Depth-averaged Velocity Distribution Research Articles

A method for modeling the lateral distributions of depth-averaged velocities behind an emergent vegetation patch

Aquatic vegetation provides ecological, hydrological, and aesthetic functions for rivers, and measuring velocity in vegetated channels is essential for river management. The paper presents a method for modeling the lateral distributions of depth-averaged velocities behind an emergent vegetation patch. Based on SKM, this approach divides the channel behind an emergent vegetation patch into pseudo-vegetation and free-flow regions, offering analytical solutions for the depth-averaged velocities in these two regions. The model incorporates several critical parameters, including the Darcy–Weisbach coefficient, lateral dimensionless eddy viscosity, drag force coefficient, and secondary flow coefficients. These coefficients are associated with bed friction, vegetation-induced resistance, secondary flow effects, and lateral momentum exchange, respectively, affecting the depth-averaged velocities. A comparison with published experimental data validates that the proposed model can predict the lateral distributions of depth-averaged velocities behind an emergent vegetation patch. A steady wake section exists behind an emergent vegetation patch for low-flow blockage. In the steady wake section, the secondary flow coefficients in pseudo-vegetation and free-flow regions remain relatively constant. Upon exiting the stable wake section, the secondary flow coefficient in the pseudo-vegetation region decreases with increasing distance from an emergent vegetation patch, and it in the free-flow region increases with increasing distance from an emergent vegetation patch. A sensitivity analysis of drag coefficient and secondary flow coefficients suggests that secondary flow coefficient in the free-flow region has a more significant effect on the lateral distributions of depth-averaged velocities compared to drag coefficient and secondary flow coefficient in the pseudo-vegetation region.

Effect of single vanes on turbulent flow

In response to growing environmental and ecological awareness, eco-friendly in-stream structures such as vanes have been implemented in different parts of the world to enhance stream conditions. FLUENT (ANSYS) was used to perform three-dimensional large eddy simulation to investigate the effect of the vanes permeability rate on flow characteristics. To evaluate the numerical model accuracy, numerical and experimental free surface profiles compared. It is observed that simulated free surface profiles agree reasonably well with measured values. The effect of different permeability rates is obvious in the flow characteristics such as depth-averaged velocity distribution, tip velocity variations, formation of the secondary flows in the flow field, turbulent kinetic energy, and mean kinetic energy contours. On average, maximum velocity values in the flow field is 1,54 times the approach velocity. Tip velocity decreases up to 30,6 % for the 70,0 % permeable vane. Maximum turbulent kinetic energy and mean kinetic energy for the 70,0 % permeable vane decrease up to 58,0 % and 43,3 %, respectively. Generally significant velocity and flow pattern variations around the impermeable vane can be attributed to the local effect of the vane structure and channel cross sectional constriction in comparison to the permeable vanes.

An Investigation on Hydraulic Aspects of Rectangular Labyrinth Pool and Weir Fishway Using FLOW-3D

Two different arrangements of the weir (i.e., straight weir and rectangular labyrinth weir) were used to evaluate the effects of geometric parameters such as weir shape, weir spacing, presence of an orifice at the weir, and bed slope on the flow regime and the relationship between discharge and depth, variation and distribution of depth-averaged velocity, turbulence characteristics, and energy dissipation at the fishway. Computational fluid dynamics simulations were performed using FLOW-3D® software to examine the effects on flow conditions. The numerical model was validated by comparing the calculated surface profiles and velocities with experimentally measured values from the literature. The results of the numerical model and experimental data showed that the root-mean-square error and mean absolute percentage error for the surface profiles and normalized velocity profiles of plunging flows were 0.014 m and 3.11%, respectively, confirming the ability of the numerical model to predict the flow characteristics of the pool and weir. A plunging flow can occur at values of L/B = 1.83 (L: distance of the weir, B: width of the channel) and streaming flow at L/B = 0.61 for each model. The rectangular labyrinth weir model has larger dimensionless discharge values (Q+) than the conventional model. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q is proportional to 1.56 and 1.47h, respectively (h: the water depth above the weir). The average depth velocity in the pool of a conventional weir is higher than that of a rectangular labyrinth weir. However, for a given discharge, bed slope, and weir spacing, the turbulent kinetic energy (TKE) and turbulence intensity (TI) values are higher for a rectangular labyrinth weir compared to conventional weir. The conventional weir has lower energy dissipation than the rectangular labyrinth weir. Lower TKE and TI values were observed at the top of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall. As the distance between the weirs and the bottom slope increased, the average depth velocity, the average value of turbulent kinetic energy and the turbulence intensity increased, and the volumetric energy dissipation in the pool decreased. The presence of an opening in the weir increased the average depth velocity and TI values and decreased the range of highest TKE within the pool, resulted in larger resting areas for fish (lower TKE), and decreased the energy dissipation rates in both models.

Boundary shear stress and apparent shear forces in compound channels with different floodplain widths

ABSTRACT The present study has studied a model to predict depth-averaged velocity distribution and boundary shear stress in compound channels with different floodplain widths. The model was verified against three different data sets of the present experiments and two data used in the literature. The results indicate that the present model can predict the depth-averaged velocity and shear stress distributions, promising to simulate the flow field and related characteristics better. The results show that the non-dimensional coefficient plays a dominant role in portraying the variation of depth-averaged velocity and shear stress distributions in compound channels with different floodplain widths. In addition, the apparent shear forces were examined by dividing the channel cross-section into seven parts, and each element carried shear forces and acted on the horizontal and vertical interfaces for three different width-to-depth ratios were discussed and analyzed. In all configurations, the horizontal interface was negative, indicating that the upper region of flow accelerates the flow in the lower main channel. In contrast, the vertical interfaces were positive, suggesting that the slower floodplain flows retards the faster main channel flows.

Experimental Study on Depth-Averaged Velocity and Bed Profile in a Braided Channel with a Mid-Bar

Braided alluvial rivers with a mid-bar are common features occurred in alluvial river that consists of bifurcation and confluence channels. The formation of the mid-bar will affect the hydraulics of river systems in terms of velocity and bed morphology. The studies corresponding to the typical braided river with a mid-bar are still ongoing. This paper is to present the finding of depth-averaged velocity, Ud and bed profile at the bifurcation and confluence channel. A channel with a mid-bar and erodible bed was used in this research. The experimental work was carried out in the Hydraulic Laboratory at Universiti Teknologi Malaysia, (UTM). In the experiment, two types of flow which are low flow and high flow rates were considered. The study found that depth-averaged velocity distributions are influenced by flow discharge and varied at the braided channel. The highest Ud velocity is 0.35 m/s occurred at the bifurcation area and the lowest Ud is 0.2 m/s that was occurred at the confluence area. This genesis to more erosion occurred at the bifurcation area compared to the confluence area.

Rivers under Ice: Evaluating Simulated Morphodynamics through a Riffle-Pool Sequence

Modeling in ice-covered rivers is limited due to added computational complexity, specifically challenges with the collection of field calibration data. Using River2D, a 2-dimensional hydrodynamic modeling software, this study simulates depth-averaged velocity and shear stress distributions under ice cover and in open-water conditions during varying flow conditions in a small, shallow riffle-pool sequence. The results demonstrated differences in velocity distribution throughout the channel and increases in discharge were found to impact the velocity magnitude under ice cover, while the spatial distribution remained consistent. A recirculating eddy found along the pool’s left bank was exacerbated under ice cover, with potential implications for silver shiner habitat suitability. Bed shear stress magnitude did not vary significantly between ice and open water, although the spatial distribution differed notably. Model validation demonstrated success in simulating water depth and velocities, and the shear stress was estimated within a reasonable margin. Using hydrodynamic models provides valuable insight into seasonal changes in velocities and shear stress when ice is present.

Transverse distribution of the streamwise velocity for the open-channel flow with floating vegetated islands.

Floating vegetation islands (FVIs) have been widely utilized in various river ecological restoration projects due to their ability to purify pollutants. FVIs float at the surface of shallow pools with their roots unanchored in the sediment. Biofilm formed by roots under islands filters nutrients and particles in the water flowing through it. Flow field disturbance will occur, and transverse distribution of flow velocity will change due to the existence of FVIs. Transport efficiency of suspended solids, nutrients, and pollutants will also be altered. A modified analytical model that considers the effects of boundary friction, drag force of vegetation, transverse shear turbulence, and secondary flow is established to model the transverse distributions of depth-averaged streamwise velocity for the open-channel flow with FVIs using the Shiono and Knight Method. The simulation results with suitable boundary conditions successfully modeled the lateral profile of the depth-averaged streamwise velocity compared with the experimental results of symmetrical and unsymmetrical arrangements of FVIs. Hence, the presented model is of guiding significance to investigate the flow characteristics of rivers with FVIs.

Analytical model for lateral depth-averaged velocity distributions in curved channels

The distribution of depth-averaged velocity is crucial to many engineering problems. This paper presents an analytical solution for the lateral depth-averaged velocity distribution in a 120° curved channel with asymmetric trapezoidal cross-sections in which the curved flow is not fully developed. The proposed analytical model was derived from the streamwise depth-integrated Reynolds-averaged Navier–Stokes equation, which considers the bed stress, Reynolds stress, secondary flow and local flow acceleration. In addition, practical boundary conditions are proposed to consider the trapezoidal cross-sections with linearly varying side beds and the flow separation at the inner bank near the bend entrance. The analytical solutions using the proposed model were found to be in good agreement with measured data. The main contributions of this study are the development of a conventional analytical model for sophisticated circumstances and the proposal of practical boundary conditions that consider flow separation.

Modeling depth-averaged streamwise velocity in straight trapezoidal compound channels with ice cover

This study considers the flow of water in ice-covered compound channels with straight trapezoidal cross-sections. For describing the lateral distribution of depth-averaged streamwise velocity in aforementioned channels, a modified analytical model, which incorporates the influences of channel bed friction, ice cover resistance, lateral shear turbulence and secondary currents, is derived by the Shiono and Knight method and a two-layer hypothesis. Then the analytical model is applied to straight compound channels with full ice cover and symmetrical shore ice. The modeled results of the two cases, which employ appropriate boundary conditions, indicate good predictions for the transverse distribution of depth-averaged streamwise velocity when compared with captured experimental results. Subsequently, the intensities and rotational directions of secondary flows and the dimensionless comprehensive eddy viscosity effect are exhaustively discussed, finding that the intensities of secondary flows in the main channel domain for the two cases present opposite changing laws as flow depth increases, and the signs of secondary flow coefficients are verified to be consistent with experimental observations. The theoretical approach used herein can supply some guidance for investigating the flow characteristics of ice-covered channels.

Analytical Model for Lateral Depth-Averaged Velocity Distributions in Rectangular Ice-Covered Channels

AbstractBased on the Reynolds-averaged Navier–Stokes equations and the Shiono and Knight method, this paper describes the development of an analytical model to predict the lateral distribution of d...

Flow characteristics of a partially-covered trapezoidal channel

Partial ice covers alter the hydraulic regime of rivers in cold regions. Border ice is a type of partial ice cover that forms on the river banks and grows toward the centre of the channel to form a full ice cover; thereby impacting freeze-up processes. Many studies have been conducted to understand flow characteristics under open channel and full ice cover conditions; however, only a few studies have focused on the effects of partial ice covers on flow characteristics in a rectangular channel. This study goes even further by investigating stream-wise velocity and shear stress distributions in a trapezoidal channel with simulated border ice. This is the very first study to investigate the effects of different border ice coverage ratios and roughness conditions on flow characteristics in a trapezoidal channel. Experiments were conducted under seven different roughness and coverage conditions. High-resolution velocity data were collected using acoustic Doppler velocimeters within the fully-developed region of the flume. The magnitude and shape of the stream-wise velocity contours were significantly altered by the presence of the partial ice and rough boundaries. Moreover, local boundary shear stress distributions were significantly impacted by the coverage and roughness conditions. Generally, stream-wise velocity and local boundary shear stress increased within the open section and decreased within the covered section. For practical purposes, depth-averaged velocity and discharge distributions were investigated for each experiment. Results from this study will improve the current knowledge of the flow in partially covered channels and can be used for design and modelling purposes.

Lateral distribution of depth average velocity & boundary shear stress in a gravel bed open channel flow

ABSTRACT Gravel bed flow is so generic condition that its study becomes fascinating as well as critical to apprehend flow characteristic. In this particular study, no bed load movement was maintained using grains of 13.5 mm (D50 value) characterised as no load condition. Depth Average Velocity (DAV) and the Boundary Shear Stress (BSS) has been experimentally estimated for five different depths for the prevailing no load condition. Furthermore, the distribution of streamwise depth-averaged velocity and boundary shear stress at different flow depths of gravel bed are also calculated using different hydraulic software packages such as CES & ANSYS FLUENT. These numerical simulation results have shown reasonably good agreement with experimental data over main channel in inbank flow. Finally, results obtained are corroborated through error analysis. The overall idea of this study was to understand flow characteristic and behaviour of gravel bed having inbank flow through experimental and numerical simulation techniques.

Depth-averaged simulation of flows in asymmetric compound channels with smooth and rough narrow floodplains

ABSTRACTDepth-averaged hydrodynamic models are predominantly used in numerical simulations of compound channel flows. One of the most popular methods for the depth-averaged simulation is Shiono and Knight method (SKM). This method accounts for the effects of bed friction, lateral turbulence and secondary flows, via three key parameters f, λ and Γ, respectively. The conventional expressions that are developed to calibrate these parameters are generally based on experiments in compound channels with wide floodplains. In this study, the application of SKM to an asymmetric compound channel with a narrow floodplain is examined in terms of the calibration requirements. Two sets of experiments that have smooth and rough floodplains are conducted and then simulated by SKM. In smooth floodplain cases, the results reveal that SKM model with the conventional calibration expressions of f, λ and Г is reasonably capable of predicting the distributions of depth-averaged velocity and boundary shear stress in the main channel. However, in the floodplain region, the expressions recommended for calibrating Г need to be modified to improve the predicted results in that region. In cases of the rough floodplain, the results indicate that only the values of λ in the main channel need to be changed from its conventional values to improve the predictions.

Flow structure at the downstream of a one-line riparian emergent tree along the floodplain edge in a compound open-channel flow

This study focuses on the effects of one-line emergent natural tree (Cupressus Macrocarpa) planted at the edge of the floodplain in a compound open-channel flow. The flow velocity and water level are measured and used to analyze the flow structure. The time averaged and depth-averaged streamwise velocity distributions with root mean square (rms) and time series of streamwise velocity distrbution are analyzed. The velocity distribution considerably changes along the compound channel. The streamwise velocity distribution fits with logarithmic distribution in the non-vegetated case, but for vegetated cases, the streamwise velocity distribution shows S shaped profile at the 1/3 part of floodplain (B f / 3) and main channel (B m / 3) close to the boundary between floodplain and main channel. Additionally, it is obtained that the presence of tree line increases turbulence intensity over the compound open-channel. Moreover, an oscillation period is obtained in the flow caused by tree line by analyzing time series of the streamwise velocity distribution. The oscillation is present everywhere in the floodplain and present at almost B m / 3 part of the main channel which is close to the junction between floodplain and main channel.

Application of the Shiono and Knight Method in asymmetric compound channels with different side slopes of the internal wall

The Shiono and Knight Method (SKM) is widely used to predict the lateral distribution of depth-averaged velocity and boundary shear stress for flows in compound channels. Three calibrating coefficients need to be estimated for applying the SKM, namely eddy viscosity coefficient (λ), friction factor (f) and secondary flow coefficient (k). There are several tested methods which can satisfactorily be used to estimate λ, f. However, the calibration of secondary flow coefficients k to account for secondary flow effects correctly is still problematic. In this paper, the calibration of secondary flow coefficients is established by employing two approaches to estimate correct values of k for simulating asymmetric compound channel with different side slopes of the internal wall. The first approach is based on Abril and Knight (2004) who suggest fixed values for main channel and floodplain regions. In the second approach, the equations developed by Devi and Khatua (2017) that relate the variation of the secondary flow coefficients with the relative depth (β) and width ratio (α) are used. The results indicate that the calibration method developed by Devi and Khatua (2017) is a better choice for calibrating the secondary flow coefficients than using the first approach which assumes a fixed value of k for different flow depths. The results also indicate that the boundary condition based on the shear force continuity can successfully be used for simulating rectangular compound channels, while the continuity of depth-averaged velocity and its gradient is accepted boundary condition in simulations of trapezoidal compound channels. However, the SKM performance for predicting the boundary shear stress over the shear layer region may not be improved by only imposing the suitable calibrated values of secondary flow coefficients. This is because difficulties of modelling the complex interaction that develops between the flows in the main channel and on the floodplain in this region.

Depth-averaged velocity and bed shear stress in unsteady open channel flow over rough bed

Very few studies have been carried out in the past in estimating depth-averaged velocity and bed shear stress in unsteady flow over rough beds. An experiment is thus conducted to investigate the vertical and lateral velocity profiles under unsteady flow conditions in a rough open channel for various flow depths. One hydrogram is repeatedly passed through the rectangular flume with a fixed rigid grass bed. Using micro Pitot tube and Acoustic Doppler Velocimeter (ADV), the flow patterns are investigated at both lateral and longitudinal positions over different cross-sections. For two typical flow depths, the velocities in both the rising limb and falling limb are observed. Hysteresis effect between stage-discharge (h ~ Q) rating curve between rising and falling limbs is illustrated. Lateral distribution of depth-averaged velocity and bed shear stress are plotted at three different cross sections and compared with the steady flow conditions. In falling limb of an unsteady flow case, both depth-averaged velocity and bed shear stress distribution in the central region is higher than that of steady flow case. However, in the rising limb, the bed shear stress of unsteady flow is less than that of steady flow case. Further, in an unsteady flow, the magnitude of depth-averaged velocity is found to increase towards the downstream sections. Along the downstream positions, bed shear stress values increase for lower flow depths and decrease for higher flow depth cases.

Transverse distribution of streamwise velocity in open-channel flow with artificial emergent vegetation

Artificial emergent vegetation can increase flow resistance and water depth to improve navigation in an open channel. An innovative and eco-friendly artificial vegetation system is analyzed in this study. First, a new method is presented to modify the depth-averaged Navier–Stokes equation by incorporating the vegetation drag force term. Two analytical formulas based on theoretical analysis are proposed to predict the lateral distribution of depth-averaged velocity in an open channel with fully and partially artificial vegetation. Then, the analytical formulas are verified by laboratory experiments. The results of the analytical model are consistent with experimental data, thereby proving that the analytical formulas can be used to predict the lateral distribution of streamwise velocity in open-channel flow with artificial emergent vegetation. The presented model can provide a significant theoretical reference for research on open channels with artificial emergent vegetation.

Numerical modeling of converging compound channel flow

This paper presents numerical analysis for prediction of depth-averaged velocity distribution of compound channels with converging flood plains. Firstly, a 3D Computational Fluid Dynamics model is used to establish the basic database under various working conditions. Numerical simulation in two phases is performed using the ANSYS-Fluent software. k-ω turbulence model is executed to solve the basic governing equations. The results have been compared with high-quality flume measurements obtained from different converging compound channels in order to investigate the numerical accuracy. Then Artificial Neural Network are trained based on the Back Propagation Neural Network technique for depth-averaged velocity prediction in different converging sections and these test results are compared with each other and with actual data. The study has focused on the ability of the software to correctly predict the complex flow phenomena that occur in channel flows.

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.

Depth-Averaged Velocity and Boundary Shear Stress Prediction in Asymmetric Compound Channels

When a river overflows, either side of its flood plain during flood is named as asymmetric compound channel; however, if two adjacent flood plains are inundated, it is called as symmetric compound channel. Due to the complex flow mechanism at the junction between main channel and flood plain, modeling of depth-averaged velocity and boundary shear stress in an asymmetric compound channels becomes an exigent task. The analytical solution of the Shiono and Knight Method accounts three governing parameters, i.e., lateral shear, bed friction and secondary flows for prediction of these flow variables. In order to investigate the influence of these governing coefficients on flow parameters, experiments were employed in asymmetric compound channels. Variation of boundary shear stress and depth-averaged velocity across the channel was investigated. Some experimental data sets from large flood channel facility and from measurements taken by other researchers have also been used in this study. The variation of three calibrating coefficients, i.e., eddy viscosity coefficient (\(\lambda \)), friction factor (f) and secondary flow coefficient (k) against the geometric and hydraulic parameters, has been studied. Expressions for secondary flow coefficients in terms of hydraulic and flow parameters have been procured for different panels which are required to get the distribution of boundary shear and depth-averaged velocity. The performance of the models has been successfully proved for experimental channels and natural river data sets.