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.     

Fine-Scale Characterization of the Turbulent Shear Layer of an Instream Pebble Cluster

This study characterizes the shear layer and associated vortex shedding around an isolated submerged pebble cluster in a gravel-bed river. The approach combines flow visualization and high frequency three-dimensional velocity (acoustic Doppler velocimeter) measurements. Two vortex shedding modes in the wake of the cluster were identified: A small scale high frequency initial instability mode and a lower frequency mode that scales with cluster height. The lower frequency mode arose from the intermittent interaction and amalgamation of the small-scale instability vortices. Reynolds shear stresses, velocity spectra, and coherence functions indicated a dominance of longitudinal-vertical shedding vortices in the wake of the cluster. Simultaneous flow visualization was required to determine the nature and behavior of the shedding modes. Quadrant analysis revealed that Q2 and Q4 events contributed 80% of the local longitudinal-vertical component Reynolds shear stress, and demonstrated a dominance of ejection events in the wake of the cluster. Through flow visualization, the behavior of the shear layer was seen to vertically expand and contract with the passage of Q2 and Q4 events, respectively.     

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.     

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.     

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.     

Turbulence Structures in Flow over Two-Dimensional Dunes

This paper presents a large eddy simulation (LES) of turbulent open channel flow over two-dimensional periodic dunes. The Reynolds number R based on the bulk velocity U(bulk) and the maximum flow depth h, is approximately 25,000. The instantaneous flow field is investigated with special emphasis on the occurrence of coherent structures. Instantaneous vortices were visualized and it is shown that separated vortices are formed downstream of the dune crest due to Kelvin–Helmholtz instabilities. Near the point of reattachment the so-called kolk-boil vortex evolves in form of a hairpin vortex. Also present are previously separated vortices, which are convected along the stoss side of the downstream dune and elevated toward the water surface. The existence of near wall streaks which reform shortly after reattachment is also shown. The spacing between two low-speed streaks is very similar to that observed previously over smooth and rough walls. For validation, profiles of the time-averaged velocities, streamwise, and wall-normal turbulent intensities and the Reynolds shear stress calculated by the LES are presented and compared with available laser Doppler velocimetry measurements and overall good agreement is found.     

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.     

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.     

Coherent Structures in the Flow Field around a Circular Cylinder with Scour Hole

Large-eddy simulation (LES) and laboratory-flume visualizations were used to investigate coherent structures present in the flow field around a circular cylinder located in a scour hole. The bathymetry corresponds to equilibrium scour conditions and is fixed in LES. The flow parameters in the simulation correspond to the experimental conditions in which the approach flow is fully turbulent. Detailed consideration is given to the interaction of the horseshoe vortex (HV) system within the scour hole with the detached shear layers formed from the cylinder, and the near bed turbulence. It is found that the overall structure of the HV system varies considerably in space and time, though a large, relatively stable, primary necklace vortex is present at practically all times inside the scour hole. The simulation captures the presence of bimodal chaotic oscillations inside the HV system, as well as the sharp increase in the resolved turbulent kinetic energy levels and pressure fluctuations reported in prior experimental investigations. High levels of the mean bed shear stress are observed beneath the primary necklace vortex, especially over the region where the bimodal oscillations are strong, as well as beneath the small junction vortex at the base of the cylinder. It is also found that the detachment and advection of patches of vorticity from the downstream part of the legs of the necklace vortices can induce large instantaneous bed shear stress values. When the critical bed shear stress value for sediment entrainment on a flat surface is adjusted for bed slope effects, the LES simulation correctly predicts that the distribution of the mean bed shear stress is consistent with equilibrium scour conditions.     

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).     

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.     

Vortex Flow Pattern in a Slab Continuous Casting Mold with Argon Gas Injection

An Eulerian-Eulerian two-fluid model was developed to study the vortex flow inside a slab continuous casting mold with argon gas injection. Interracial momentum transfer that accommodated various interracial forces including drag force, lift force, virtual mass force, and turbulent dispersion force was considered. Predicted results agree well vaith experimental measurements of the water model in two-phase flow pattern and vortex flow structures. Three typical flow patterns with different argon steel ratios （ASRs） have been obtained： ＂double roll＂, ＂three roll＂, and ＂single roll＂. The flow pattern inside the mold alternates among the three types or it may attain some intermedi ate condition. With increasing ASR, the positions of vortices move from the submerged entry nozzle to the narrow face of the mold, and the sizes of vortices are reduced gradually. The rotating directions of vortices are all from high velocity area to low velocity area. Two mechanisms of vortex formation on the top surface have been suggested, i. e. , congruous shear flow and incongruous shear flow.     

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.     

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.     

Large-Eddy Simulation of High Reynolds Number Turbulent Flow Past a Square Cylinder

Flow past a square cylinder at a Reynolds number of 21,400 has been studied numerically using the large-eddy simulation technique. A dynamic subgrid-scale stress model has been used for the small scales of turbulence. The time- and span-averaged axial and transverse velocities in the downstream of the cylinder are in good agreement with the experimental results. The distribution of turbulent normal and shear stresses is also well predicted. The coherent and incoherent components of turbulent fluctuations at some specified phases have been separated and their relative magnitudes downstream of the cylinder have been compared. The comparison shows more coherence in the near wake than the far wake, while the coherent and incoherent components are of comparable magnitude in the far wake. The far wake shows irregular phase-averaged structures.     

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).     

Investigation of Twin Vortices near the Interface in Turbulent Compound Open-Channel Flows Using DNS Data

The direct numerical simulation of turbulent flows in a compound open channel is described. Mean flows and turbulence structures are provided, and are compared with numerical and measured data available in the literature. The simulated results show that twin vortices are generated near the interface of the main channel and the floodplain and that their maximum magnitude is about 5% of the bulk streamwise velocity. Near the interface, the simulated wall shear stress reaches a maximum, contrary to experimental data. A quadrant analysis shows that both sweeps and ejections become the main contributor to the production of Reynolds shear stresses near the interface. Through the conditional quadrant analysis, it is demonstrated how the directional tendency of dominant coherent structures determines the production of Reynolds shear stress and the pattern of twin vortices near the interface. In addition, the time-dependent characteristics of three-dimensional vortical structures in a compound open-channel flow were investigated using direct numerical simulation (DNS) data.     

Analysis of Velocity Lag in Sediment-Laden Open Channel Flows

Laboratory experiments have recently confirmed that the streamwise particle velocity is largely less than that of the fluid in sediment-laden flows. This velocity lag is investigated analytically in the present study based on the drag force exerting on a particle in the presence of other neighbors. The normalized drag force or the hindrance coefficient is found generally dependent on the particle concentration, particle Reynolds number, and specific gravity. The velocity lag is then derived by relating the hindrance coefficient to the shear stress distribution for uniform sediment-laden open channel flows. The analysis shows that the profile of the velocity lag, when normalized by the shear velocity, is associated with the shear Reynolds number, dimensionless particle diameter, and specific gravity. For the dilute condition, the velocity lag distribution varies only with the shear Reynolds number, and the lag can be ignored if the shear Reynolds number is less than unity. The theoretical predictions are comparable to limited experimental results.     

Pressure Distribution in Cavitating Circular Cylinder Wakes

The present study examines the effect of cavitation on the base pressure coefficient of a circular cylinder. The tests are conducted at near-constant Reynolds numbers (≈105) and a wide range of cavitation numbers. The degree of cavitation varies from noncavitating flow, to inception, to near-choking conditions. Pressure measurements along the wake axis are also obtained at various cavitation numbers. The similarity of the wake axis pressure distribution is investigated.