Limitations of Depth-Averaged Modeling for Shallow Wakes

Large-scale horizontal vortical structures are generic features of shallow flows which are often modeled using the two-dimensional (2D) depth-averaged equations. Such modeling is investigated for the well-defined case of shallow wakes of a conical island of small side slope for which a three-dimensional (3D) boundary-layer (3DBL) model has previously been validated through comparison with experiment. The 3DBL model used a 3D, two-mixing-length, eddy-viscosity turbulence model with a vertical mixing length of classical Prandtl form and a horizontal mixing length some multiple of this. A multiple of six gave good predictions. This mixing length approach is reduced to depth-averaged form, giving a horizontal mixing length of about half the water depth. The shallow wakes may be vortex shedding or steady/stable and are conventionally defined by a stability parameter. The critical value above which a stable wake is formed is considerably overestimated by the depth-averaged model (for a range of mixing lengths) and the length of stable wake bubble is considerably underestimated. It seems likely that this is because the amplification of friction coefficient due to horizontal strain rates is not represented. However, when vortex shedding is prominent the 2D and 3DBL wake structures are quite similar. These results show, for example, the limitations of depth-averaged models for the prediction of solute dispersion.     

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.     

Treatment of Stagnant Zones in Riverine Advection-Dispersion

Advection-dispersion in streams encounters pockets of stagnant or dead zones in the flow, which trap the injected tracer. Treatment of stagnant or dead zones for dispersion is presented using one-dimensional advection-dispersion equation. A method is suggested for simultaneous estimation of dispersion coefficient, apparent (or effective) velocity, and effective injected mass of tracer, from a temporal concentration profile observed at a downstream section. The method is robust and uses a nonlinear optimization. Using the method procedure for estimation of adsorption coefficient for riverine advection-dispersion has also been suggested. The effective velocity is related to the stagnant zone fraction (average fraction of cross-sectional area attributed to stagnant zones) and adsorption. The application of the method on published data sets show that the parameter-estimates are reliable and the observed concentration profiles are closely reproduced. The analytical procedure described for the treatment of stagnant zones may have a wide application in civil engineering as well as other fields. The amount of chemicals released from the industrial units or by an accident can be estimated.     

Detached Eddy Simulation Investigation of Turbulence at a Circular Pier with Scour Hole

This paper uses results from detached eddy simulation to reveal the dynamics of large-scale coherent eddies in the flow around a circular pier with an equilibrium scour hole. This is important for the sediment transport because the local scour process is controlled to a large extent by the large-scale coherent structures present in the near-bed region. The present paper investigates the dynamics of these coherent structures, their interactions and their role in entraining sediment in the later stages of the scour process when the horseshoe vortex system is stabilized by the presence of a large scour hole. The pier Reynolds number was 2.06×105, outside the range of well-resolved large-eddy simulation (LES). Additionally, scale effects are investigated based on comparison with LES results obtained at a much lower Reynolds number of 16,000 in a previous investigation. The paper provides a detailed study of the dynamics of the main necklace vortices of the horseshoe vortex system, including an investigation of the bimodal oscillations, their effect on the amplification of the turbulence within the scour hole and the interactions of the necklace vortices with the downflow. Several mechanisms for the growth of the downstream part of the scour hole in the later stages of the scour process are discussed. Similar to the low-Reynolds-number simulation, and consistent with experimental observations, the presence of strong upwelling motions near the symmetry plane resulted in the suppression of the large-scale vortex shedding in the wake. The fact that the nondimensional values of the turbulent kinetic energy and pressure RMS fluctuations in the higher Reynolds number simulation were consistently lower inside the regions of high turbulence amplification associated with the main necklace vortex, the separated shear layers and the near-wake shows that changes in the flow and turbulence due to the Reynolds number and scour hole geometry can be quantitatively significant over Reynolds numbers between 104 and 105.     

Eddy Taxonomy Methodology around a Submerged Barb Obstacle within a Fixed Rough Bed

Past research in environmental hydraulics has established the consideration that small- and large-scale turbulent eddy structures correspond to fast and slow fluctuations within a velocity time series measured at a fixed location. This work embraces this concept and develops an eddy taxonomy methodology to classify the prominent small- and large-scale eddies in the vicinity of an obstacle within a fixed rough bed. The previously documented visual interpretation technique is used in conjunction with a novel technique, which utilizes the statistical skew parameter, to quantify the moving-average time step at which large-scale eddies may be isolated from small-scale eddies. Thereafter, triple decomposition theory is employed and prominent spatial and temporal scales (i.e., integral length scales and periodicity) of small- and large-scale eddies are calculated. The eddy taxonomy methodology is implemented using acoustic Doppler velocimeter time-series measurements captured in the vicinity of an experimental model of a submerged barb obstacle—a hydraulic structure used for bank protection and increasing aquatic diversity. Implementation of the eddy taxonomy methodology using the streamwise velocity (u) time series and streamwise-vertical Reynolds stress (uw) time series provide similar results for the time step necessary to decompose large- from small-scale eddies. Eddy taxonomy results indicate the presence of large-scale, macroturbulent eddies throughout the barb test section with periodicity and length scales that agree with literature reported values. Additionally, small-scale bed derived eddies are most pronounced in the deflected flow regions where the barb obstacle has less influence upon the flow, while multiple small-scale eddies, including ejection, wake, and Kelvin–Helmotz associated eddies, persist in the downstream overtopping and wake regions of the barb obstacle.     

Analysis and Prediction of Transverse Mixing Coefficients in Natural Channels

An experimental study has been undertaken using a naturally formed meandering channel to obtain unique tracer and hydrodynamic data. The velocity data presented are from laser Doppler anemometer measurements; tracer data were collected using an array of fluorometers in continuous flow through mode. Techniques for the prediction of the primary and secondary velocity flow fields are explored, and shown to be accurate. Analysis of the tracer data by the generalized method of moments using the cumulative transverse discharge approach is undertaken. The coefficient of transverse mixing is shown to exhibit considerable longitudinal variation over the meander cycle. A new integrated approach for predicting transverse mixing coefficients is developed and explored and has been validated against the data set. This approach requires only three parameters as input, namely, longitudinal planform curvature, cross-sectional shape, and total discharge, and has been shown capable of accurately predicting the longitudinal variation of the transverse mixing coefficient over the meander cycle.     

Large Scale Particle Image Velocimetry for Low Velocity and Shallow Water Flows

Large scale particle image velocimetry (LSPIV) is an extension of quantitative imaging techniques for measurements of water surface velocities using inexpensive standard video equipment. The present Technical Note describes capabilities and limitations of LSPIV for low velocity shallow flows. Measurements in low velocity shallow flume flows were performed to investigate the LSPIV sensitivity to seeding density and time interval between successive images. The results show that the accuracy of the LSPIV technique does not deteriorate as the flow velocity is reduced to as low as 0.015 m/s provided an adequate seeding and suitable time difference between images are selected. The results suggest that LSPIV is well-suited for flow fields with small velocities that are often below the limit of detection of most conventional devices.     

Convection Velocity of Vortex Structures in the Near Wake of a Circular Cylinder

The convection velocity of vortex structures in the near wake of a circular cylinder was experimentally investigated over the region 1.6–2.5 ? x/D ? 12.0 for R = 160–12,000. Dye injection technique of flow visualization and two completely noninvasive laser Doppler velocimeters were employed for R ? 320 and ?400, respectively. The convection velocity, Uc, is defined as the mean traveling velocity of vortex cores passing a streamwise separation during a mean elapsed time. For R ? 320, Uc was determined directly from the motion of dye-marked vortex cores filmed by a video camera. In the cases of R ≥ 400, the positions of peak vorticity and half of the half-velocity-defect width at each downstream section were first used to identify the mean path of vortex cores (i.e., the most probable trajectory of the vortex structures), along which spatial correlation measurements were then performed to determine the mean elapsed time corresponding to the maximum cross correlation. The present results show that, in laminar and transitional wakes, the ratio Uc/Uo increases from 0.53 to 0.84 over a region of 1.6 ? x/D ? 6.0 and then tends to be a constant of 0.84 for x/D ≥ 6.0. In a turbulent wake, Uc/Uo also increases from a certain value at a point downstream from the position of vortex formation to a mean value of about 0.86 at x/D ≥ 5.0–6.0, and then changes little with the increase of x/D. In addition, it is found that the dependence of Uc/Uo on R almost disappears for x/D ≥ 5.0.     

The physical and mathematical modelling of the flow field in the mold region in continuous casting systems: Part II. The mathematical representation of the turbulent flow field

A mathematical representation is developed for the turbulent flow field, temperature field, and tracer distribution in the upper region of the liquid pool in continuous casting. The problem is formulated through the statement of the two-dimensional turbulent flow equa-tions, which were then solved numerically, using the adaptation of a technique described by Spalding and coworkers. The computed results for the velocity fields were found to be in good qualitative agreement with the results of water model studies for both straight and radial flow nozzles. Furthermore, the predictions based on the model for the temperature and tracer profiles within the pool seem to be consistent with expectations. R. T. YADOYA, formerly Graduate Student, State University of New York at Buffalo     

Reynolds Number Effects on the Near-Exit Region of Turbulent Jets

In this paper, attention has been focused on the near-exit region of a round turbulent free jet to study the large-scale coherent structures and to document the signatures of the vortices over a range of Reynolds numbers. Particle image velocimeter measurements were conducted at three jet exit Reynolds numbers of 10,000, 30,000, and 55,000. The large-scale structures in the near field (X/D<12) were investigated by performing a proper orthogonal decomposition analysis of the velocity fields. A vortex identification algorithm was complemented by swirling strength maps to identify the vortex centers, rotational sense, size, and circulation of the vortices. The influence of the Reynolds number on the distribution of the number, size, and circulation of the identified vortices was studied. Proper orthogonal decomposition of the velocity fields revealed that Reynolds number has a strong influence on the mean circulation of vortices. The present results show that the axial location where vortices first appear and the number of vortices close to the nozzle exit (X/D<5) are dependent on the Reynolds number.     

Numerical Simulation of Street Canyon Flows with Simple Building Geometries

The velocity and pressure fields of the flow over street canyons formed by groups of buildings are studied numerically. The flow fields are computed by solving the time-dependent incompressible Navier–Stokes equations using the fractional step method. The numerical model is validated by simulating flows over a square cylinder at different Reynolds numbers. The Strouhal numbers, which reflect the dynamic flow characteristics, agree well with published experimental data over a wide range of Reynolds numbers. The wind field model is then applied to two street canyon configurations. First, flows inside street canyons formed by four identical buildings are simulated. The incidental flow is raised by the most upstream building and becomes parallel to the ground at the rooftop level of the fourth building downstream, resulting in a clockwise rotating vortex in downstream street canyons with an inflow from left to right. Second, flows inside street canyons formed by two identical buildings are simulated. In this case, a primary eddy that is counterclockwise rotating may be formed due to flow separation at the front corner of the upstream building. A clockwise rotating primary eddy is formed in the wake area of the separate zone above the street canyon, which drives the counterclockwise rotating eddy in the street canyon. The result indicates that rooftop level flows cannot be assumed parallel to the ground as some modelers have done in their studies. Studies also show that flow regimes in the street canyon will remain unchanged while the inflow velocity is greatly increased from 0.1 to 6.0?m/s. In addition, the wind velocities in the street canyon have a linear response to the inflow velocity.     

Effect of Electromagnetic Ruler Braking (EMBr) on Transient Turbulent Flow in Continuous Slab Casting using Large Eddy Simulations

Static electromagnetic braking (EMBr) fields affect greatly the turbulent flow pattern in steel continuous casting, which leads to potential benefits such as decreasing flow instability, surface defects, and inclusion entrapment if applied correctly. To gain a fundamental understanding of how EMBr affects transient turbulent flow, the current work applies large eddy simulations (LES) to investigate the effect of three EMBr ruler brake configurations on transient turbulent flow through the bifurcated nozzle and mold of a liquid-metal GaInSn model of a typical steel slab-casting process, but with deep nozzle submergence and insulated walls with no solidifying shell. The LES calculations are performed using an in-house graphic-processing-unit-based computational-fluid-dynamics code (LES-CU-FLOW) on a mesh of ~7?million brick cells. The LES model is validated first via ultrasonic velocimetry measurements in this system. It is then applied to quantify the mean and instantaneous flow structures, Reynolds stresses, turbulent kinetic energy and its budgets, and proper orthogonal modes of four cases. Positioning the strongest part of the ruler magnetic field over the nozzle bottom suppresses turbulence in this region, thus reducing nozzle well swirl and its alternation. This process leads to strong and focused jets entering the mold cavity making large-scale and low-frequency (<0.02?Hz) flow variations in the mold with detrimental surface velocity variations. Lowering the ruler below nozzle deflects the jets upward, leading to faster surface velocities than the other cases. The double-ruler and no-EMBr cases have the most stable flow. The magnetic field generates large-scale vortical structures tending toward two-dimensional (2-D) turbulence. To avoid detrimental large-scale, low-frequency flow variations, it is recommended to avoid strong magnetic fields across the nozzle well and port regions.     

Mass Balance in Eulerian-Lagrangian Transport Simulations in Estuaries

This paper investigates the generation of flow mass errors in finite-element shallow water models and the effect of these errors in the mass conservation of Eulerian-Lagrangian transport simulations. Flow mass errors are shown to be similar for several primitive and wave equation formulations. These errors occur primarily in areas of steep bathymetric gradients and near complex boundaries. Forcing Eulerian-Lagrangian transport simulations with nonconservative flow fields generates important mass imbalances, which can be mitigated by refining the flow grid. Comparatively, refining the transport grid only reduces marginally the mass errors.     

Modeling of macrosegregation caused by volumetric deformation in a coherent mushy zone

A two-phase volume-averaged continuum model is presented that quantifies macrosegregation formation during solidification of metallic alloys caused by deformation of the dendritic network and associated melt flow in the coherent part of the mushy zone. Also, the macrosegregation formation associated with the solidification shrinkage (inverse segregation) is taken into account. Based on experimental evidence established elsewhere, volumetric viscoplastic deformation (densification/dilatation) of the coherent dendritic network is included in the model. While the thermomechanical model previously outlined (M. M’Hamdi, A. Mo, and C.L. Martin: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 2081–93) has been used to calculate the temperature and velocity fields associated with the thermally induced deformations and shrinkage driven melt flow, the solute conservation equation including both the liquid and a solid volume-averaged velocity is solved in the present study. In modeling examples, the macrosegregation formation caused by mechanically imposed as well as by thermally induced deformations has been calculated. The modeling results for an Al-4 wt pct Cu alloy indicate that even quite small volumetric strains (≈2 pct), which can be associated with thermally induced deformations, can lead to a macroscopic composition variation in the final casting comparable to that resulting from the solidification shrinkage induced melt flow. These results can be explained by the relatively large volumetric viscoplastic deformation in the coherent mush resulting from the applied constitutive model, as well as the relatively large difference in composition for the studied Al-Cu alloy in the solid and liquid phases at high solid fractions at which the deformation takes place.     

Flow Details near River Groynes: Experimental Investigation

Experiments have been carried out in a fixed-bed flume for a schematized straight river reach with groynes on one side to study the dynamics of the flow near groynes. The flume had a geometrical scale of 1∶40, based on typical dimensions of the Dutch River Waal. Both emergent and submerged groynes were studied. The measurements demonstrate the differences in the nature of the turbulence between submerged and emerged groynes stages; and provide insight into the flow pattern in the vicinity of groynes, the shape and the extent of the mixing layer at different flow stages, and the dynamic behavior of the velocity along the mixing layer between the main channel and the groyne fields. A parameterization of the turbulence characteristics of the flow near groynes is presented. Large-scale velocity fluctuations are found in all test cases, with timescales that vary with the flow stage. The large-scale u and v velocity fluctuations are in phase in the center of the mixing layer and out of phase for the points on the boundaries of the mixing layer.     

Particle Image Velocimetry Measurements of the Mean Flow Characteristics in a Bubble Plume

A direct measurement method for the velocity field in multiphase flows using the particle image velocimetry (PIV) and particle tracking velocimetry (PTV) methods is developed to study the flow characteristics of an unbounded bubble plume in quiescent, unstratified ambient conditions. A single camera is used to obtain images containing both bubbles and fluid tracer particles. Using gray-scale thresholding, phase-separated images of the bubbles are produced, and bubble velocities are obtained from these images using the standard PTV method. Regular PIV is applied to the mixed fluid images, and bubble vectors are removed using a velocity threshold and vector median filter that is calibrated to the PTV result. From the separate velocity fields, the time-averaged flow characteristics of a bubble plume are studied. Gaussian velocity profiles match the entrained fluid velocity, and top-hat velocity profiles match the bubble velocity. Time-averaged values are also presented of velocity, plume width, entrained fluid volume flux, and void fraction as a function of height. From these data, the entrainment coefficient for the entrained ambient fluid is calculated and lies between 0.08 near the plume source and 0.05 in the upper reaches. The results for the entrainment coefficient, together with those from the literature, are correlated to a nondimensional velocity, given by the ratio of the bubble slip velocity us to a characteristic velocity in the plume (B/z)1/3, where B = kinematic buoyancy flux and z is the height above the source.     

320m~3充气机械搅拌式浮选机内气液两相流的数值模拟

随着经济发展对矿产资源需求的不断增长,大型浮选机以其高效率和低能耗优势已成为国际潮流;作为辅助设计和效能评估的重要工具,CFD技术已成为进行大型浮选机研究、设计的关键技术手段之一。本文利用CFD技术针对320 m3充气机械搅拌式浮选机槽内气液两相流进行仿真计算,在确定合适模型的情况下,将得到的气、液流场、液面气液流速、叶轮功耗等在浮选机工业清水试验中较为重要的参数与工业试验所得的数据进行对比。结果表明,所选用的数学模型可以较准确地描述浮选机槽内气液流场,可以为浮选机的设计、改进提供依据。     

Linear Stability Analysis of Lateral Motions in Compound Open Channels

A linear stability analysis of lateral motions in shallow flow open channels with a free surface is presented. Unlike previous studies, this work does not employ the rigid-lid assumption. Computations revealed that the rigid-lid assumption works well for weak shear flows and∕or small Froude numbers. However, the validity of the rigid-lid assumption is reduced as the Froude number increases. Also, when Reynolds numbers are larger than 1,000, the stability domain is insensitive to the Reynolds number for all Froude numbers. The size of the stability domain is found strongly affected by the velocity and length scales of base velocity and the shape of the velocity profile. The analysis shows that the stability domains obtained by the Manning formula are larger than those obtained by the Chézy formula for the same Froude number. The analysis shows that a compound channel, whose floodplain has larger flow resistance than the main channel does, has larger lateral transport of flow mass, momentum, and energy.     

Numerical Simulation of Obstructed Round Buoyant Jets in a Static Uniform Ambient

The k-ε turbulence closure model is used to simulate obstructed round buoyant jets in a static uniform ambient, and the results compare well with available experimental data. On the basis of the axial line velocity distribution, three regions in the flow behind the disk are identified: the wake region, the transitional region, and the self-similarity region. The length of the wake region, which varies with flow and geometrical parameters, and the existence of self-similarity are also addressed.     

Estimation of Average Stream Velocity

Stream tracer studies provide information supporting diverse applications in environmental research and management. Average stream velocity through a reach is often estimated from tracer temporal profiles. This Technical Note addresses the calculation of average reach velocity. It is shown here that, under steady flow, average reach velocity over a fixed distance equals the spatial harmonic mean velocity. Similarly, the average reach velocity from the point of tracer injection to a fixed downstream measurement site is equal to downstream distance divided by the harmonic mean tracer time-of-travel, rather than the commonly used temporal centroid.