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.     

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.     

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.     

Effect of Convergence on Nonlinear Flow in Porous Media

The behavior of flow through porous media has been the subject of study for a long time. The relationship relating friction factor and Reynolds number using the square root of intrinsic permeability as the characteristic length is examined for flow in porous media with converging boundaries. An experimental investigation of the effect of convergence of streamlines on the linear and nonlinear parameters for different radial flow lines in a converging permeameter for different ratios of radii of the test section is also studied. In the present case, crushed rocks of sizes 11.64 and 4.73 mm were used as media and water as fluid, to develop curves relating friction factor and Reynolds number for different radial flow lines with different ratios of radii of the test section of the permeameter.     

Effect of Transitions on Flow past a Square Cylinder at Low Reynolds Number

Numerical simulations have been performed for three-dimensional flow past a square cylinder. The cylinders are placed normal to the incoming uniform flow. The results are based on higher order spatial and temporal discretization. The computations are carried out for a range of Reynolds number (100-325). The flow is found to be two-dimensional at R = 160 while it becomes three-dimensional at R = 163.5. Both Mode-A and Mode-A* are observed to be quite prominent and distinct at R = 175 though they are present in a range of Reynolds number. The spanwise wavelength for Mode-A is higher than at R = 250 where finer-scale structures are observed called Mode-B. The decay rate for primary vortices in Mode-A* is the fastest and it is the lowest for Mode-B. The magnitude of secondary vortices of Mode-A* is quite high compared to Mode-A, but of comparable magnitude to Mode-B. The effect of transitions on the instantaneous flow and root mean square fluctuations are quite significant while the time-averaged flow does not show any noticeable variation.     

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.     

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.     

Investigation of Two- and Three-Dimensional Models of Transitional Flow Past a Square Cylinder

The present study is a comparison of two- and three-dimensional models of flow past a square cylinder at a Reynolds number of 250. The models are computational in nature. The governing equations have been solved by the Marker and Cell (MAC) method with higher order spatial and temporal discretization. Essential differences have been observed in the predictions of the two models. Results reveal that the rms values of the aerodynamic forces in the two-dimensional simulation are higher. These are related to higher stochastic fluctuations near the cylinder surface and a shorter spread of the fluctuating fields. The three-dimensional model shows a longer shear layer and the fluctuations are smaller. An interesting observation of the present study is that the fluctuations are the highest at the points of inflexion in the time-averaged velocity profile. The findings of the present study have been discussed with the help of physical reasoning along with the transport equations of velocity fluctuations.     

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.     

Validation of Forchheimer's Law for Flow through Porous Media with Converging Boundaries

Modifications to the Forchheimer equation, which describes the flow behavior through coarse porous media, to account for the convergence of streamlines are made and experimentally verified. The applicability of a resistance law relating friction factor and Reynolds number using the square root of intrinsic permeability as the characteristic length is examined for flow with converging boundaries, and theoretical curves similar to Moody diagram for pipe flow are developed. The effect of convergence of streamlines on the linear and nonlinear parameters is demonstrated.     

Turbulent Flow through Idealized Emergent Vegetation

This paper presents results of several large-eddy simulations (LES) of turbulent flow in an open channel through staggered arrays of rigid, emergent cylinders, which can be regarded as idealized vegetation. In this study, two cylinder Reynolds numbers, RD = 1,340 and RD = 500, and three vegetation densities are considered. The LES of the lowest density and at RD = 1,340 corresponds to a recently completed laboratory experiment, the data of which is used to validate the simulations. Fairly good agreement between calculated and measured first- and second-order statistics along measurement profiles is found, confirming the accuracy of the simulations. The high resolution of the simulations enables an explicit calculation of drag forces, decomposed into pressure and friction drag, that are exerted on the cylinders. The effect of the cylinder Reynolds number and the cylinder density on the drag and hence on the flow resistance is quantified and in agreement with previous experimental studies. Turbulence structures are visualized through instantaneous pressure fluctuations, isosurfaces of the Q-criterion and contours of vertical vorticity in horizontal planes. Analysis of velocity time signals and distributions of drag and lift forces over time reveals that flow and turbulence are more influenced by the vegetation density than by the cylinder Reynolds number.     

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.     

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.     

Revisited Analysis of Pressure Drop in Flow through Crushed Rocks

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

LES and RANS Studies of Oscillating Flows over Flat Plate

Oscillatory flows over a flat plate are studied by using Large Eddy Simulation (LES) and Reynolds-Average Navier-Stokes (RANS) methods. A dynamic subgrid scale (SGS) model is employed in LES, while the Saffman's turbulence model in RANS. The mean velocity profile, the turbulence intensity, and the wall shear stress are computed and compared with earlier experimental and numerical works. The results indicate that the flow behaviors are quite different during the accelerating and decelerating phases of the oscillating cycle. The transition from laminar to turbulent is also investigated as a function of the Reynolds number, R, which represents the square of the ratio of the oscillation amplitude at free stream to the thickness of the Stokes layer at the plate. The present results both from LES and RANS show that the transition occurs in the range of 5 × 104 < R < 5 × 105. The evolution of the flow structure in the Stokes layer during the transition from laminar to turbulent is clearly demonstrated from the numerical results. The friction coefficient of the amplitude of oscillatory surface shear stress varies as R?0.5 with a phase angle of 45° in laminar regime and transition to R?0.23 with a phase angle of about 10° in turbulence regime. These variations in the surface shear stress with the Reynolds number are in excellent agreement with the earlier experimental results of Kamphuis and the numerical results of Blondeaux. The excellent agreement between the LES and RANS demonstrated that Saffman's turbulence model, as originally intended by Saffman, is applicable for unsteady flows.     

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.     

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.     

Flow Heterogeneity over 3D Cluster Microform: Laboratory and Numerical Investigation

The present study examines the flow around a self-occurring cluster bed form and the use of general computation fluid dynamics methods for hydraulic and geophysical flow applications. This is accomplished through a comprehensive experimental/numerical investigation. In the laboratory, cluster bed forms are first formed from movable sediment, and laser Doppler velocimeter measurements of two-dimensional fluid velocity are then taken around a formed cluster. A three-dimensional (3D) Reynolds averaged Navier-Stokes simulation of the physical cluster and flow conditions is then conducted using near-wall, shear stress transport (SST) turbulence modeling with the inclusion of hydraulic roughness, ks (R = 31,150, ks/h = 0.1, ks+ = 274, i.e., in the fully rough regime). SST near-wall modeling is advantageous compared to the more widely used wall functions approach for flows with significant roughness and flow separation because the model equations can be integrated down to the wall. Therefore, SST near-wall modeling makes no a priori assumption that the law of the wall is valid throughout the wall region of the flow. Additionally, it has the ability to intrinsically handle boundary roughness through the boundary condition for turbulent specific dissipation at the wall, allowing for wall functions to be bypassed in accounting for roughness effects. The study shows that in the wall region surrounding the cluster, flow is 3D and quite complex, with different scales of embedded flow structures dominating the cluster wake and leading to flow heterogeneities in pressure and bed-shear stress. Results also indicate that near-wall modeling with SST compared favorably with the experimental flow data without tuning of model constants.     

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).