Flow resistance and its prediction methods in compound channels

A series of experiments was carried out in a large symmetric compound channel composed of a rough main channel and rough floodplains to investigate the resistance characteristics of inbank and overbank flows. The effective Manning, Darcy-Weisbach, Chezy coefficients and the relative Nikuradse roughness height were analyzed. Many different representative methods for predicting the composite roughness were systematically summarized. Besides the measured data, a vast number of laboratory data and field data for compound channels were collected and used to check the validity of these methods for different subsection divisions including the vertical, horizontal, diagonal and bisectional divisions. The computation showed that these methods resulted in big errors in assessing the composite roughness in compound channels, and the reasons were analyzed in detail. The error magnitude is related to the subsection divisions.

Predictive model for stage-discharge curve in compound channels with vegetated floodplains

The governing equation of the discharge per unit width, derived from the flow continuity equation and the momentum equation in the vegetated compound chan- nel, is established. The analytical solution to the discharge per unit width is presented, including the effects of bed friction, lateral momentum transfer, drag force, and secondary flows. A simple＇ but available numerical integral method, i.e., the compound trapezoidM formula, is used to calculate the approximate solutions of the sub-area discharge and the total discharge. A comparison with the published experimental data from the U. K. Flood Channel Facility （UK-FCF） demonstrates that this model is capable of predicting not only the stage-discharge curve but also the sub-area discharge in the vegetated com- pound channel. The effects of the two crucial parameters, i.e., the divided number of the integral interval and the secondary flow coefficient, on the total discharge are discussed and analyzed.

Two-dimensional analytical solution for compound channel flows with vegetated floodplains

This paper presents a two-dimensional analytical solution for compound channel flows with vegetated floodplains. The depth-integrated N-S equation is used for analyzing the steady uniform flow. The effects of the vegetation are considered as the drag force item. The secondary currents are also taken into account in the governing equations, and the preliminary estimation of the secondary current intensity coefficient K is discussed. The predicted results for the straight channels and the apex cross-section of meandering channels agree well with experimental data, which shows that the analytical model presented here can be applied to predict the flow in compound channels with vegetated floodplains.

Two dimensional analytical solution for a partially vegetated compound channel flow

The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the unit volume where the effect of the vegetation on the flow is considered as a drag force item, The compound channel is divided into 3 sub-regions in the transverse direction, and the coefficients in every region＇s differential equations were solved simultaneously. Thus, the analytical solution of the transverse distribution of the depth-averaged velocity for uniform flow in a partially vegetated compound channel was obtained. The results can be used to predict the transverse distribution of bed shear stress, which has an important effect on the transportation of sediment. By comparing the analytical results with the measured data, the analytical solution in this paper is shown to be sufficiently accurate to predict most hydraulic features for engineering design purposes.

Study on resistance coefficient in compound channels

This paper presents a further study of the Manning and Darcy-Weisbach resistance coefficients, as they play a significant role in assessing the cross-sectional mean velocity, conveyance capacity and determining the lateral distribution of depth mean velocity and local boundary shear stress in compound channels. The relationships between the local, zonal and overall resistance coefficients, and a wide range of geometries and different roughness between the main channel and the flood plain are established by analyzing a vast amount of experimental data from a British Science and Engineering Research Council Flood Channel Facility （SERC-FCF）. And the experimental results also show that the overall Darcy-Weisbach resistance coefficient for a compound channel is the function of Reynolds number, but the function relationship is different from that for a single channel. By comparing and analyzing the conventional methods with the experimental data to predict composite roughness in compound channels, it is found that these methods are not suitable for compound channels. Moreover, the reason why the conventional methods cannot assess correctly the conveyance capacity of compound channels is also analyzed in this paper.

Simple analytical model for depth-averaged velocity in meandering compound channels

A simple but applicable analytical model is presented to predict the lat- eral distribution of the depth-averaged velocity in meandering compound channels. The governing equation with curvilinear coordinates is derived from the momentum equation and the flow continuity equation under the condition of quasi-uniform flow. A series of experiments are conducted in a large-scale meandering compound channel. Based on the experimental data, a magnitude analysis is carried out for the governing equation, and two lower-order shear stress terms are ignored. Four groups of experimental data from different sources are used to verify the predictive capability of this model, and good predictions are obtained. Finally, the determination of the velocity parameter and the limitation of this model are discussed.

Analysis of flow around impermeable groynes on one side of symmetrical compound channel:An experimental study

This paper presents the results of an experimental study on the influences of floodplain impermeable groynes on flow structure, velocity, and water depth around the groyne（s）. A wooden symmetrical compound channel was used. Groyne models with three different groyne relative lengths, 0.5, 0.75, and 1.0, were used on one floodplain with single and series arrangements. Analysis of the experimental results using the measured flow velocity and water depth values showed that flow structure, velocity, and water depth mainly depend on groyne relative length and the relative distance between series groynes. The flow velocity at the main channel centerline increased by about 40%, 60%, and 85%, and in other parts on the horizontal plane at the floodplain mid-water, depth by about 75%, 125%, and 175% of its original value in eases of one-side floodplain groyne（s） with relative lengths of 0.5, 0.75, and 1.0, respectively. The effective distance between two groynes in series arrangement ranges from 3 to 4 times the groyne length. Using an impermeable groyne with a large relative length in river floodplains increases the generation of eddy and roller zones downstream of the groyne, leading to more scouring and deposition. To avoid that, the groyne relative length must be kept below half the floodplain width,

Investigating the Effect of Relative Width on Momentum Transfer between Main Channel and Floodplain in Rough Rectangular Compound Channel Sunder Varius Relative Depth Condition

Compound section is referred to a section the surface of which is made of several sub-sections with different flow characteristics. The difference in the hydraulic and geometry characteristics causes a complexity in flow hydraulic and creates an interaction between the main channel and floodplains, resulting in an apparent shear stress and a transverse momentum transfer. The amount of such a stress plays an important role in many river engineering measures [1]. Due to the flow complexity, the common approximate analytical methods are not enough to identify the flow profile. The FLOW3D Software with its great features in three-dimensional analysis of flow field is used as a tool to investigate the shear stress in a direct symmetrical compound rectangular channel. After the simulation of models, it is found that an increase in the relative width and relative depth parameters decreases the percentage of apparent shear stress and an increase in the relative roughness causes it to be increased [2].

Analytical Models for Velocity Distributions in Compound Channels with Emerged and Submerged Vegetated Floodplains

The lateral distributions of depth-averaged velocity in open compound channels with emerged and submerged vegetated floodplains were analyzed based on the analytical solution of the depth-integrated Reynolds-Averaged Navier-Stokes equation with a term to account for the effects of vegetation.The three cases considered for open channels were two-stage rectangular channel with emerged vegetated floodplain,rectangular channel with submerged vegetated corner,and two-stage rectangular channel with submerged vegetated floodplain,respectively.To predict the depth-averaged velocity with submerged vegetated floodplains,we proposed a new method based on a two-layer approach where flow above and through the vegetation layer was described separately.Moreover,further experiments in the two-stage rectangular channel with submerged vegetated floodplain were carried out to verify the results.The analytical solutions of the cases indicated that the corresponding analytical depth-averaged velocity distributions agree well with the simulated and experimental prediction.The analytical solutions of the cases with theoretical foundation and without programming calculation were reasonable and applicable,which were more convenient than numerical simulations.The analytical solutions provided a way for future researches to solve the problems of submerged vegetation and discontinuous phenomenon of depth-averaged velocity at the stage point for compound channels.Understanding the hydraulics of flow in compound channels with vegetated floodplains is very important for supporting the management of fluvial processes.

Experimental Study of the Effects of Submerged Dikes on the Energy and Momentum Coefficients in Compound Channel

This paper aims to understand the flow structure around submerged dike in the main channel and flood plain of a compound cross section. The study undertaken to develop this understanding was carried out in a laboratory flume using a submerged vane installed at a 90 degree angle to the bank. In order to study the flow structures, the flow velocity was measured using a three-dimensional Acoustic Doppler Velocity meter (micro-ADV) with data collection rate of 50 Hz. These flow velocity measurements were taken at 500 points on a regular grid. As the tests were undertaken with turbulent flow, these conditions were subcritical. Furthermore, all the tests were undertaken using a fixed bed. The results obtained showed that the momentum transfer and the kinetic energy reduced in two directions. Also the energy and momentum coefficients decreased significantly with the installation of the submerged vane inside the main channel. Finally, streamlines were found to deviate from the side walls of channel into the main channel.

Numerical investigation of flow through vegetated multi-stage compound channel

This paper addresses the problem of the renormalization group k turbulence modeling of a vegetated multi-stage compound channel. Results from Micro acoustic Doppler velocimeter（ADV） tests are used with time and spatial averaging（doubleaveraging method） in the analysis of the flow field and the characterization. Comparisons of the mean velocity, the Reynolds stress, and the turbulent energy distribution show the validity of the computational method. The mean velocity profile sees an obvious deceleration in the terraces because of vegetation. Secondary flow exists mainly at the junction of the main channel and the vegetation region on the first terrace. The bed shear stress in the main channel is much greater than that in the terraces. The difference of the bed shear stress between two terraces is insignificant, and the presence of vegetation can effectively reduce the bed shear stress.

The characteristics of secondary flows in compound channels with vegetated floodplains

The experiments were conducted in compound channels with vegetated floodplains for investigating the influence of vegetation types on the characteristics of secondary flows. In terms of the streamwise and transverse velocities and the depth-averaged velocity, the secondary flow coefficient, M, is proposed, with good physical meanings, and it may characterize the rotational direction and the intensity of the secondary currents. The experimental results show that, for the cases without vegetation and with grass, the rotational directions of the secondary flows are all antielockwise while for the cases with shrubs, they are all changed to the clockwise direction in the whole cross-section. However, when trees are planted, the secondary flows rotate in the anticlockwise direction in the main channel and in the clockwise direction on the floodplain. In addition, for all cases, the intensities of the secondary currents on the floodplain are stronger than those in the main channel.

NUMERICAL MODELING OF COMPOUND CHANNEL FLOWS

A numerical model capable of predicting flow characteristics in a compound channel was established with the 3-D steady continuity and momentum equations along with the transport equations for turbulence kinetic energy and dissipation rate. Closure was achieved with the aid of algebraic relations for turbulent shear stresses. The above equations were discretized with implicit difference approach and solved with a step method along the flow direction. The computational results showing the lateral distribution of vertical average velocities and the latio of total flow in the compound channel agree well with the available experimental data.

Behavior of near-field dilution of thermal buoyant jet discharged horizontally in compound open-channel

The RNG κ-ε model considering the buoyancy effect, which is solved by the hybrid finite analytic method, is used to simulate the mixture of the horizontal round thermal buoyant jet in compound open channel flow. The mixing features near the spout and flowing characteristic of the secondary currents are studied by numerical simulation. Meanwhile, （1） the distribution of the measured isovels for stream-wise velocity, （2） secondary currents, （3） the distribution of the measured isovels for temperature of typical cross-section near the spout, were obtained by the three-dimensional Micro ADV and the temperature measuring device. Compared with experimental data, the RNG κ-ε model based on buoyancy effect can preferably simulate the jet which performs the bifurcation phenomenon, jet reattachment （Conada effect） and beach secondary currents phenomenon with the effect of ambient flow, buoyancy, and secondary currents of compound section and so on.

Estimation of discharge and its distribution in compound channels

Results of research into a compound channel having width ratio （a） in excess of 11 are presented in the form of boun-dary shear distributions across the compound cross section. New relationship is derived between the percentage of shear carried by the flood plains （%S fp ） and the percentage of area occupied by the flood plains （%Afp ） . The equation so derived is taken as the basis to develop a new methodology to predict the stage discharge relationship specifically for wide compound channels using Darcy＇s friction factor （ f ） for the main channel and flood plain regions. The methodology also is used for compound channels with smaller width ratios by applying the appropriate relation for %S fp derived earlier by different researchers and seems to work well. Next, as a corollary to the methodology, separate formulae are proposed to estimate flow distribution in main channel and flood plain regions. The proposed method and its corollary are tested for their validity against well-published small-scale data series of pre-vious researchers along with some large-scale data series from EPSRC-FCF （A-Series） compound channel experiments and very good agreement is observed between the measured values and predicted values for total flow as well as zonal distribution of flow. The methodology is also applied to some compound river section data published in literature and is found to serve well the purpose of predicting flow in real world application. This new method gives the least RMS value of error for discharge prediction compared with some other well-known methods used for estimating stage-discharge relation in compound channels by considering all data sets.

RESEARCH ON SYSTEM DYNAMICS MODEL OF CONVEYANCE CAPACITY IN SYMMETRIC COMPOUND CHANNELS

Stage-discharge curves are particularly important in river basin management. For a compound channel, the stage-discharge curve is often difficult to be extrapolated to yield estimates of level for a given frequency of flow. By analyzing a large number of experimental data from Science and Engineering Research Council Flood Channel Facility (SERC-FCF) and applying system dynamics method, the authors established system dynamics model of conveyance capacity when rivers flow in an overbank mode, spilling onto the adjoining flood plain. The model was applied to a compound channel. And the corresponding simulated results are shown to attain high accurcy.

EVALUATION OF STAGE-DISCHARGE RELATIONSHIP IN COMPOUND CHANNELS

Experimental results were compared with the computed results obtained from the nine most well-known methods for computation of discharge in a compound channel. The results demonstrate a high accuracy of the divided channel method with the horizontal division lines, while the length of division line is included within the calculation of the wetted perimeter. In addition, as relative depth increases, the results of the all methods converge to each other and also in case of steeper slopes in lower relative depths, more agreements between different calculated methods and experimental results were observed. Furthermore, the results show the effects of the maximum momentum transfer on the horizontal interface between the main channel and flood plains, while further angular distance from the horizontal interface toward the vertical interface between main channel and flood plains causes gradual decrease of momentum transfer effects.

Dispersion features of pollutants in a compound channel with vegetated floodplains

The planting of the vegetation on the floodplain helps the ecological restoration,which is the main form of the river’s ecological corridor.Therefore,the current research of the river dynamics focuses on the water movement under a compound channel with the vegetated floodplains.Two simulated vegetation species are selected in this paper for the flume simulation experiments of the floodplain vegetation,and the compound channel is divided into three subregions in the transverse direction.The Navier-Stokes equation and the eddy viscosity theory are applied to obtain the transverse distribution of the depth-averaged velocity and the results agree well with the experimental data.This paper proposes a new method based on the analytical solution of the flow velocity distribution to calculate the average flow velocity in each section.Calculation results can effectively simulate the average flow velocity of the measured sections.The description of the pollutant transport processes in a moving stream requires a refined determination of the dispersion coefficients in the compound channel.The process of the pollutant concentrations in each zone and the reasons for their occurrence are elucidated on the basis of the experimental results.Simultaneously,the measured values of the longitudinal dispersion coefficients are obtained by the“routing procedure,”and a two-zone model of the pollutant dispersion is constructed on the basis of the hydrodynamic study.The prediction method for the longitudinal dispersion coefficients is also presented.Applying the predicted and measured section average flow velocities to the two-zone model to predict the longitudinal dispersion coefficient,and the average relative errors are only 4.17%,7.15%,respectively.This result indicates that the two-zone model can effectively predict the longitudinal dispersion coefficients.The calculation methods for the longitudinal dispersion coefficients from—various studies are compared.The results reveal that the predicted values of these calculation methods are all larger than the measured values,indicating that the vegetation has a considerable influence on the dispersion process.This study comprehensively shows the dispersion features of the pollutants and provides a theoretical basis for the planning and the design of the vegetated ecological corridors.

A simple method for estimating bed shear stress in smooth and vegetated compound channels

Instead of a large number of measurements of the streamwise velocity, a simple method is proposed to estimate the bed shear stress in smooth and vegetated compound channels, based on the Darcy-Weisbach equation. This method contains a dimension- less parameter Ai, to represent the relationship between the bed shear stress and the velocity close to the channel bed （Ub）, which is determined in each divided domain. This method is verified in two smooth compound channels with different geometries, and in one compound channel with emergent floodplain vegetation. The comparison of predicted and measured bed shear stresses indicates the good predictive capability of this method, particularly in the mixing region. This method is further discussed for a channel with submerged vegetation. Once the values of Ai in the main channel and the floodplain are determined, this method is a practical tool

Hydraulic calculation of steady uniform flows in trapezoidal compound open channels

Hydraulic calculation of steady uniform flows in trapezoidal compound open channels is studied. Based on the force balance of water in each sub-section, the average velocities of the main channel, side slope, and floodplain are derived. The lateral momentum exchanges between the sub-sections are expressed by using the apparent shear stress. To verify the model, seven groups of UK Flood Channel Facility （UK-FCF） measured data with a relative water depth between the floodplain and the main channel varying from 0.057 to 0.4 are used for comparison. The result shows that the calculated velocity is larger than the measured data when the relative water depth is small, while it is less than or close to the measured value in the case of a larger relative water depth. The influence of the apparent shear stress on the calculation of velocity on the floodplain is not obvious, while it is much greater on the main channel. The three-stage model is compared with Liu’s two-stage model, showing that the former can give a better prediction for a three-stage trapezoidal compound channel. Finally, the apparent shear stress is calculated and compared with the measured data. The result shows that the chosen values of the momentum transfer coefficients are appropriate.