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.     

Depth-Averaged Two-Dimensional Numerical Modeling of Unsteady Flow and Nonuniform Sediment Transport in Open Channels

A depth-averaged two-dimensional (2D) numerical model for unsteady flow and nonuniform sediment transport in open channels is established using the finite volume method on a nonstaggered, curvilinear grid. The 2D shallow water equations are solved by the SIMPLE(C) algorithms with the Rhie and Chow’s momentum interpolation technique. The proposed sediment transport model adopts a nonequilibrium approach for nonuniform total-load sediment transport. The bed load and suspended load are calculated separately or jointly according to sediment transport mode. The sediment transport capacity is determined by four formulas which are capable of accounting for the hiding and exposure effects among different size classes. An empirical formula is proposed to consider the effects of the gravity on the sediment transport capacity and the bed-load movement direction in channels with steep slopes. Flow and sediment transport are simulated in a decoupled manner, but the sediment module adopts a coupling procedure for the computations of sediment transport, bed change, and bed material sorting. The model has been tested against several experimental and field cases, showing good agreement between the simulated results and measured data.     

Numerical Error in Weighting Function-Based Unsteady Friction Models for Pipe Transients

The accurate simulation of pressure transients in pipelines and pipe networks is becoming increasingly important in water engineering. Applications such as inverse transient analysis for condition assessment, leak detection, and pipe roughness calibration require accurate modeling of transients for longer simulation periods that, in many situations, requires improved modeling of unsteady frictional behavior. In addition, the numerical algorithm used for unsteady friction should be highly efficient, as inverse analysis requires the transient model to be run many times. A popular model of unsteady friction that is applicable to a short-duration transient event type is the weighting function-based type, as first derived by Zielke in 1968. Approximation of the weighting function with a sum of exponential terms allows for a considerable increase in computation speed using recursive algorithms. A neglected topic in the application of such models is evaluation of numerical error. This paper presents a discussion and quantification of the numerical errors that occur when using weighting function-based models for the simulation of unsteady friction in pipe transients. Comparisons of numerical error arising from approximations are made in the Fourier domain where exact solutions can be determined. Additionally, the relative importance of error in unsteady friction modeling and unsteady friction itself in the context of general simulation is discussed.     

Volume of Fluid Model for Turbulence Numerical Simulation of Stepped Spillway Overflow

The stepped spillway has increasingly become an effective energy dissipator. When the hydraulic performance of the overflow is clearly known, the energy dissipation could be increased. However, the study of stepped spillway overflow has been based only on model tests until now. In this paper, the k–? turbulence model is used to simulate the complex turbulence overflow. The unstructured grid is used to fit the irregular boundaries and the volume of fluid method is introduced to solve the complex free-surface problem. The free surface, velocities, and pressures on the stepped spillway are obtained by the turbulence numerical simulation. Furthermore, the simulation results compare well with measured data. The study indicates that the turbulence numerical simulation is an efficient and useful method for the complex stepped spillway overflow.     

Applicability of Quasisteady and Axisymmetric Turbulence Models in Water Hammer

Two of the existing turbulence water hammer models, namely the two-layer and the five-layer eddy viscosity models, are implemented and analyzed and the accuracy of their quasi-steady and axisymmetric assumptions evaluated. In addition, a dimensionless parameter P (ratio of the time scale of radial diffusion of shear to the time scale of wave propagation) for assessing the accuracy of quasi-steady turbulence modeling in water hammer problems is developed and applied. It is found that the results of both models are in reasonable agreement, confirming that the turbulence modeling of water hammer flows is insensitive to the magnitude and distribution of the eddy viscosity within the pipe core. Comparison of model results with available data shows that the quasi-steady assumption becomes more accurate as the dimensionless parameter P increases. Furthermore, the analysis shows that the quasi-steady assumption is highly accurate as long as the simulation time is below the diffusion time scale and that this assumption causes an almost linear increase in the difference between model results and data with time. The accuracy of the flow axisymmetry assumption is evaluated by applying both models to a water hammer problem where flow asymmetry has been observed experimentally. It is found that the difference between models and data grows exponentially and reaches 100% after six wave periods.     

Systematic Evaluation of One-Dimensional Unsteady Friction Models in Simple Pipelines

In this paper, basic unsteady flow types and transient event types are categorized, and then unsteady friction models are tested for each type of transient event. One important feature of any unsteady friction model is its ability to correctly model frictional dissipation in unsteady flow conditions under a wide a range of possible transient event types. This is of importance to the simulation of transients in pipe networks or pipelines with various devices in which a complex series of unsteady flow types are common. Two common one-dimensional unsteady friction models are considered, namely, the constant coefficient instantaneous acceleration-based model and the convolution-based model. The modified instantaneous acceleration-based model, although an improvement, is shown to fail for certain transient event types. Additionally, numerical errors arising from the approximate implementation of the instantaneous acceleration-based model are determined, suggesting some previous good fits with experimental data are due to numerical error rather than the unsteady friction model. The convolution-based model is successful for all transient event types. Both approaches are tested against experimental data from a laboratory pipeline.     

Wall Shear Stress in the Early Stage of Unsteady Turbulent Pipe Flow

Conventionally, wall shear stress in an unsteady turbulent pipe flow is decomposed into a quasi-steady component and an “unsteady wall shear stress” component. Whereas the former is evaluated by using “standard” steady flow correlations, extensive research has been carried out to develop methods to predict the latter leading to various unsteady friction models. A different approach of decomposition is used in the present paper whereby the wall shear in an unsteady flow is split into the initial steady value and perturbations from it. It is shown that in the early stages of an unsteady turbulent pipe flow, these perturbations are well described by a laminar-flow formulation. This allows simple expressions to be derived for unsteady friction predictions, which are in good agreement with experimental and computational results.     

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.     

One-Dimensional Numerical Model for Nonuniform Sediment Transport under Unsteady Flows in Channel Networks

In this study, the proposed one-dimensional model simulates the nonequilibrium transport of nonuniform total load under unsteady flow conditions in dendritic channel networks with hydraulic structures. The equations of sediment transport, bed changes, and bed-material sorting are solved in a coupling procedure with a direct solution technique, while still decoupled from the flow model. This coupled model for sediment calculation is more stable and less likely to produce negative values for bed-material gradation than the traditional fully decoupled model. The sediment transport capacity is calculated by one of four formulas, which have taken into consideration the hiding and exposure mechanism of nonuniform sediment transport. The fluvial erosion at bank toes and the mass failure of banks are simulated to complement the modeling of bed morphological changes in channels. The tests in several cases show that the present model is capable of predicting sediment transport, bed changes, and bed-material sorting in various situations, with reasonable accuracy and reliability.     

Applicability of Kinematic, Noninertia, and Quasi-Steady Dynamic Wave Models to Unsteady Flow Routing

Propagation of flood waves in an open channel can be mathematically approximated by the Saint-Venant equations (dynamic wave) or by their simplifications including the kinematic wave, noninertia wave, gravity wave, and quasi-steady dynamic wave models. All of these wave approximations differ not only in the physical propagation mechanism, but also in the degree of complexity involved in computation. In order to efficiently implement the approximate wave models for flood routing, their criteria of applicability should be developed. The applicability of the kinematic wave, noninertia wave, and quasi-steady dynamic wave approximations to the full dynamic wave equations for unsteady flow routing is examined by comparing the propagation characteristics of a sinusoidal perturbation to the steady gradually varying flow for different simplified wave models. Development of the applicability criteria provides a guideline for selecting an appropriate wave model for unsteady flow modeling, thus enabling an assessment of the capabilities and limitations of different simplified wave models. By using the linear stability analysis, the derived criteria can be expressed in terms of dimensionless physical parameters that represent the unsteadiness of the wave disturbance, characteristics of the downstream boundary condition (backwater effect), and the location along the channel. The developed criteria are for a specific point and time, thereby providing a more refined indication than the integrated criteria based on the testing for a hydrograph found commonly in the literature. In this study, we have justified whether the simplified wave models such as the kinematic, noninertia, or gravity wave models would be appropriate and reliable approximations to the full Saint-Venant equations with a comparable accuracy for a given flow condition. The downstream backwater effect has been taken into consideration in the developed criteria for broader engineering applications. One hypothetical example is presented for illustration.     

Conservative Scheme for Numerical Modeling of Flow in Natural Geometry

A numerical model is proposed to compute one-dimensional open channel flows in natural streams involving steep, nonrectangular, and nonprismatic channels and including subcritical, supercritical, and transcritical flows. The Saint-Venant equations, written in a conservative form, are solved by employing a predictor-corrector finite volume method. A recently proposed reformulation of the source terms related to the channel topography allows the mass and momentum fluxes to be precisely balanced. Conceptually and algorithmically simple, the present model requires neither the solution of the Riemann problem at each cell interface nor any special additional correction to capture discontinuities in the solution such as artificial viscosity or shock-capturing techniques. The resulting scheme has been extensively tested under steady and unsteady flow conditions by reproducing various open channel geometries, both ideal and real, with nonuniform grids and without any interpolation of topographic survey data. The proposed model provides a versatile, stable, and robust tool for simulating transcritical sections and conserving mass.     

Modeling Unsteady Flow Characteristics of Hydropeaking Operations and Their Implications on Fish Habitat

Reservoir releases associated with energy production and flood mitigation need to be reconciled with efforts to maintain healthy ecosystems in regulated rivers. Unsteady flow phenomena caused by hydropeaking operations typically affect riverbed erosion and fish displacement. A three-dimensional hydrodynamic model is used to simulate the flow characteristics during the passage of the rising limb of an observed hydropeaking event in a gravel-bed reach of Smith River, Virginia. The calculated time-dependent water surface elevations, velocities, and shear stresses are compared with field measurements. Further, comparison based on numerical simulations of this historical and a hypothetical “staggering” hydropeaking event reveals that the latter has the capability of reducing the area subject to erosion and prolonging refugia availability for juvenile brown trout. Issues related to the adoption of either a truly dynamic modeling approach or a quasi-steady methodology for simulating unsteady flows are examined through a proposed unsteadiness flow parameter. The insights obtained from this study can assist in properly accounting for the impact of hydropeaking operations on fish habitat and instream flow management.     

3D Numerical Modeling of Flow and Sediment Transport in Laboratory Channel Bends

The development of a fully three-dimensional finite volume morphodynamic model, for simulating fluid and sediment transport in curved open channels with rigid walls, is described. For flow field simulation, the Reynolds-averaged Navier–Stokes equations are solved numerically, without reliance on the assumption of hydrostatic pressure distribution, in a curvilinear nonorthogonal coordinate system. Turbulence closure is provided by either a low-Reynolds number k?ω turbulence model or the standard k?ε turbulence model, both of which apply a Boussinesq eddy viscosity. The sediment concentration distribution is obtained using the convection-diffusion equation and the sediment continuity equation is applied to calculate channel bed evolution, based on consideration of both bed load and suspended sediment load. The governing equations are solved in a collocated grid system. Experimental data obtained from a laboratory study of flow in an S-shaped channel are utilized to check the accuracy of the model’s hydrodynamic computations. Also, data from a different laboratory study, of equilibrium bed morphology associated with flow through 90° and 135° channel bends, are used to validate the model’s simulated bed evolution. The numerically-modeled fluid and sediment transportation show generally good agreement with the measured data. The calculated results with both turbulence models show that the low-Reynolds k?ω model better predicts flow and sediment transport through channel bends than the standard k?ε model.     

Experimental and Numerical Investigation of Bed-Load Transport under Unsteady Flows

The dynamic behavior of bed-load sediment transport under unsteady flow conditions is experimentally and numerically investigated. A series of experiments are conducted in a rectangular flume (18?m in length, 0.80?m in width) with various triangular and trapezoidal shaped hydrographs. The flume bed of 8?cm in height consists of scraped uniform small gravel of D50 = 4.8??mm. Analysis of the experimental results showed that bed-load transport rates followed the temporal variation of the triangular and trapezoidal hydrographs with a time lag on the average of 11 and 30?s, respectively. The experimental data were also qualitatively investigated employing the unsteady-flow parameter and total flow work index. The analysis results revealed that total yield increased exponentially with the total flow work. An original expression which is based on the net acceleration concept was proposed for the unsteadiness parameter. Analysis of the results then revealed that the total yield increased exponentially with the increase in the value of the proposed unsteadiness parameter. Further analysis of the experimental results revealed that total flow work has an inverse exponential variation relation with the lag time. A one-dimensional numerical model that employs the governing equations for the conservation of mass for water and sediment and the momentum was also developed to simulate the experimental results. The momentum equation was approximated by the diffusion wave approach, and the kinematic wave theory approach was employed to relate the bed sediment flux to the sediment concentration. The model successfully simulated measured sedimentographs. It predicted sediment yield, on the average, with errors of 7% and 15% of peak loads for the triangular and trapezoidal hydrograph experiments, respectively.     

Numerical Simulation of Equal and Opposing Subcritical Flow Junctions

This study presents measured and computational results of a flow pattern at a junction with equal and opposing flows in the upstream channel that collide and turn 90° into the branch channel. The computational results are obtained using a two-dimensional, depth-averaged model with the k-ε turbulent closure scheme. The aim is to predict the recirculation zones that form as the flow turns into the branch channel. The simulated depth and velocity profiles in the upstream main and the downstream branch channels are found to compare well with the measurements made in the physical model for various inlet Froude numbers and width ratios of the main channel to the branch channel. The absolute relative error between the measured and computed contraction coefficient, a measure of the recirculation zone size, is less than 4.7%. The computational model is then used to develop curves for the contraction coefficient for various inlet Froude numbers and ratios of main channel width to the branch channel width for design purposes.     

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.     

Numerical and Physical Simulation of Flow Patterns in a Swirling Flow Tundish

Swirling flow tundish is a new kind of tundish which has shown good effects on flotation of inclusion and reduction of inclusion content. In this paper, studies have been carried out on the flow fields in a one‐strand slab tundish. A full scale model of the flow patterns in the water model tundish was developed using a self‐developed code. RTD curves under different experimental conditions were obtained from both physical and numerical simulations. The effects of the swirling flow chamber geometry and the flowrate on flow patters in the tundish were discussed and compared with results from the numerical simulation. Validation of the self‐developed codes was achieved by comparing the physical and numerical results of the RTD curves and the mean rotational velocities in swirling flow tundish. As a result, significant rotational flow in the swirling flow chamber and asymmetrical flow pattern in the whole tundish were confirmed and the effects of these parameters on dead zone and mean residence time were also obtained. Further and more comprehensive studies are needed to optimize the design and application of such tundishes.     

FLS分解炉二维流场的数值模拟计算

针对一实际尺寸FLS分解炉内的湍流流场建立数学模型 ,给出该数学模型的数学解法 .详细地对炉内的流场进行了数值模拟 ,数值计算结果给出速度、湍流动能等参数的分布 ,为分析分解炉内的传热、传质及化学反应过程提供了理论依据。     

Numerical Modeling of Bed Evolution in Channel Bends

A two-dimensional numerical model is developed to predict the time variation of bed deformation in alluvial channel bends. In this model, the depth-averaged unsteady water flow equations along with the sediment continuity equation are solved by using the Beam and Warming alternating-direction implicit scheme. Unlike the present models based on Cartesian or cylindrical coordinate systems and steady flow equations, a body-fitted coordinate system and unsteady flow equations are used so that unsteady effects and natural channels may be modeled accurately. The effective stresses associated with the flow equations are modeled by using a constant eddy-viscosity approach. This study is restricted to beds of uniform particles, i.e., armoring and grain-sorting effects are neglected. To verify the model, the computed results are compared with the data measured in 140° and 180° curved laboratory flumes with straight reaches up- and downstream of the bend. The model predictions agree better with the measured data than those obtained by previous numerical models. The model is used to investigate the process of evolution and stability of bed deformation in circular bends.