Integrating numerical and regression methods for estimating discharge coefficients of intake structures with wingwalls in irrigation networks

Numerical modeling and discharge coefficient analysis of semi-elliptical sharp-crested weirs

ABSTRACT Natural flood management (NFM) uses natural features and processes to manage flood risk. Although natural processes in river flow are well known, their use to manage floods has been only deeply analyzed since recent years, and the hydraulic behavior and performance of some measures is not yet fully understood. Leaky woody dams (LWD) are one example of the application of NFM, which is very complex to understand, and many uncertainties are still unresolved. In practical applications, the effect of LWD is modeled with different assumptions (Manning's n , geometry changes, porosity, etc.), but none of them represent the real physics of the problem. This paper presents novel lab experiments that attempt to simulate LWD in a river channel. The experiments were developed in a straight research flume. The performance of the LWD in terms of outflow capacity and the effect in terms of increase in water levels upstream and velocities downstream have been analyzed. The orifice + weir model has been proposed as the more realistic model to simulate the flow through LWD, and empirical coefficients of discharge for applications in analytical methods and in numerical models have been obtained. The results help to understand the hydraulic behavior of LWD, and the coefficients of discharge obtained can be useful to reduce uncertainties in numerical modeling for practical applications.

ABSTRACT Gas pipelines are prone to leakage due to time, corrosion damage and construction. In order to evaluate and control leakage risk effectively, it is necessary to predict the flow coefficient accurately. Until now, there has not been a reliable tool that can accurately predict the discharge coefficient after leakage. In this work, the impact of different influencing factors on the discharge coefficient was analyzed. The prediction performance of five machine learning (ML) models and deep learning model, including Decision Tree (DT), Extra Trees (ET), Random Forest (RF), Gradient Tree Boosting (CATBoost), eXtreme Gradient Boosting (XGBoost), and Convolutional Neural Network (CNN) were employed to predict discharge coefficients is compared and evaluated. Results show that the CNN model exhibited the best prediction performance with a R 2 of 0.99998 in test data, and the maximum error is less than 4% in dataset. In addition, the predictive capabilities of the ML method are optimized for model architecture parameters by the Bayesian algorithm and K-fold cross-validation. A variety of feature analysis techniques are employed to select different optimal feature variables as input values to reduce the number of original variables used when modeling while preserving as much information as possible. The result show that the weber number, indispensable to the input parameters, served as a fundamental descriptor in the accurate prediction of the discharge coefficient. The artificial intelligence technology provides a powerful tool for accurately predicting liquid nitrogen discharge coefficients, which helps to improve the source term model for liquid nitrogen leakage safety analysis.

The sensitivities of the cavitation inception conditions and the cavitation discharge coefficient, together with the path independence and uniqueness of inception, underpin reliable use of cavitating Venturi tube under ambient conditions. With a downstream sweep rate of 1/6 °/s verified in preliminary tests, forward and backward quasi-dynamic cavitation evolution processes were sampled to construct pressure- and flow-rate-control paths for the Venturi tube used in this study. Analysis of the control paths shows that, as the critical inlet pressure approaches infinity, the critical pressure ratio and the cavitation discharge coefficient approach characteristic values of 0.6364 and 0.5573. With ±3% practical equivalence margins, they become insensitive to the critical inlet pressure above thresholds of 2.4496 and 1.7167 MPa, respectively. The inception conditions are unique; hysteresis in the critical pressure ratio emerges for critical inlet pressures of 0.40–0.45 MPa, and path independence no longer holds for critical inlet pressure exceeding 0.45 MPa. The findings indicate that detecting and controlling Venturi cavitation under ambient conditions must account for the sensitivities and path-dependence of cavitation characteristics, and they provide a useful baseline reference.

ABSTRACT Global warming has altered hydroclimatic factors that are fundamental to ecosystem functioning, and socioeconomic development. The resulting changes, compounded by human activities, have reshaped the hydrological regimes and threatened the sustainability of basin ecosystems. This study analyzes hydroclimatic and anthropogenic factors and integrates them in a regression model to assess their effects on river discharge, while also examining LULC changes in the basin. Trend tests revealed significant increases in temperatures, with maximum temperature change rate of 0.005°C/month. Rainfall showed a significant increase at higher elevations, such as Fukuyama, with a rate of 0.124 mm/month, whereas snowfall demonstrated a significant decline of −0.094 cm/month, with potential impacts on spring irrigation. Regression analysis indicated that rainfall had the strongest influence on discharge (coefficient = 0.3745, p < 2 × 10−¹⁶), followed by temperature-snowfall interaction. Irrigation had a small but statistically significant negative effect on discharge. LULC analysis revealed that forest cover expanded from 81.6% to 89.5%, while cropland and grassland declined by 24.1% and 51.5%, respectively, largely due to population decline and land abandonment. These findings demonstrate how combined climatic and anthropogenic factors influence discharge variability and ecosystem resilience, providing critical insights for adaptive land and water management under climate change.

The labyrinth weir is an effective hydraulic structure, offering high discharge efficiency and economic advantages, making it a suitable option for dam construction or rehabilitation projects. Owing to its complex geometry, significant research efforts have been dedicated to enhancing its hydraulic performance. Since the beginning of this century, Computational Fluid Dynamics (CFD) has emerged as a vital approach, complementing traditional methods in the design of hydraulic structures. This study employs CFD ANSYS FLUENT to examine the discharge coefficient of a semicircular labyrinth weir, featuring a cyclic arrangement and a half-round crest profile. The numerical models and simulations address two-phase flow (air and water) under incompressible and free-surface conditions. The CFD ANSYS FLUENT approach used is multiphase flow modeling using the Volume of Fluid method to track the free water surface. For turbulence effects, it is complemented with the standard k-ε model and the Semi-Implicit Method for Pressure Linked Equations algorithm for pressure–velocity coupling. In addition, for boundary conditions, the flow velocity was defined as the inlet to the channel and atmospheric pressure as the outlet, and the walls of the channel and weir are considered solid, stationary, and non-sliding walls. The model was validated with experimental data reported in the literature. The results indicate that the semicircular labyrinth weir achieves greater discharge capacity when the headwater ratio HT/P increases for HT/P ≤ 0.25. A regression analysis mathematical model was also developed, using the HT/P ratio, to predict the discharge coefficient for 0.05 ≤ HT/P ≤ 1. Relative to other geometrical configurations, the semicircular labyrinth weir demonstrated a discharge capacity that was up to 88% higher than that of the trapezoidal labyrinth weir. Both weir and cycle efficiency were assessed, and maximum weir efficiency was observed when HT/P ≤ 0.1, while cycle efficiency peaked at HT/P ≤ 0.25. The geometric configuration under analysis demonstrated greater economic efficiency by providing a reduced total length and enhanced discharge capacity relative to trapezoidal designs, especially when the sidewall angle α is considered as α ≤ 12°. The study concludes by presenting a design sequence detailing the required concrete volume for construction, which is subsequently compared to the specifications of a trapezoidal labyrinth weir.

Experimental and computational analysis of circular eccentric venturi meters: Discharge coefficients and flow regimes

Abstract Focusing on the development requirements for enhancing the shock absorption performance of landing gears, this paper proposes an optimization method for landing dynamics based on parameter sensitivity. Taking a specific aircraft landing gear as the object, its landing impact dynamics model was constructed. The Sobol global sensitivity analysis method was used to quantitatively evaluate how key shock absorber parameters—both structural and pneumatic-hydraulic—affect performance metrics such as ground loads and stroke. The results show that the oil chamber parameters—specifically the discharge coefficient, main orifice area, and pressurized oil area—have the greatest impact. Among these, the discharge coefficient has a total effect index as high as 56.67%. Based on this, the orifice area was selected as the optimization variable, with the goal of reducing the maximum landing vertical load. Considering engineering constraints such as stroke, a genetic algorithm was applied for optimization and verified through experiments. The optimized maximum vertical load was significantly reduced by 12.7%, effectively improving the shock absorption performance.

This study comprehensively investigated the hydraulic behavior of labyrinthine side weirs in open channels using newly developed statistical approaches based on experimental data compiled from the literature. The model used in this study is a multiple linear regression model. The main objective was to reveal the complex relationships between the discharge coefficient (Cd) and the dimensionless flow parameters and the discharge. Experimental data showed that Cd values exhibit a nonlinear relationship with the flow regimes, which is characterized by the dimensionless h/w ratio with the optimal hydraulic performance region being h/w=2.0−2.6. Furthermore, a general decreasing trend in Cd was observed as the discharge (Q) increased, with a particularly dramatic decrease at high flow rates above 10 L/s, indicating potential choking effects at high discharges. A model was developed to estimate the flow coefficients using SPSS statistical software. While this model successfully captured the general trends, it showed significant deviations from the experimental data in certain flow regimes. Regression analyses revealed that the model can predict with high accuracy in low and medium-high flow rate ranges (e.g., R2=0.91 for 6-8 L/s, R2=0.95 for 11-12.5 L/s), but that there is a significant decrease in predictive power at very high flow rates (R2=0.70 for 17-23 L/s). These findings point to limitations in the generalizability of the model and the need for more sophisticated modeling approaches, especially for the complex flow dynamics in high flow regimes. Regression analyses showed that the model performed with high accuracy in medium flow ranges (R2=0.91 and R2=0.95), but its predictive power decreased at high flow rates (R2=0.70). These findings contribute to the hydraulic design of labyrinth weirs and underscore the need for advanced predictive tools in high-flow scenarios. The obtained data provide significant contributions to the hydraulic design principles of labyrinth weirs and provide a scientific basis for the development of more effective and reliable tools for water resources engineering applications.

ABSTRACT An experimental methodology was applied in this research to examine the outcomes of gate positioning and the performance of a sill with an orifice under sluice gates on the discharge coefficient. For this purpose, rectangular sills with the number of orifices one, two, three, and four under flow rate ranging from 150 to 750 liters per minute and the opening height of the gates 2 and 3 cm were investigated. The findings indicated that incorporating a sill with an orifice under the sluice gates enhanced the discharge coefficient by 37% compared to when the gate was absent. Increasing the number of orifices in the sill resulted in a 5 to 23% reduction in the discharge coefficient compared to the condition with no orifice. Finally, a prototype equation was developed to estimate the discharge coefficient (Cd) of the gate with a sill containing an orifice, demonstrating a high coefficient of determination and an acceptable root mean square error.

Correction: Investigating the Discharge Coefficient in Crump Weirs Under Increasing Flow Rate Conditions (Unsteady Flow)

In this study, experimental work was performed to represent the flow within an open channel and through a compound weir of semi-circular and trapezoidal sections for different flow conditions. This study aims to evaluate the hydraulic performance of the compound weir by finding the value of the coefficient of discharge, Cd, and deriving an equation linking the value of Cd to the rest of the hydraulic and geometric parameters governing the flow conditions. Fifteen laboratory models of a sharp-crested compound weir were tested inside a laboratory channel with dimensions of 0.3 m wide, 0.45 m high, and 15 m long. The dimensions of the compound weir opening were changed while maintaining the general shape, which consisted of a trapezoidal part with a different side slope (θ) and a semicircular part that remained constant. The effects of water depth over the crest of compound weir (h), the depth of water upstream compound weir (hu), the diameter of the semi-circular part (D), the width of the first base of the trapezoidal part (b1), the width of the second base of the trapezoidal part (b2), the perpendicular height of the trapezoidal part, and the slope of the trapezoidal side (θ) were taken into consideration in deriving a non-dimensional formula representing the relationship between these parameters and Cd. Using Excel 365 and SPSS 26 software, a non-linear relationship was derived to estimate Cd, and a good value of the coefficient of determination (R2) was achieved.

This study investigates the impact of groove implementation on the hydraulic performance of sharp-edged trapezoidal side weirs, focusing on discharge coefficients and shear stress behavior. The simulation processes were carried out using the VOF (Volume of fluid) methodology in combination with the RNG (Re-normalize group) model for turbulence. The validation with experimental data by comparison showed that the relative error in the range of 0.4-2.6%. It was found from the results that the discharge coefficient increases in the no-grooved model and decreases in the grooved model. The identified variation of the discharge coefficient range through different Froude numbers lies between 0.6 and 0.8, where the discharge coefficient of the no-grooved model is larger by 2.68% compared to that of the grooved model. The grooved model was more effective for lower flow rates, while the no-grooved model was more effective for higher flow rates. In all cases, in both models, the discharge coefficient increases with the Froude number, with a greater increase observed in the no-grooved configuration (19.64% higher). The research indicated that grooves significantly reduce shear stresses at the crest of the weir, reducing further damage to the structure. The variation in shear stress between the two models was most evident under high flow conditions, demonstrating the efficiency of the grooved model in reducing harmful stresses and energy dissipating.

Thermal management of aero-engine supersonic convergent–divergent nozzles under extreme flow conditions remains a critical challenge. This study investigates the flow interactions and cooling performance of novel expanding and branching film hole configurations in a two-dimensional supersonic nozzle using Reynolds-Averaged Navier–Stokes and Delayed Detached Eddy Simulation (DDES) methods, and anti-kidney vortices are identified as an effective cooling mechanism. A baseline cylindrical hole is compared against three expanding holes (forward-inclined, fan-shaped, and dust-pan) and three branching holes (backward-bending, forward-bending, and dumbbell) under a low coolant-to-mainstream mass flow ratio of 0.0079%. Results reveal that shock/expansion waves induced by coolant injection exhibit limited propagation due to low secondary flow rates. Branching holes generate anti-kidney vortices that suppress traditional kidney vortex dominance, enhancing cooling effectiveness by up to 28.65% and improving spanwise uniformity by 47.74% compared to cylindrical holes. Expanding holes, particularly the fan-shaped design, increase cooling uniformity by 19.86% but exhibit shorter high-effectiveness regions. Transient DDES analyses highlight coherent vortex structures (e.g., hairpin vortices) and asymmetrical coolant distribution influenced by vortex evolutions. Despite minor reductions in discharge coefficient by 0.12% and thrust coefficient by 0.01%, all configurations introduce negligible aerodynamic losses. This work provides critical insights into vortex-driven cooling mechanisms and establishes design guidelines for high-efficiency supersonic nozzle thermal protection systems.

Abstract The micro-flow control system, serving as a critical component of the air-breathing electric propulsion storage and supply system, is responsible for precise delivery of captured rarefied atmospheric gas. As a key technology in air-breathing electric propulsion, its performance directly determines the operational stability and efficiency of the thruster. An essential flow regulation approach involves adjusting upstream pressure and modifying micro-orifice dimensions. Micro-orifices (micron-scale throat-diameter conical entrance sonic nozzles) act as flow output elements in this system. This study investigates the flow characteristics of these micro-orifices under low Reynolds number conditions (Re &lt; 2000), with the upstream side maintained at standard atmospheric pressure and the downstream connected to a vacuum chamber (40-120 μm orifices) via pressure controllers. Experimental analysis revealed that when the Reynolds number is below 2000, the critical back pressure ratio (CBPR) of the micro-orifices is approximately 0.19. The discharge coefficient C d exhibits an increasing trend at Reynolds numbers below 900, while oscillating between 0.88 and 0.94 when the Reynolds number exceeds 900. Compared to conventional micron-scale arc-shaped sonic nozzles (CBPR = 0.53, C d = 0.98), the studied micro-orifices demonstrate reduced CBPR and C d values, indicating greater deviation between actual and theoretical flow rates under low Reynolds conditions. These findings provide theoretical foundation and technical references for optimizing micro-flow control systems in air-breathing electric propulsion applications.

For evaluating the heat transfer performance in a jet impingement cooling system featuring W-shaped rib turbulators, an experimental investigation was completed. Six different configurations, including three W-rib pitches (P/e=18, 9, and 6) and two jet-to-target surface spacings (z/d=3 and 6), were considered to completely assess their influence on the heat transfer, pressure loss, and crossflow of a relatively long impingement channel with an in-line array of 4×12 impinging jets. Moreover, the regionally averaged heat transfer coefficients were evaluated based on two different reference temperatures: jet inlet temperature and local bulk temperature. Each configuration was experimentally tested at four Reynolds numbers, based on the jet diameter (Re=10,000–60,000), using the copper plate experimental method. The results show that the heat transfer enhancement can reach up to 25% in the narrow channel with the P/e=6 configuration. Also, the crossflow can deteriorate or enhance the local heat transfer along the channel. The discharge coefficients showed minimal variations, and the pressure loss increased in the W-rib channels is between 1.3 and 2.5 times the smooth channel pressure loss. Finally, a design correlation was developed for the area-averaged Nusselt number estimation in W-rib roughened impingement channels.

Control valves, as the core components of flow control and pressure-regulating pipeline systems, critically influence operational safety and maintenance efficiency. Although cavitation induced by valve throttling is inherently challenging to eliminate, effective suppression strategies are essential to ensure valve reliability. Among these, post-valve pipeline expansion technology has emerged as a promising approach due to its structural simplicity and high efficiency. This study investigates the cavitation suppression mechanism of the sudden expansion body in two typical control valves (plunger valves and fixed cone valves) through integrated theoretical analysis, physical experiments, and numerical simulations. A quantitative correlation is established among the valve discharge coefficient, expansion ratio, and cavitation number. The results demonstrate that the sudden expansion body significantly enhances the valve’s anti-cavitation performance, albeit with diminishing returns as the expansion ratio increases. Furthermore, based on hydraulic stability criteria and cost–benefit analysis, an optimal expansion ratio of 4.00 is proposed for single-valve circular expansion pipelines. This finding provides a practical trade-off between cavitation suppression efficacy and manufacturing costs, offering valuable insights for industrial applications.

ABSTRACT Grate inlets are crucial to urban stormwater drainage, influencing network efficiency and flood risk. Previous studies lack data on discharge capacity and coefficients of sump inlets under clogging conditions. This study experimentally investigates the hydraulic characteristics of sump grate inlets under varying degrees of clogging in the broad-crested weir (BCW) mode. The results show that the discharge coefficient in BCW mode C w remains relatively stable, averaging 0.858 ± 7% across a wide range of clogging conditions, with a perimeter contraction coefficient ranging from 0.178 to 1. Additionally, a clear functional relationship between the discharge coefficient C w and the Froude number Frw was obtained. This relationship enables a quantitative assessment of the sum of kinetic energy coefficient and the equivalent coefficient of hydraulic resistance of the inlet. These findings provide some insights for the design and modelling of stormwater sump grate inlets in weir mode, taking into account clogging effects.

Accurately predicting the discharge coefficient (Cd) in weir structures is crucial for improving hydraulic designs and ensuring their safe operation. This study focuses on developing and testing advanced Machine Learning (ML) models to estimate Cd in Semicircular Labyrinth Weirs (SCLWs). The models explored include a Tabular Neural Network (TabNet) optimized with the Moth Flame Optimization algorithm (TabNet-MFO), an Extreme Learning Machine (ELM) enhanced with the Jaya and Firefly Algorithms (ELM-JFO), a Decision Tree (DT), and a Light Gradient Boosting Machine (LightGBM). One of the key innovations in this study is the introduction of the TabNet-MFO framework. Through sensitivity analysis, using tools like the Explainable Boosting Machine (EBM) and SHapley Additive exPlanations (SHAP), the study found that the ratio of upstream flow depth to weir height (h/P) is the most significant factor affecting Cd predictions. Other important factors include the number of weir cycles (N) and the ratio of crest length to weir height (lC/P). The dataset was split into 75% for train and 25% for validation. The performance of each model was gauged using a number of statistical indicators. They were the coefficient of determination (R2), the Root Mean Square Error (RMSE), the symmetric Mean Absolute Percentage Error (sMAPE), the Scatter Index (SI), and the Weighted Mean Absolute Percentage Error, or WMAPE and along with Taylor diagrams and the Performance Index (PI) for comparison. In the training phase, the ELM-JFO model delivered the best results in predicting Cd, with a PI of 166 and a normalized centered RMSE (E’) of 0.0052. The TabNet-MFO model also performed well, with a PI of 142 and an E’ of 0.0068. The LightGBM and DT models produced good results as well, with PIs of 89.45 and 89.36, respectively. In the testing phase, the TabNet-MFO model remained the top performer (PI = 81.92, E’ = 0.0118), followed by ELM-JFO (PI = 69.71, E’ = 0.0139). LightGBM and DT showed lower accuracy, with PIs of 60.62 and 47.55 and E’ values of 0.0159 and 0.0199, respectively. The novelty of this research lies in combining interpretable and hybrid ML techniques for Cd estimation, offering a reliable alternative to traditional empirical and regression-based methods. These results show the potential of ML in improving flow prediction accuracy and supporting better hydraulic structure design.