Shallow Turbulent Flows by Video Imaging Method

Shallow turbulent flows were produced in a tank of small thickness to study the friction effects on large-scale turbulent motion of small depth. The tank was constructed of two parallel walls. The space between the parallel walls (4.4, 1.57, and 0.59 cm) was small compared with the height (107 cm) and the width (212 cm) of the tank, and was varied during the experiments for different friction effects. Turbulent flows were produced by the injection of water in the form of starting jets into the tank filled with water. The large-scale turbulent flow in the small space between the walls of the tank is confined to essentially two-dimensional motion, and the motion is retarded by the force of friction. Dye was injected with the source fluid as the tracer for the highly unsteady and quasitwo-dimensional turbulent motion. From the initiation of the turbulent motion at the source to the final interaction of the jets with the tank bottom, the entire sequence of events was recorded by a pair of video cameras. The depth-averaged concentration of the dye was analyzed using the recorded video images.     

Power Law Velocity Profile in Fully Developed Turbulent Pipe and Channel Flows

The power law velocity profile has been analyzed in terms of the envelope of the friction factor which gives the friction factor log law. The power law index α and prefactor C are shown as the function of the friction Reynolds number, as well as the function of the alternate variable the nondimensional friction velocity. The fully developed turbulent superpipe flow data of McKeon et al. and fully developed channel flow data of Zanoun et al. have been analyzed and the power law index α and prefactor C data have been estimated, first as a function of the friction Reynolds number and second as function of the nondimensional friction velocity. Based on analysis, several correlations have been proposed that have been supported by the data.     

Approximation of Turbulent Wall Shear Stresses in Highly Transient Pipe Flows

Theoretical predictions of wall shear stresses in unsteady turbulent flows in pipes are developed for all flow conditions from fully smooth to fully rough and for Reynolds numbers from 103 to 108. A weighting function approach is used, based on a two-region viscosity distribution in the pipe cross section that is consistent with the Colebrook–White expression for steady-state wall friction. The basic model is developed in an analytical form and the resulting weighting function is then approximated as a sum of exponentials using a modified form of an approximation due to Trikha. A straightforward method is presented for the determination of appropriate values of coefficients for any particular Reynolds number and pipe roughness ratio. The end result is a method that can be used relatively easily by analysts seeking to model unsteady flows in pipes and ducts.     

Hydrodynamic Behavior of Asymmetric Oscillatory Boundary Layers at Low Reynolds Numbers

An experimental and numerical study has been carried out to study the wave boundary layers under asymmetric waves. The experiments were conducted in an oscillating tunnel using a simple mechanical system to generate an asymmetric oscillatory motion similar to cnoidal waves. The velocities were measured by laser Doppler velocimetry and the bottom shear stress was calculated from the cross-stream velocity profile. A low Reynolds number k–ε model was used to predict the hydrodynamic properties of the cnoidal wave boundary layers. After validating the model with the experimental data, a series of numerical experiments were carried out to study the transitional behavior of these boundary layers by virtue of friction factor and phase difference between mean free-stream velocity and bottom shear stress. Finally a stability diagram was drawn to demarcate the laminar, transition, and fully turbulent regimes using the numerical results. The present study would be useful for the hydraulic and coastal engineers interested in calculating bottom shear stress in order to compute the sediment transport in coastal environments.     

Timescale Behavior of the Wall Shear Stress in Unsteady Laminar Pipe Flows

Based on two-dimensional (2D) flow model simulations, the effects of the radial structure of the flow (e.g., the nonuniformity of the velocity profile) on the pipe wall shear stress, τw, are determined in terms of bulk parameters such as to allow improved 1D modeling of unsteady contribution of τw. An unsteady generalization, for both laminar and turbulent flows, of the quasi-stationary relationship between τw and the friction slope, J, decomposes the additional unsteady contribution into an instantaneous energy dissipation term and an inertial term (that is, based on the local average acceleration-deceleration effects). The relative importance of these two effects is investigated in a transient laminar flow and an analysis of the range of applicability of this kind of approach of representing unsteady friction is presented. Finally, the relation between the additional inertial term and Boussinesq momentum coefficient, is clarified. Although laminar pipe flows are a special case in engineering practice, solutions in this flow regime can provide some insight into the behavior of the transient wall shear stress, and serve as a preliminary step to the solutions of unsteady turbulent pipe flows.     

Semianalytical Model for Solid Concentration in Turbulent Pipe Flows with Dispersed Particles

This paper presents a semianalytical model for the radial distribution of the solid concentration in a fully developed vertical turbulent pipe two-phase flow. A simplified momentum equation in the radial direction for solid phase in a two-phase flow with dilute suspended particles was first obtained. A linear empirical closure relation for the mean gas and solid velocities along the pipe direction was constructed using published experimental data. By incorporating the closure relation, an analytical solution to the simplified solid momentum equation with the appropriate boundary conditions at the pipe center and wall was obtained. The results from this semianalytical model are able to describe the core-annulus phenomenon commonly occurring in two-phase turbulent pipe flows. Very good agreements were found between the model predictions and published experimental data.     

Flow Characteristics of Skimming Flows in Stepped Channels

Skimming flows in stepped channels are systematically investigated under a wide range of channel slopes (5.7°?θ?55°). The flow conditions of skimming flows are classified into two flow regimes, and the hydraulic conditions required to form a quasi-uniform flow are determined. An aerated flow depth of a skimming flow is estimated from the assumption that the residual energy at the end of a stepped channel coincides with the energy at the toe of the jump formed immediately downstream of the stepped channel. In a quasi-uniform flow region, the friction factor of skimming flows is represented by the relative step height and the channel slope. The friction factor for the channel slope of θ=19° appears to have a maximum. The residual energy of skimming flows is formulated for both nonuniform and quasi-uniform flow regions. Further, a hydraulic-design chart for a stepped channel is presented.     

Friction Factor of Meandering Flows

An expression for the friction factor of rough turbulent meandering flows is suggested: flow cross section is rectangular, the plan shape of the meandering channel is sine-generated. This expression gives the value of the friction factor as a function of position (which is determined by, among other factors, the local channel curvature) and channel sinuosity. The validity of the present expression is tested against results of laboratory measurements. The measurements were carried out in two meandering channels, one typifying “small” sinuosity, the other “large” sinuosity. It is found that the vertically averaged flows in these two channels exhibit two distinctly different (“in-” and “out-going”) flow patterns, depending on whether the channel sinuosity is “large” or “small.” These two radically different flow pictures cannot be supplied by the vertically averaged equations of motion if they are solved for a constant friction factor. The present consideration of the friction factor as a function of position and channel sinuosity is found to yield the computed vertically averaged flows that are in agreement with the flow pictures measured for both large and small values of sinuosity.     

Numerical Study of the Transition Regime between the Skimming and Wake Interference Flows in a Water Flume by Using the Lattice-Model Approach

A numerical study to describe the transition regime between the skimming and wake interference flows due to the influence of an idealized bed roughness in a water flume was carried out here using the lattice model approach. The model reproduced the skimming, transition, and wake interference regimes for different aspect ratios that determine the bed roughness geometry. The simulated turbulent structures were visualized by drawing the trajectories of a large number of passive tracer particles released in the computational domain, and the results agreed with those reported by the research works. The dimensionless streamwise and vertical turbulent intensities were calculated at five test sections. The results obtained supported the visualized flow patterns permitting us to detect the presence of a shear layer developed at the top of the roughness element, whose strength varied according to the flow regime simulated.     

Turbulent Flow Friction Factor Calculation Using a Mathematically Exact Alternative to the Colebrook–White Equation

We present a novel, mathematically equivalent representation of the Colebrook–White equation to compute friction factor for turbulent flow in rough pipes. This new form is simple, no iterative calculations are necessary, and is well suited for accurate friction factor estimation. A limiting case of this equation provided friction factor estimates with a maximum absolute error of 0.029 and a maximum percentage error of 1% over a 20×500 grid of ε/D and R values (10?6 ? ε/D ? 5×10?2; 4×103相似文献   

Salinity-Induced Density Stratification in Near-Laminar Open-Channel Flows

Salt tracer experiments are a cost-effective tool widely used in studies of flow and transport in free surface flows. Whereas in a large majority of rivers and streams, fully turbulent conditions achieve rapid vertical mixing of injected tracers, this is not necessarily the case with very low Reynolds number flows as encountered e.g., in wetland ponds. There, often laminar to near-laminar transitional flow regimes prevail, and the fact that solutions of elevated salinity are distinctly heavier than water may result in the development of stable density layers, trapping part of the salt tracer and distorting the breakthrough curve recorded at the outlet. In this study, the conditions under which density stratification develops due to salt injection are analyzed, and a criterion is presented which permits an intended salt tracer experiment to be judged at the planning stage already.     

Hydraulic Radius for Evaluating Resistance Induced by Simulated Emergent Vegetation in Open-Channel Flows

The resistance induced by simulated emergent vegetation in open-channel flows has been interpreted differently in the literature, largely attributable to inconsistent uses of velocity and length scales in the definition of friction factor or drag coefficient and Reynolds number. By drawing analogies between pipe flows and vegetated channel flows, this study proposes a new friction function with the Reynolds number that is redefined by using a vegetation-related hydraulic radius. The new relationship is useful for consolidating various experimental data across a wide range of vegetation density. The results clearly show a monotonic decrease of the drag coefficient with the new Reynolds number, which is qualitatively comparable to other drag coefficient relationships for nonvegetated flows. This study also proposes a procedure for correcting sidewall and bed effects in the evaluation of vegetation drag.     

Revisited Analysis of Pressure Drop in Flow through Crushed Rocks

Experimental data of pressure drop in flow through crushed rocks are reanalyzed with the capillary model in comparison with a model based on the square root of permeability as characteristic length. The capillary model is described by two parameters: the pore diameter and the tortuosity. The comparison leads to relationships between the structural parameters, Reynolds number, and friction factor of each model. The interest of the capillary model is that a single equation can predict all the experimental data expressed in terms of a pore friction factor as a function of pore Reynolds number. The equation, which is the sum of a viscous term and an inertial one, is valid for the whole Reynolds number domain. The equation can be used for the determination of the limits of the Darcy and turbulent flow regimes. According to the criterion used to neglect the viscous or the inertial term, the flow regimes limits can be expressed by a simple numerical value.     

Stone Stability in Nonuniform Flow

This paper presents the results of an experimental study on stone stability under nonuniform turbulent flow, in particular expanding flow. Detailed measurements of both flow and turbulence and the bed stability are described. Than various manners of quantifying the hydraulic loads exerted on the stones on a bed are extensively reviewed and extended. On the basis of the data, a new relationship between flow parameters and bed damage—expressed as a stone entrainment formula—has been established for nonuniform flow. As the present data is in line with existing data on other flows, the present relation seems applicable for other types of nonuniform flow as well. Such a relationship could provide more consistent design criteria and allow an estimate of the cumulative damage over time, which is important for making decisions regarding maintenance frequency and lifetime analysis of hydraulic structures.     

Mathematical Prediction of Cylinder Wake during Synchronization

For flows past a cylinder with a transversely oscillatory external forcing, a rapid phase change of π during synchronization has been noted in experimental studies in both laminar and turbulent regimes. In the present analysis, the Stuart–Landau (SL) model that was validated in unforced vortex shedding proves to be a feasible way in predicting this phase change. In addition, using this model other phenomena observed in experimental studies are also noted. These include the possible occurrence of hysteresis, and the broadening of frequency range undergoing phase change with the increase of forcing amplitude.     

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.     

Dynamics of Air Flow in Sewer Conduit Headspace

Pressurization in sanitary sewer conduit atmosphere is modeled using computational fluid dynamics techniques. The modeling approach considers both turbulent and laminar flow regimes. The turbulent model takes into consideration the turbulence-driven secondary currents associated with the sewer headspace and hence the Reynolds equations governing the air flow field are closed with an anisotropic closure model which comprises the use of the eddy viscosity concept for the turbulent shear stresses and semiempirical relations for the turbulent normal stresses. The resulting formulations are numerically integrated. The turbulent model outputs are verified with experimental data reported in the literature. Satisfactory agreement is obtained between numerical simulations and experimental data. Mathematical formulas and curves as functions of longitudinal pressure gradient, wastewater velocity, and sewer headspace geometry are developed for the cross-sectional average streamwise velocity.     

Analytical Relationships for Designing Multiple Outlets Pipelines

In this paper an analytical procedure taking into account the nonuniform outflow profile for hydraulic analysis and design of multiple outlets pipelines, is presented. Energy relations are improved based on the average friction drop approach with a simple exponential function, to express the nonuniform outflow concept. To determine friction head losses, the Darcy-Weisbach formula is used here; and the kinetic head change is considered whereas minor head losses are neglected. Several mathematical relationships are also derived for computing extreme pressure heads and their locations of occurrence along the pipeline. The presented method also provides specific lengths of the segments in which the different flow regimes occur along its length. This method simulates pressure and outflow profiles along trickle and sprinkler irrigation laterals and manifolds, as well as gated pipes. The presented technique was applied to several computational examples to clarify its precision for trickle and sprinkler lateral design and the analytical results were compared with those obtained using the numerical step-by-step method. The comparison test for the various design combinations indicated that, the proposed method is found to be sufficiently accurate in all design cases for both trickle and sprinkler lateral design. The analytical development is simple, direct, and easily adaptable to solve hydraulic design problems of various types of single-diameter mutiple-outlet pipelines in different flow regimes and uniform line slope cases. It is preferred to the numerical techniques which need large amounts of execution time and complex computer operations.     

Vertical Dispersion of Fine and Coarse Sediments in Turbulent Open-Channel Flows

Through using a kinetic model for particles in turbulent solid–liquid flows, underlying mechanisms of sediment vertical dispersion as well as sediment diffusion coefficient are investigated. Four hydrodynamic mechanisms, namely gravitational settling, turbulent diffusion, effect of lift force, and that of sediment stress gradient, coexist in two-dimensional (2D) uniform and steady open-channel flows. The sediment diffusion coefficient consists of two independent components: one accounts for the advective transport of sediment probability density distribution function due to sediment velocity fluctuations, and the other results from sediment–eddy interactions. Predictions of the kinetic model are in good agreement with experimental data of 2D open-channel flows. In such flows, it is shown that: (1) the parameter γ (i.e., the inverse of the turbulent Schmidt number) may be greater than unity and increases toward the bed, being close to unity for fine sediments and considerably large for coarse ones; (2) effects of lift force and sediment stress gradient become significant and need to be considered below the 0.1 flow depth; and (3) large errors may arise from the traditional advection–diffusion equation when it is applied to flows with coarse sediments and/or high concentrations.