Aspects of Inlet Boundary Prescription for a Turbulent Flow Field

In the literature on turbulent flow various combinations of velocity, turbulence kinetic energy, and eddy viscosity models have been proposed for the inlet boundary to a flow field. There appears to be no rational criterion for specifying inlet boundary conditions. The present study proposes a criterion to select the inlet boundary conditions by treating the inlet boundary as a part of the flow field. Using this criterion, any prescribed variation of velocity, turbulence kinetic energy k, and rate of dissipation of kinetic energy ε, must satisfy the governing flow field equations at the inlet boundary. Analysis of previously used profiles of velocity, kinetic energy, and dissipation of kinetic energy in the literature indicates that most of these do not satisfy the flow field equations. To substantiate the importance of inlet boundary conditions, several reported numerical simulations using k-ε turbulence models are reconsidered to determine if there is any linkage between the residual errors at the inlet boundary and the errors in the flow field simulation. Based on such an analysis, it is both logical and practical to hypothesize the inlet boundary as a part of flow field.     

Two-Dimensional Simulation Model of Sediment Removal and Flow in Rectangular Sedimentation Basin

A steady, two-dimensional numerical model was created to study the hydrodynamics of a rectangular sedimentation basin under turbulent conditions. The strip integral method was used to formulate the flow equations, using a forward marching scheme for solving the governing partial differential equations of continuity, momentum, advection–diffusion, turbulent kinetic energy, and its dissipation. In this way the flow equations were converted to a set of ordinary differential equations (ODEs) in terms of the key physical parameters. These parameters, along with a set of shape functions, describe flow variables including the velocity, the concentration of suspended sediments, and both the kinetic energy and its dissipation rate. Four Gaussian distributions were investigated, one corresponding to each flow parameter. In order to calculate the turbulent shear stresses, a two-equation turbulence model (i.e., k-ε model) was used. A fourth order Runge–Kutta method numerically integrates the set of ODEs. Simulation results were compared with experimental data, and close agreement (generally within 5–10%) was observed.     

Numerical Solution of Fully Developed Flow with Vegetative Resistance

This paper presents a numerical solution of the Reynolds averaged Navier-Stokes and the near-wall k- (turbulent kinetic energy) and ω- (specific dissipation or dissipation per unit kinetic energy) transport equations, which are modified to include vegetative drag terms. For similar treatment of the model coefficients, the use of the near-wall k-ω model produces similar results to previous models that employed the standard k-ε models with wall functions. The study shows that reasonable predictions of streamwise velocity and Reynolds stress profiles can be achieved by adopting universal values for all model coefficients, but the calculated energy gradient can have significant error. The study also indicates that predictions of streamwise turbulence intensity are significantly improved by adopting the universal values of Cfk = 0.05 and Cfω = 0.16 rather than the theoretically based values, Cfk = 1.0 and Cfω = β/αβ?Cfk.     

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.     

Steady and Unsteady Simulations of Turbulent Flow and Transport in Ultraviolet Disinfection Channels

The effects of unsteadiness in the turbulent flow through a staggered array of circular cylinders, modeling an ultraviolet disinfection system, are studied by means of solutions of the two-dimensional Reynolds-averaged Navier–Stokes equations incorporating the standard k–? turbulence model. Time averaging is applied to the unsteady solution, and the time-averaged characteristics are compared with a solution where a steady flow is a priori assumed, as well as with time-averaged measurements. Differences between the predictions of time-averaged and the steady-flow models are found to be largest in the entrance region of the array, and to decline in importance in the downstream direction. Comparison with measurements indicate that, while the time-averaged unsteady model predictions exhibited better agreement in some respects, the turbulent kinetic energy remained substantially underpredicted. Predictions of head losses through the array are also discussed.     

Shallow Turbulent Flow Simulation Using Two-Length-Scale Model

Numerical simulations of the planar starting jets were conducted using a two-length-scale turbulence model and a hydraulic code to study the effect of friction on 2D turbulence in shallow open-channel flow. The simulation results were compared with the data of the starting jets obtained in a recent series of laboratory experiments conducted in a large tank of small thickness. Dividing the turbulence energies into large and small scales, and calculating the energies with separate models, the observed friction effects on the 2D large-scale turbulent motion were correctly simulated by a two-length-scale turbulence model. To maintain the large-scale turbulence in the shallow shear flow, the production of turbulence energy by the transverse shear must be greater than the dissipation of the energy by friction. The critical gradient bed-friction number obtained from the simulations of the starting jets was Sc ? 0.08, which is consistent with the experimental observations in other shallow turbulent flows.     

Vertical Mixing in the Fully Developed Turbulent Layer of Sediment-Laden Open-Channel Flow

Eulerian equations for the vertical flux and momentum of suspended particles in dilute sediment-laden open-channel flow in equilibrium have been derived using the two-fluid approach. Reynolds averaging has been applied in order to allow validation of individual terms with experimental data. Consideration of the various terms of the vertical momentum balance with experimental flume data indicates that the drag force has to be separated into a mean and a turbulent contribution with different timescales, respectively, the (gravitational) particle timescale and the integral turbulence timescale. The resulting formulation further provides a new theoretical closure for the turbulent Schmidt number.     

Numerical Modeling of Three-Dimensional Flow Field Around Circular Piers

A three-dimensional numerical model FLUENT is used to simulate the separated turbulent flow around vertical circular piers in clear water. Computations are performed using different turbulence models and results are compared with several sets of experimental data available in the literature. Despite commonly perceived weakness of the k-ε model in resolving three-dimensional (3D) open channel and geophysical flows, several variants of this turbulence model are found to have performed satisfactorily in reproducing the measured velocity profiles. However, model results obtained using the k-ε models show some discrepancy with the measured bed shear stress. The Reynolds stress model performed quite well in simulating velocity distribution on flat bed and scour hole as well as shear stress distribution on flat bed around circular piers. The study demonstrates that a robust 3D hydrodynamic model can effectively supplement experimental studies in understanding the complex flow field and the scour initiation process around piers of various size, shape, and dimension.     

Mean Flow and Turbulence Structure in Vertical Slot Fishways

This paper presents the results of an experimental study on the mean and turbulence structures of flow in a vertical slot fishway with slopes of 5.06 and 10.52%. Two flow patterns existed in the fishway and for each one, two flow regions were formed in the pools: a jet flow region and a recirculating flow region. The mean kinetic energy decays rapidly in the jet region and the dissipation rate in most of the areas in the pool is less than 200?W/m3. For the jet flow, the nondimensional mean velocity profile across the jet agrees very well with that of a plane turbulent jet in the central part of the jet with some scatter near its boundaries. Its maximum velocity decays faster compared to a plane turbulent jet in a large stagnant ambient. The jet presents different turbulence structure for the two flow patterns and for each pattern, the turbulence characteristics appear different between the left and right halves of the jet. However, the turbulence characteristics show some similarity for each case. The normalized energy dissipation rate shows some similarity and has a maximum value on the center of the jet. The results are believed to provide useful insight on the turbulence characteristics of flow in vertical slot fishways and can be used to verify numerical models and also for guidance in the design of fishways in the future.     

Numerical Evaluation of Two k-ε Turbulence Model for Predicting Flow and Solidification in Continuous Casting Slab

ListofSymbol　　cp———Specificheat ,J·kg-1·℃ -1;　　C1,C2 ,Cμ———Turbulentmodelconstants ;　　Dnoz———EquivalentdynamicdiameterofSEN ,m ;　　fs,f1———Solidfractionandliquidfraction ;　　f1,f2 ,fμ———Turbulentmodelterms ;　　g———Gravitationalacceleration ,m·s-2 ;　　k———Turbulencekineticenergy ,m2 ·s-2 ;　　k1———Laminarthermalconductivity ,W·m-1·℃-1;　　ks———Thermalconductivityofsolidsteel,W·m-1·℃ -1;　　p———Pressure ,Pa ;　　Prt———TurbulentPran…     

Unobstructed and Obstructed Turbulent Flow in Gravel Bed Rivers

An acoustic Doppler velocimeter was used to characterize turbulence in two gravel bed rivers. Data were collected in unobstructed flow and compared to recent investigations. Additional data collected in the wake of emergent boulders indicate that mean flow velocity, turbulent kinetic energy, gradients in the streamwise velocity, and Reynolds stress downstream from large rocks deviate from unobstructed flow results, but similar turbulence patterns are found behind each boulder. Results of this study are discussed with regard to natural channel design and fish habitat.     

Measurement and modeling of turbulence in the gas/liquid two-phase zone during gas injection

Averaged and turbulent fluctuating liquid velocities in the gas/liquid plume zone of a gas-stirred water model ladle were measured with a combined laser Doppler anemometer (LDA) and elec-trical probe technique. The measured turbulence fields, void fraction distribution, and gas and liquid velocities in the plume zone were used for evaluation of various turbulence models. It was found that, among all of the turbulence models tested, only a modified k-ε model, with extra source terms to take into account the generation and dissipation resulting from the inter-action of the bubbles with the liquid, yielded good agreement with both the mean liquid flow field and the turbulent kinetic energy distribution. However, the values of the coefficients orig-inally proposed by their authors were found inapplicable to the bubbly plume situation; more appropriate values of the coefficients were determined based on comparison with experimental measurement.     

Particle Image Velocimetry Study of Flow near Trashrack Models

This paper provides results of an experimental study of turbulent flow near trashrack models that are comprised of an array of three rectangular bars. The bar thickness, bar depth, and center-to-center spacing were maintained constant. The flow characteristics were studied by aligning the bars with the approach flow and conducting measurements at three different approach freestream velocities. Subsequently, the freestream velocity was kept constant and detailed measurements were conducted for four different bar inclinations relative to the approach flow. For each test condition, a high-resolution particle image velocimetry (PIV) technique was used to conduct detailed velocity measurements in streamwise-spanwise planes at middepth of flow. From these measurements, isocontours and profiles of the mean velocities, turbulence intensities, Reynolds shear stress, and production term in the transport equation for the turbulent kinetic energy were obtained to study the flow characteristics around and downstream of the aligned and inclined bars. Flow characteristics near hydroelectric station trashracks are important for efficient turbine operation and reduction of fish entrainment.     

Modeling of a Rough-Wall Oscillatory Boundary Layer Using Two-Equation Turbulence Models

The standard k?ω turbulence model and two versions of blended k?ω/k?ε models have been used to study the characteristics of a one-dimensional oscillatory boundary layer on a rough surface. The wall boundary condition for the specific dissipation rate of turbulent kinetic energy at the wall is specified in terms of a function based on wall roughness. A detailed comparison has been made for mean velocity, turbulent kinetic energy, Reynolds stress, and wall shear stress with the available experimental data. The three models predict the above properties reasonably well. In particular, the prediction of turbulent kinetic energy for the rough case by the blended models is much better than that for smooth oscillatory boundary layers as reported in previous studies. As a result of the present study, the use of one of the blended models in calculating the sediment transport in coastal environments may be recommended.     

Turbulent Boundary Layer Flows Above a Porous Surface Subject to Flow Injection

A new analytical expression for velocity profile in a fully developed turbulent boundary layer above a porous surface subject to flow injection is derived by solving the coupled Reynolds equations and turbulent kinetic energy equation. The advection of turbulent kinetic energy is considered during the derivation, whereas the earlier studies have neglected it. The new solution reduces to the universal logarithmic law in the case of no flow injection. For the small injection, the solution can be expanded into a series form in terms of the normalized injection velocity. The leading order terms are found to be equivalent to those in the earlier works in which the advection of turbulent kinetic energy has been neglected in the derivation. The new solution can provide more accurate prediction of bed shear stress for a wide range of flow injection rate, fluid type (e.g., from air to water), and surface roughness. On the other hand, the earlier theories may significantly underestimate bed shear stress under high injection rates.     

Turbulent Flow near Vertical Angled Fish Screen

Mean and turbulent flow characteristics on the upstream and downstream sides of the screen in a flow diversion channel have important implications for operation and maintenance (e.g., sedimentation) and for assessing fish behavior related to flow turbulence. This technical note extends an earlier study on mean flow near screens to turbulence characteristics. Acoustic Doppler velocimeter was used to explore three-dimensional mean and turbulent flow characteristics on the upstream and downstream sides of vertical angled fish screens. The present study confirms the two-dimensional mean velocity observations of the previous experimental work and shows that the vertical mean velocities are less than 10% of the local magnitudes of longitudinal velocity and hence can be ignored. Horizontal components of the mean velocity on the downstream side of the screen were relatively small, but the turbulent velocity fluctuations were two to three times as intense as those measured on the upstream side.     

Characteristics of Shear Layer Structure in Skimming Flow over a Vertical Drop Pool

The characteristics of shear layer structure between the sliding jet and the pool for skimming flows over a vertical drop pool were investigated experimentally, using flow visualization technique and high speed particle image velocimetry. Four series of experiments having different end sill ratios (h/H = 0.12, 0.43, 0.71 and 1.0, where h=end sill height and H=drop height) with various approaching flow discharges were performed to measure the detailed quantitative velocity fields of the shear layer. The mean velocities and turbulence properties were obtained by ensemble averaging the repeated measurements. From the velocity profiles, it is found that the growth of the shear layer in the downward direction as the jet slides down the pool represents the momentum exchange. Analyzing the distribution of measured velocity, the similarity profile of the mean velocity at different cross sections along the shear layer was obtained. The proposed characteristic scales provided unique similarity profiles having promising regression coefficient. The selection of these characteristic scales is also discussed. Further, the spatial variations of mean velocity profiles, turbulence intensities, in-plane turbulent kinetic energy, and Reynolds shear stress were also elucidated in detail. The imperative observation is that the Reynolds shear stress dominates the major part along the shear layer as compared to the viscous shear stress. The study also provides an insight into the flow phenomena through the velocity and turbulent characteristics.     

Effect of Turbulence Modeling on the Melt Flow and Inclusions Transport in a Steel Filtration Experiment

The current article deals with the effect of turbulence modeling on inclusions transport and melt flow in an induction crucible furnace (ICF), which was employed in order to investigate the efficiency and the performance of a ceramic filter. Furthermore, the influence of the discrete random-walk dispersion model on the behavior of inclusions in the ICF was investigated. Different turbulence models were employed in order to predict the turbulent melt flow. The numerical results show that the flow field is affected by the turbulence modeling method. Moreover, the distribution of the turbulent kinetic energy depends considerably on the choice of the turbulence model. In addition, the turbulence model and dispersion model also affect the inclusion transport in the melt. The filtration rate is also affected by the choice of the turbulence model.     

Oblique Flow over Dredged Channels.?I: Flow Description

A 3D investigation of flow across long, straight channels aligned obliquely to the flow direction has been conducted. The applied mathematical model solves the Reynolds-averaged Navier-Stokes equations using a k-ε model for turbulence closure in a curvilinear coordinate system. The uniformity along the channel alignment allows the three momentum equations to be solved in a 2D computational domain. With respect to a steady current entering a channel obliquely, two important flow features arise: (1) The flow will be refracted in the direction of the channel alignment, which may be described by depth-averaged models; and (2) a secondary flow will be introduced due to shear in the velocity profile. This can only be described using a 3D approach. The secondary flow will cause a horizontal deflection of streamlines over the vertical. Only by capturing the 3D flow behavior can the direction and magnitude of the bed shear stress be well modeled. When crossing a channel obliquely, the flow is gradually accelerated in the direction of the channel alignment. Results of the numerical flow model are compared with existing experimental data and good agreement is found.