Use of artificial neural networks for prediction of discharge coefficient of triangular labyrinth side weir in curved channels

Side weirs have been extensively used in hydraulic and environmental engineering applications. The discharge coefficient of the triangular labyrinth side weirs is 1.5-4.5 times higher than that of rectangular side weirs. This study aims to estimate the discharge coefficient (C_d) of triangular labyrinth side weir in curved channel by using artificial neural networks (ANN). In this study, 7963 laboratory test results are used for determining the C_d. The performance of the ANN model is compared with multiple nonlinear and linear regression models. Root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficient (R) statistics are used as comparing criteria for the evaluation of the models’ performances. Based on the comparisons, it was found that the neural computing technique could be employed successfully in modeling discharge coefficient from the available experimental data. There were good agreements between the measured values and the values obtained using the ANN model. It was found that the ANN model with RMSE of 0.1658 in validation stage is superior in estimation of discharge coefficient than the multiple nonlinear and linear regression models with RMSE of 0.2054 and 0.2926, respectively.     

Predicting discharge capacity of triangular labyrinth side weir located on a straight channel by using an adaptive neuro-fuzzy technique

Side weirs are widely used for flow diversion in irrigation, land drainage, urban sewage systems and also in intake structures. It is essential to correctly predict the discharge coefficient for hydraulic engineers involved in the technical and economical design of side weirs. In this study, the discharge capacity of triangular labyrinth side weirs is estimated by using adaptive neuro-fuzzy inference system (ANFIS). Two thousand five hundred laboratory test results are used for determining discharge coefficient of triangular labyrinth side weirs. The performance of the ANFIS model is compared with multi nonlinear regression models. Root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficient (R) statistics are used as comparing criteria for the evaluation of the models’ performances. Based on the comparisons, it was found that the ANFIS technique could be employed successfully in modeling discharge coefficient from the available experimental data. There are good agreements between the measured values and the values obtained using the ANFIS model. It is found that the ANFIS model with RMSE of 0.0699 in validation stage is superior in estimation of discharge coefficient than the multiple nonlinear and linear regression models with RMSE of 0.1019 and 0.1507, respectively.     

Predicting discharge coefficient of triangular labyrinth weir using extreme learning machine,artificial neural network and genetic programming

Weirs are a type of hydraulic structure used to direct and transfer water flows in the canals and overflows in the dams. The important index in computing flow discharge over the weir is discharge coefficient (C _d). The aim of this study is accurate determination of the C _d in triangular labyrinth side weirs by applying three intelligence models [i.e., artificial neural network (ANN), genetic programming (GP) and extreme learning machine (ELM)]. The calculated discharge coefficients were then compared with some experimental results. In order to examine the accuracy of C _d predictions by ANN, GP and ELM methods, five statistical indices including coefficient of determination (R ²), root-mean-square error (RMSE), mean absolute percentage error (MAPE), SI and δ have been used. Results showed that R ² values in the ELM, ANN and GP methods were 0.993, 0.886 and 0.884, respectively, at training stage and 0.971, 0.965 and 0.963, respectively, at test stage. The ELM method, having MAPE, RMSE, SI and δ values of 0.81, 0.0059, 0.0082 and 0.81, respectively, at the training stage and 0.89, 0.0063, 0.0089 and 0.88, respectively, at the test stage, was superior to ANN and GP methods. The ANN model ranked next to the ELM model.

     

Turbulent Flow in the Vicinity of Side Weirs in Subcritical Conditions

Side weirs are installed on the main channels wall in sewage disposal systems and irrigation networks to divert the flow. In this paper, the flow pattern in rectangular channels along a side weir is predicted using the Volume of Fluid (VOF) scheme and the standard k–ε and RNG k–ε turbulence models. A comparison between the numerical and experimental results shows the high accuracy of the numerical model. For example, the values of root mean square error (RMSE), mean absolute relative error (MARE) and correlation coefficient (R) for the lateral velocity on z = 0.183 m level are calculated 3.782, 0.399 and 0.993, respectively. According to the simulation results, as the flow approaches to the side weir plane the flow field pressure decreases suddenly and at the end of the side weir the pressure increases. Also, by advancing the flow towards the downstream of the side weir the turbulent kinetic energy of the flow within the rectangular channel decreases. For all levels, the turbulent length scale value suddenly increases by reaching the flow to the end of the side weir.     

An expert system for predicting aeration performance of weirs by using ANFIS

A free overfall jet from a weir plunging into downstream water causes entrainment of the air bubbles if the free overfall jet velocity exceeds a certain critical value and hence aeration occurs. This study investigates the free overfall jets from triangular sharp-crested weirs and effect on their air entrainment rate and the aeration efficiency. An expert system based on adaptive network based fuzzy inference system (ANFIS) was obtained for predicting air entrainment rate and aeration efficiency of weirs. The performance of ANFIS model was compared with multi nonlinear and linear regression models. There were good agreements between the measured values and the values obtained using the ANFIS model.     

Neural networks for estimation of discharge capacity of triangular labyrinth side-weir located on a straight channel

Side-weirs are flow diversion devices widely used in irrigation, land drainage, and urban sewage systems. It is essential to correctly predict the discharge coefficient for hydraulic engineers involved in the technical and economical design of side-weirs. In this study, the discharge capacity of triangular labyrinth side-weirs is estimated by using artificial neural networks (ANN). Two thousand five hundred laboratory test results are used for determining discharge coefficient of triangular labyrinth side-weirs. The performance of the ANN model is compared with multi nonlinear regression models. Root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficient (R) statistics are used as comparing criteria for the evaluation of the models’ performances. Based on the comparisons, it was found that the neural computing technique could be employed successfully in modelling discharge coefficient from the available experimental data. There were good agreements between the measured values and the values obtained using the ANN model. It was found that the ANN model with RMSE of 0.0674 in validation stage is superior in estimation of discharge coefficient than the multiple nonlinear and linear regression models with RMSE of 0.1019 and 0.1507, respectively.     

Computational simulation of flow over stepped spillways

Numerical simulations of water flow over stepped spillways with different step configurations are presented. The finite element computational fluid dynamics module of the ADINA software was used to predict the main characteristics of the flow. This included the determination of the water surface, the development of skimming flow over corner vortices, and the determination of energy dissipation. Since the actual flow is turbulent, the k-ε flow model was used. A two-phase solution process was adopted in order to optimize the overall simulation efficiency. In the first phase, a simple yet reasonable water surface consisting of three straight lines was used as an initial guess and was treated as a fixed wall. In the second phase, the results from the first phase were used as initial conditions and the water surface was treated as a free surface that evolved to attain a steady state configuration. For all the cases considered, the predicted water surface profile over the entire length of the spillway was in close agreement with the experimentally measured water surface profile. The predicted energy dissipation was also comparable to the experimentally attained values.     

Computational modeling of flow over an ogee spillway

This paper presents an investigation into the hydraulics of regular ogee-profile spillways. The free-surfaces of the fluid for several flow heads as measured in the hydraulics laboratory are used as benchmarks. The finite element computational fluid dynamics software, ADINA, was used to predict the free surface over an ogee spillway and thus model the flow field. Since the actual flow is turbulent the k-ε flow model was used. For the cases considered in this paper, ADINA predicted reasonable free surface results that are consistent with general flow characteristics over spillways. The results are also in close agreement with measured free-surface profiles over the entire length of the spillway.     

Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump

A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number. Turbulence is treated using RANS approach RNG k-ε. A Volume Of Fluid (VOF) method is used to track the air–water interface, consequently aeration is modeled using an Eulerian–Eulerian approach. Structured meshes of cubic elements are used to discretize the channel geometry. The numerical model accuracy is assessed comparing representative hydraulic jump variables (sequent depth ratio, roller length, mean velocity profiles, velocity decay or free surface profile) to experimental data. The model results are also compared to previous studies to broaden the result validation. Both codes reproduced the phenomenon under study concurring with experimental data, although special care must be taken when swirling flows occur. Both models can be used to reproduce the hydraulic performance of energy dissipation structures at low Reynolds numbers.     

Modeling of wetting–drying transitions in free surface flows over complex topographies

Numerical techniques development for the modeling and simulation of free surface flows has generated great interests over the last decades. In hydraulic engineering, the objectives include the predictions of dam break waves' propagation, fluvial floods and other catastrophic flooding phenomenon, the modeling of estuarine and coastal circulations, and the design and optimization of hydraulic structures. Most of the flooding events involve wetting and drying lands which are critical for the numerical modeling, especially when dealing with complex topographies. Extreme slopes and abrupt changes in irregular geometries, have often led to significant numerical errors and stability difficulties, and these are more critical for propagations over complex dry beds. This paper presents a simple and efficient numerical model for the wetting and drying effects over complex bathymetries. An overview of the key methods that have been suggested since the pioneering studies is first presented. A 2-D cell-centered finite-volume scheme is then proposed for solving the shallow-water equations using both structured and unstructured fixed meshes. Steady state C-property and global mass conservation properties are satisfied using appropriate numerical fluxes and wet/dry interfaces treatments. The resulting numerical model proved stable and robust and was validated through some benchmarks tests, including comparisons with exact solutions and experimental data, and a real case of wetting–drying simulation in a portion of the river “Rivière des Prairies” in a suburb of Laval, Quebec.     

带形状参数的Bernstein-Bézier曲面

虽然三角域上的曲面造型方法能有效解决不规则产品的几何造型问题, 在实际工程中有着广泛的应用, 但由于其结构的特殊性和复杂性, 目前对三角域曲面的扩展研究并不多。为了丰富三角域曲面的理论, 针对如何增强三角域曲面形状表示的灵活性进行了专门的研究。首先构造了一组三角域上含一个参数的四次多项式基函数, 它是三角域上二次Bernstein基函数的扩展。然后用递推的方式定义了三角域上含一个参数的n+2次多项式基函数, 它是三角域上n次Bernstein基函数的扩展。基于新的n+2次多项式基函数, 定义了相应的n阶三角域曲面。分析了基函数和曲面的性质, 新曲面不仅具备三角域上Bernstein Bézier曲面的基本性质, 而且还可以在不改变控制顶点的情况下, 通过改变参数的值来自由调整曲面的形状。     

Numerical simulation of viscous flow over non-smooth surfaces

The incompressible viscous flow over several non-smooth surfaces is simulated numerically by using the lattice Boltzmann method. A numerical strategy for dealing with a curved boundary with second-order accuracy for velocity field is presented. The drag evaluation is performed by the momentum-exchange method. The streamline contours are obtained over surfaces with different shapes, including circular concave, circular convex, triangular concave, triangular convex, regular sinusoidal wavy and irregular sinusoidal wavy, are obtained. The flow patterns are discussed in detail. The velocity profiles over different kinds of non-smooth surfaces are investigated. The numerical results show that the lattice Boltzmann method is reliable, accurate, easy to implement, and can provide valuable help for some engineering practices.     

Numerical simulation of free surface flows on a fish bypass

A computational fluid dynamics (CFD) model is developed to better understand the complex flow field inside a free surface fish bypass constructed at Rocky Reach Dam. This facility consists of two identical parallel channels, with fish screens on the side walls of each channel, and a pump station recirculating 96% of incoming flows into the forebay. The model is based on the Reynolds-averaged Navier-Stokes (RANS) equations, with a standard κ-ε turbulence model. The volume of fluid (VOF) method is used to predict free surface elevations. A proportional controller is implemented in the model to achieve a target flow rate at the pump exits. The pressure drop in the fish screens is modeled using porous media. Quantitative validation and visualization of the flow field characteristics indicate that CFD modeling may be a useful tool for fish passage design.     

Using intelligent methods to predict air-demand ratio in venturi weirs

Artificial intelligent methods are today extensively used in many areas. They are known as powerful tools to solve engineering problems with uncertainties. The purpose of this study was to develop a model, using artificial intelligent methods, for estimating air-demand ratio in venturi weirs. For this aim, Adaptive Network based Fuzzy Inference Systems (ANFIS) and Artificial Neural Network (ANNs) methods were used. The test results revealed that ANFIS model predicted the measured values at higher accuracy than ANNs model. Average correlation coefficients (R²) in ANFIS models were achieved equal to 0.9623 for β = 0.75 and 0.9666 for β = 0.50. Extremely good agreement between the predicted and measured values confirms that ANFIS model can be successfully used to predict air-demand ratio in venturi weirs.     

Three-dimensional free surface simulation

A 3D boundary element method with linear triangular element has been developed for the simulation of the free surface subjected to the surface tension force. A liquid droplet and a liquid jet are chosen to be the studying cases for the free surface simulation. The codes include 3D Laplace's solver, grid generation, and free surface module for the calculation of surface normal vector, surface curvature, and tangential velocity. Distortion of a droplet has shown the corresponding mode oscillation by specifying a given order of Legendre function for the initial velocity potential. And, the comparison of computational results and the predicted values from the dispersion equation, which serves as the analytical solution for the growth rate, for the temporal instability analysis on a liquid jet shows a very good agreement. This has shown that the proposed model is capable of the complex 3D liquid jet simulation.     

CFD simulations of wave-current-body interactions including greenwater and wet deck slamming

A numerical method for the solution of unsteady Navier-Stokes equations has been employed in conjunction with an interface-preserving level-set method for the simulation of greenwater effect on offshore structures and ships. In this method, the free surface flows are modeled as immiscible air-water two-phase flows and the free surface itself is represented by the zero level-set function. The Navier-Stokes equations for both the water and air flows are formulated in moving curvilinear coordinate system and discretized using the finite-analytic method on a non-staggered multi-block grid system. Large eddy simulation (LES) approach is used with Smagorinsky model to account for the effects of turbulence induced by violent free surface motions. A chimera domain decomposition approach is implemented using overlapping, embedding, or matching grids to facilitate the simulation of complex flow around practical configurations. The overset grid system also greatly simplified the simulation of arbitrary translational and rotational motions among various computational blocks. Calculations were performed first for dam-breaking flow and free jet problems involving violent free surface motions. The level-set Navier-Stokes method was then employed for the simulation of slamming of a hemisphere, greenwater on offshore structure and ships, and wet deck slamming of an X-Craft in pitch and heave motions. The numerical results clearly demonstrated the capability of the level-set method to deal with violent free surface flows involving breaking waves, water droplets, trapped air bubbles, and wave-current-body interactions.     

三角网格模型体素特征分割

针对现有机械制造领域网格模型分割结果缺少工程含义的现状,提出了一种三角网格模型体素特征分割方法。首先在对三角网格模型分割的基础上,对由网格分割得到的每个子网格进行曲面类型识别,然后在基本体素及典型结构显著特征表示的基础上,把识别出的曲面集合与基本体素及典型结构进行匹配,从而将分割结果分类为自由曲面、基本体素和复杂体素,实现具有工程含义的体素特征分割。该方法可以降低模型重构的难度,加快模型重构的速度。     

Flow pattern around an appended tanker hull form in simple maneuvering conditions

A detailed computational study is presented of the flow pattern around the Esso Osaka with rudder in simple maneuvering conditions: “static rudder” and “pure drift”. The objectives are: (1) apply RANS for maneuvering simulation; (2) perform verification and validation on field quantities; (3) characterize flow pattern; and (4) correlate behavior of the integral quantities with the flow field. The general-purpose code CFDSHIP-IOWA is used. The free surface is neglected and the two-equation k-ω turbulence model is used. The levels of verification of the velocity components for the “straight-ahead”, “static rudder” and “pure drift” conditions show ranges from 5.5% to 28.3% of free stream, U₀, for the axial velocity U and 2.5-29.1%U₀ for the cross flow (V, W). Qualitative validation against limited experimental data shows encouraging results with respect to trends and levels. The flow pattern is characterized by fore and aft body bilge and side vortices, which are similar for “straight-ahead” and “static rudder” conditions, except in close vicinity of the rudder. The “pure drift” condition shows strong asymmetry on windward vs. leeward sides and a more complex vortex system with additional bilge vortices. Similarities and differences with data for other tanker, container, and surface combatant hulls and relation between flow pattern and forces and moments are discussed. Future work focuses on influence of propeller.     

Computational fluid dynamics (CFD) software tools for microfluidic applications - A case study

This paper reports on an exemplary study of the performance of commercial computational fluid dynamic (CFD) software programs when applied as engineering tool for microfluidic applications. Four commercial finite volume codes (CFD-ACE+, CFX, Flow-3D and Fluent) have been evaluated by performing CFD-simulations of typical microfluidic engineering problems being relevant for a large variety of lab-on-a-chip (LOAC) applications. Following problems are considered as examples: multi lamination by a split and recombine mixer, flow patterning on a rotating platform (sometimes termed “lab-on-a-disk”), bubble dynamics in micro channels and the so called TopSpot^® droplet generator for micro array printing. Hereby mainly the capability of the software programs to deal with free surface flows including surface tension and flow patterning of two fluids has been studied. In all investigated programs the free surfaces are treated by the volume-of-fluid (VOF) method and flow patterning is visualised with a scalar marker method. The study assesses the simulation results obtained by the different programs for the mentioned application cases in terms of consistency of results, computational speed and comparison with experimental data if available.     

Application of two different neural network techniques to lateral outflow over rectangular side weirs located on a straight channel

Side weirs are structures often used in irrigation techniques, sewer networks and flood protection. This study aims to obtain sharp-crested rectangular side weirs discharge coefficients in the straight channel by using artificial neural network model for a total of 843 experiments. The performance of the feed forward neural networks (FFNN) and radial basis neural networks (RBNN) are compared with multiple nonlinear and linear regression models. Root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficient (R) statistics are used for the evaluation of the models’ performances. Comparison results indicated that the neural computing techniques could be employed successfully in modeling discharge coefficient. The FFNN is found to be better than the RBNN. It is found that the FFNN model with RMSE of 0.037 in test period is superior in estimation of discharge coefficient than the multiple nonlinear and linear regression models with RMSE of 0.054 and 0.106, respectively.