Compound Open Channel Research Articles

Mathematical expression of discharge capacity of compound open channels using MARS technique

In this paper, analytical methods, artificial neural network (ANN) and multivariate adaptive regression splines (MARS) techniques were utilised to estimate the discharge capacity of compound open channels (COC). To this end, related datasets were collected from literature. The results showed that the divided channel method with a coefficient of determination (R 2) value of 0.76 and root mean square error (RMSE) value of 0.162 has the best performance, among the various analytical methods tested. The performance of applied soft computing models with R 2=0.97 and RMSE = 0.03 was found to be more accurate than analytical approaches. Comparison of MARS with the ANN model, in terms of developed discrepancy ratio (DDR) index, showed that the accuracy of MARS model was better than that of MLP model. Reviewing the structure of the derived MARS model showed that the longitudinal slope of the channel (S), relative flow depth (H r ) and relative area (A r ) have a high impact on modelling and forecasting the discharge capacity of COCs.

Stage discharge prediction in heterogeneous compound open channel roughness

Prediction of flow discharge in the rivers performs important role in flood management. Using the compound open channel concept, the real condition in natural streams can be accurately estimated. A compound open channel includes a main channel and floodplains that usually floodplains are rougher than the main channel. Several empirical approaches have been proposed for estimating the discharge of flow in the compound open channels. In this study, the accuracy of the empirical approaches including Single Channel Method, Divided Channel Method (DCM), and Coherence Method were assessed to estimate the discharge of flow in heterogeneous compound channel roughness. To this purpose series of experiments were programmed and performed at the hydraulic laboratory of Tehran University. To compare the obtained results with previous studies, 396 data related to discharges of flow in the compound open channel were collected and used for evaluating the performance of applied methods. Results showed that DCM with assuming the virtual perpendicular line as boundry line between sub-sections (main channel and floodplains) with coefficient of determination more than the 0.90 has suitable performance through the empirical approaches and can be used for practical works.

Flow discharge estimation in compound open channel using theoretical approaches

Estimating the value of discharge in water ways is an important factor in the flood controlling projects. Recently by advances in flood management, investigators have proposed to use the concept of compound section for modeling the flow characteristics in the natural waterways such as rivers. Several conceptual and theoretical approaches based on the idea of compound section have been proposed for estimating the discharge in rivers. In this study, the performances of the theoretical methods were assessed using performing series of experiments in straight prismatic compound open channel and also analyzing the published data in the literature. Analyzing the performance of theoretical methods shows that Divided Channel Method including vertical bounded line with the determination of coefficient (0.91) and root mean square error (0.02) is an accurate method through the theoretical approaches and only this method has suitable ability to apply for practical purposes.

Prediction of flow discharge in compound open channels using adaptive neuro fuzzy inference system method

Discharge estimation in rivers is the most important parameter in flood management. Predicting discharge in the compound open channel by analytical approach leads to solving a system of complex nonlinear equations. In many complex mathematical problems that lead to solving complex problems, an artificial intelligence model could be used. In this study, the adaptive neuro fuzzy inference system (ANFIS) is used for modeling and predicting of flow discharge in the compound open channel. Comparison of results showed that the divided channel method with horizontal division lines with the Coefficient of determination (0.76) and root mean square error (0.162) is accurate among the analytical approaches. The ANFIS model with the coefficient of determination (0.98) and root mean square error (0.029) for the testing stage has suitable performance for predicting the discharge of flow in the compound open channel. During the development of the ANFIS model, found that the relative depth, ratio of hydraulics radius and ratio of the area are the most influencing parameters in discharge prediction by the ANFIS model.

Predictive modeling of discharge of flow in compound open channel using radial basis neural network

Predicting the flow discharge in open channel is the main parameters in the flood management. The concept of the compound open channel is the accurate approach for modeling the natural streams. Several ways as analytical approaches and artificial intelligence methods have been proposed for predicting the discharge in rivers in term of compound open channel concepts. In this paper the single channel method (SCM), coherence method (COHM), and divided channel method (DCM) as common analytical approaches were used to predict the discharge in the compound open channel and in follow to achieve more accuracy in flow discharge prediction the radian basis neural network (RBF) was developed. The performance of RBF was compared with other types of transfer function governed on neurons of neural network. The results showed that the DCM with horizontal separated boundary among the subsections with correlation of determination (R2 = 0.76) is accurate through the analytical approaches. Assessing the results of the MLP model showed that this model with (R2 = 0.95) is a bit more accurate than the RBF (R2 = 0.85) and analytical approaches.

Analyzing the distribution of momentum and energy coefficients in compound open channel

Study on the open channel hydraulic is a main part in the river engineering. Compound open channel is a new and accurate concept for modeling of the river engineering modeling. Studies on the flow discharge, velocity distribution, shear stress distribution are the main parameters in the compound open channel studies. Flow discharge calculation in rivers is one of the parameter in flood management. In this paper the hydraulic characteristic of open compound open channel is studied. In this regard distribution of Momentum Coefficient (β), Energy Coefficient (α), head discharge relationship, specific energy curve was evaluated. The head discharge curve of compound open channel was calculated by Single-Channel Method, Divided-Channel Method, and modified divided-channel method (MDCM). The results show that the compound section for canal has significant effect on the distribution of α and β. Calculation of flow discharge in compound open channel by MDCM shows the more values in compere to other analytical approaches.

Hydraulics of combining flow in a right-angled compound open channel junction

Although combining flows are common in natural streams, no comprehensive experimental data has been compiled to characterize the three-dimensional flow field within the compound channel confluence. The present study examines the time-averaged flow structure at confluence over a rigid bed. Current knowledge of channel confluence, based on laboratory observation indicates that cross flow interactions exert a significant influence on confluence events. Secondary current and turbulent stresses are reproduced well by the hydraulic model and found greater in the interface region as relative flow ratio decreases. Velocity fields in combining flow region arising from varying discharge ratios are presented. A zone of depression in surface elevation in compound channel junction is observed as well. The flow field in compound channel is seen to be moderately different from that of simple channel junction. This study contributes to a better knowledge of hydraulic key processes into fundamental aspect of combining flow dynamics.

Longitudinal dispersion in waterways with vegetated floodplain

Floodplains have a vital role in biocomplexity in ecosystem structure and function. Because of their long-term spontaneous development, vegetation established on the floodplains can influence ecological and environmental conditions of floodplains. Accidental contaminant spills in rivers can affect the water quality over long distances. In this situation, one-dimensional approaches can be used to describe the mass transport phenomena when longitudinal dispersion is the primary mechanism responsible for spreading the tracer cloud and for reducing peak concentrations. The longitudinal dispersion coefficients in simple shape channels have been studied extensively by many researchers; however, the flow conditions in the more complex geometries are completely different than those of simple channels. In this study, longitudinal dispersion phenomenon in a compound open channel is investigated experimentally. Tracer tests were conducted for both smooth and vegetated floodplain and for different flow conditions. Concentration profiles were extracted from the images taken before and during a passage of the tracer cloud using the image processing technique. It was found that the longitudinal dispersion coefficient increases by implanting vegetation over the floodplain as well as increasing the relative depth. Also, an attempt was made to compare the results of the present study with those of the predicted by some of the well-known empirical relationships available in the literature. Using three statistical parameters including NRMSE, DR and ME, the most accurate models for predicting the longitudinal dispersion coefficient in compound channels are proposed.

Predictive modeling of discharge in compound open channel by support vector machine technique

Modeling of river phonemes is one of the main parts in Hydraulic engineering studies. Predicting the discharge in the compound open channel is the main subject of the river engineer researches. In this study the support vector machine (SVM) technique is used to predict the discharge in the compound open channel. The result of the error indexes shows that the best accuracy of the SVM by correlation coefficient 0.99 is related to the SVM model which includes the radial basis function (RBF) as kernel function. During the SVM model process obtained 0.00005 for the gamma coefficient, epsilon is equal to 0.1 and C = 1.

Assessment of stage–discharge predictors for compound open-channels

The accurate prediction of flood levels and velocities is a prerequisite to any appropriate management of river valleys, where the mitigation of environmental, economic or human losses caused by flood events is of paramount importance. During these events, rivers frequently acquire a compound channel configuration.Due to the 3D nature of compound channel flows, the stage–discharge curves are not as easily predicted as in single channels. Despite the availability of 2D and 3D flow models that may solve this question, 1D methods are often preferred due to the reduced data required and to the much shorter processing time. In the last five decades, important research efforts have been devoted to the improvement of 1D predictors of stage–discharge curves in compound channels. In this study, the accuracy of seven of those methods is assessed by comparing their predictions with a large experimental dataset, comprising symmetrical and asymmetrical compound channels with vertical and inclined main channel sidewalls, and smooth and rough floodplains. To the authors’ best knowledge, this is the most comprehensive assessment of stage–discharge predictors for straight compound channels since it involves the highest number of predictors applied to the widest data set.It was concluded that the methods that account for the momentum transfer between the main channel and the floodplains display considerably better results than the traditional methods. For relative depth (ratio between floodplain and main channel flow depths) higher than 0.25, predicted discharges for the methods that account for the turbulent momentum exchange are within 5% of observed values. Depending on whether the flow depth or the flow discharge is the pertinent variable, two different methods seem to be the most appropriate to produce precise and safe predictions.

Flood hydrograph estimation using an adjoint shallow-water model

This paper describes the estimation of the flood discharge hydrograph for a compound open channel floodplain using data assimilation. The hydrograph was produced iteratively using an adjoint shallow-water model with time-series data of observed water levels. Data assimilation was applied to a flood event that occurred in mid-September 1998 along a 20 km stretch of the lower Tone River in Japan. Both the estimated hydrograph and the flow field simulated using the hydrograph were verified by comparison with the results of aerial photographic analysis. Results show that the hydrograph based on the stage–discharge was overestimated, but it was reasonably corrected by the data assimilation technique used for this study. In addition, the resulting relation during the flood event exhibited a hysteresis loop characteristic, which is typical of compound open channel flows during flooding.

Computation of gradually varied flow in compound open channel networks

Although, natural channels are rarely rectangular or trapezoidal in cross section, these cross sections are assumed for the computation of steady, gradually varied flow in open channel networks. The accuracy of the computed results, therefore, becomes questionable due to differences in the hydraulic and geometric characteristics of the main channel and floodplains. To overcome these limitations, an algorithm is presented in this paper to compute steady, gradually varied flow in an open-channel network with compound cross sections. As compared to the presently available methods, the methodology is more general and suitable for application to compound and trapezoidal channel cross sections in series channels, tree-type or looped networks. In this method, the energy and continuity equations are solved for steady, gradually varied flow by the Newton–Raphson method and the proposed methodology is applied to tree-type and looped-channel networks. An algorithm is presented to determine multiple critical depths in a compound channel. Modifications in channel geometry are presented to avoid the occurrence of multiple critical depths. The occurrence of only one critical depth in a compound cross section with modified geometry is demonstrated for a tree-type channel network.

Φ-indices approach and multivariable regression analysis for prediction of discharge in asymmetric straight compound open channel flows

This study is related to flow measurement structures of asymmetric compound cross section mostly suggested for sediment laden-rivers, streams and wadis. Nine different models of asymmetrical rectangular cross sections were tested for a wide range of discharges. In each model, the stages and corresponding discharges were measured. From these measurements, the average discharges utilizing the Φ-indices Approach were determined. In addition, a multivariable regression model was derived with high accuracy for the prediction of discharge in asymmetric compound channels using five dimensionless parameters.The measured discharges were compared with the predicted ones obtained from the Φ-indices methods with vertical, horizontal and diagonal interface planes; FI-V, FI-D and FI-H, respectively, with the use of three well-known methods for the computation of the apparent shear stress acting on the interface perimeter, τa, and the multivariable regression model for discharge prediction. At lower relative depth values, almost all the tested methods predict discharge with acceptable accuracy. In addition, as the relative depth increases, the results demonstrate a suitable accuracy of the FI-V with the vertical division lines and the multivariable regression model method. The multivariable regression model presented has been identified as the best-fit model in 26 cases out of 29 through minimization of the mean squared errors.

Simulation of flow in compound open-channel using a discontinuous Galerkin finite-element method with Smagorinsky turbulence closure

The small-scale spatial variability of eddy viscosity which is characteristic for the turbulent shear stress in compound open-channel flows was studied and investigated in this paper. Different options including a constant value, zero-equation, one-equation, two-equation, and Smagorinsky turbulence models for parameterizing the eddy viscosity were developed in the framework of the discontinuous Galerkin finite-element SLIM model and applied for presenting the complex velocity profile in two different experimental data sets of laboratory flumes. A very good qualitative agreement was achieved between numerical results and measurement data for both velocity and flow depth of all experimental data sets in general. In addition, the calculation results showed that the turbulent Smagorinsky empiricism allowed a better presentation of non-uniform velocity in the floodplain and transition regions between plain and main channels than the others in all calculated cases. This empiricism predicted a very close variation of eddy viscosity in comparison with the results calculated by the depth-averaged Reynolds' stress and the lateral gradient of longitudinal velocity. The eddy viscosity varies significantly in the channel section; in particular the small values often occurred around the middle location of floodplains and the central location of the main channel while the large values appeared in the transition regions, presenting different minimum and maximum values of eddy viscosity in each flow region. The effects of eddy viscosity variation on lateral distribution of velocity profile were also investigated and discussed.

Mathematical modeling of flow discharge over compound sharp-crested weirs

Water measurements play a pivotal role in hydraulic and environmental management of river systems, irrigation and drainage networks, and sewer conduits. Due to effective limitations of simple sharp crested weirs, recently compound sharp crested weirs have attracted great attention of civil engineers. With this type of weir, flow discharge is measured with a reasonable sensitivity over a wide range of flow rates. In this paper, the Shiono and Knight (SKM) quasi 2-D mathematical model has been numerically solved for discharge prediction of compound weirs, based on the assumption of flow similarity between compound sharp crested weirs and compound open channels. The modeled results are compared with the experimental data and the conventional method (linear combination of theoretical equations of simple weirs). The comparisons revealed that the proposed method shows improved discharge calculation within 3.8 percent absolute mean error while the traditional method has more than 12.5 percent error.

3D Simulation of Velocity Profile of Turbulent Flow in Open Channel with Complex Geometry

Abstract Simulation of open channel flow or river flow presents unique challenge to numerical simulators, which is widely used in the applications of computational fluid dynamics. The prediction is extremely difficult because the flow in open channel is usually transient and turbulent, the geometry is irregular and curved, and the free-surface elevation is varying with time. The results from a 3D non-linear k– ɛ turbulence model are presented to investigate the flow structure, the velocity distribution and mass transport process in a meandering compound open channel and a straight open channel. The 3D numerical model for calculating flow is set up in cylinder coordinates in order to calculate the complex boundary channel. The finite volume method is used to disperse the governing equations and the SIMPLE algorithm is applied to acquire the coupling of velocity and pressure. The non-linear k– ɛ turbulent model has good useful value because of taking into account the anisotropy and not increasing the computational time. The main contributions of this study are developing a numerical method that can be applied to predict the flow in river bends with various bend curvatures and different width-depth ratios. This study demonstrates that the 3D non-linear k– ɛ turbulence model can be used for analyzing flow structures, the velocity distribution and pollutant transport in the complex boundary open channel, this model is applicable for real river and wetland problem.

Turbulent non-uniform flows in straight compound open-channels

The reported experimental study assesses the effects of flow non-uniformity on the momentum flux in straight compound channels. Two flumes were used, featuring vertical and sloping banks. Starting with uniform flow condition, various imbalances in the upstream discharge distribution were introduced. This resulted in a time-averaged lateral flow and advective transport of momentum, which interacted with the shear-layer turbulence generated by the compound geometry. To investigate this interaction, the three contributions to transverse momentum flux (depth-averaged flow, shear-layer turbulence and dispersive term of spanwise velocity) are assessed. The first two contributions were strengthened by the sloping banks, while the third becomes important for the case of the vertical bank. With a lateral flow towards the main channel, the first contribution rises at the expense of the second. With a lateral flow towards the floodplain, the first two contributions have the same order of magnitude, and the Boussinesq approach is invalidated.

Estimation of the error on the mean velocity and on the Reynolds stress due to a misoriented ADV probe in the horizontal plane: Case of experiments in a compound open-channel

This study aims at evaluating the error on the horizontal components of the mean-velocity and of the Reynolds stress measurements due to a misorientation of an Acoustic Doppler Velocimeter (ADV) in the horizontal plane. The misorientation of the ADV is represented by a misalignment angle, which is the angle between the ADV coordinate frame and the reference frame. The error due to the misorientation is first analytically determined. Thereafter, using experiments in a compound channel, the error is evaluated based on an angle of 2.5° representing the maximum possible angle of misalignment by human eyes adjustment. While the maximal error does not exceed 5% for the longitudinal mean velocity and 14% for the normal Reynolds stresses, it can be larger than 100% for the lateral mean velocity and largely greater than 100% for the Reynolds shear stress. Such a degree of error appears to be similar to those worked out for classical flows from the literature with a mean velocity gradient mainly occurring in the horizontal plane (mixing layers, plane jets) or in the vertical plane (boundary layers). This error is finally compared with the uncertainty due to the various sources of noise that perturbate the turbulence measurement. This study reveals that both are comparable, therefore indicating that the error due to the probe misorientation should not be neglected, as it is too often the case.

Prediction of flow resistance in a compound open channel

Flooding in a river is a complex phenomenon which affects the livelihood and economic condition of the region. During flooding flow overtops the river course and spreads around the flood plain resulting in a two-course compound channel. It has been observed that the flow velocity in the flood plain is slower than that in the actual river course. This can produce a large shear layer between sections of the flow and produces turbulent structures which generate extra resistance and uncertainty in flow prediction. Researchers have adopted various numerical, analytical, and empirical models to analyze this situation. Generally, a one-dimensional empirical model is used for flow prediction assuming that the flow in the compound open channel is uniform. However, flow in a compound channel is quasi-uniform due to the transfer of momentum in sub-sections and sudden change of depths laterally. Hence, it is essential to analyze the turbulent structures prevalent in the situation. Therefore, in this study, an effort has been made to analyze the turbulent structure involved in flooding using large eddy simulation (LES) method to estimate the resistance. Further, a combination of an artificial neural network (ANN) and a fuzzy logic (FL) is considered to predict flow resistance in a compound open channel.

Application of Shiono and Knight Method to Compound Open Channel Flow with One-Line Emergent Vegetation

A quasi two-dimensional model was developed to calculate depth-averaged velocity and bed shear stress in a straight compound channel with one-line emergent vegetated at the floodplain edge. Reduction in volume of water due to vegetation is modelled as porosity. Drag force due to vegetation is modelled as an additional momentum source term in the Navier-Stokes equation. Estimation methods for model parameters—friction factor, roughness height due to drag force, porosity, eddy viscosity and advection term-are discussed. The predictive capability of the model is assessed against experimental data with regard to distributions of depth-averaged velocity and boundary shear stress. The results show that the quasi 2D model well reproduces a reasonable simulation of the flow field under relative water depths of 0.24 and 0.52.