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.     

Investigation of Flow Upstream of Orifices

A physical model study is conducted to investigate the flow field upstream of orifices. In particular, new experimental data for the upstream flow pattern resulting from multiple orifices, an orifice near a free surface, and a large orifice (where the pressure gradient across the orifice cannot be ignored) are collected and presented. A new potential flow solution for flow behind orifices is developed to include pressure gradient effects as well as to accurately superpose the solution due to multiple orifices and determine a solution close to orifices. The proposed solution compares well with the measured data for multiple orifices and for an orifice near a free surface. For a large orifice, the skew in the velocity profile in the vertical direction due to the pressure gradient is accurately predicted.     

Physical and Numerical Simulation of Fluid Flow and Solidification at the Twin‐Roll Strip Casting Process

The fluid flow in a twin‐roll strip caster is investigated by physical and numerical simulation on a 1:1‐scale water model. A laser‐optical measurement technique (Laser Doppler Anemometry ‐ LDA) is used to validate the numerical results for the water flow. The numerical simulations are then transferred to the melt flow in the strip caster. The investigations are focused on different SEN concepts (submerged entry nozzle), a single‐nozzle system with two outlet ports and a double‐nozzle system with one outlet port each. The Influence of these concepts on the velocity, turbulence, and temperature distribution inside the liquid pool between the casting rolls and on the solidification and growth of the strip shells are investigated by numerical simulations (Computational Fluid Dynamics ‐ CFD). The non‐isothermal melt flow is calculated considering the solidification enthalpy as well as the behaviour of the solidifying melt. In addition to the numerical simulations of the melt flow inside the pool the temperature distribution in the cast strip is simulated. The SEN concept directly correlates with the temperature distribution Inside the strip. Furthermore, the surface temperature of the strip below the outlet of the roll gap is measured using a line‐scanner and is compared with the CFD simulation. In order to simulate the shape of the free surface in the liquid pool, CFD simulations of the water flow in the physical model are carried out using a Volume of Fluid model (VoF). This two‐phase model is able to reproduce free surface waves.     

Velocity Distribution of Turbulent Open-Channel Flow with Bed Suction

This study investigates theoretically and experimentally the velocity distributions of turbulent open channel flow with bed suction. A velocity profile with a slip velocity at the bed surface and an origin displacement under the bed surface is proposed and discussed. Based on this assumption, a modified logarithmic law is derived. The measured experimental velocity distribution verifies the accuracy of the theoretically derived profile. The data show a significant increase in the near bed velocity and a velocity reduction near the water surface, resulting in the formation of a more uniform velocity distribution. The values of the origin displacement, slip velocity and shear velocity are found to increase with increasing relative suction. The measured data show the occurrence of two flow regions in the suction zone: a transitional region in which the velocity readjusts rapidly; and an “equilibrium” region.     

Simulation of Flow and Mass Dispersion in Meandering Channels

This paper reports the development of an enhanced two-dimensional (2D) numerical model for the simulation of flow hydrodynamics and mass transport in meandering channels. The hydrodynamic model is based on the solution of the depth-averaged flow continuity and momentum equations where the density of flow varies with the concentration of transported mass. The governing equation for mass transport model is the depth-averaged convection and diffusion equation. The dispersion terms arisen from the integration of the product of the discrepancy between the mean and the actual vertical velocity distribution were included in the momentum equations to take into account the effect of secondary current. Two laboratory experimental cases, flow in mildly and sharply curved channels, were selected to test the hydrodynamic model. The comparison of the simulated velocity and water surface elevation with the measurements indicated that the inclusion of the dispersion terms has improved the simulation results. A laboratory experiment study of dye spreading in a sine-generated channel, in which dye was released at the inner bank, centerline, and outer bank, respectively, was chosen to verify the mass transport model. The simulated concentration field indicated that the Schmidt number can be used as a calibration parameter when dispersion is computed using a 2D approach with a simplified turbulence model.     

Velocity Profile and Flow Resistance Models for Developing Chute Flow

A developing boundary layer starts at the spillway crest until it reaches the free surface at the so-called inception point, where the natural air entrainment is initiated. A detailed reanalysis of the turbulent velocity profiles on steep chutes is made herein, including mean values for the parameters of the complete turbulent velocity profile in the turbulent rough flow regime, given by the log-wake law. Accounting both for the laws of the wall and the wake, a new rational approach is proposed for a power-law velocity profile within the boundary layer of turbulent rough chute flow. This novel approach directly includes the power-law parameters and does not require for a profile matching, as is currently required. The results obtained for the turbulent velocity profiles were applied to analytically determine the resistance characteristics for chute flows. The results apply to the developing flow zone upstream of air inception in chute spillways.     

Laminar and Turbulent Bottom Boundary Layer Induced by Nonlinear Water Waves

Results of a numerical study to investigate wave-induced boundary layer flows are reported. In this study, the writers consider a coupled viscous-inviscid approach, in which the fully nonlinear free surface boundary conditions are satisfied in the inviscid flow calculation, while the viscous flow near the seabed is solved via the Reynolds-averaged Navier-Stokes equations, instead of the thin boundary layer equation. To simulate the turbulent flow, a two-layer k-ε model is applied. Coupling of the viscous and inviscid computations is accomplished by the direct matching of the velocity and pressure distributions on the matching boundaries. Validation of the numerical model is carried out separately for the inviscid and viscous models, and the coupling approach as a whole. The numerical results are compared with theoretical solutions and available experimental data. A parametric study of the laminar and turbulent boundary layers for highly and weakly nonlinear waves is performed using the coupled viscous-inviscid approach. The results are compared with corresponding U-tube simulations, and the discrepancy is highlighted and discussed.     

Simulation of a 3D Numerical Viscous Wave Tank

A numerical scheme was developed to solve the unsteady three-dimensional (3D) Navier–Stokes equations and the fully nonlinear free surface boundary conditions for simulating a 3D numerical viscous wave tank. The finite-analytic method was used to discretize the partial differential equations, and the marker-and-cell method was extended to treat the 3D free surfaces. A piston-type wave generator was incorporated in the computational domain to generate the desired incident waves. This wave tank model was applied to simulate the generation and propagation of a solitary wave in the wave tank and the diffraction of periodic waves by a semiinfinite breakwater. The computation was carried out by a PC cluster established by connecting several personal computers. The message passing interface (MPI) parallel language and MPICH software were used to write the computer code for parallel computing. High consistency between the numerical results and the theoretical solutions for the wave and velocity profiles confirms the accuracy of the proposed wave tank model.     

BIEM Modeling of 3D Circulation and Transport in Stratified Estuaries

Here the boundary integral equation method (BIEM) is used for 3D modeling of hydrodynamics and pollutant transport in stratified estuaries. The flow computations are made using a newly developed BIEM solution. The transport modeling has been done using an Eulerian-Lagrangian BIEM (ELBIEM) model. In ELBIEM, the advection part in the transport equation is treated by the concept of the Eulerian-Lagrangian scheme, which overcomes the limitation of traditional BIEM to deal with an arbitrary velocity field. The coupling of the 3D shallow water BIEM model and advection-diffusion ELBIEM model enables one to effectively deal with fluctuation of free surface and density stratification in an estuary. The main advantages of the BIEM model include reduction in computational dimensions, ease in discretization and data preparation, accurate free surface simulation, less numerical diffusion and dispersion problems, and direct flux solution at boundaries. The numerical simulation results are compared with other model results and found to be satisfactory. The illustrated case study shows the effectiveness of the model in the simulation of mass, momentum, and heat transfer due to air-water interaction in stratified estuary problems.     

RANS∕Laplace Calculations of Nonlinear Waves Induced by Surface-Piercing Bodies

An interactive zonal numerical method has been developed for the prediction of free surface flows around surface-piercing bodies, including both viscous and nonlinear wave effects. In this study, a Laplace solver for potential flow body-wave problems is used in conjunction with a Reynolds-averaged Navier-Stokes (RANS) method for accurate resolution of viscous, nonlinear free surface flows around a vertical strut and a series 60 ship hull. The Laplace equation for potential flow is solved in the far field to provide the nonlinear waves generated by the body. The RANS method is used in the near field to resolve the turbulent boundary layers, wakes, and nonlinear waves around the body. Both the kinematic and dynamic boundary conditions are satisfied on the exact free surface to ensure accurate resolution of the divergent and transverse waves. The viscous-inviscid interaction between the potential flow and viscous flow regions is captured through a direct matching of the velocity and pressure fields in an overlapping RANS and potential flow computational region. The numerical results demonstrate the capability of an interactive RANS∕Laplace coupling method for accurate and efficient resolution of the body boundary layer, the viscous wake, and the nonlinear waves induced by surface-piercing bodies.     

3D Analytic Model for Testing Numerical Tidal Models

A 3D analytic solution is presented for tides in channels with arbitrary lateral depth variation. The solution is valid for narrow channels in which the lateral variation of the amplitude of tidal elevation is small. The error introduced by the solution is on the order of a few percent in a tidal channel of a few kilometers in width. The solution allows an arbitrary lateral depth variation and thus provides a wide choice of depth functions, especially those with large bottom slopes. The largest amplitude of the along-estuary velocity appears on the surface in the deepest water. The depth-averaged velocity is the largest in the deepest water. The time of flood (ebb) in deep water lags that in shallow water. The time of flood (ebb) on the surface lags that at the bottom. Since this solution is simple and allows arbitrary lateral depth variations, it can be used to demonstrate the first-order tidal flow in narrow tidal channels of variable depth, and to test high-resolution numerical models with large depth gradients.     

Dam Break in Channels with 90° Bend

In practice, dam-break modeling is generally performed using a one-dimensional (1D) approach for its limited requirements in data and computation. However, for valleys with multiple sharp bends, such a 1D model may fail for predicting as well the maximum water level as the wave arrival time. This paper presents an experimental study of a dam-break flow in an initially dry channel with a 90° bend, with refined measurements of water level and velocity field. The measured data are compared to some numerical results computed with finite-volume schemes associated with Roe-type flux calculation. The 1D approach reveals the expected limits, while a full two-dimensional (2D) approach provides fine level prediction and rather satisfactory information about the arrival time. A hybrid approach is now proposed, mixing the 1D model for the straight reaches and local 2D models for the bends. The compatibility of the Roe fluxes at the interfaces requires a careful formulation, but the resulting scheme seems able to capture reflection and diffraction processes in such a way that the results are really good in what concerns the water level.     

Experimental Study and 3D Numerical Simulations for a Free-Overflow Spillway

The main objectives of the present work were to investigate the flow field over a spillway and to simulate the flow by means of a three-dimensional (3D) numerical model. Depending on the wall curvature, the boundary layer parameters decreased or increased with increasing distance along the spillway. The growth of the boundary layer along the spillway is better described as a function of Reynolds number than the normalized streamwise length. A simplified form of the 3D momentum equation can be used to obtain a rough estimate of the skin friction. The velocity profile in the boundary layer along the spillway is described by a velocity–defect relationship. Numerical models provide a cost-effective means of simulating spillway flows. In this study, the water surface profiles and the discharge coefficients for a laboratory spillway were predicted within an accuracy range of 1.5–2.9%. The simulations were sensitive to the choice of the wall function, grid spacing, and Reynolds number. A nonequilibrium wall function with a grid spacing equal to a distance of 30 wall units gave good results.     

基于单相LBM模拟大平板反重力充型过程

采用单相格子Boltzmann方法研究大平板的反重力充型过程,该模型不需考虑气相格子的变化,从而提高了计算效率.针对该方法,本文新提出了一种权重系数重新分配的方法来处理格点中的液相排出及分配问题.首先用该模型计算了单浇口条件下的大平板型腔反重力充填过程,以相同参数下的高速相机成像的水力充填实验为参照,数值模拟的流场特征及流体形态与实验结果吻合良好.另外,还采用线速度分布云图,并提出了自由表面的高度差判据来分析充型过程中的流场区域特征和流体平稳程度.在此基础上,继续用该模型研究了双浇口和圆柱扰流条件下的大平板反重力充型过程.双浇口条件下由于浇道间的互相影响,流场中形成的漩涡多于单浇口;圆柱扰流条件下的充填方式会降低流体的晃动程度,提高充型的稳定性.      

Curvilinear Flow Profiles Based on Reynolds Averaging

A new theoretical approach is presented for the derivation of free surface profiles of two-dimensional steady and unsteady flows by solving the Reynolds-averaged Navier-Stokes equations applied to the turbulent flow regime. This approach enables us to compute the steady and unsteady curvilinear flows having small curvatures, such as free overfall and constant velocity surge. In addition, the applications of the theory to the second-order waves are illustrated through the problems of small height bore and second-order tide.     

Case Study of an S-Shaped Spillway Using Physical and Numerical Models

The spillway studied in this paper was designed as an “S” shape in plan view, characterized in two curved conduits, steep slopes, and small curvature radiuses. An approach of the combination of physical and numerical models was adopted to study the hydraulic characteristics and examine the feasibility of the design. By setting proper sills whose specific layouts were determined by numbers of experiments at the bottom of the curved conduits, the flow pattern was significantly improved. The k–ε turbulence model was used to simulate the three-dimensional turbulent flow. The free water surface was determined by the volume of fluid method, and the governing equations were solved by the finite volume method. Simulated results of the free water surface and the velocity are in good agreement with measured data. It is shown that S shaped spillways are feasible in practical projects. Moreover, numerical simulations are useful for the design and analysis of S shaped spillways.     

Two-Dimensional Analysis of Dam-Break Flow in Vertical Plane

This work presents numerical computations for the analysis of Dam-Break Flow using two-dimensional flow equations in a vertical plane. The numerical model uses the general approach of the simplified marker and cell method combined with the volume of fluid approach for the surface tracking. The time evolution of flow depth at the dam site and the evolution of the pressure distribution are investigated for both wet and dry bed conditions. The effect of the initially nonhydrostatic state on the long term surface profile and wave velocity are studied. These long term effects are found to be marginal in the case of wet-bed conditions, but are significant in dry-bed conditions. The dry-bed tip velocity immediately after the dam break, computed numerically, compares well with analytical results published previously. The time taken to obtain a constant flow depth at the dam site increases with decreasing initial depth ratio. The numerical result for this time elapse for dry-bed conditions is close to the experimentally obtained value.     

Numerical Solution of 2D Free Surface Flow to Ditch Drains in Anisotropic Soils

A numerical solution of two-dimensional free surface flow to ditch drains in homogeneous and anisotropic soils is presented. The differential equation governing two dimensional ground-water flow in anisotropic soils is solved by the alternating direction implicit (ADI) method of finite difference. In the approach the method is modified to make it applicable for curved boundaries. This simplified approach does not involve any kind of smoothing or linearization technique. The model solutions for ditch drainage with constant replenishment and instantaneous drawdown are found to be in close agreement with the finite-difference and finite-element solutions proposed by other researchers.     

Form Drag of Fences Placed in Disturbed Turbulent Boundary Layers

Wind tunnel studies on the drag characteristics of solid and porous fences placed in the turbulent boundary layer disturbed by the presence of an upstream fence are reported. The analysis of the data reveals that the outer region of the approach velocity profile also influences the drag, contrary to the implication from the relationship of Ranga Raju et al. that only the velocity distribution in the inner region is of consequence so far as the drag is concerned. A unique relationship has been obtained for the drag coefficient based on the average velocity over the height of the fence in terms of the porosity, the shape factor of the approach boundary layer, and an additional parameter characterizing the approach velocity distribution over the height of the fence. This relationship is valid for 2D solid and porous fences placed in a flow with a zero pressure gradient for the cases of disturbed and undisturbed boundary layers developed over smooth, transitional, and rough surfaces.