Simulation of Flow past an Open-Channel Floor Slot

In the past, solutions to the problem of flow past a floor slot in a rectangular open channel used to divert flow from one stream to another were obtained mainly on the basis of model tests or through the development of simplified theoretical expressions. In the present study, the free-surface turbulence model is applied to obtain the flow parameters such as pressure head distribution, velocity distribution, and water surface profile. The predictions of the proposed numerical model are validated using previous experimental data. In particular, the model predictions agree well with the test data related to flow parameters. The study indicates that the free-surface turbulence model developed is an efficient and useful tool for predicting characteristics of free surface flows such as flow past a floor slot. For flow past an open-channel floor slot, a model that is properly validated can be used to predict the flow characteristics under various flow configurations encountered in the field, without resorting to expensive experimental procedures.     

Experimental Study of 3D Pump-Intake Flows with and without Cross Flow

Detailed measurements of three-dimensional turbulent flows within a rectangular single-pump bay area of a right-angle water intake model with and without cross flow were obtained using an acoustic Doppler velocimeter (ADV) in order to elucidate swirling flow characteristics within the pump sump. Without cross flow, the pump-approach flow distributions were characterized by nearly uniform streamwise velocities in the pump bay and weak free-surface vortices near the pump column. With cross flow, the three-dimensional mean velocity measurements revealed the existence of a large recirculation zone upstream of the pump column such that strong streamwise velocities were present at higher depths and near the left sidewall, while the reverse current concentrated at lower depths along the right sidewall. Flow patterns in the latter case were also characterized by strong free-surface vortices in the vicinity of the pump column and a strong floor-attached subsurface vortex underneath the pump bell. Uncertainty analysis for ADV velocity measurements showed good quality data, with uncertainty in mean velocities varying from 2.5 to 6.4%. These experimental data were utilized in validating inviscid numerical solutions.     

Turbulence Characteristics in Flows Subjected to Boundary Injection and Suction

The influence of seepage (lateral flow) on the turbulence characteristics in free-surface flows over an immobile rough boundary is investigated. Steady flows having zero-pressure gradient over an immobile rough boundary created by uniform gravels of 4.1 mm in size were simulated experimentally with injection (upward seepage) and suction (downward seepage) applied through the boundary. A Vectrino (acoustic Doppler velocimeter) was used to measure the instantaneous velocities, which are analyzed to explore second- and third-order correlations, turbulent kinetic energy, turbulent energy budget, and conditional Reynolds shear stresses. It is observed that the second-order correlations decrease in presence of injection and increase in suction. The turbulent diffusivity and mixing length increase in presence of injection and decrease in suction. The third-order correlations suggest that the ejections are prevalent over the entire flow depth. The near-boundary flow is significantly influenced by the existence of upward seepage, which is manifested by a reduction in streamwise flux and the vertical advection of streamwise Reynolds normal stress. In addition, the upward flux and the streamwise advection of vertical Reynolds normal stress are also affected. The streamwise flux of turbulent kinetic is found to migrate upstream, while the vertical flux of turbulent kinetic energy is transported upward. The fluxes increase in presence of injection and decrease in suction. Energy budget evidences a lag between the turbulent dissipation and production and an opposing trend in the turbulent and pressure energy diffusions. A quadrant analysis for the conditional Reynolds shear stresses reveals that the ejection and sweep events are the primary contributions toward the total Reynolds shear stress production, with ejections dominating over the entire flow depth. The effect of seepage is shown to affect the magnitude of such events. However, in case of sweeps, this phenomenon is the opposite. The mean-time of occurrence of ejections and that of sweeps in suction are more persistent than those in no-seepage and injection.     

3D Unsteady RANS Modeling of Complex Hydraulic Engineering Flows. II: Model Validation and Flow Physics

A chimera overset grid flow solver is developed for solving the unsteady Reynolds-averaged Navier-Stokes (RANS) equations in arbitrarily complex, multiconnected domains. The details of the numerical method were presented in Part I of this paper. In this work, the method is validated and applied to investigate the physics of flow past a real-life bridge foundation mounted on a fixed flat bed. It is shown that the numerical model can reproduce large-scale unsteady vortices that contain a significant portion of the total turbulence kinetic energy. These coherent motions cannot be captured in previous steady three-dimensional (3D) models. To validate the importance of the unsteady motions, experiments are conducted in the Georgia Institute of Technology scour flume facility. The measured mean velocity and turbulence kinetic energy profiles are compared with the numerical simulation results and are shown to be in good agreement with the numerical simulations. A series of numerical tests is carried out to examine the sensitivity of the solutions to grid refinement and investigate the effect of inflow and far-field boundary conditions. As further validation of the numerical results, the sensitivity of the turbulence kinetic energy profiles on either side of the complex pier bent to a slight asymmetry of the approach flow observed in the experiments is reproduced by the numerical model. In addition, the computed flat-bed flow characteristics are analyzed in comparison with the scour patterns observed in the laboratory to identify key flow features responsible for the initiation of scour. Regions of maximum shear velocity are shown to correspond to maximum scour depths in the shear zone to either side of the upstream pier, but numerical values of vertical velocity are found to be very important in explaining scour and deposition patterns immediately upstream and downstream of the pier bent.     

Three-Dimensional Numerical Study of Flows in Open-Channel Junctions

An open-channel junction flow is encountered in many hydraulic structures ranging from wastewater treatment facilities to fish passage conveyance structures. An extensive number of experimental studies have been conducted but a comprehensive three-dimensional numerical study of junction flow characteristics has not been performed and reported. In this paper, a three-dimensional numerical model is developed to investigate the open-channel junction flow. The main objective is to present the validation of a three-dimensional numerical model with high-quality experimental data and compare additional simulations with classical one-dimensional water surface calculations. The three-dimensional model is first validated using the experimental data of a 90° junction flow under two flow conditions. Good agreement is obtained between the model simulation and the experimental measurements. The model is then applied to investigate the effect of the junction angle on the flow characteristics and a discussion of the results is presented.     

Multilayer Averaged and Moment Equations for One-Dimensional Open-Channel Flows

A model is developed to account for the vertical distribution of velocity and nonhydrostatic pressure in one-dimensional open-channel flows. The model is based on both classical multilayer models and depth-averaged and moment equations. The establishment of its governing equations and the flow simulation are performed over a number of flow layers as in classical multilayer models. However, the model also allows for vertical distributions within a flow layer by including both Boussinesq terms and effective stress terms due to depth-averaging operations. These terms are evaluated on the basis of vertically linearly approximated profiles of velocity and pressure. The resulting additional coefficients can be solved by the moment equations for the relevant layers. Three verifications demonstrate satisfactory simulations for water surface profile, as well as vertical distributions for horizontal velocity, vertical velocity, and nonhydrostatic pressure. Sensitivity analysis shows that the model can be applied with fewer flow layers, more flexibility of layer division, and less computational cost than classical multilayer models, without a remarkable compromise in accuracy.     

Unified Modeling of Fluid or Granular Flows on Dam-Break Case

The stopping process of debris-flow pulses is a complex phenomenon that expresses both the characteristics of a non-Newtonian fluid when it flows and those of a soil when it comes to a stop. In order to capture this phenomenon, we have developed a model based on a Navier-Stokes approach with a constitutive law including a Drucker-Prager yield criterion. The latter permits us to continuously describe the passage of granular material from the flowing (viscous) to the stopped (viscoplastic) status. In addition to being easy to implement, this approach has the advantage of being straightforwardly expandable to full three-dimensional modeling. In order to evaluate this approach, we have implemented it using finite elements. This implementation uses a Galerkin finite-element approximation with a least-squares stabilization procedure. The free surface is treated by means of a level-set approach to cope with the complex geometry of a flowing pulse. The rheological model and the free-surface treatment are tested in an analytical problem and in a dam-break test.     

Modeling 3D Supercritical Flow with Extended Shallow-Water Approach

Despite the three-dimensional (3D) nature of the flow, the classical shallow-water equations are often used to simulate supercritical flow in channel transitions. A closer comparison with experimental data, however, often shows large discrepancies in the height and pattern of the shock waves that increase with the Froude number. An extension to the classical shallow-water approach is derived considering higher-order distribution functions for pressure and horizontal and vertical velocities, therefore taking nonhydrostatic pressure distribution and vertical momentum into account. The approach is applied to highly supercritical flow in a channel contraction (F0 = 4.0), a channel junction (F0 ≈ 4.5 for both branches), and a channel expansion (F0 = 8.0). Specific problems of such flows—wetting and drying of computational cells and wave breaking due to steep free-surface gradients—are discussed and solved numerically. The solutions with the extended approach are compared both with experimental data and classical shallow-water computations, and the influence of the additional terms considering the 3D nature of such flows is illustrated.     

Fully Nonhydrostatic Modeling of Surface Waves

A fully nonhydrostatic model is tested by simulating a range of surface-wave motions, including linear dispersive waves, nonlinear Stokes waves, wave propagation over bottom topographies, and wave–current interaction. The model uses an efficient implicit method to solve the unsteady, three-dimensional, Navier-Stokes equations and the fully nonlinear free-surface boundary conditions. A new top-layer pressure treatment is incorporated to fully include the nonhydrostatic pressure effect. The model results are verified against either analytical solutions or experimental data. It is found that the model using a small number of vertical layers is capable of accurately simulating both the free-surface elevation and vertical flow structure. By further examining the model’s performance of resolving wave dispersion and nonlinearity, the model’s efficiency and accuracy are demonstrated.     

Velocity Distribution in the Roughness Layer of Rough-Bed Flows

Several models for the vertical distribution of the double-averaged (in time and in the plane parallel to the mean bed) longitudinal velocity in the flow region between roughness troughs and roughness tops are suggested. We found that the same model for velocity distribution may be applicable to a range of flow conditions and roughness types, which share some common features. The suggested models for velocity distribution in the near-bed region are: (1) Constant velocity; (2) exponential velocity distribution; and (3) linear velocity distribution. The measured velocity distributions may be approximated by a single model or by a combination of models depending on roughness geometry and flow conditions. The validity of these models for velocity distribution is supported by laboratory data.     

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.     

Turbulence Modeling of Flows over Circular Spillways

To predict the characteristics of flows over circular spillways, a turbulence model based on the Reynolds stress model (RSM) is presented. Circular spillways are used to regulate water levels in reservoirs. The flow over the spillway is rapidly varied with highly curvilinear streamlines. The isotropic eddy-viscosity models such as k-ε models are based on the Boussinesq eddy viscosity approximation that assumes the components of the turbulence Reynolds stress tensor linearly vary with the mean rate of strain tensor. Hence, they cannot very precisely predict the characteristics of flows over the spillway. On the other hand, the non-isotropic turbulence models such as the turbulence Reynolds stress models (RSM) that calculate all the components of the Reynolds stress tensor can accurately predict the characteristics of these flows. The k-ε models and RSM were applied in the present study to obtain the flow parameters such as the pressure and velocity distributions as well as water surface profiles. The previously published experimental results were used to validate the simulation predictions. For flow over a circular spillway, RSM appears to properly validate the characteristics of the flow under various conditions in the field, without recourse to expensive experimental procedures.     

Numerical and Experimental Study of Dividing Open-Channel Flows

Dividing flows in open channels are commonly encountered in hydraulic engineering systems. They are inherently three-dimensional (3D) in character. Past experimental studies were mostly limited to the collection of test data on the assumption that the flow was 1D or 2D. In the present experimental study, the flow is treated as 3D and test results are obtained for the flow characteristics of dividing flows in a 90°, sharp-edged, rectangular open-channel junction formed by channels of equal width. Depth measurements are made using point gauges, while velocity measurements are obtained using a Dantec laser Doppler anemometer over grids defined throughout the junction region. A 3D turbulence model is also developed to investigate the dividing open-channel flow characteristics. The predicted flow characteristics are validated using experimental data. Following proper model validation, the numerical model developed can yield design data pertaining to flow characteristics for different discharge and area ratios for other dividing flow configurations encountered in engineering practice. Energy and momentum coefficients based on the present 3D model yield more realistic energy losses and momentum transfers for dividing flow configurations. Data related to secondary flows provide information vital to bank stability, if the branch channel sides are erodible.     

Transient Flow into a Partially Penetrating Well during the Constant-Head Test in Unconfined Aquifers

This study derives a semianalytical solution for drawdown distribution during a constant-head test at a partially penetrating well in an unconfined aquifer. The constant-head condition is used to describe the boundary along the screen. In addition, a free-surface condition is used to delineate the upper boundary of the unconfined aquifer. The Laplace-domain solution is then derived using separation of variables and Laplace transform. This solution can be used to identify the aquifer parameters from the data of the constant-head test when integrated with an optimization scheme or to investigate the effects of vertical flow caused by the partially penetrating well and free-surface boundary in an unconfined aquifer.     

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.     

Applicability of Sediment Transport Capacity Formulas to Dam-Break Flows over Movable Beds

In this paper, we investigate the extent to which well-known sediment transport capacity formulas can be used in one-dimensional (1D) numerical modeling of dam-break waves over movable beds. The 1D model considered here is a one-layer model based on the shallow-water equations, a bed update (Exner) equation, a space-lag equation for the nonequilibrium sediment transport and an empirical formula calculating the sediment transport capacity of the flow. The model incorporates a variety of sediment transport capacity formulas proposed by Meyer-Peter and Müller, Bagnold, Engelund and Hansen, Ackers and White, Smart and Jaeggi, van Rijn, Rickenmann, Cheng, Abrahams and Camenen, and Larson. We examine the performance of each formula by simulating four idealized laboratory cases on dam-break waves over sandy beds. Comparisons between numerical results and measurements show that for each case better predictions are obtained using a particular formula, but overall, formulas proposed by Meyer-Peter and Müller (with the factor 8 being replaced by 12), Smart and J?ggi, Cheng, Abrahams and Camenen, and Larson rank as the best predictors for the entire range of conditions studied here. Moreover, results show that in the cases where a bed step exists, implementing a mass failure mechanism in the numerical modeling plays an important role in reproducing the bed and water profiles.     

Depth-Averaged Model of Open-Channel Flows over an Arbitrary 3D Surface and Its Applications to Analysis of Water Surface Profile

A new set of depth-averaged equations is introduced to study the flow over an arbitrary three-dimensional (3D) surface. These equations are derived based on a generalized curvilinear coordinate system attached to the 3D bed surface, therefore it allows us to include the effect of centrifugal force due to the bottom curvature. These general equations make it possible to analyze flows over complex terrain without the limitation of mild slope assumption used in conventional depth-averaged models. This new model is then applied to calculate the water surface profiles of (1) flow over a cylindrical surface; (2) flow over a circular surface; and (3) flow with an air-core vortex at a vertical intake. A simple hydraulic experiment is conducted in the laboratory to observe the water surface profile of flow over a circular surface. The results obtained from the model are in good agreement with experimental measurements and calculation by an empirical formula. Consequently, it demonstrates the applicability of the model in cases of flow over a highly curved bottom.     

Modeling of One-Dimensional, Unsteady, Free-Surface, and Pressurized Flows

The utilization of mathematical models in hydraulic engineering for the analysis of one-dimensional, unsteady free-surface, and pressurized flows is discussed, with an emphasis when the models performed well as well as when they did not. For illustration purposes, the applications to a number of real-life projects are presented, outlining limitations, successes, and failures.     

Coherent Structure Dynamics in Turbulent Flows Past In-Stream Structures: Some Insights Gained via Numerical Simulation

Large-scale coherent vortical structures in natural streams and rivers dominate flow and transport processes and impact the stability of stream banks, the diversity and abundance of organisms, and the quality of running waters in aquatic ecosystems. Thus, understanding and being able to model the dynamics of energetic coherent structures in such flows at ecologically relevant scales are crucial prerequisites for developing a science-based ecosystem restoration framework. We review recent progress toward the development of coherent-structure-resolving (CSR) computational fluid dynamics techniques, based on hybrid URANS/LES modeling strategies, for simulating turbulent flows in open-channels with hydraulic structures. CSR simulations of the turbulent horseshoe vortex (THSV) past bed-mounted piers explained the physical mechanism leading to the experimentally documented bimodal velocity fluctuations of the vortex and underscored the importance of the Reynolds number as a key parameter governing the THSV dynamics. Simulations of high Reynolds number flows past surface-piercing, groynelike structures in open channels revealed the complexity of the recirculating region at the upstream face of the groyne, underscored the interaction of the flow in this region with the energetic shear layer shed from the point of separation at the upstream side wall, and demonstrated the importance of flow depth in the vorticity dynamics of such flows. The paper also identifies areas for future work and modeling challenges that need to be addressed for the computational tools to be able to accurately predict flow and transport processes in real-life aquatic environments.     

Three-Dimensional Numerical Simulation of Compound Channel Flows

A three-dimensional numerical study is presented for the calculation of turbulent flow in compound channels. The flow simulations are performed by solving the three-dimensional Reynolds-averaged continuity and Navier–Stokes equations with the k?ε turbulence model for steady-state flow. The flow equations are solved numerically with a general-purpose finite-volume code. The results are compared with the experimental data obtained from the UK Flood Channel Facility. The simulated distributions of primary velocity, bed shear stress, turbulent kinetic energy, and Reynolds stresses are used to investigate the accuracy of the model prediction. The results show that, using an estimated roughness height, the primary velocity distributions and the bed shear stress are predicted reasonably well for inbank flows in channels of high aspect ratio (width/depth ≥ 10) and for high overbank flows with values of the relative flow depth greater than 0.25.