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.     

Depth-Averaged Drag Coefficient for Modeling Flow through Suspended Canopies

Aquatic suspended canopies are porous obstacles that extend down from the free-surface but have a gap between the canopy and bed. Examples of suspended canopies include those formed by aquaculture structures or floating vegetation. The major difference between suspended canopies and the more common submerged canopies, which are located on the bottom boundary, is the influence of the bottom boundary layer beneath the suspended canopy. Data from laboratory experiments are presented which explore aspects of the flow through and beneath suspended canopies constructed from rigid cylinders. The experiments, using both acoustic Doppler and two-dimensional (2D) particle tracking velocimetry, give details of the flow structure that may be divided vertically into a bottom boundary layer, a canopy shear layer, and an internal canopy layer. The experimental data show that the penetration of the shear layer into the canopy is limited by the distance between the canopy and bottom boundary layer. Peaks in velocity spectra indicate an interaction between the bottom boundary and canopy shear layer. An analytical model is also developed that can be used to calculate a drag coefficient that includes the effect of both canopy drag and bed friction. This drag coefficient is suitable for use in 2D (depth-averaged) hydrodynamic modeling. The model also allows the average velocity within and beneath the canopy to be calculated, and is used to investigate the effect of canopy density and thickness on both total drag and bottom friction.     

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.     

Numerical Simulation on Flow Control for Drag Reduction of Revolution Body Using Dimpled Surface

Numerical simulation on the flow fields near the dimpled and the smooth revolution bodies are performed and compared by using SST k-ω turbulence model, to explain the reasons of friction and base drag reductions on the bionic dim-pled surface and the control behaviors of dimpled surface to boundary layer near wall of the revolution body. The simulation results show that the dimpled surface reduces the skin friction drag through reducing the velocity gradient and turbulent in-tensity , and reduces the base drag through weakening the pumping action on the flow behind the revolution body caused by the external flow; the low speed rotating vortexes in the dimples segregate the external flow and the revolution body; and the low speed rotating vortexes forming in the bottom of dimples can produce negative skin friction.     

Open Channel Flow through Different Forms of Submerged Flexible Vegetation

Laboratory experiments are used to explore the effect of two forms of flexible vegetation on the turbulence structure within a submerged canopy and in the surface flow region above. The two simulated plant forms involve flexible rods (stipes) of constant height, and the same rods with a frond foliage attached. These plant forms were arranged in a regular staggered configuration, set at the same stipe density. The plant geometry and its mechanical properties have been scaled from a real aquatic plant using Froudian similarity, and the methods used for quantifying the bending stiffness, flexural rigidity, and drag force–velocity relationship of the vegetation are outlined. Experimental results reveal that within the plant layer, the velocity profile no longer follows the logarithmic law profile, and the mean velocity for the rod/frond canopy is less than half of that observed for the simple rod array. In addition to the mean flow field, the turbulence intensities indicate that the additional superficial area of the fronds alters the momentum transfer between the within-canopy and surface flow regions. While the frond foliage induces larger drag forces, shear-generated turbulence is reduced due to the inhibition of momentum exchange by the frond surface area. It is known that the additional drag exerted by plants reduces the mean flow velocity within vegetated regions relative to unvegetated ones, but this research indicates that plant form can have a significant effect on the mean flow field and, therefore, potentially influence riverine and wetland system management strategies.     

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.     

Settling Characteristics of Calcareous Sand

This paper provides quantitative comparisons and relationships for the fall velocities and drag coefficients of 998 calcareous sand grains collected on Oahu, Hawaii. Laboratory analyses of the grains provide the three orthogonal dimensions, fall velocity, and density, from which the nominal diameter, drag coefficient, Reynolds number, and shape factor are evaluated for each grain. The fall velocity and drag coefficient expressed, respectively, as functions of nominal diameter and Reynolds number show strong correlation over a wide range of Corey shape factors. The present relationships are validated with published data based on quartz grains. Analysis of the data by flow regime shows that particle shape has a stronger influence on the settling characteristics when turbulent boundary layers develop around the grains.     

Spatially Averaged Open-Channel Flow over Rough Bed

In this paper it is suggested that the double-averaged (in temporal and in spatial domains) momentum equations should be used as a natural basis for the hydraulics of rough-bed open-channel flows, especially with small relative submergence. The relationships for the vertical distribution of the total stress for the simplest case of 2D, steady, uniform, spatially averaged flow over a rough bed with flat free surface are derived. These relationships explicitly include the form-induced stresses and form drag as components of the total stress. Using this approach, we define three types of rough-bed flows: (1) Flow with high relative submergence; (2) flow with small relative submergence; and (3) flow over a partially inundated rough bed. The relationships for the double-averaged velocity distribution and hydraulic resistance for all three flow types are derived and compared with measurements where possible. The double-averaged turbulent and form-induced intensities and stresses for the case of regular spherical-segment-type roughness show the dominant role of the double-averaged turbulence stresses and form drag in momentum transfer in the near-bed region.     

Simulation of Free Surface Flow over Spillway

A numerical approach is proposed to simulate and study the effect of geometry on the free surface flow over a tunnel spillway. A three-step solution procedure is proposed to speed up the solution. The first step is to obtain an approximate free surface profile and mean velocity distribution, assuming 1D steady flow. Next, the 3D turbulent flow field is computed while the water surface profile is kept fixed. Finally, the water surface is set free to move and generate waves. The governing equations for weakly compressible flow (compressible hydrodynamic flow) are solved with an explicit finite volume method. A boundary fitted grid system is used to accurately resolve the flow near the free surface with steep waves. A mixed Lagrangian-Eulerian approach is proposed to calculate the new free surface position. The numerical results of a time-averaged free surface profile as well as pressure and velocity distribution have been compared with some experimental data.     

Large-Eddy Simulation of Turbulent Flow over a Fixed Two-Dimensional Dune

Turbulent open-channel flow over a two-dimensional dune is studied using an established large-eddy simulation code. The free surface is approximated as a shear free boundary. Turbulence statistics and instantaneous flow structures are examined. Numerical results from two computational grids agree with each other, and are also in good agreement with recently obtained experimental data. The mean velocity profiles show significant changes along the dune and there is no region that conforms to the standard law-of-the-wall. Profiles of the Reynolds stresses show distinct peaks marking the shear layer that originates from flow separation at the dune crest. Secondary peaks found further from the dune are ascribed to the shear layer over the upstream dune. Details of the separated flow and development of the flow after reattachment are well predicted. Quadrant analysis of the Reynolds shear stress shows that turbulent ejections dominate the near-wall motions. Complex water surface flow structures are visualized.     

Three-Dimensional Mean Velocity Analysis of a 30 Degree Bend Flow

The 3D velocity profiles of the 30° bend flow of Flack and Johnston have been analyzed in terms of the existing 3D turbulent boundary layer theories. Various cross-flow and near-wall similarity models were tested. Coles's cross-flow model described the velocity profiles satisfactorily. The wall function matched the data well, and the experimentally determined wake functions collapsed into a narrow band, which was however different from the originally suggested wake function. A new form of wake function has been proposed. Among the near-wall models, Hornung and Joubert's and Prahlad's models matched the data very well and excellent near-wall similarity from the wall to the boundary layer edge was achieved. This is rather unexpected in a 3D turbulent boundary layer flow with large skewing. The excellent performance of these two near-wall models could not be attributed to any particular reason.     

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.     

开槽阳极对铝电解气液两相流及气泡分布特性影响的数值模拟

基于计算流体动力学原理,建立了全尺度三阳极铝电解槽内气液两相流三维CFD-PBM耦合计算模型,采用Grace曳力系数模型和Simonin湍流扩散力模型分别计算气液相间曳力和湍流扩散力,研究和讨论了开槽阳极对阳极底掌区域内气液两相流体流动及气泡分布特性的影响。结果表明,电解质流场预测结果与文献测试结果吻合良好;对阳极进行开槽可明显加快气泡的逸出方式,从而改变电解质流场和气体体积分数分布;长度方向开槽可明显降低气体体积分数和减小气泡索特平均直径。     

Rough Wall Boundary Layer on Plates in Open Channels

Experiments were performed to measure the characteristics of a turbulent boundary layer developing on a rough surface placed in an open channel flow at close proximity to the free surface. Streamwise velocity measurements were made with a one-component laser Doppler velocimeter system at the top of the spherical roughness elements. Measurements at three stations downstream of the plate leading edge show the growth of the boundary layer on the rough wall and its interaction with the exterior open-channel flow and the free surface. Resorting to the turbulence profile provides an alternative definition of the boundary layer thickness. The near-wall flow follows the well-known logarithmic law with a shift due to roughness. In the outer layer, there are two opposing effects: the free surface tends to decrease the wake component while the roughness tends to increase it. The streamwise turbulence intensity is affected by the shear and turbulence in the exterior flow, the effect of the free surface being greater than that of wall roughness.     

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.     

Oxygen Demand by a Sediment Bed of Finite Length

A model of sedimentary oxygen demand (SOD) for a sediment bed of finite length is presented. The responses of diffusive oxygen transfer in turbulent flow above the sediment surface and of microbial activity inside the sediment to a developing diffusive boundary layer are modeled numerically. The developing diffusive boundary layer above the sediment/water interface is modeled based on shear velocity and turbulent boundary layer concepts, and dissolved oxygen (DO) uptake inside the sediment is modeled as a function of the microbial growth rate. The model predicts that the diffusive boundary layer above the sediment/water interface thickens in flow direction, and that DO penetration depth into the sediment is practically constant over the length of the sediment bed. The effect of the developing diffusive boundary layer on SOD is minor, except at very low shear/flow velocities (shear velocity U*<0.01?cm/s) and/or high microbial density inside the sediment. The average SOD over the sediment bed therefore varies only slightly with its length. SOD varies somewhat in flow direction, i.e., SOD is largest near the leading edge (x = 0), decreases with distance, and finally, approaches a nearly constant value for fully developed boundary layer. Including microbial activity in the sediment makes the change of SOD in flow direction much smaller than is predicted by a pure vertical diffusive flux model. The diffusive boundary layer is nearly fully developed at a dimensionless distance x+ = 10,000, regardless of microbial activity inside the sediment. Longer sediment beds are required to eliminate the small leading edge effect on any measured average SOD value. SOD depends strongly on the diffusion coefficient of DO inside the sediment bed. This effect becomes more significant as shear/flow velocity is increased. Overall, SOD is found to be controlled principally by shear velocity of the water flowing above the sediment/water interface, microbial activity inside the sediment, and diffusion of DO inside the sediment. The length of the sediment bed is of lesser influence.     

狭缝射流冲击柱状凸形表面流动换热特性

采用数值方法研究了狭缝射流冲击柱状凸形表面的流动换热特性,通过四种湍流模型计算结果与实验数据对比,确定了湍流模型适用性.以压力梯度分布为依据,重点分析了狭缝射流沿柱状凸形表面的流动结构和边界层分离特点及柱状凸形表面的强化换热特性.结果表明:RNG k-ε和Realizable k-ε模型具有预测适应性;狭缝射流冲击至柱状凸形表面,气体沿表面运动,速度降低,并在流动下游发生边界层分离;量纲一的逆压梯度随量纲一的曲率半径(D/B)的减小而增大,使得边界层分离更早出现;驻点区域换热Nu随量纲一的曲率半径(D/B)的减小而获得增强,但流动进入下游后,D/B对换热基本无影响;压力梯度是影响狭缝射流冲击柱状凸形表面换热分布的重要因素.      

Turbulence Characteristics in Gradual Channel Transition

A field study was conducted to determine the effects of a channel transition on turbulence characteristics. Detailed three-dimensional (3D) flow measurements were collected at a cross section that is located downstream of a gradual channel expansion. These measurements were obtained via an acoustic doppler velocimeter and include the 3D velocity field, the mean local velocities, the turbulent intensities, the frictional characteristics of the flow, the secondary velocity along the transverse plane, and the instantaneous shear stress components in the streamwise and transverse directions. Analysis of the 3D flow data indicates that the turbulent flow on the outer bank of the channel is anisotropic. Such anisotropy of turbulence, which is attributed to the gradual expansion in the channel and bed roughness, yields the development of a secondary flow of Prandtl’s second kind as reported in 1952. In particular, it was found that turbulent intensities in the vertical and transverse directions on the outer bank section are different in magnitude creating turbulence anisotropy in the cross-sectional plane and secondary flows of the second kind. Turbulent intensities increase toward the free surface indicating the transfer of a higher-momentum flux from the channel bed to the free surface, which contradicts common wisdom. Results for the normalized stress components in the streamwise and transverse direction show similar behavior to the intensities. Moreover, the nonlinear distribution of stresses is indicative of the oscillatory nature of the flow induced by the secondary flows of Prandtl’s second kind. A similar behavior was found for flows in straight rectangular channels over different roughness. Finally, a comparison between the secondary current velocity with the mainstream velocity indicates that secondary flow of Prandtl’s second kind is present within the right half of the measured cross section.     

Mean Flow and Turbulence Structure of Open-Channel Flow through Non-Emergent Vegetation

The ability of turbulence models, based on two equation closure schemes (the k-ε and the k-ω formulations) to compute the mean flow and turbulence structure in open channels with rigid, nonemergent vegetation is analyzed. The procedure, developed by Raupach and Shaw (1982), for atmospheric flows over plant canopies is used to transform the 3D problem into a more tractable 1D framework by averaging the conservation laws over space and time. With this methodology, form∕drag related terms arise as a consequence of the averaging procedure, and do not need to be introduced artificially in the governing equations. This approach resolves the apparent ambiguity in previously reported values of the drag-related weighting coefficients in the equations for the turbulent kinetic energy and dissipation rates. The working hypothesis for the numerical models is that the flux gradient approximation applies to spatial∕temporal averaged conservation laws, so that the eddy viscosity concept can be used. Numerical results are compared against experimental observations, including mean velocities, turbulence intensities, Reynolds stresses, and different terms in the turbulent kinetic energy budget. The models are used to further estimate vegetation-induced flow resistance. In agreement with field observations, Manning's coefficient is almost uniform for some critical plant density and then increases linearly.     

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.