computational fluid dynamics

Morning glory spillways play a critical role in water flow management in dams and reservoirs, influenced significantly by the discharge coefficient. This coefficient determines the efficiency and risk of spillway performance under flood conditions. In this study, using 80 experimental datasets collected from two morning glory spillway inlet sections with square and circular zigzag shapes (featuring 4, 8, and 12 zigzags), two machine learning models—Support Vector Machine (SVM) and Gene Expression Programming (GEP)—were applied to simulate the discharge coefficient. Independent variables included the number of zigzags (n), Froude number (Fr), relative water head (H/P), and spillway shape index (R/D). Performance metrics (RMSE, MAE, R²) were employed to evaluate the accuracy of the models. Among various SVM models, the RBF kernel with γ = 0.1 yielded the most optimal results. The training and testing phases for the circular spillway showed (RMSE, MAE, R²) values of (0.9262, 0.0696, 0.0848) and (0.9820, 0.0346, 0.0398), respectively, while for the square spillway, these values were (0.9707, 0.073, 0.0904) and (0.9334, 0.0676, 0.0787). The GEP model demonstrated superior performance, particularly for the circular spillway with three genes, a head size of 9, and 45 chromosomes, yielding (RMSE, MAE, R²) values of (0.9778, 0.0375, 0.0451) and (0.9811, 0.0315, 0.0396) in the training and testing phases, respectively. For the square section, the GEP model with 55 chromosomes achieved (RMSE, MAE, R²) values of (0.9741, 0.0494, 0.0597) and (0.9591, 0.0503, 0.0594) for training and testing, respectively.

Intouduction:

Groynes at water intake locations significantly increase the flow diverted from rivers by optimizing incoming water control. Vaghefi and Ghodsian (2017) experimentally studied flow patterns around a T-shaped Groyne within a 90-degree arc using a moving bed. Shaker and Kashfipour (2013) compared flow velocity and shear stress distribution with and without Groynes. Behnam-Talab et al. (2018) simulated porous Groynes using FLOW-3D software. Shahinejad et al. (2022) applied a multi-objective algorithm to optimize T-shaped Groyne dimensions, achieving superior results, compared to previous designs. Zare and Honer (2016) investigated how simple Groynes reduce lateral erosion in river arches under laboratory conditions, emphasizing the influence of Groynes on erosion patterns. These studies collectively highlight the importance of Groyne design in enhancing water extraction and mitigating erosion.The review of literatures confirms that both laboratory and numerical studies have been conducted to examine the characteristics of various types of Groynes and the impact of flow patterns on them. However, there is a lack of studies addressing the simultaneous application and comparison of numerical and data-driven models in the investigation of geometric and hydraulic characteristics, particularly concerning the effect on the amount of diverted discharge from a canal into intake featuring T-shaped and L-shaped Groynes. Consequently, this research aims to evaluate the performance of two MLMs, specifically SVM and GEP in comparison with the Computational Fluid Dynamics (CFD)-based FLOW-3D model, on a laboratory scale.

Groynes play a crucial role in river engineering by regulating river flow. This study assesses the efficacy of two machine learning algorithms—support vector machine (SVM) and gene expression programming (GEP)—in comparison with FLOW-3D software for simulating diverted flow in a laboratory setting. The experimental model was tested in a laboratory flume with T-shaped and L-shaped Groynes positioned at 90 and 135-degree angles to channel the discharge into the intake system. The machine learning models incorporated three independent variables: the flow Froude number, the angle of water intake, and the relative length of the Groynes. Out of 96 laboratory data points, 70% were allocated for model training and 30% for model testing. Model performance was assessed using the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) indices.

 The results indicated that the GEP model surpassed the SVM model. For the L-shaped Groyne, the values for (R², MAE, RMSE) during both the training and testing phases were (0.9325, 0.9878, 1.2536) and (0.9836, 0.4102, 0.6325), respectively. For the T-shaped Groyne, the corresponding values were (0.9025, 1.2534, 1.8502) during training and (0.9873, 0.3337, 0.4972) during testing. In the FLOW-3D model, after calibration and validation, a Manning's roughness coefficient of 0.035 and the Prandtl's mixing length model were chosen for turbulence simulation. The performance indices during the testing phase for the L-shaped and T-shaped Groynes were (0.9607, 0.9363, 1.2070) and (0.9513, 1.1256, 1.3759), respectively. The GEP model showed a relative advantage over the FLOW-3D model.

Concutions:

 This study compares the performance of MLMs (SVM, GEP) with FLOW-3D in simulating diverted flow using T-shaped and L-shaped Groynes. Results from laboratory flume tests showed GEP outperformed SVM and FLOW-3D, particularly in simulating flow diversion, evaluated by RMSE, MAE, and R² performance indices.

Hydraulic jump is a type of rapid variable currents, which has surface turbulence and twisting of water from the beginning to the end, and is known as an energy-wasting phenomenon. In this research, the numerical simulation of hydraulic jump was done in the case of initial negative step of 3 and 6 cm, bed roughness of 2 cm and reverse slope of 1.5 and 3%. RNG and k-ε disturbance models were used in this research. Also, two types of uniform and non-uniform grids were used. According to the numerical modeling results, the RNG turbulence model calculated the turbulence of the flow field more accurately compared to the K-ε turbulence model. The statistical indices of NRMSE, R2 and d for the numerical simulation results of the water surface profile were obtained as 10.1, 0.993 and 0.994 respectively. Also, the values of these indices were calculated for the speed profile simulation results, respectively 16.36, 0.944 and 0.97. The error of the numerical model in calculating the values of the velocity profile was higher compared to the water level profile, which can be attributed to the severe flow turbulence and instantaneous velocity fluctuations in any vertical direction within the range of occurrence of hydraulic jump and intensification of air-water mixing. Comparison of the simulation results with the laboratory results of water surface profile, velocity profile, conjugate depth ratio, rolling length and hydraulic jump length and energy loss ratio shows the capability of the numerical model in the three-dimensional simulation of the free hydraulic jump flow field.

Density difference causes density flow. Density flow is the the movement of the forehead, body, and tail of the heavy fluid into the ambient flow, and the buoyancy or gravity force causes the drive force. The movement of dense current under clear water creates a shear layer at the interface between clear water and density fluid. Therefore, at the interface, many cuts and vortices are created and this causes the entrainment of smooth water and density flow, which reduces the amount of density difference and the buoyancy force. Hosseini & Fattahi (2020) showed that the variations in the waterway shape causes higher velocity of density flow and decreases the flow thickness. Also, increasing the density of density flow, increases the maximum velocity in velocity profiles. This increase in the maximum velocity of the density flow is more pronounced in streams with higher inlet flow. The velocity profile patterns in the wall and jet area of the density flow body are influenced by the flow regime.

In this research, the density flow is illustrated in 3 different models according to Figure 1. The opening rate of the density flow valve is considered to be 1 cm. In this research, we have tried to show the effect of curvature at 180 ° bend and sinusoidal shape restricted channel and the flood plain. In this simulation the channel with 4 different longitudinal slopes, 0.002, 0.005, 0.008 and 0.02, are modeled and also 4 different densities, 0.00667, 0.00727, 0.00859 and 0.01 g / cm3, and 4 f Froude numbers, 1.2, 3, 5 and 8, have been used. Moreover six different mesh gridding for the flood plain and six different mish gridding for the channel are considered. it should be mentioned that 6 types of turbulence models ( The k-e model (standard, RNG, investigable), the kw model (standard, SST) and the RSM model (linear strain-pressure) are used.

Four types of networks were selected for finite channel with sinusoidal curvature. Figure (3) compares the different mesh gridding with the tested mesh and it was observed that in the range close to the bed, at high speeds, meshes with dimensions of 60 × 20 × 140 are very close to the experimental model developed by Hosseini & Fattahi (2020). Also, considering all 3 optimal models for turbulence models, k-ε models can be considered more optimal than k-ω and RSM models. The effects of the increasing slope of the flume bed in the wall area is more tangible than in the jet area while Froude number and input density are the same. On the other hand, increasing the slope of the channel bed from 0.2% to 2%, reduces the density flow thickness along the channel. As a result, the flow velocity shows an increase in the density flow which causes the growth of the drive force and will increase the turbulent flow velocity by increasing the inlet Froude number from 1.22 to 8. In all laboratory data, the density current concentration profile in the jet area shows a higher dispersion of 47% than the wall area. By increasing the slope of the channel from 0.2% to 2%, the dispersion rate increases by 65%. Richardson data and entrainment ratio in model No.1 increased by 10% compared to the experimental model and also these data increased by 19% in model No.2 compared to the experimental model.

In this research, we tried to simulate the three-dimensional density flow in models with 180 degree bend and limited sinusoidal curvature as well as sinusoidal patterns with plain flood. Also, the most optimal computational mesh, turbulence model, slope, density and Froude number are investigated as long as the studies include the depth profiles of velocity, density, turbulence, etc. in a situation where the channels are curved. Moreover, by increasing the number of Froude numbers from 1.22 to 8, due to model number 1 with 180 degree curvature, the pattern of density profile decreases by 19% and 21.3% compared to models number 2 and 3, respectively. Also, in all laboratory data, the density current concentration profile in the jet area shows a higher dispersion of 47% than the wall area. With increasing the slope of the channel from 0.2% to 2%, the dispersion rate increases by 65%. Richardson number has established a significant relationship with the entrainment ratio, which has a correlation of 0.71. Also the numerical entrainment ratio (for all three models) increased by 4.4% compared to the experimental model.AcknowledgmentsWe would like to thank Water and Hydraulic Laboratory of Shiraz University for their effective cooperation.

One of the most important issues to be considered in trapezoidal channels is the effect of side slope effects on the shear stress and jump characteristics including energy loss, jump length and conjugate depths ratio which have been studied in this study. For this purpose, at first, model has been calibrated by using an experimental results published for trapezoidal channel of 45 degree side slope, the RGN model was selected from the turbulent models, and then the model for different hydraulic conditions (Froude number between 1.5 to 12) and two slopes of 60 and 75 degrees has been performed and the results have been obtained. Due to the shear stress importance, which is usually not investigated in experimental researches, in this study the distribution of bed shear stress has been calculated in all three channels side slopes, and also the hydraulic jump characteristics. The results of this study on the three side slopes show different behavior of hydraulic jumps and shear stress in trapezoidal channel of 45 degree side slope, in which the asymmetry of jump is very tangible and the shear stress concentration is observed on the left side of the channel wall. Comparison of the shear stress results show a significant reduction in shear stress after jump which the maximum amount of this reduction is related to the trapezoidal channel of 45 degree side slope. It was also found that by increasing the side slope the amounts of shear stress and the sequent depths ratio increase, and the amounts of energy loss and length of jump decrease.

The use of stepped spillways has been increasingly on the rise due to their low cost and high efficiency. Hence، growing attention has been paid to the studies in this field by dam engineers; however، most of these studies have focused on the stepped spillways with uniform step height at the cost of ignoring non-uniform step heights، which also demand particular attention. In this study، a physical model of Herat Dam for a 1. 3-m high stepped spillway with a slope of 19. 2 ° was used to verify the numerical model. Then، three types of stepped configurations were tested using computational fluid dynamics in the ANSYS CFX software for the flow range of. Further، a two-phase flow simulation was carried out for each configuration and all discharge ranges. The results were compared in terms of flow pattern، energy dissipation and aeration point. The results showed minor difference in terms of energy dissipation for nappe regime flow and marked difference in terms of skimming regime flow.