Compound Open Channel Research Articles

Experimental and numerical study of unsteady flows in a compound open channel

Unsteady flows are investigated in a compound open-channel flume, consisting of a Main Channel (MC) and an adjacent Flood Plain (FP). Two types of inflow hydrographs are studied, i.e., a discharge hydrograph with, at any time: a slightly unbalanced inflow partition between MC and FP (Case I); and a noticeably unbalanced inflow partition (Case II). Ensemble averages of the time-varying discharges, water depths and velocities are estimated based on 100 successive runs. The main focus of the experimental study is on assessing (i) the time-varying lateral discharge and depth-averaged Reynolds stress at the MC/FP interface, and (ii) the influence of the inflow partition on the downstream flow parameters. The experimental flows are then simulated using a 1D (one-dimensional) code that was adapted to implement the 1D+ Independent Sub-sections Model (ISM) (Proust et al. in Water Resour Res 45:1–16, 2009). The numerical study aims at validating the ISM under unsteady flow conditions, using classical 1D simulations as benchmark. It is experimentally found that 90 successive runs are required to get convergence of the ensemble averages of sub-section discharges and flow depth, while interfacial velocity is not fully converged after 100 runs. The influence of the inflow partition on the downstream parameters is felt along the whole flume. The ISM simulations are closer to the measurements than the classical 1D simulations. The ISM can accurately predict the time-varying flow depths and interfacial lateral discharge, and can approximate the interfacial Reynolds stresses.

Discharge estimation in a compound channel with converging and diverging floodplains using ANN–PSO and MARS

Abstract The discharge estimation in rivers is crucial in implementing flood management techniques and essential flood defence and drainage systems. During the normal flood season, water flows solely in the main channel. During a flood, rivers comprise a main channel and floodplains, collectively called a compound channel. Computing the discharge is challenging in non-prismatic compound channels where the floodplains converge or diverge in a longitudinal direction. Various soft computing techniques have nowadays become popular in the field of water resource engineering to solve these complex problems. This paper uses a hybrid soft computing technique – artificial neural network and particle swarm optimization (ANN–PSO) and multivariate adaptive regression splines (MARS) to model the discharge in non-prismatic compound open channels. The analysis considers nine non-dimensional parameters – bed slope, relative flow depth, relative longitudinal distance, hydraulic radius ratio, angle of convergence or divergence, flow aspect ratio, relative friction factor, and area ratio – as influencing factors. A gamma test is carried out to determine the optimal combination of input variables. The developed MARS model has produced satisfactory results, with a mean absolute percentage error (MAPE) of less than 7% and an R2 value of more than 0.90.

Modeling of discharge in compound open channels with convergent and divergent floodplains using soft computing methods

Abstract In this research, the estimation of discharge in compound open channels with convergent and divergent floodplains using soft computing methods, including the neural fuzzy group method of data handling (NF-GMDH), support vector regression (SVR), and M5 tree algorithm were performed. For this purpose, the geometric and hydraulic characteristics of the flow, including relative roughness (ff), relative area (Ar), relative hydraulic radius (Rr), relative dimension of the flow aspects (δ*), relative width (β), relative flow depth (Dr), relative longitudinal distance (Xr), convergent or divergent angle (θ) of the floodplain and longitudinal slope (So) of the bed were used as input variables and discharge was considered as the target (output) variable. The results showed that the statistical indices of the NF-GMDH in the testing stage are RMSENF-GMDH = 0.004, R2NF-GMDH = 0.923 and in the same stage for SVR are RMSESVR= 0.002 and R2SVR = 0.941 and finally for M5 tree algorithm are RMSEM5 = 0.002, R2M5= 0.931. The evaluation of the structure of the M5 tree algorithm showed that the most effective parameters are ff, Dr, Rr, δ*, and θ which confirm the important parameters specified by MARS, GMDH, and GEP algorithms used by previous researchers.

On asymmetric compound open channel flows with two distinct width floodplains: revisiting interfacial mixing layer and flow structures

On asymmetric compound open channel flows with two distinct width floodplains: revisiting interfacial mixing layer and flow structures

Effect of vegetation on flow hydraulics in compound open channels with non-prismatic floodplains

Abstract The present paper aims to evaluate the effect of emergent rigid vegetation density on the flow's turbulence structure and hydraulic parameters at the non-prismatic floodplains. The experiments were performed using the physical model of the asymmetric non-prismatic compound channel. The results show that the velocity distribution in the vegetation flow is more influenced by the drag force caused by the vegetation than by the bed shear stress and does not follow the law of logarithmic velocity distribution throughout the non-prismatic section. The intense velocity gradient at the interface of the main channel and the floodplain leads to the development of strong secondary currents, increased Reynolds shear stresses, apparent shear stresses and momentum exchange in this region. Vegetation also decreases mean kinetic energy in the floodplain and increases it in the main channel. The mean turbulence exchange coefficient for the non-prismatic compound channels without vegetation was 0.23 and for the divergent and convergent compound channels was 0.035 and 0.020, respectively. The comparison of the local drag coefficient results shows that the fluctuations of this parameter are greater in the divergent section than in the convergent section due to the strong secondary currents in the interface.

Numerical analysis of sediment transport and depth averaged flow velocity in non-prismatic compound channels

The flow velocity in compound open channels is greatly affected by the geometry of both the main channel (MC) and floodplain (FP). In this study, a numerical investigation of the joint effect between the FP divergence angle and the size of suspended sediment particles on sediment transport and flow depth-averaged velocity (DAV) in non-prismatic diverging compound channels was conducted. In addition, the influence of relative flow depth on the DAV in different flow directions (i.e., stream-wise and span-wise) was examined. Three divergence angles of 4.0, 6.3 and 11.3°, four sediment particle sizes of 1, 5, 50 and 500 µm and two relative depths of the FP with respect to the MC of 0.20 and 0.40 were considered during simulations. A Computational Fluid Dynamics (CFD) software ANSYS-Fluent was used to perform the required simulation scenarios and the DAV was expressed in terms of a dimensionless velocity (i.e., relative depth-averaged velocity; RDAV) to generalize the use of the obtained results. Results revealed that the span-wise RDAV gradient between the MC and FP at the middle and the end sections of the divergence reach is much larger in the case of higher divergence angle. Moreover, the presence of coarse sediment particles in the sediment-laden flow resulted in an augmentation in the fluctuations of span-wise and stream-wise RDAVs as compared to those obtained in the case of fine sediment particles. Results also showed that the span-wise RDAV gradient between the two subsections (MC and FP) increases with decreasing the relative flow depth. Sediment particle size had a considerable impact on the span-wise RDAV values, especially in the case of lower relative depth. As the sediment particle size increases, the distortion in the span-wise RDAV distribution curves increases. However, the stream-wise RDAV along the MC and FP decreases, as the sediment particle size decreases, especially in the case of higher relative depth. Based on the results, it can be concluded that the span-wise DAV gradient was greatly affected by the FP divergence angle and sediment particle size. The fluctuations in the span-wise DAV gradient were more pronounced in the case of higher divergence angles and coarser sediment particles. The stream-wise DAV distribution along the MC and FP was mainly influenced by the relative depth and sediment particle size. The stream-wise DAV dip along the MC and FP was more explicit in the case of higher relative depths and finer sediment particles.

Shear layers in two-stage compound channels investigated with LS-PIV

Flow experiments are conducted in a two-stage compound open-channel, with varying intensity of the velocity difference between the main channel (deep part) and the floodplain (shallower part), using a large-scale free surface PIV technique (LS-PIV). For all investigated flows, a shear layer develops at the interface between main channel and floodplain, characterised by a peak of turbulent shear stress. Yet, two different kinds of shear layer could be identified. The first kind is characterised by the presence of large-scale quasi-periodic structures of Kelvin-Helmholtz type which are growing in downstream direction, whereas the second kind is characterised by smaller-scale vortical structures without quasi-periodicity and which do not grow in downstream direction. The shear parameter lambda =(U_2-U_1)/(U_2+U_1), where U_1 and U_2 are defined as the velocities outside the shear layer, is identified as a key parameter to distinguish between these two types of shear layers, supporting a result from Proust et al. (Water Resour Res 53: 3387–3406, 2017). A physical interpretation of the lambda-criterion is proposed, based on the inhibiting effect of ambient turbulence (the turbulence level outside the shear layer) on the emergence of Kelvin-Helmholtz structures. Accordingly, the threshold value of lambda, above which large-scale structures can develop, is dependent on the level of the ambient turbulence. Despite their very different behaviours, the two types of shear layer have the same efficiency to generate turbulent shear stress for a given velocity difference across the shear layer, except for lambda-values close to the threshold value.

Large Eddy Simulation of Compound Open Channel Flows with Floodplain Vegetation

Floodplain vegetation is of great importance in velocity distribution and turbulent coherent structure within compound open channel flows. As the large eddy simulation (LES) technique can provide detailed instantaneous flow dynamics and coherent turbulent structure predictions, it is of great importance to perform LES simulations of compound open channel flows with floodplain vegetation. In the present study, a wall-modeled large eddy simulation (WMLES) method was employed to simulate the compound open channel flows with floodplain vegetation. The vegetation-induced resistance effect was modeled with the drag force method. The WMLES model, incorporating the drag force method, was verified against flume measurements and an analytical solution of vegetated open channel flows. Numerical simulations were conducted with a depth ratio of 0.5 and four different floodplain vegetation densities (frk = 0, 0.28 m−1, 1.13 m−1 and 2.26 m−1). The main flow velocity, secondary flow, bed shear stress and vortex coherent structure, based on the Q criterion, were obtained and analyzed. Based on the numerical results, the influences of floodplain vegetation density on the flow field and turbulent structure of compound open channel flows were summarized and discussed. Compared to the case without floodplain vegetation, the streamwise velocity in the main channel increased by 10.8%, 19.9% and 24.4% with the frk = 0.28 m−1, 1.13 m−1 and 2.26 m−1, respectively. The results also indicated that, when the floodplain vegetation density increased, the following occurred: the velocity increased in the main channel, while the velocity decreased in the floodplain; the transverse momentum exchange was enhanced; and the strip structures were more concentrated near the junction area of compound open channel flows.

Genetic algorithm-assisted data-driven model for boundary shear distribution and stage-discharge: Compound open channel flows

In this paper, a unified method has been proposed for the percentage shear force carried by floodplains using fewer non-dimensional parameters such as the floodplain's percentage area, the ratio of Manning’s roughness and the depth ratio. This new data-driven dynamic model for percentage shear force is obtained using a genetic algorithm (GA) program, a well-documented machine-learning software, which can examine the existing relationship among the variables and explore the influencing factors. GA facilitated a unified relationship between apparent shear force and the chosen parameters. The new proposed model is simple and accurate compared to the previous models, which were either complex or distinct for different configurations. The efficiency of the new model shows that the most predicted test case results are under the 5% error cap. The cohesive expression derived for smooth and roughened compound channels is the most significant advantage of the GA-based data-driven model, providing a simple and easy-use formula for engineers to apply for broad applications. Compared with the other available approaches, the model proposed provides the most accurate discharge prediction for various unique datasets.

Momentum Transfer–Equivalent States Assumption of the Apparent Shear Stress in Compound Open-Channel Flow

The use of apparent shear stress at the interface between the adjacent subregions of a cross section to represent the effect of momentum transfer is a common method for the one-dimensional calculation of compound open-channel flow. The apparent shear stress of the dividing lines is affected by the compound geometry and boundary conditions. The expressions of the apparent shear stress established with previous studies are very different. Empirical treatment was proposed in this study to simplify the expressions based on a momentum transfer–equivalent states assumption, in which (1) the apparent shear stress was assumed to be the difference of the momentum transfer from two sides of a dividing line, and (2) two assumed equivalent states were employed to define the equivalent value of the momentum transfer. The apparent shear stress could be calculated based on the deviation of the momentum transfer from its equivalent value. The new expressions were used to calculate the discharges and the boundary shear force. Comparisons between the calculated results based on different methods and the measured data showed that the proposed method improved the calculation of the subregion boundary shear force and the discharges in the compound cross sections.

Hydrodynamic performance and placement characterization of axial hydro-kinetic turbine in a compound open-channel

In this study, performance of an in-stream hydro-kinetic turbine and its impacts on a simplified river channel (known as a compound open-channel) flow has been numerically examined. To this end, a steady Reynolds-Averaged Navier-Stokes solver has been employed together with the moving reference method to simulate the turbine rotation as well as the Reynolds Stress Model (RSM) as the turbulence closure. The results showed that the presence of a hydro-kinetic turbine causes dramatic changes in the natural flow structure of the compound channel, which varies depending on the location of turbine installation. Comparison of turbine installation in various locations in the cross-section of the channel showed that minimum effects on the natural flow conditions have been occurred in the installation at the main-channel being far from the bed. It has also been observed that the bed shear stress remains virtually constant for different hydro-kinetic turbine locations. Values of the power coefficient indicate that the highest value of maximum power coefficient is obtained where the hydro-kinetic turbine is installed at the interaction zone of the compound open-channel. This observation implies that cellular secondary currents of the compound channel have positive effects on the turbine power. Finally, it is noted that the thrust coefficient variation with the installation location is insignificant compared to the variation of this coefficient with respect to the inlet velocity and the ratio of the blade flow speed to the flow speed.

Study on Conveyance Coefficient Influenced by Momentum Exchange Under Steady and Unsteady Flows in Compound Open Channels

Study on Conveyance Coefficient Influenced by Momentum Exchange Under Steady and Unsteady Flows in Compound Open Channels

Discharge modeling in compound channels with non-prismatic floodplains using GMDH and MARS models

Abstract In this study, modeling of discharge was performed in compound open channels with non-prismatic floodplains (CCNPF) using soft computation models including multivariate adaptive regression splines (MARS) and group method of data handling (GMDH), and then their results were compared with the multilayer perceptron neural networks (MLPNN). In addition to the total discharge, the discharge separation between the floodplain and main channel was modeled and predicted. The parameters of relative roughness coefficient, the relative area of flow cross-section, relative hydraulic radius, bed slope, the relative width of water surface, relative depth, convergence or divergence angle, relative longitudinal distance as inputs, and discharge were considered as models output. The results demonstrated that the statistical indices of MARS, GMDH, and MLPNN models in the testing stage are R2 = 0.962(RMSE = 0.003), 0.930(RMSE = 0.004), and 0.933(RMSE = 0.004) respectively. Examination of statistical error indices shows that all the developed models have the appropriate accuracy to estimate the flow discharge in CCNPF. Examination of the structure of developed GMDH and MARS models demonstrated that the relative parameters: roughness, area, hydraulic radius, flow aspect ratio, depth, and angle of convergence or divergence of floodplain have the greatest impact on modeling and estimation of discharge.

Analysis and validation of mathematical models of secondary velocities along vertical and transverse directions in wide open-channel turbulent flows

Cellular secondary flows are inevitably present in turbulent flows through ducts, natural or artificial channels, and compound channels. Secondary currents significantly modify the characteristics of turbulent quantities, the pattern of primary flow velocity by causing dip-phenomenon. To understand the detailed mechanism and hidden cause, modelling of secondary flow velocities is crucial. In this study, proper mathematical models of secondary flow velocities along vertical and transverse directions are proposed for steady and uniform turbulent flow through wide open channels with equal smooth and rough bed strips. Starting from the continuity and the Reynolds averaged Navier–Stokes equations, governing equation for secondary velocity is derived first and then using appropriate boundary conditions (no-slip boundary conditions at channel bottom and free surface, and maximum vertical velocity in magnitude at the interface of two cellular secondary cells and at mid-depth of the channel. All these conditions are consistent with several experimental observations). A new model of the streamwise Reynolds shear stress is proposed for the entire cross-sectional plane and using it, the analytical solutions are obtained. Proposed models include the effects of viscosity of the fluid and the eddy viscosity model of turbulence. All suggested models are validated with existing experimental data in rectangular open-channel flows, compound open channel flows, and duct flows, and satisfactory results are obtained. Furthermore, models are also compared with existing empirical models from literature to show the effectiveness and superiority of proposed models. Apart from these, the obtained results from this study are used to investigate the effects of vertical and transverse secondary flow velocities on the settling velocity vector in a cross-sectional plane. Effective alternative models for the settling velocity vector are suggested. The model of settling velocity vector is also compared with the existing model. Finally, all results are justified from physical viewpoints.

Numerical Modeling of Compound Channels for Determining Kinetic Energy and Momentum Correction Coefficients Using the OpenFOAM Software

Abstract The non-uniformity of the flow velocity distribution in each section of compound channels and in the main channel-floodplain interface area causes errors in estimating water surface profile, flood routing, pollution transfer, and so on. To reduce the impacts of non-uniformity on the exact calculation of kinetic energy and momentum, α and β correction coefficients are used, respectively. However, the determination method of these coefficients is a challenging issue in river engineering. This study used the OpenFOAM Software to determine these coefficients numerically for two laboratory models of compound open channels of which the data are available, using the single-phase pimpleFoam solver to do modeling in the mentioned software and the k-ωSST turbulence model to calculate the flow characteristics. Based on the results, the highest difference (13%) between the results estimated by the software and those obtained from the lab experiments was seen in the low flow depth where the flow left the main channel and entered the floodplain of a very shallow depth, possibly due to the grid generation of this area. This difference decreased as the flow depth increased, and its average was 6.65% for α coefficient and 2.32% for β coefficient in all cases, which means the results of numerical modeling and the experimental data conformed well, and the OpenFOAM software can be successfully used in flow modeling and analyzing flow characteristics in compound channels.

Impact of depth ratio on flow structure and turbulence characteristics of compound open channel flows

Compound open channel flows appear in most natural rivers are of great importance in river management and flood control. In this study, large eddy simulations were carried out to simulate the compound open channel flows with four different depth ratios (hr = 0.10, 0.25, 0.50, and 0.75). The main flow velocity, secondary flow, Reynolds stress, and bed shear stress were obtained from numerical simulations. The depth-averaged streamwise momentum equation was used to quantify the lateral momentum exchange between the main channel and floodplain. The instantaneous coherent structures were presented by the Q criterion method. The impact of hr on flow structure and turbulence characteristics was analyzed. The results showed that with the increase of hr, the high velocity area in the main channel shifted to the floodplain, and the dip phenomenon became more obvious; the Reynolds stress largely contributed to the lateral momentum exchange within the flows near the side walls of floodplain; and the vortex structures were found to significantly increase in the floodplain region.

Practical secondary flow contribution for meandering compound open channels

Practical secondary flow contribution for meandering compound open channels

Linear-scale models for discharge estimation: asymmetric compound open channel flows

In this study, three recent methods of discharge estimation are evaluated, namely, the interacting divided channel method, the modified divided channel method and the momentum transfer divided channel method, which include momentum exchange on the interface for prediction of discharge. These methods are compared intensively using 22 experimental flume data sets with six river data sets taken from the literature comprising 204 test runs in total. These data sets are categorised as asymmetric compound channels with a wide range of width ratio (B/b), aspect ratio (b/h) and bed slope ([Formula: see text]), where [Formula: see text] is the total width of channel at the bankfull condition, [Formula: see text] is the main channel bed width and [Formula: see text] is the bankfull main channel height. All these three methods are capable of predicting both overall and zonal discharge for small- to large-scale channels, including natural rivers. However, the interacting divided channel method is the least erroneous, with an average percentage error of 5.83%. Further investigations should include in-depth discussion on zonal discharge prediction, particularly for floodplain discharge, which has been an area of concern and interest in the areas of the water environment and sustainable design of rivers.

Experimental Study on Flow Characteristics in a Compound Open Channel with Flexible Vegetation

In order to study the effect of flexible vegetation for the flow in open channels with flood plains, a series of experiments were carried out in a laboratory flume with a two-stage floodplain. Four cases, i.e., dense parallel arrangement, normal parallel arrangement, sparse parallel arrangement and no vegetation condition, were designed with fixed water depth and discharge. By using three dimensional (3D) laser Doppler velocimeter (LDV) and other instruments, under the condition of the four cases,3D flow velocities, water level and turbulence intensity were measured, The experimental results show that, compared with the non-vegetation situation, the arrangement of grasses on the floodplain will increase the water surface gradient, hydraulic gradient and turbulence intensity to a certain extent.

Boundary Shear Stress Distribution in Curved Compound Open Channels

AbstractAn analytical model for evaluation of boundary shear stress in compound open-channel bends is developed. Perpendicular volumetric elements are generated in all cross sections of a bend. Eac...