Flow Characteristics around a Circular Cylinder Placed Horizontally above a Plane Boundary

Flow characteristics around a circular cylinder positioned near a plane boundary (on which laminar boundary layer flow develops in the absence of circular cylinder), are investigated for Reynolds numbers R ranging from 7.8×102 to 1.15×104. Particle image velocimetry and fiber laser Doppler velocimetry were used to measure the velocity fields and velocity time histories, respectively. Flow structures are particularly revealed using flow visualization technique at R = 7.8×102 for gap ratios G/D (where G is the net gap between the surface of circular cylinder and the plane boundary), varying from 0 to 4. Based on the experimental results, the variation of Strouhal number of shedding vortex (or eddy) with G/D, the mechanism of vortex shedding suppression, and the streamwise velocity profiles of the upper shear layers and gap flows for small G/D are all discussed. Although the regular, alternate vortex shedding is suppressed for G/D<0.5, the periodicity could be detected due to the vortex (or eddy) shedding from the upper shear layer of the circular cylinder. Gap flow switching randomly is found and first put forward to be the main reason of multipeak or broadband spectral characteristics of the shedding event at a certain small gap ratio. It is also found that the streamwise velocity profiles of the upper shear layer, where periodic shedding eddies originate, exhibit well-behaved similarity. In addition, a unique similarity of mean streamwise velocity profiles of the gap flows is demonstrated for G/D ? 0.3. For R<4×103, the S increases as G/D decreases to its maximum around G/D ? 0.5 and then decreases as G/D decreases. For R ≥ 4×103, although most of the previous studies indicate that the S is insensitive to G/D, the present study shows that S still increases as G/D decreases but the variations of S are in a small range (i.e., 0.18 ? S ? 0.22).     

Suction Removal of Sediment from between Armor Blocks. II: Waves

When a stone/armor layer on a sand bed is exposed to flow, the sand underneath will be agitated by the flow turbulence. When the flow velocity reaches a critical value, the sand will be sucked (winnowed out) from between the armor blocks. In a previous investigation, we studied suction removal of sediment in steady currents. The present study is an extension of our previous investigation to waves. The critical condition for the onset of suction is determined. It is found that the onset of suction is governed by three parameters: (1) the sediment mobility number (based on the sediment size); (2) the ratio of sediment size to stone size, d/D; and (3) the Keulegan-Carpenter (KC) number, based on the armor block/stone size. The variation of the critical mobility number for suction as a function of d/D and KC is determined for the ranges of the parameters 0.001相似文献   

Simultaneous Particle Image Velocimetry and Laser Doppler Velocimetry Measurements of Periodical Oscillatory Horseshoe Vortex System near Square Cylinder-Base Plate Juncture

This paper presents simultaneous measurements using particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) techniques on the study of a horseshoe vortex system. The horseshoe vortex system is generated near the juncture of a vertical square cylinder and a horizontal base plate. The combination of PIV and LDV not only gives the spatial distribution and time history of velocity near the juncture for spatial and time domain analyses, it also allows phase averaging the PIV velocity data to reduce noise and, in a turbulent flow, result in turbulence statistics. A flow visualization technique displaying particle streaklines has also been used to help the classification of the vortex system and visualize the flow motion and vortex evolution. The classification of the horseshoe vortex was briefly categorized as steady, periodical oscillatory, and turbulence-like chaotic vortex systems through the use of the flow visualization technique and time-domain spectral analysis. Phase-averaged flow characteristics of the periodical oscillatory vortex system with a Reynolds number of 2,250 are presented in detail through the use of PIV and LDV as well as the flow visualization technique.     

Scour at Submerged Cylindrical Obstacles under Steady Flow

Results of an experimental study on clear-water scour at submerged cylindrical obstacles (circular cylinders) in uniform bed sediments under steady flow are presented. The scour depths at submerged circular cylinders are compared with the scour depths at corresponding unsubmerged cylinders (extended above the free surface of flow) of the same diameters under similar flow and bed sediment conditions. The scour depth decreases with an increase in submergence ratio. A submergence factor is introduced to determine the scour depth at a submerged cylinder from the information of the scour depth at an unsubmerged cylinder of the same diameter. In addition, the flow fields along the upstream vertical plane of symmetry of unsubmerged and submerged cylinders are presented through vector plots, which reveal that the dimension and strength of the horseshoe vortex decreases with an increase in submergence ratio. The horseshoe vortex circulations, which decrease with an increase in submergence ratio, are computed from the vorticity contours by using the Stokes theorem.     

Terminal Velocity of Cylinders Rolling in Uniform Flows

Ordnance remediation projects suggest that understanding the motion of cylinders (the approximate shape of ordnance) in flows would help to predict regions of ordnance mobility, to prioritize remediation efforts, and to improve the design of engineering works to trap ordnance. In simplified experiments, the characteristics of motion of smooth, unrestrained cylinders in contact with a smooth horizontal bed were investigated in flume experiments with steady, uniform flows. Eight cylinders were tested with varying specific gravities and diameters. At low flows, the cylinders follow trends similar to those noted in sediment particle studies. Incipient motion velocities were highest for the heavier cylinders. At high flows, the terminal velocity of the cylinders was limited to 60–80% of the free-stream flow. Potential flow derivations imply a maximum velocity ratio of 71%. Use of potential flow theory was considered valid (as an estimator) based on previous studies of boundary-layer control that suggest the moving surface of the cylinder minimizes the wake downstream of the cylinder, and therefore only a thin boundary layer is present around the cylinder.     

Transition and Chaos in Two-Dimensional Flow past a Square Cylinder

The unsteady wake of a long square cylinder has been numerically analyzed in the present study. Velocity signals at selected locations in the near-wake and the instantaneous forces on the cylinder have been recorded from the numerical model at various Reynolds numbers. These form the basis of investigating the dynamic behavior of the flow system. Results of the present work show the following. Flow past a square cylinder undergoes a sequence of transitions from a steady pattern up to a Reynolds number of 40 to a chaotic one around a Reynolds number of 600. The transition to chaos is manifested through a quasi-periodic route that includes the frequency-locking phenomenon. The quasi-periodicity is seen to set in with two or more Hopf bifurcations. The transition to chaos in the wake of a bluff object is related to the three-dimensionality of the flow. In a 2D simulation, this appears in the form of new harmonics in the velocity traces. The quasi-periodic route to chaos has been established through different characterization tools, such as the spectra, autocorrelation function, time-delay reconstruction, and the Poincaré section. Chaotic behavior is quantified through the calculation of Lyapunov exponent and fractal dimension.     

Wave Generation in Open Channels by Vortex Shedding from Channel Obstructions

Transverse surface waves were produced in a rectangular open channel in the region where the otherwise steady, uniform, flow passed through a cluster of vertical circular cylinders. The cylinders could represent either naturally occurring obstacles such as vegetation or man-made structures such as a group of piles driven into the bed of a river. The waves were produced from the periodic forces created by the vortex shedding from the cylinders. These forces generated and then amplified transverse waves in the channel. In some experiments the waves had amplitudes of 35% of the mean flow depth. These resonance-generated waves produce a seiching that can occur in hydraulic models as well as prototype systems. Both laboratory experiments and a theory-based analysis were used to determine the relationship between the amplitude of the vortex-generated wave, average velocity of the approach flow, viscosity of the fluid, width of the rectangular channel, depth of flow, cylinder diameter, and cylinder placement configuration.     

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.     

Turbulent flow field over fluvial obstacle marks generated in a laboratory flume

The study is aimed at investigating the mean flow and turbulence characteristics in scour geometry developed near a circular cylinder of length 10cm placed over the sand bed transverse to the flow. The obstacle placed on a sand bed, on the way of a unidirectional flow, develops a crescent-shaped scour mark on the bed. The scour is caused by generation of vortex developed on the upstream side of the obstacle. Sand grains eroded by this vortex, are deposited on the downstream side of the obstacle as wakes. The turbulent flow field within the scour mark was measured in a laboratory flume using an Acoustic Doppler Velocimeter (ADV). The scour marks named as current crescents preserved in geological record are traditionally used as indicators of palaeocurrent direction. The distribution of mean velocity components, turbulent intensities and Reynolds stresses at different positions of the mark are presented. The experimental evidence also shows that the geometric characteristics of the scour mark (width) depend primarily on the cylinder aspect ratio, cylinder Reynolds number and sediment Froude number.     

Flow around Cylinders in Open Channels

This paper presents the results of an experimental study of flow around cylindrical objects in an open channel. Cylindrical objects of equal diameter and four heights were tested under similar flow conditions producing four different levels of submergence, including a surface piercing bridge-pier-like cylinder. Different flow elements and their locations were identified using a set of flow visualization tests. Observations made from the flow visualization tests were then verified by measurements of bed-shear stress and deflected flow velocity around the cylinders. Horse-shoe vortex systems were found to appear closer to the submerged cylinders compared to a surface piercing cylinder. The increase in dimensionless bed-shear stress is found to be inversely related to the level of submergence of the cylinders. Bed-shear stress results presented in this paper will be valuable for a qualitative understanding of the scour potential of flow around submerged cylinders. Mean velocity profiles in the deflected flow region were analyzed in terms of the theories of three-dimensional turbulent boundary layer. Submergence of a cylinder has been found to suppress alternate vortex shedding and produce stronger three-dimensional flows in the downstream wake. Perry and Joubert’s model was found to be sufficiently accurate to predict the deflected velocity magnitudes around submerged cylinders. Overall, the present study will provide valuable knowledge of hydraulics of flow around submerged structures (e.g., simple fish habitat structures).     

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.     

Effects of Bed Roughness on Flow around Bed-Mounted Cylinders in Open Channels

This paper presents the results of an experimental study of flow around cylindrical objects on a rough bed in an open channel. This is an extension of a previous study of flow around cylinders on a smooth bed. The purpose of this study is to explore the effects of bed roughness on the characteristics of the deflected flow around cylindrical objects and the resulting bed-shear stress distributions. Similar to the previous study cylindrical objects of equal diameter and four heights were tested under similar flow conditions producing four different levels of submergence. Bed shear stress and deflected flow velocities were measured by a thin yaw-type Preston probe after a set of flow visualization tests. Flow visualization tests showed that the horse-shoe vortex systems on the rough bed occupy a relatively greater width compared to the smooth bed. Unlike smooth bed observations, the flow separation point upstream of the cylinder was not dependent on the level of submergence as the separation points were found to appear within a short range of x = ?1D to ?1.2D. Bed shear stress has been found to increase significantly near the shoulder of the cylinders, and its ratio with respect to the approach bed-shear stress was twice as large compared to the smooth bed case. Mean velocity profiles were analyzed in terms of three-dimensional turbulent boundary layer theories. Bed roughness was found to oppose the effect of the lateral pressure gradient that causes skewing in the boundary layer. Perry and Joubert’s model has been found to be equally accurate on smooth and rough beds for predicting the deflected velocity magnitudes around cylinders. The present study will enhance the knowledge of hydraulics of flow around bed-mounted objects (e.g. fish-rocks) in natural streams.     

Influence of Inlet Shear on Structure of Wake behind a Square Cylinder

The force coefficients and the frequency of vortex shedding in the wake of a square cylinder exposed to a uniform shear flow and the flow structure around it were numerically investigated. The Reynolds number defined on the basis of cylinder width was in the range of 250–1,500. The shear parameter, namely the transverse velocity gradient, which is nondimensionalized using the obstacle width and the average incoming velocity, was varied between 0 and 0.2. Analyses were performed for a number of flow parameters using various combinations of Reynolds number and shear parameters. Results show that mean and root-mean-square values of drag coefficient initially decrease up to certain values of the shear rate and then increase with increase in shear parameter. The root-mean-square values of lift coefficient show a similar behavior. The Strouhal number decreases uniformly with increase in shear parameter. At higher shear rates, the von Kármán vortex street comprising alternating vortices breaks, and the far wake shows mainly clockwise vortices.     

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.     

Numerical Modeling of Local Scour below a Piggyback Pipeline in Currents

Local scour below a piggyback pipeline in steady currents is investigated numerically. A piggyback pipeline comprises two pipelines that are arranged in the so-called piggyback configuration with the small pipeline being located directly above the large pipeline. The Reynolds-averaged Navier–Stokes equations and the transport equation for suspended sediment concentration are solved using a finite element method. The bed scour profile is determined through solving sediment mass conservation equation. The numerical model is validated against experimental data available in literature on scour below a single pipeline. Computations are carried out for the diameter ratio [the small pipe diameter (d) to the larger one (D)] of 0.2 and the gap (G, between the two pipelines) to the large diameter ratio G/D ranging from 0.0 to 0.5. It is found that the flow and the scour profiles are influenced significantly by the gap ratio.     

Interaction between Rotating Elliptic Cylinder and Fixed Circular Cylinder

The general planar motion of an elliptic cylinder through an inviscid and incompressible fluid in the vicinity of a fixed circular cylinder is investigated analytically. The velocity potential is derived by using the successive-image method and the perturbation method, and it is used to determine the hydrodynamic interactions between them. In a relative coordinate system moving with the uniform flow, the kinetic energy of the fluid is expressed as a function of 15 generalized added masses due to the motion of these two cylinders. The generalized added masses are then employed to determine the translational and rotational motion of the elliptic cylinder based on the dynamic equations of motion that are obtained from Lagrange's equations of motion. Numerical results show that the initial configuration of the elliptic cylinder greatly affects its subsequent motions.     

Laboratory Measurements of Flow and Turbulence in Discontinuous Distributions of Ligulate Seagrass

Turbulent flow characteristics were investigated in laboratory flume studies of a ligulate plant canopy interrupted by a gap representing discontinuities observed in seagrass prairies. The reliability of velocity measurements obtained using an acoustic Doppler velocimeter within the canopy was shown using specifically designed experiments. In relatively fast flow (mean velocity 5.5?cm?s?1), the mean flow profile was logarithmic above the canopy, had an inflection point near its top, and uniformly low values within it. Within the gap, a recirculation cell formed. Reynolds stress maxima were approximately coincident with the mean flow inflection point. Quadrant analysis revealed an ejection-dominated upper layer, a sweep-dominated region around the top of the canopy and within the gap, and no dominant quadrant within the canopy. In slower flow (mean velocity 1.7?cm?s?1) the plants were quasiemergent and the flow fields more uniform. Sweeps similarly dominated the region near the top of the canopy and within the gap. In both flows, autocorrelation of longitudinal velocity fluctuations showed a Lagrangian time scale maximum at the downstream end of the gap.     

Experimental Investigation of Flow Past a Square Cylinder at an Angle of Incidence

Flow past a square cylinder placed at an angle to the incoming flow is experimentally investigated using particle image velocimetry, hot wire anemometry, and flow visualization. The Reynolds number based on cylinder size and the average incoming velocity is set equal to 410. Data for four cylinder orientations (θ = 0, 22.5, 30, and 45°) and two aspect ratios [AR = 16 and 28] are reported. Results are presented in terms of drag coefficient, Strouhal number, time averaged velocity, stream traces, turbulence intensity, power spectra, and vorticity field. In addition, flow visualization images in the near wake of the cylinder are discussed. The shape and size of the recirculation bubble downstream of the cylinder are strong functions of orientation. A minimum in drag coefficient and maximum in Strouhal number is observed at a cylinder orientation of 22.5°. The v-velocity profile and time-average stream traces show that the wake and the separation process are asymmetric at orientations of 22.5 and 30°. The corresponding power spectra show additional peaks related to secondary vortical structures that arise from nonlinear interaction between the Karman vortices. The flow visualization images show the streamwise separation distance between the alternating vortices to be a function of cylinder orientation. Further, the flow approaches three dimensionality early, i.e., closer to the cylinder surface for the 22.5° orientation. The drag coefficient decreases with an increase in aspect ratio, while the Strouhal number is seen to increase with aspect ratio. The turbulence intensity is higher for the large aspect ratio cylinder and the maximum turbulence intensity appears at an earlier streamwise location. The overall dependence of drag coefficient and Strouhal number on orientation is preserved for the two aspect ratios studied.     

Three-Dimensional and Depth-Averaged Large-Eddy Simulations of Some Shallow Water Flows

Three-dimensional (3D) and two-dimensional (2D) depth-averaged (DA) large-eddy simulations (LES) are presented for three different shallow-water flows involving large-scale horizontal structures: a mixing layer, the flow around a circular cylinder, and the flow in a groyne field. The results are compared with each other and also with experiments. In the 3D-LES, most of the energy-containing turbulent motions, including the larger subdepth-scale motions, are resolved, while in the 2D-DA-LES the effect of the 3D subdepth-scale turbulence is represented by a quadratic bottom-friction model and a simple eddy-viscosity model. In the case of the mixing layer, an additional stochastic backscatter model is necessary to account for the energy transfer from the subdepth-scale turbulence to the 2D structures in order to generate the latter. The 3D-LES results are generally in good agreement with the experiments, including the evolution of the horizontal structures. The much more economic 2D-DA-LES are somewhat less realistic in detail but also produce results that are generally of sufficient accuracy for practical purposes.     

Characteristics of Steady Horseshoe Vortex System near Junction of Square Cylinder and Base Plate

This paper presents an experimental investigation on the characteristics of a horseshoe vortex system near the juncture of a square cylinder and a horizontal base plate, using particle image velocimetry and flow visualization technique. Experiments were conducted for Reynolds numbers (based on the free stream velocity and the width of square cylinder) ranging from 2.0×102 to 6.0×103. The flow patterns are first classified into four major regimes: Steady horseshoe vortex system, periodic oscillation vortex system with small displacement, periodic breakaway vortex system, and irregular vortex system. The classifications can be demonstrated as a figure of Reynolds number versus the ratio of the height of square cylinder to undisturbed boundary layer thickness. The study then mainly focused on the characteristics of steady horseshoe vortex system (corresponding to Reynolds numbers ranging from 2.0×102 to 2.5×103). The nondimensional characteristics, including the horizontal and vertical distances from the primary vortex core to frontal face of the vertical square cylinder and bottom boundary of the base plate, respectively, the height of stagnation point at frontal face of the square cylinder, and the down-flow discharge as well as circulation of the primary vortex, all increase with increase of the ratio of the height of square cylinder to undisturbed boundary layer thickness. However, they all decrease with the increase of the aspect ratio (i.e., the height-to-width ratio) of the square cylinder. The study provides essential properties of a steady horseshoe vortex system and gives an insight for related engineering applications. It can be served as a basis for more complicated horseshoe vortex systems occurring at high Reynolds numbers.