Determination of Boundary Shear Stress and Reynolds Shear Stress in Smooth Rectangular Channel Flows

A method for computing three-dimensional Reynolds shear stresses and boundary shear stress distribution in smooth rectangular channels is developed by applying an order of magnitude analysis to integrate the Reynolds equations. A simplified relationship between the lateral and vertical terms is hypothesized for which the Reynolds equations become solvable. This relationship has the form of a power law with an exponent of n = 1, 2, or infinity. The semiempirical equations for the boundary shear distribution and the distribution of Reynolds shear stresses are compared with measured data in open channels. The power-law exponent of 2 gave the best overall results while n=infinity gave good results near the boundary.     

Modeling Depth-Averaged Velocity and Boundary Shear in Trapezoidal Channels with Secondary Flows

The Shiono and Knight method (SKM) offers a new approach to calculating the lateral distributions of depth-averaged velocity and boundary shear stress for flows in straight prismatic channels. It accounts for bed shear, lateral shear, and secondary flow effects via 3 coefficients—f,λ, and Γ—thus incorporating some key 3D flow feature into a lateral distribution model for streamwise motion. The SKM incorporates the effects of secondary flows by specifying an appropriate value for the Γ parameter depending on the sense of direction of the secondary flows, commensurate with the derivative of the term Hρ(UV)d. The values of the transverse velocities, V, have been shown to be consistent with observation. A wide range of boundary shear stress data for trapezoidal channels from different sources has been used to validate the model. The accuracy of the predictions is good, despite the simplicity of the model, although some calibration problems remain. The SKM thus offers an alternative methodology to the more traditional computational fluid dynamics (CFD) approach, giving velocities and boundary shear stress for practical problems, but at much less computational effort than CFD.     

Shear Stress in Smooth Rectangular Open-Channel Flows

The average bed and sidewall shear stresses in smooth rectangular open-channel flows are determined after solving the continuity and momentum equations. The analysis shows that the shear stresses are function of three components: (1) gravitational; (2) secondary flows; and (3) interfacial shear stress. An analytical solution in terms of series expansion is obtained for the case of constant eddy viscosity without secondary currents. In comparison with laboratory measurements, it slightly overestimates the average bed shear stress measurements but underestimates the average sidewall shear stress by 17% when the width–depth ratio becomes large. A second approximation is formulated after introducing two empirical correction factors. The second approximation agrees very well (R2>0.99 and average relative error less than 6%) with experimental measurements over a wide range of width–depth ratios.     

Boundary Shear Distribution in Straight Ducts and Open Channels

A semianalytical model was developed to predict boundary shear distribution in straight, noncircular ducts and open channels. The model was developed using a simplified streamwise vorticity equation, which involves only secondary Reynolds stress terms. These terms are representative of transverse turbulence anisotropy and nonhomogeneity. Transverse anisotropy is modeled using a universal function. Shear stresses are incorporated into the model by applying the momentum transfer model. An empirical model was employed to calculate the effect of the channel boundary on shear stresses. The final equation was applied to calculate boundary shear distribution in triangular ducts and trapezoidal open channels. The model predictions were well correlated with experimental data.     

URANS Computations of Shallow Grid Turbulence

This paper describes the unsteady Reynolds-averaged Navier–Stokes (URANS) computations of a quasi-two-dimensional (2D) grid turbulence in shallow open-channel flows, generated downstream of multiple piers aligned at regular intervals over the channel width. In shallow open-channel flows, the vertical confinement of the flow generally suppresses the three dimensionality and attains two-dimensional features with up-cascading of turbulent kinetic energy from small-scale toward large-scale structures. In this study, 2D depth averaged and 3D Reynolds-averaged equations with linear and nonlinear URANS turbulence models are applied to a shallow open-channel flow downstream of multiple piers and numerical results are discussed through a comparison with the experimental results performed by Uijttewaal and Jirka in 2003. We employed 0-equation models and k-ε models for the 2D and 3D computations, respectively. In 2D computations, vortices downstream of the grid occurred synchronously in the computation with both the linear and nonlinear 0-equation models. In the 3D computations, vortex merging and up-cascading of the kinetic energy were captured when artificial disturbance is added at the inlet. The measured decay of the turbulent kinetic energy in the streamwise direction, with a slope of ?1.3, was well captured by computation with the 3D models with inlet disturbance. The flow sensitivity on the inlet disturbance was rather small in the wide range of the disturbance ratios.     

Nonlinear Mixing Length Model for Prediction of Secondary Currents in Uniform Channel Flows

A nonlinear turbulence model for numerical solution of uniform channel flow is presented. Turbulent stresses are evaluated from a nonlinear mixing length model that relates turbulent stresses to quadratic products of the mean rate of strain and the mean vorticity. The definition of the mixing length, based on a three-dimensional integral measure of boundary proximity, eliminates the need for solution of additional transport equations for the turbulence quantities. Experimental data from the literature for closed and open-channel flows are utilized to validate the model. The model produced the secondary flow vortices successfully. Velocity field and wall shear stresses affected by secondary flow vortices are accurately computed. Bulging of velocity contour lines toward the corners and dipping phenomena of maximum velocity are successfully simulated.     

Semianalytical Model for Shear Stress Distribution in Simple and Compound Open Channels

Semianalytical equations were derived for distribution of shear stress in straight open channels with rectangular, trapezoidal, and compound cross sections. These equations are based on a simplified streamwise vorticity equation that includes secondary Reynolds stresses. Reynolds stresses were then modeled and their different terms were evaluated based on the work of previous researchers and experimental data. Substitution of these terms into the simplified vorticity equation yielded the relative shear stress distribution equation along the width of different channel cross sections. In compound channels the effect of additional secondary flows due to the shear layer between the main channel and the flood plain were also considered. Comparisons between predictions of the model and experimental data, predictions of other analytical or three dimensional numerical models with advanced turbulent closures, were made with good agreement.     

Flow Heterogeneity over 3D Cluster Microform: Laboratory and Numerical Investigation

The present study examines the flow around a self-occurring cluster bed form and the use of general computation fluid dynamics methods for hydraulic and geophysical flow applications. This is accomplished through a comprehensive experimental/numerical investigation. In the laboratory, cluster bed forms are first formed from movable sediment, and laser Doppler velocimeter measurements of two-dimensional fluid velocity are then taken around a formed cluster. A three-dimensional (3D) Reynolds averaged Navier-Stokes simulation of the physical cluster and flow conditions is then conducted using near-wall, shear stress transport (SST) turbulence modeling with the inclusion of hydraulic roughness, ks (R = 31,150, ks/h = 0.1, ks+ = 274, i.e., in the fully rough regime). SST near-wall modeling is advantageous compared to the more widely used wall functions approach for flows with significant roughness and flow separation because the model equations can be integrated down to the wall. Therefore, SST near-wall modeling makes no a priori assumption that the law of the wall is valid throughout the wall region of the flow. Additionally, it has the ability to intrinsically handle boundary roughness through the boundary condition for turbulent specific dissipation at the wall, allowing for wall functions to be bypassed in accounting for roughness effects. The study shows that in the wall region surrounding the cluster, flow is 3D and quite complex, with different scales of embedded flow structures dominating the cluster wake and leading to flow heterogeneities in pressure and bed-shear stress. Results also indicate that near-wall modeling with SST compared favorably with the experimental flow data without tuning of model constants.     

VOF Model for Simulation of a Free Overfall in Trapezoidal Channels

In the past, solutions to open channel flow problems involving free surfaces were generally found on the basis of experimental data or through the development of theoretical expressions using simplified assumptions. The volume of fluid (VOF) turbulence model is applied to obtain characteristics of three-dimensional open channel flows involving free surfaces. In particular, the VOF model is used to determine the pressure head distributions, velocity distributions, and water surface profiles for the free overfall in a trapezoidal open channel. The predictions of the proposed model are validated using existing experimental data.     

Installation of Torpedo Anchors: Numerical Modeling

Torpedo anchors are used as foundations for mooring deep-water offshore facilities, including risers and floating structures. They are cone-tipped cylindrical steel pipes ballasted with concrete and scrap metal and penetrate the seabed by the kinetic energy they acquire during free fall through the water. A mooring line is usually connected at the top of the anchor. The design of such anchors involves estimation of the embedment depth as well as short-term and long-term pullout capacities. This paper describes the development of a computational procedure that leads to prediction of torpedo-anchor embedment depth. The procedure relies on a computational fluid dynamics (CFD) model for evaluation of the resisting forces on the anchor. In the model, the soil is represented as a viscous fluid and the procedure is applied to axially symmetric penetration of the seabed. The CFD approach provides estimates of not only the embedment depth but the pressure and shear distributions on the soil-anchor interface and in the soil.     

Depth-Averaged Shear Stress and Velocity in Open-Channel Flows

Turbulent momentum and velocity always have the greatest gradient along wall-normal direction in straight channel flows; this has led to the hypothesis that surplus energy within any control volume in a three-dimensional flow will be transferred toward its nearest boundary to dissipate. Starting from this, the boundary shear stress, the Reynolds shear stress, and the velocity profiles along normal lines of smooth boundary may be determined. This paper is a continuous effort to investigate depth-average shear stress and velocity in rough channels. Equations of the depth-averaged shear stress in typical open channels have been derived based on a theoretical relation between the depth-averaged shear stress and boundary shear stress. Equation of depth mean velocity in a rough channel is also obtained and the effects of water surface (or dip phenomenon) and roughness are included. Experimental data available in the literature have been used for verification that shows that the model reasonably agrees with the measured data.     

Turbulent Stresses and Secondary Currents in a Tidal-Forced Channel with Significant Curvature and Asymmetric Bed Forms

Acoustic Doppler current profilers are deployed to measure both the mean flow and turbulent properties in a channel with significant curvature. Direct measurements of the Reynolds stress show a significant asymmetry over the tidal cycle where stresses are enhanced during the flood tide and less prominent over the ebb tide. This asymmetry is corroborated by logarithmic fits using 10?min averaged velocity data. A smaller yet similar tendency asymmetry in drag coefficient is inferred by fitting the velocity and estimated large-scale pressure gradient to a one-dimensional along-channel momentum balance. This smaller asymmetry is consistent with recent modeling work simulating regional flows in the vicinity of the study site. The asymmetry in drag suggests the importance of previously reported bed forms for this channel and demonstrates spatial and temporarily variations in bed stress. Secondary circulation patterns observed in a relatively straight section of channel appear driven by local curvature rather than being remotely forced by the regions of significant curvature only a few hundred meters from the measurement site.     

Junction and Drop-Shaft Boundary Conditions for Modeling Free-Surface, Pressurized, and Mixed Free-Surface Pressurized Transient Flows

A junction and drop-shaft boundary conditions (BCs) for one-dimensional modeling of transient flows in single-phase conditions (pure liquid) are formulated, implemented and their accuracy are evaluated using two computational fluid dynamics (CFD) models. The BCs are formulated in the case when mixed flows are simulated using two sets of governing equations, the Saint-Venant equations for the free-surface regions and the compressible water hammer equations for the pressurized regions. The proposed BCs handle all possible flow regimes and their combinations. The flow in each pipe can range from free surface to pressurized flow and the water depth at the junction or drop shaft can take on all possible levels. The BCs are applied to the following three cases: (1) a three-way merging flow; (2) a three-way dividing flow; and (3) a drop shaft connected to a single-horizontal pipe subjected to a rapid variation of the water surface level in the drop shaft. The flow regime for the first two cases range from free surface to pressurized flows, while for the third case, the flow regime is pure pressurized flow. For the third case, laboratory results as well as CFD results were used for evaluating its accuracy. The results suggest that the junction and drop-shaft BCs can be used for modeling transient free-surface, pressurized, and mixed flow conditions with good accuracy.     

Numerical Calculation of Turbulence Structure in Depth-Varying Unsteady Open-Channel Flows

Unsteady depth-varying open-channel flows are really observed in flood rivers. Owing to highly accurate laser Doppler anemometers (LDA), some valuable experimental databases of depth-varying unsteady open-channel flows are now available. However, these LDA measurements are more difficult to conduct in open-channel flows at higher unsteadiness, in comparison with unsteady wall-bounded flows such as oscillatory boundary layers and duct flows. Therefore, in this study, a low-Reynolds-number k–ε model involved with a function of unsteadiness effect was developed and some numerical calculations were conducted using the volume of fluid method as a free-surface condition. The present calculated values were in good agreement with the existing LDA data in the whole flow depth from the wall to the time-dependent free surface. These values were also compared with those of unsteady wall-bounded flows. The present calculations were able to predict the distributions of turbulence generation and its dissipation, and consequently the unsteadiness effect on turbulence structure was discussed on the basis of the outer-variable unsteadiness parameter α, which is correlated with the inner-variable unsteadiness parameter ω+ in unsteady wall-bounded flows.     

Transverse Dispersion Caused by Secondary Flow in Curved Channels

A new theoretical equation is proposed to describe the streamwise variations of the transverse velocity along a curved channel with a constant curvature. Furthermore, based on this theoretical equation for the transverse velocity, a new equation for the transverse dispersion coefficient is developed to incorporate the effect of the secondary flow on the transverse dispersion in curved channels. The new equations for the transverse velocity and dispersion coefficient are verified with experimental data sets that were obtained from laboratory experiments conducted in two different channels. The results show that the proposed velocity equation properly describes the streamwise variations of the secondary flow developed in the curved channels. The reach-averaged values of the transverse dispersion coefficient calculated by the new equation are in relatively good agreement with the observed values from the laboratory channels. Sensitivity analysis reveals that both the secondary flow and the transverse dispersion coefficient are proportional to the roughness factor, and in inverse proportion to the aspect ratio of the channel.     

Rough Wall Boundary Layer on Plates in Open Channels

Experiments were performed to measure the characteristics of a turbulent boundary layer developing on a rough surface placed in an open channel flow at close proximity to the free surface. Streamwise velocity measurements were made with a one-component laser Doppler velocimeter system at the top of the spherical roughness elements. Measurements at three stations downstream of the plate leading edge show the growth of the boundary layer on the rough wall and its interaction with the exterior open-channel flow and the free surface. Resorting to the turbulence profile provides an alternative definition of the boundary layer thickness. The near-wall flow follows the well-known logarithmic law with a shift due to roughness. In the outer layer, there are two opposing effects: the free surface tends to decrease the wake component while the roughness tends to increase it. The streamwise turbulence intensity is affected by the shear and turbulence in the exterior flow, the effect of the free surface being greater than that of wall roughness.     

Flow around Cylinders in Open Channels

This paper presents the results of an experimental study of flow around cylindrical objects in an open channel. Cylindrical objects of equal diameter and four heights were tested under similar flow conditions producing four different levels of submergence, including a surface piercing bridge-pier-like cylinder. Different flow elements and their locations were identified using a set of flow visualization tests. Observations made from the flow visualization tests were then verified by measurements of bed-shear stress and deflected flow velocity around the cylinders. Horse-shoe vortex systems were found to appear closer to the submerged cylinders compared to a surface piercing cylinder. The increase in dimensionless bed-shear stress is found to be inversely related to the level of submergence of the cylinders. Bed-shear stress results presented in this paper will be valuable for a qualitative understanding of the scour potential of flow around submerged cylinders. Mean velocity profiles in the deflected flow region were analyzed in terms of the theories of three-dimensional turbulent boundary layer. Submergence of a cylinder has been found to suppress alternate vortex shedding and produce stronger three-dimensional flows in the downstream wake. Perry and Joubert’s model was found to be sufficiently accurate to predict the deflected velocity magnitudes around submerged cylinders. Overall, the present study will provide valuable knowledge of hydraulics of flow around submerged structures (e.g., simple fish habitat structures).     

Investigation into the Total Dissolved Gas Dynamics of Wells Dam Using a Two-Phase Flow Model

Bubbles entrained by spilled water at hydroelectric projects increase the concentration of total dissolved gas (TDG), which may lead to gas bubble disease in fish. In this paper, the TDG dynamics downstream of Wells Dam are investigated using a two-phase flow model that accounts for the effect of the bubbles on the flow field. The TDG is calculated with a transport equation in which the source is the bubble/liquid mass transfer, a function of the gas volume fraction and bubble size. The model uses anisotropic turbulence modeling and includes attenuation of normal fluctuation at the free surface to capture the flow field and TDG mixing. The model is validated using velocity and TDG field data. Simulations under two plant operational configurations are performed to gain a better understanding of the effect of spill operations on the production, transport, and mixing of TDG. Model results indicate that concentrated spill releases create surface jets that result in the lowest TDG concentration downstream. On the other hand, spreading the spill release, with moderate flow through each gate, produces the highest TDG values downstream as a result of more air available for dissolution and smaller degasification at the free surface.     

Numerical Modeling of Abutment Scour with the Focus on the Incipient Motion on Sloping Beds

A three-dimensional computational fluid dynamics model is applied to predict local scour around an abutment in a rectangular laboratory flume. When modeling local scour, steep bed slopes up to the angle of repose occur. To predict the depth and the shape of the local scour correctly, the reduction of the critical shear stress due to the sloping bed must be taken into account. The focus of this study is to investigate different formulas for the threshold of noncohesive sediment motion on sloping beds. Some formulas only take the transversal angle (perpendicular to the flow direction) into account, but others also consider the longitudinal angle (streamwise direction). The numerical model solves the transient Reynolds-averaged Navier-Stokes equations in all three dimensions to compute the water flow. Sediment continuity in combination with an empirical formula is used to capture the bed load transport and the resulting bed changes. When the sloping bed exceeds the angle of repose, the bed slope is corrected with a sand-slide algorithm. The results from the numerical simulations are compared with data from physical experiments. The reduction of the bed shear stress on the sloping bed improves the results of the numerical simulation distinctly. The best results are obtained with the formulas that use both the transversal and the longitudinal angle for the reduction of the critical bed shear stress.