameterization and low-weight physics regularization for well-test parameter inversion in long horizontal wells intersecting multiple faults. The proposed method takes the multiple-fault pressure response of a long horizontal well as the target problem. Both the pressure–drawdown curve and the pressure–drawdown derivative curve are used as data constraints. At the same time, parameter scaling and stage-wise training are introduced to jointly invert the reservoir permeability, fault transmissibility coefficient, skin factor, and effective producing length of the horizontal well. Considering that the simplified line-source forward model is not fully consistent with the two-dimensional pressure-diffusion equation and the fault-interface residuals, a physics-loss consistency test is performed to determine safe weighting ranges for the PDE residual and the fault-interface residual. These residuals are then incorporated into the training process as low-weight physics regularization terms to improve the physical plausibility of the inversion results. Results from the base case, different fault types, multiple-fault combinations, noise-robustness tests, ablation experiments, and method comparisons show that the proposed method can stably fit pressure–drawdown and pressure–drawdown derivative curves and effectively identify key well-test parameters in single-fault cases and some multiple-fault cases. In single-fault cases, the order of magnitude of the fault transmissibility coefficient can be identified stably. Reliable inversion performance is obtained for medium- to high-transmissibility faults and some multiple-fault combinations. In contrast, ambiguity remains between sealing faults and strong-baffle faults in multiple low-transmissibility fault combinations. The results further indicate that, under multiple random initializations, the physics-regularized neural inversion framework provides improved inversion stability in the tested synthetic low-transmissibility multiple-fault cases compared with the traditional least-squares method. Therefore, the proposed framework can serve as an intelligent auxiliary tool for well-test parameter inversion and fault-connectivity evaluation in complex fault-block reservoirs. Nevertheless, fine discrimination of low-transmissibility faults and interpretation of highly noisy field data still require joint constraints from geological, seismic, and production-dynamic information. A preliminary reduced field PINN fitting test using the well X falloff event further provides an engineering-scale applicability check for real pressure-transient data, with a pressure NRMSE of 2.457% for the extracted shut-in response. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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20 pages, 35328 KB  
Article
Efficient Temporal Prediction of Compressible Flows in Irregular Domains Using Fourier Neural Operators
by Yifan Nie and Qiaoxin Li
Mathematics 2026, 14(11), 1851; https://doi.org/10.3390/math14111851 - 26 May 2026
Viewed by 369
Abstract
This paper investigates the temporal evolution of high-speed compressible fluids governed by the two-dimensional Euler equations in irregular flow fields using the Fourier Neural Operator (FNO). We reconstruct the irregular flow field point set into sequential format compatible with FNO input requirements, and [...] Read more.
This paper investigates the temporal evolution of high-speed compressible fluids governed by the two-dimensional Euler equations in irregular flow fields using the Fourier Neural Operator (FNO). We reconstruct the irregular flow field point set into sequential format compatible with FNO input requirements, and then embed temporal bundling technique within a recurrent neural network (RNN) for multi-step prediction. We further employ a composite loss function to balance errors across different physical quantities. Experiments are conducted on three different types of irregular flow fields, including orthogonal and non-orthogonal grid configurations. Then we comprehensively analyze the physical component loss curves, flow field visualizations, and physical profiles. On non-orthogonal grids, our method consistently achieves improvements in both computational efficiency and error compared to other baseline models. Results demonstrate that our approach achieves high accuracy, as evidenced by maximum relative L2 errors of (0.75%,0.56%,0.35%) for (p,T,u) respectively (where p, T, and u denote pressure, temperature, and velocity magnitude), and offers substantial improvements in computational efficiency over traditional numerical methods. Within this data-driven context, the method accurately and efficiently simulates the temporal evolution of high-speed compressible flows in irregular domains. Full article
(This article belongs to the Section E: Applied Mathematics)
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9 pages, 1440 KB  
Proceeding Paper
Numerical Investigation of Unsteady Fluid Flow Inside Air Cooling Ducts with Tilted Heat Exchanger for Electrified Aero Engines
by Prabhjot Singh, Florian Nils Schmidt, Sebastian Merbold, Ralf Rudnik and Stefanie de Graaf
Eng. Proc. 2026, 133(1), 161; https://doi.org/10.3390/engproc2026133161 - 20 May 2026
Viewed by 291
Abstract
Integrating a heat exchanger (HEX) into the cooling duct of a high-power fuel-cell-based aircraft presents a critical trade-off between thermal performance and aerodynamic penalties. The present study addresses this challenge through the design and system-level analysis of a HEX integrated into the cooling [...] Read more.
Integrating a heat exchanger (HEX) into the cooling duct of a high-power fuel-cell-based aircraft presents a critical trade-off between thermal performance and aerodynamic penalties. The present study addresses this challenge through the design and system-level analysis of a HEX integrated into the cooling duct. Developed as part of the Clean Aviation project FAME, the design features a rectangular inlet, a circular outlet, and a tilted HEX. The evaluation is performed using high-fidelity Large Eddy Simulations (LESs). The HEX is modeled with a porous media approach based on the Darcy–Forchheimer equation, while the simulations are carried out using a self-adapted version of the pisoFoam solver, termed pisoTempFoam, to account for heat transfer. The study reveals that while component-level design choices, such as a straight inlet and tilted HEX configuration, successfully mitigate local flow separation and duct-induced losses, a critical system-level performance issue emerges. The analysis demonstrates that the cooling duct design, when subjected to realistic operational conditions, generates the high pressure head to overcome the resistance of the HEX. The external aerodynamic analysis also indicates that the HEX resistance is a critical factor, and without overcoming it the system fails to capture the required air mass flow rate, compromising thermal management. The findings highlight the necessity to optimize the design, by an adapted duct shape or an auxiliary fan, to overcome the HEX-induced pressure drop. The porous media approach is thereby validated as an effective tool for rapid system-level design analysis, despite its inherent limitation in capturing detailed downstream turbulence. Full article
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19 pages, 2939 KB  
Article
Study on the Mass Loss Characteristics of Underwater Explosion Bubble Pulsation
by Tan Lu, Yuan Gao, Libo Ding and He Zhang
Appl. Sci. 2026, 16(10), 4888; https://doi.org/10.3390/app16104888 - 14 May 2026
Viewed by 344
Abstract
The underwater explosion bubble is one of the primary loads generated by underwater explosive detonations, and the presence of complex detonation products results in its unique physical evolution characteristics. Based on classical bubble dynamics theory, this paper introduces the JWL equation of state [...] Read more.
The underwater explosion bubble is one of the primary loads generated by underwater explosive detonations, and the presence of complex detonation products results in its unique physical evolution characteristics. Based on classical bubble dynamics theory, this paper introduces the JWL equation of state for explosives and the instantaneous detonation assumption to determine the initial boundary conditions of the explosion bubble, establishing a second-order analytical model. Addressing the mass loss during bubble pulsation, the physical mechanisms of convective mass transfer in the boundary layer and the inertial scattering of insoluble elements are analyzed. Accordingly, a modified dynamic model incorporating mass loss is established. The accuracy and reliability of the proposed model are verified through comparison with experimental data from underwater explosions. The results indicate that the inertial scattering of insoluble elements is the dominant mechanism governing bubble mass loss, while the macroscopic effects of the mass loss of detonation products primarily manifest during the secondary pressure pulsation and subsequent evolution stages. This study provides reliable theoretical predictions within the primary pulsation cycles of explosion bubble pulsation characteristics, providing theoretical support for further elucidating the underlying mechanisms of underwater explosion bubble dynamics. Full article
(This article belongs to the Section Applied Physics General)
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20 pages, 501 KB  
Article
Pandemics and Tourism: Empirical Evidence from Greek Hospitality Industry During the COVID-19 Period
by Andromaxi Papadam, Gaby Gavriilidis and Theodore Metaxas
Tour. Hosp. 2026, 7(5), 121; https://doi.org/10.3390/tourhosp7050121 - 27 Apr 2026
Viewed by 1073
Abstract
This study aims to examine the impact of the COVID-19 pandemic on the hospitality sector in Greece during the COVID-19 period. To this end, questionnaires were distributed in 320 enterprises operating throughout Greece exclusively in the hospitality industry. Structural equation modeling (SEM) was [...] Read more.
This study aims to examine the impact of the COVID-19 pandemic on the hospitality sector in Greece during the COVID-19 period. To this end, questionnaires were distributed in 320 enterprises operating throughout Greece exclusively in the hospitality industry. Structural equation modeling (SEM) was employed for analyzing data. The results reveal a structured transmission pathway: Business Survival Anxiety and Psychological Distress intensify Financial Strain; financial pressure constrains Strategic Capability; and diminished strategic flexibility shapes firms’ evaluation of the crisis’s overall impact. Financial Strain emerges as the central mediating mechanism, bridging managerial perceptions and organisational outcomes. These findings confirm that crisis impact is embedded in firm-level dynamics, where psychological pressures, resource constraints, and strategic contraction interact systematically. Ultimately, the study shows that the severity of the pandemic was not assessed solely in terms of immediate revenue loss, but in relation to the erosion of strategic capacity—innovation, investment potential, and long-term competitiveness. Resilience in tourism therefore depends on the alignment between psychological stability, financial robustness, and strategic adaptability. Full article
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15 pages, 5064 KB  
Article
Physics-Guided Machine Learning with Flowing Material Balance Integration: A Novel Approach for Reliable Production Forecasting and Well Performance Analytics
by Eghbal Motaei, Tarek Ganat and Hai T. Nguyen
Energies 2026, 19(9), 2022; https://doi.org/10.3390/en19092022 - 22 Apr 2026
Viewed by 682
Abstract
Reliable production forecasting is a critical task for evaluating asset valuation and commercial performance in oil and gas reservoirs. Conventional short-term forecasting methods, such as Arps’ decline curve analysis, rely on simple mathematical curve fitting and often oversimplify reservoir performance. On the other [...] Read more.
Reliable production forecasting is a critical task for evaluating asset valuation and commercial performance in oil and gas reservoirs. Conventional short-term forecasting methods, such as Arps’ decline curve analysis, rely on simple mathematical curve fitting and often oversimplify reservoir performance. On the other hand, long-term forecasting requires complex multidisciplinary models that integrate geophysics, reservoir engineering, and production engineering, but these approaches are time-consuming and have high turnaround times. To bridge the gap between long and short-term production forecasts, reduced-physics models such as Blasingame type curves have been developed, incorporating transient well behaviour derived from diffusivity equations and Darcy’s law. These models assume homogeneity and uniform reservoir properties, enabling faster results while honouring pressure performance. However, despite their efficiency, they still face limitations in reliability, particularly when extended to long-term forecasts. This paper proposes a hybrid modelling approach that integrates flowing material balance (FMB) concepts into physics-informed neural networks (PiNNs) and machine learning models to improve the accuracy and reliability of production forecasting. The proposed methodology introduces two hybrid strategies: physics-informed models enriched with FMB feature, and PiNNs. The first proposed hybrid model uses a created FMB-derived feature as input to neural networks. The second PiNN model embeds data-driven loss functions with a physics-based envelope to reflect reservoir response into the machine learning model. The primary loss function is mean squared error, ensuring minimization of data misfit between predicted and observed production rates. The study validates both proposed physically informed neural network models through performance metrics such as RMSE, MAE, MAPE, and R2. Results application on field data shows that the integration of FMB into neural network models using the PiNN concept guides the neural network models to predict the production rates with higher reliability over the full span of the tested data period, which was the last year of unseen production data. Additionally, the proposed PiNN model is able to predict the well productivity index via hyper-tuning of the PiNN model. Furthermore, the PiNN is not improving the metric performance of conventional neural networks, as it has to satisfy an additional material balance equation. This is due to a lower degree of freedom in the PiNN models. Full article
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31 pages, 5309 KB  
Article
Analysis of Embankment Seepage Responses Based on Physics-Informed Neural Networks Surrogate Model
by Cekai Fu, Qiang Wang, Chenfei Shao, Yanxin Xu and Sen Zheng
Water 2026, 18(6), 749; https://doi.org/10.3390/w18060749 - 23 Mar 2026
Viewed by 603
Abstract
Accurate and efficient analysis of embankment seepage is of vital importance for scientific assessment of embankment safety. Conventional numerical simulation techniques for embankment seepage analysis suffer from high computational cost and low efficiency. To address this issue, this paper proposes an embankment seepage [...] Read more.
Accurate and efficient analysis of embankment seepage is of vital importance for scientific assessment of embankment safety. Conventional numerical simulation techniques for embankment seepage analysis suffer from high computational cost and low efficiency. To address this issue, this paper proposes an embankment seepage response analysis method based on physical information neural network (PINN). Initially, this method considering the fluid–solid coupling and spatial variability of soil parameters of the embankment. Consequently, a numerical simulation method was developed using the finite difference method to analyze the seepage response. On this basis, a neural network loss function for the surrogate model is introduced by integrating the governing equations for fluid–solid coupling of embankments with boundary conditions. This integration incorporates physical restrictions into the seepage analysis, hence improving its interpretability. Furthermore, a feature sequence is derived from the soil parameter field via a Variational Autoencoder (VAE) to diminish input dimensionality and improve training accuracy. The feature sequence and hydraulic loading function as the model input, while the output is the piezometric head obtained from the pore water pressure. The PINN model is trained by numerical simulation results to establish the surrogate model for seepage responses analysis. A case study on the practical embankment engineering is employed to confirm the feasibility and efficacy of the proposed strategy. Comparative tests demonstrate that the PINN surrogate model markedly enhances computational accuracy relative to conventional baseline models. Overall, this approach offers a trustworthy and effective method for rapid and accurate assessment of embankment seepage characteristics. Full article
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28 pages, 4897 KB  
Article
Flow Unsteadiness Analysis in the High-Altitude Aircraft Dual-Fan System and Geometric Optimization Control Strategies
by Wentao Zhao, Jianxiong Ye, Tingqi Zhao, Lin Li and Gaoan Zheng
Processes 2026, 14(6), 993; https://doi.org/10.3390/pr14060993 - 20 Mar 2026
Viewed by 516
Abstract
When high-altitude aircraft operate in a low-density environment, the flow instability within their internal ducts poses a severe challenge to aerodynamic design and operational safety. Especially in the intake system of the tandem dual-fan configuration, the asymmetric flow caused by rotating machinery coupled [...] Read more.
When high-altitude aircraft operate in a low-density environment, the flow instability within their internal ducts poses a severe challenge to aerodynamic design and operational safety. Especially in the intake system of the tandem dual-fan configuration, the asymmetric flow caused by rotating machinery coupled with the low-density effect exacerbates flow distortion, momentum dissipation, and efficiency loss and may even trigger system instability risks such as rotational stall or surge. To address these challenges, this paper establishes a high-fidelity dynamic model of the internal flow field of the aircraft, based on the Reynolds-averaged Navier–Stokes equations and the SST k-ω turbulence model, combined with dynamic mesh technology. It reveals the unstable mechanism caused by angular momentum accumulation under co-rotation conditions and its intrinsic correlation with the degradation of aerodynamic performance. Inspired by the concept of micro-flow regulation, an active flow control strategy integrating discrete auxiliary injection and local geometric shape optimization is proposed. Numerical results show that by reasonably arranging auxiliary injection holes in the intake duct and optimizing local geometric fillets, the uniformity of intake flow can be effectively improved, and the formation of large-scale vortex structures can be suppressed. This method increases the system’s flow capacity by approximately 47.4%, significantly improves the total pressure recovery coefficient and fan aerodynamic efficiency, and reduces the amplitude of low-frequency pressure fluctuations by approximately 23.1%. Research shows that in high-altitude low-Reynolds-number conditions, micro-flow regulation combined with geometric reconstruction can effectively suppress flow instability induced by rotating machinery. This achievement provides a theoretical basis and feasible engineering path for aerodynamic stability design and optimization of key components, such as the aircraft intake and exhaust systems and thermal management systems, and is of significant value for improving the overall performance and reliability of high-altitude long-endurance aircraft. Full article
(This article belongs to the Section Process Control, Modeling and Optimization)
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22 pages, 3319 KB  
Article
Study, Modelling and Computing of Pressure Losses in GH2 Pipelines
by Akshay Bambore, Patrick Hendrick and Jean Philippe Ponthot
Energies 2026, 19(4), 885; https://doi.org/10.3390/en19040885 - 8 Feb 2026
Viewed by 595
Abstract
The Wallonia region of Belgium aims to transition to a modern hydrogen infrastructure. Given the relatively low density of hydrogen gas, it is important to understand its nature and behavior during transport through pipelines. This study aims to observe the pressure loss in [...] Read more.
The Wallonia region of Belgium aims to transition to a modern hydrogen infrastructure. Given the relatively low density of hydrogen gas, it is important to understand its nature and behavior during transport through pipelines. This study aims to observe the pressure loss in pipelines due to surface roughness with H2 and other singular losses to find a solution to minimize the amount of pressure loss that occurs during transportation. This study involves numerical methods and gas equation models to determine the pressure loss. This analysis includes the properties of hydrogen gas, the pipeline material used, the friction factor, pipeline efficiency, and other relevant properties of hydrogen and pipelines. To address this challenge, the study integrates numerical fluid dynamics methods with structural modelling of pipeline walls. It accounts for long-term friction effects, erosion over several years, radial pressure gradients (mixing pressure drop), acceleration effects, and gravity influences, considering the non-ideal behavior of gaseous hydrogen (GH2). This study provides a systematic comparison between AGA-based analytical models and CFD simulations using a scaled pipeline approach, enabling reliable estimation of pressure losses in long-distance hydrogen pipelines. The proposed methodology integrates scaling, numerical validation, and CFD simulation to compute pressure losses in a hydrogen pipeline. Full article
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