Boundary Shear Stress Distribution Research Articles

Sustainable gene expression programming model for shear stress prediction in nonprismatic compound channels

Open channel flow resistance and channel stability can be determined from boundary shear stress distribution. Overbank floods cross the main channel and pours the floodplain. The momentum change between the main channel and floodplains creates complicated flow shapes in compound channels. This alters floodplain and main channel shear stress. River floodplains also support agriculture and development activities due to which floodplain shape changes along the flow length, creating a converging, diverging or skewed compound channels. Traditional empirical formulas cannot accurately estimate shear force distribution. Thus, creative and accurate methods remain in demand. Gene expression programming, an innovative approach, has been utilized in this study to develop a new equation for compound channel with converging floodplains in terms of nondimensional geometric and flow variables to estimate the boundary shear force carried by floodplains. The proposed GEP-based method is best when compared to previously developed methods. The findings indicate that the predicted percentage shear force carried by floodplains determined using GEP is in good agreement with the experimental data (R2 = 0.96 and RMSE = 3.395 for the training data and R2 = 0.95 and RMSE = 4.022 for the testing data).

Experimental study of the flow field in compound channels with converging and inclined floodplains

ABSTRACT This paper presents experimental results of overbank flow in compound channels with converging and inclined floodplains. Velocity and boundary shear stress distributions at different selected sections along the narrowing part of the flume for two convergence angles of 3.81° and 11.31° were measured. The study indicated that the velocity and boundary shear stress increase along the flume, especially in the second half of the converging part of the flume. It was shown that the maximum velocity at the end of the converging transition can be over than twice as much as at the beginning section. By using the experimental data and force–momentum balance, the apparent shear forces at the vertical interface between the main channel and floodplains were investigated. The apparent shear forces at the vertical interface of the flume subsections increased with the increase of the convergence angle and relative depth, reached a peak at the relative depth of 0.4, and then decreased.

Estimation of Boundary Shear Stress Distribution in a Trapezoidal Cross-Section Channel with Composite Roughness

The estimation of boundary shear stress distribution in a channel is a challenge in some hydraulic or environment investigations. A new partition model of a trapezoidal cross-section in a prismatic channel with composite roughness has been introduced based on a concept of a standardized cross-section using the “zero-shear stress” division lines. Based on this new model, an “equal local-region velocity” assumption, which can be regarded as an improvement of Einstein’s (1942) “equal velocity” assumption, has been proposed that is based on a discussion on the mechanism of energy transfer and velocity distribution at two sides of a dividing line. This assumption along with some empirical treatments have been employed to establish a new method to estimate the boundary shear stress of a side-wall or bed. Comparisons show that the proposed method can be applied to composite roughness cases and provides better prediction performance compared to other methods.

Flow investigation around cylinders assembled in a confined straight channel geometry

The paper is dedicated to experimental and numerical investigations of the dynamics of 3D-flow around a cylinder with 10 mm diameter. The cylinder is positioned in a confined geometry represented by a long straight channel with 50 mm width and 10 mm height. The study analyses the dependence on the Re-number of the path lines distributions in the vicinity of the immersed cylinder. The visualized flow patterns are fairly reproduced by the numerical solutions of the Navier-Stokes equations up to Re = 1000. The velocity and wall stresses are computed in the vicinity of the cylinder. One main goal of the present work is established by the correlation between the flow pattern, wake boundary and wall shear stress distributions down-stream the cylinder.

Prediction of boundary shear stress distribution in straight open channels using velocity distribution

Conventional methods for measuring local shear stress on the wetted perimeter of open channels are related to the measurement of the very low velocity close to the boundary. Measuring near-zero velocity values with high fluctuations has always been a difficult task for fluid flow near solid boundaries. To solve the observation problems, a new model was developed to estimate the distribution of boundary shear stress from the velocity distribution in open channels with different cross-sectional shapes. To estimate the shear stress at a point on the wetted perimeter by the model, the velocity must be measured at a point with a known normal distance to the boundary. The experimental work of some other researchers on channels with various cross-sectional shapes, including rectangular, trapezoidal, partially full circular, and compound shapes, was used to evaluate the performance of the proposed model. Optimized exponent coefficients for the model were found using the multivariate Newton method with the minimum of the mean absolute percentage error (MAPE) between the model and experimental data as the objective function. Subsequently, the calculated shear stress distributions along the wetted perimeter were compared with the experimental data. The most important advantage of the proposed model is its inherent simplicity. The mean MAPE value for the seven selected cross-sections was 6.9%. The best results were found in the cross-sections with less discontinuity of the wetted perimeter, including the compound, trapezoidal, and partially full circular pipes. In contrast, for the rectangular cross-section with an angle between the bed and walls of 90°, MAPE increased due to the large discontinuities.

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...

Streamflow, Sediment Transport, and Geomorphic Change during the 2011 Flood on the Missouri River Near Bismarck–Mandan, ND

AbstractGeomorphic change from extreme events in large managed rivers has implications for river management. A steady‐state, quasi‐three‐dimensional hydrodynamic model was applied to a 29‐km reach of the Missouri River using 2011 flood data. Model results for an extreme flow (500‐year recurrence interval [RI]) and an elevated managed flow (75‐year RI) were used to assess sediment mobility through examination of the spatial distribution of boundary or bed shear stress (τb) and longitudinal patterns of average τb, velocity, and kurtosis of τb. Kurtosis of τb was used as an indicator of planform channel complexity and can be applied to other river systems. From differences in longitudinal patterns of sediment mobility for the two flows we can infer: (1) under extreme flow, the channel behaves as a single‐thread channel controlled primarily by flow, which enhances the meander pattern; (2) under elevated managed flows, the channel behaves as multithread channel controlled by the interaction of flow with bed and channel topography, resulting in a more complex channel; and (3) for both flows, the model reach lacks a consistent pattern of deposition or erosion, which indicates migration of areas of erosion and deposition within the reach. Despite caveats and limitations, the analysis provides useful information about geomorphic change under extreme flow and potential implications for river management. Although a 500‐year RI is rare, extreme hydrologic events such as this are predicted to increase in frequency.

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.

Experimental Research on Boundary Shear Stress in Typical Meandering Channel

A novel instrument named Micro-Electro-Mechanical System (MEMS) flexible hot-film shear stress sensor was used to study the boundary shear stress distribution in the generalized natural meandering open channel, and the mean sidewall shear stress distribution along the meandering channel, and the lateral boundary shear stress distribution in the typical cross-section of the meandering channel was analysed. Based on the measurement of the boundary shear stress, a semi-empirical semi-theoretical computing approach of the boundary shear stress was derived including the effects of the secondary flow, sidewall roughness factor, eddy viscosity and the additional Reynolds stress, and more importantly, for the first time, it combined the effects of the cross-section central angle and the Reynolds number into the expressions. Afterwards, a comparison between the previous research and this study was developed. Following the result, we found that the semi-empirical semi-theoretical boundary shear stress distribution algorithm can predict the boundary shear stress distribution precisely. Finally, a single factor analysis was conducted on the relationship between the average sidewall shear stress on the convex and concave bank and the flow rate, water depth, slope ratio, or the cross-section central angle of the open channel bend. The functional relationship with each of the above factors was established, and then the distance from the location of the extreme sidewall shear stress to the bottom of the open channel was deduced based on the statistical theory.

Boundary Shear Stress Distribution in Straight Compound Channel Flow Using Artificial Neural Network

Boundary shear stress distribution of a compound channel is generally influenced by the geometric, roughness, and hydraulic parameters. Experiments are performed on both homogeneous and nonhomogeneous compound channels to study the dependency of variables on the boundary shear distribution. This study proposes an artificial neural network (ANN) model for the prediction of boundary shear stress distribution in straight compound channels. The most influential parameters such as width ratio, relative flow depth, aspect ratio, Reynolds number, and Froude number are considered as input parameters. A large number of experimental data sets comprising wide ranges of width ratio, relative flow depth, roughness ratio, Reynolds number, Froude number, bed slope, and aspect ratio with the present experimental data series are used for both training and validation of the model. Previous models can provide good results only for specific ranges of independent parameters, whereas back-propagation neural network (BPNN) models are capable of performing well for global ranges of independent parameters. This is because BPNN is able to perform nonlinear mapping between the dependent and independent variables during the training. The efficacy of the models is verified with the standard statistical error analysis using the global data sets.

Prediction of apparent shear stress in an asymmetric compound channel

There is always an exchange of momentum between the deep main channel and its shallow floodplains of a compound channel section. When rivers have single side floodplains, they are known as asymmetric compound channels. Momentum transfer phenomenon has the effect of increasing floodplain shear and decreasing the main channel shear. In symmetrical compound channels, the momentum transfer occurs from both sides of the main channel to the floodplains whereas, for an asymmetrical compound channel, there is a stronger interaction takes place as compared to the symmetrical case. This causes more non-uniform boundary shear stress distribution as compared to the symmetrical cases. Experiments are conducted to measure the boundary shear stress distribution of an asymmetric compound channel that helps to quantify the momentum transfer in terms of apparent shear stress at the interface. Analysis of the apparent shear is useful in deciding the choice of appropriate interface planes for stage–discharge relationship of a compound channel. In the present work, an improved expression to predict the apparent shear stress, especially in an asymmetrical compound channel is developed. The strength of the new expression to predict apparent shear stress is also found to be better than the models of other investigators.

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.

Analytical solution of non-uniform flow in compound channel

The present work investigates the analysis of depth-averaged velocity and boundary shear stress distribution in compound channels with non-uniform flow condition. A quasi two-dimensional model is proposed to assess the flow variables by accounting the physical processes that are specific to non-uniform flow. For analyzing the flow behavior, experimental data sets concerning compound channels with narrowing and enlarging floodplains of previous investigators are considered. The model accounts the influence of momentum transfer on the flow variables through additional shear stresses that are developed in non-uniform flow. Three types of effective stresses produced by molecular viscosity, turbulent and dispersion on the vertical planes are discussed. An analytical solution to the model is presented. Terms associated with the effective stresses are investigated relating them to the geometric and hydraulic parameters. The significance of lateral variation of energy slope is further investigated. For both homogenous and heterogeneous non-prismatic channels, the approach is examined to predict the flow variables with reasonable accuracy.

Numerical modeling of flow field in compound channels with non-prismatic floodplains

In this paper an attempt has been made to study flow field in compound channels with non-prismatic floodplains. A three dimensional computational fluid dynamic (CFD) model is used to calculate the velocity distribution, secondary flow circulation and boundary shear stress in non-prismatic compound channels with two different convergence angles of 3.81o and 11.31o. The ANSYS-CFX software and k-e turbulence model is used to solve Reynolds Averaged Navier-Stokes (RANS) equations. The results of the numerical modeling were then compared to the experimental data on non-prismatic compound channels with the same convergence angles. The study shows that, more or less, the k-e turbulence model is capable of predicting the velocity and boundary shear stress distributions along the flume fairly well, especially for convergence angle of 3.81o. Also by increasing relative depth, discrepancy between numerical and experimental data decreases. The results of modeling show that the k-eturbulence model is able to predict secondary flow circulations in the main channel, created by the mass exchange between the floodplains and the main channel.

Experimental investigation of the flow characteristics beneath partial ice covers

In northern climates where water bodies are subjected to sub-freezing temperatures for part of the year it is important to know how the presence of ice impacts the flow characteristics of channels. While many studies have been conducted in channels that are fully open or completely covered with ice, little is known about the hydraulic characteristics of channels with only a partial cover. The goal of this study was to examine the impact of border ice on the discharge and corresponding streamwise velocity distribution in a channel. Using acoustic Doppler velocimetry, detailed three-dimensional velocity measurements were collected in a fully developed cross section of a rectangular flume under steady flow conditions with a symmetrical ice cover extending from both walls. The influence of different extents of partial ice coverages and different Froude numbers was explored. The partial ice cover was found to impact the flow distribution within the channel and a classification system was developed to divide the channel cross-section into open, transitional and covered sections. Partial ice coverage extent was found to have a relative width of transition to be consistent while increasing Froude was found to produce a smaller transition region. Boundary shear stress distributions on the boundaries were examined and a detailed analysis beneath the ice cover is presented. The presented data set represents the most thorough experimental examination of flow characteristics beneath a partial ice cover.

An analysis of shear stress distribution in circular channels with sediment deposition based on Gene Expression Programming

Knowledge of the boundary shear stress distribution in channels is important because it is a key factor affecting on erosion and sedimentation rates. The presence of sediment deposits in sewers is often reported during operation, and circular channels are frequently used in sewer networks. Gene expression programming (GEP) is applied in this study to determine an equation for evaluating the shear stress distribution along the wetted perimeter of a circular channel with a flat bed, because of the presence of sediment on the bed. In view of the parameters affecting the shear stress distribution, five dimensionless parameters are applied to develop six GEP models to be used with 905 experimental data. The impact of the shear stress parameters is studied using the six GEP models and by dividing the wetted perimeter into wall and bed sections. Two equations are extracted from the GEP models’ output to estimate wall and bed shear stresses. The best model results are compared with a well-known equation based on the entropy concept. The GEP model predictions of wall and bed shear stresses are very similar to the experimental outcomes, whereas the entropy-based model overestimates the shear stress distribution. The proposed GEP models demonstrate superior performance in estimating the shear stress distribution with a mean absolute percentage error (MAPE) of 3.79% compared to an existing equation with MAPE of 9.52%.

Numerical solution of depth-averaged velocity and boundary shear stress distribution in converging compound channels

In prismatic compound channels, the water level remains uniform throughout the length of the channel. But in case of non-prismatic compound channels, the flow becomes non-uniform and complex. This paper examines the use of Lateral Distribution Method (LDM) and its modifications in the computation of depth-averaged velocity and boundary shear stress distribution in a compound channel for both prismatic and non-prismatic floodplains. The modification of LDM has been done considering the friction slope and secondary current effect. Finite difference scheme has been used for discretizing the Modified LDM using MATLAB tool. For the present study, different prismatic and non-prismatic compound channels having converging flood plains have been considered to evaluate the strength of Modified LDM over other numerical approaches like LDM and Conveyance and Afflux Estimation system.

Modelling boundary shear stress distribution in open channels using a face recognition technique

This paper describes a novel application of a pattern recognition technique for predicting boundary shear stress distribution in open channels. In this approach, a synthetic database of images representing normalized shear stress distributions is formed from a training data set using recurrence plot (RP) analysis. The face recognition algorithm is then employed to synthesize the RPs and transform the original database into short-dimension vectors containing similarity weights proportional to the principal components of the distribution of images. These vectors capture the intrinsic properties of the boundary shear stress distribution of the cases in the training set, and are sensitive to variations of the corresponding hydraulic parameters. The process of transforming one-dimensional data series into vectors of weights is invertible, and therefore, shear stress distributions for unseen cases can be predicted. The developed method is applied to predict boundary shear stress distributions in smooth trapezoidal and circular channels and the results show a cross correlation coefficient above 92%, mean square errors within 0.04% and 4.48%, respectively, and average shear stress fluctuations within 2% and 5%, respectively, thus indicating that the proposed method is capable of providing accurate estimations of the boundary shear stress distribution in open channels.