FLOW PAST TWO CYLINDERS IN TANDEM: INSTANTANEOUS AND AVERAGED FLOW STRUCTURE

A technique of high-image-density particle image velocimetry is employed to characterize the instantaneous and averaged patterns of velocity, vorticity and Reynolds stress due to flow past two cylinders in tandem. These features of the flow patterns are characterized in the gap region as a function of the distance between the cylinders. In turn, they are related to the patterns in the near-wake of the two-cylinder system. Along the gap between the cylinders, small-scale concentrations of vorticity are formed in the separated shear layers. These concentrations buffet the surface boundary layer on the downstream cylinder, and thereby influence the eventual shedding of large-scale vortices. Within the gap, the instantaneous structure of the recirculation zones can exhibit both symmetrical and asymmetrical patterns. In the near-wake of the downstream cylinder, the form of the vortex shedding, as well as the averaged patterns of the flow structure, are substantially altered, relative to the case of a single cylinder. The width of the near-wake, as represented by averaged patterns of vorticity, is substantially narrower and the magnitudes of the peak Reynolds stress are significantly attenuated. On the other hand, if the gap region is sufficiently large such that Kármán-like vortices form between the cylinders, the near-wake of the downstream cylinder shows distinctive patterns, and both the wake width and the magnitude of the Reynolds stresses become larger, relative to those at smaller gap width.     

Experimental measurement of flow past cavities of different shapes

Experiments are carried out in order to investigate the flow structure past a rectangular, triangular and semi-circular cavity of length-to-depth ratio of 2:1 using the Particle Image Velocimetry (PIV) technique. The experiments are performed in a large scale water channel with three different upstream velocities resulting in Reynolds numbers of 1230, 1460 and 1700, based on inflow momentum thickness, for each cavity type. Contours of constant averaged streamwise and transverse components of velocity, contours of constant averaged vorticity, Reynolds stress and streamline plots for each cavity type for the aforementioned three Reynolds numbers are presented. In addition, streamwise velocity, Reynolds stress and turbulence intensity values are compared for all cavity types. Effect of cavity shape on flow structure within the cavity is discussed in detail. Moreover, spectrum of instantaneous streamwise velocity fluctuations in shear layer near the downstream of the leading corner and the upstream of the trailing corner of the cavities are obtained and it was found that no organized oscillations are present in the flow; rectangular and triangular cavities have the largest amplitudes while semi-circular cavity has the smallest. Calculated turbulence intensities also reveal that the maximum turbulence intensities occur at cavity lid in the centerline section and rectangular and triangular cavities have larger turbulence intensity compared to semi-circular cavity.     

NEAR-WAKE FLOW STRUCTURE OF A CYLINDER WITH A HELICAL SURFACE PERTURBATION

The near-wake of a circular cylinder having a helical wire pattern about its surface is characterized using a technique of high-image-density velocimetry. Patterns of vorticity in three orthogonal planes show substantial influence of a wire having a diameter an order of magnitude smaller than the cylinder diameter. The distinctive patterns of vorticity in these three planes are associated with lack of formation of large-scale Kármán-like clusters of vorticity (ω_z) in the near-wake region of the cylinder. The instantaneous structure of the separating spanwise vorticity (ω_z) layers on either side of the cylinder involve small-scale concentrations of vorticity analogous to the well-known Kelvin–Helmholtz vortices from a smooth cylinder. Moreover, a dual vorticity layer, i.e., two adjacent layers of like vorticity (ω_z), can form from one side of the cylinder. Along the span of the cylinder, distributions of instantaneous velocity and transverse vorticity (ω_y) show a spatially periodic sequence of wake-like patterns, each of which has features in common with the very near-wake of a two-dimensional bluff body, including a large velocity defect bounded by vorticity layers with embedded small-scale vorticity concentrations. In the cross-flow plane of the wake, patterns of streamwise vorticity (ω_x) show small-scale, counter-rotating pairs of vorticity concentrations (ω_x) emanating from the inclined helical perturbation, rather than isolated concentrations of vorticity of like sign, which would indicate single streamwise vortices. All of the aforementioned patterns of small-scale vorticity concentrations are scaled according to the local wake width/local pitch of the helical wire pattern in the respective plane of observation.     

Time-resolved PIV measurements of the interaction of polystyrene beads with near-wall-coherent structures in a turbulent channel flow

Time-resolved PIV measurements were performed in a dilute particle-laden flow tracking near-neutrally buoyant polystyrene beads and the velocity field of a near wall turbulent boundary layer. Data were taken in a vertical light sheet aligned in the streamwise direction at the center of a horizontal, closed loop, transparent square water channel facility. In addition, low speed measurements were performed characterizing the effects of the dispersed phase on mean and turbulence flow quantities. Reynolds shear stress slightly differed from clear water conditions whereas fluid mean and rms values were not affected. A case study for several beads revealed a clear relation between their movement and near-wall coherent structures. Several structures having 2D vorticity signatures of near-wall hairpin vortices and hairpin packets, directly affected bead movement. A statistical analysis showed that the mean streamwise velocity of ascending beads lagged behind the mean fluid velocity and bead rms values were higher than fluid ones. Particle Reynolds numbers based on the magnitude of the instantaneous relative velocity vector peaked near the wall; values not exceeding 100, too low for vortex shedding to occur. Quadrant analysis showed a clear preference for ascending beads to reside in ejections while for descending beads the preference for sweeps was less.     

Construction of three-dimensional images of flow structure via particle tracking techniques

Construction of three-dimensional images of flow structure, based on the quantitative velocity field, is assessed for cases where experimental data are obtained using particle tracking technique. The experimental data are in the form of contiguous planes of particle images. These contiguous data planes are assumed to correspond to successive spatial realizations in steady flow, or to phase-referenced realizations in an unsteady flow.Given the particle images on contiguous planes, the in-plane velocity fields are determined. Then, the out-of-plane velocity field is obtained using a spectral interpolation method. Application of this method allows, in principle, construction of the three-dimensional vorticity field and the streamline patterns.A critical assessment is made of the uncertainties arising from the in-plane interpolation of the velocity field obtained from particle tracking and the evaluation of the out-of-plane velocity component. The consequences of such uncertainties on the reconstructed vorticity distributions and streamline patterns are addressed for two basic types of vortex flows: a columnar vortex, for which the streamlines are not closed and are spatially periodic in the streamwise direction; and for a spherical (Hill's) vortex exhibiting closed streamline patterns, and no spatial periodicity.     

Structure of the turbulent boundary layer over a rod-roughened wall

Turbulent coherent structures near a rod-roughened wall are scrutinized by analyzing instantaneous flow fields obtained from direct numerical simulations (DNSs) of a turbulent boundary layer (TBL). The roughness elements used are periodically arranged two-dimensional spanwise rods, and the roughness height is k/δ = 0.05 where δ is the boundary layer thickness. The Reynolds number based on the momentum thickness is varied in the range Re_θ = 300–1400. The effect of surface roughness is examined by comparing the characteristics of the TBLs over smooth and rough walls. Although introduction of roughness elements onto the smooth wall affects the Reynolds stresses throughout the entire boundary layer when scaled by the friction velocity, the roughness has little effect on the vorticity fluctuations in the outer layer. Pressure-strain tensors of the transport equation for the Reynolds stresses and quadrant analysis disclose that the redistribution of turbulent kinetic energy of the rough wall is similar to that of the smooth wall, and that the roughness has little effect on the relative contributions of ejection and sweep motions in the outer layer. To elucidate the modifications of the near-wall vortical structure induced by surface roughness, we used two-point correlations, joint weighted probability density function, and linear stochastic estimation. Finally, we demonstrate the existence of coherent structures in the instantaneous flow field over the rod-roughened surface.     

The Tilting Mechanism of a Longitudinal Vortical Structure in a Homogeneous Shear Flow with and Without Spanwise Rotation

A longitudinal vortical structure is typically observed in near-wall turbulence. This vortical structure is elongated in the streamwise direction, though it is also tilted in the spanwise direction. The sense of this spanwise tilting is determined by the sign of the streamwise vorticity associated with the vortex, and longitudinal vortical structures with a different streamwise vorticity become asymmetric (mirror symmetric). The tilting must be due to the combined effects of the non-linear terms and mean spanwise vorticity associated with the mean shear. However, the detailed mechanism of the tilting is not well known. To study the tilting in detail, we performed direct numerical simulations of a homogeneous shear flow where the longitudinal vortical structures similar to those in the near-wall region are observed. In particular, the effects of spanwise system rotation as well as the Reynolds number on the vortical structure are studied. As a result, we found that spanwise system rotation has more marked effects on the vortical structure than the Reynolds number. When the system rotation is imposed in the same direction as the mean spanwise vorticity, the tilting is enhanced, while the system rotation of the opposite direction attenuates it. We also found that when the longitudinal vortical structure is tilted in the spanwise direction, it is sandwiched between the streamwise vorticity of the opposite sign. The cyclonic rotation enhances the streamwise vorticity of the opposite sign, though the longitudinal vortical structure at the center is attenuated. In the anticyclonic case, the streamwise vorticity of the opposite sign almost disappears and the longitudinal vortical structure is isolated from the surrounding flow.     

Imaging of the self-excited oscillation of flow past a cavity during generation of a flow tone

Flow through a pipeline-cavity system can give rise to pronounced flow tones, even when the inflow boundary layer is fully turbulent. Such tones arise from the coupling between the inherent instability of the shear flow past the cavity and a resonant acoustic mode of the system. A technique of high-image-density particle image velocimetry is employed in conjunction with a special test section, which allows effective laser illumination and digital acquisition of patterns of particle images. This approach leads to patterns of velocity, vorticity, streamline topology and hydrodynamic contributions to the acoustic power integral. Comparison of global, instantaneous images with time- and phase-averaged representations provides insight into the small-scale and large-scale concentrations of vorticity, and their consequences on the topological features of streamline patterns, as well as the streamwise and transverse projections of the hydrodynamic contribution to the acoustic power integral. Furthermore, these global approaches allow the definition of effective wavelengths and phase speeds of the vortical structures, which can lead to guidance for physical models of the dimensionless frequency of oscillation.     

Large Eddy Simulation of boundary layer transition over an isolated ramp-type micro roughness element

Boundary layer transition over an isolated surface roughness element is investigated by means of numerical simulation. Large Eddy Simulation (LES) flow-modeling approach is employed to study flow characteristics and transition phenomenon past a roughness element immersed within an incoming developing boundary layer, at a height-based Reynolds number of 1170. LES numerical results are compared to experimental data from literature showing the time-averaged velocity distribution, the velocity fluctuation statistics and the instantaneous flow topology.Despite slight difference in the intensity of streamwise velocity fluctuations, the present LES results and experimental data show very good agreement. The mean flow visualization shows streamwise counter-rotating vortices pairs formation downstream of the obstacle. The primary pair induces an upwash motion and a momentum deficit that creates a Kelvin-Helmholtz type flow instability. The instantaneous flow topology reveals the formation of coherent K-H vortices downstream that produce turbulent fluctuations in the wake of the roughness element. These vortices are streched and lifted up when moving downstream. The velocity fluctuations results show that the onset of the turbulence is dominated by the energy transfer of large-scale vortices.     

Modification of the large-scale features of high Reynolds number wall turbulence by passive surface obtrusions

A high Reynolds number boundary-layer wind-tunnel facility at New Mexico State University was fitted with a regularly distributed braille surface. The surface was such that braille dots were closely packed in the streamwise direction and sparsely spaced in the spanwise direction. This novel surface had an unexpected influence on the flow: the energy of the very large-scale features of wall turbulence (approximately six-times the boundary-layer thickness in length) became significantly attenuated, even into the logarithmic region. To the author’s knowledge, this is the first experimental study to report a modification of ‘superstructures’ in a rough-wall turbulent boundary layer. The result gives rise to the possibility that flow control through very small, passive surface roughness may be possible at high Reynolds numbers, without the prohibitive drag penalty anticipated heretofore. Evidence was also found for the uninhibited existence of the near-wall cycle, well known to smooth-wall-turbulence researchers, in the spanwise space between roughness elements.     

An experimental investigation into the effect of vortex generators on the near-wake flow of a circular cylinder

The effect of the streamwise vortex generators on the near-wake flow structure of a circular cylinder was experimentally investigated. Digital particle image velocimetry (DPIV) measurements were performed in a large circulating water tunnel facility at a Reynolds number of 41,300 where the flow around a bare cylinder was expected to be at the sub-critical flow state. In order to capture various flow properties and to provide a detailed wake flow topology, the DPIV images were analysed with three different but complementary flow field decomposition techniques which are Reynolds averaging, phase averaging and proper orthogonal decomposition (POD). The effect of the vortex generators was clearly demonstrated both in qualitative and in quantitative manner. Various topological features such as vorticity and stress distribution of the flow fields as well as many other key flow characteristics including the length scales and the Strouhal number were discussed in the study. To the best of the authors’ knowledge, the study presents the first DPIV visualization of the near-wake flow of a circular cylinder fitted with the vortex generators in the open literature.     

PIV measurements of the near-wake behind a sinusoidal cylinder

The three-dimensional near-wake structures behind a sinusoidal cylinder have been investigated using a particle image velocimetry (PIV) measurement technique at Re=3,000. The mean velocity fields and spatial distributions of ensemble-averaged turbulence statistics for flows around the sinusoidal and corresponding smooth cylinders were compared. The near-wake behind the sinusoidal cylinder exhibited pronounced spanwise periodic variations in the flow structure. Well-organized streamwise vortices with alternating positive and negative vorticity were observed along the span of the sinusoidal cylinder. They suppress the formation of the large-scale spanwise vortices and decrease the overall turbulent kinetic energy in the near-wake of the sinusoidal cylinder. The sinusoidal surface geometry significantly modifies the near-wake structure and strongly controls the three-dimensional vortices formed in the near-wake.     

Structure of wake of a sharp-edged bluff body in a shallow channel flow

The flow field downstream of a bluff body in a typical open channel flow was explored by two-dimensional particle image velocimetry. Measurements are obtained in horizontal planes at the near-bed, mid-depth and near-surface locations downstream of the body up to a streamwise distance of 10D, where D is the width of the body. The dimensionless streamwise defect velocity profile of the wake flow matches well with the data of a previous investigation and does not reflect any dependency on the distance from the bed. However, the nature of development of the recirculation region is found to be different at the three vertical locations. The time-averaged streamline pattern indicates the existence of a unique nodal pattern close to the bed. The variation of the half-width is also found to be affected by the presence of the bed and the free surface. The bed friction arrests the transverse growth of the shear layer, and the free-surface helps to redistribute the turbulent kinetic energy in the streamwise and transverse directions. Swirling strength analysis is carried out to compare the behavior and statistics of the vortex population in the vertical direction. The prevailing magnitude of the swirling strength is found to be different at the three vertical locations. Bed friction assists to dissipate vorticity rapidly, and therefore reduces the probability of appearance of strong vortices close to the bed.     

Aerodynamic forces and three-dimensional flow structures in the mean wake of a surface-mounted finite-height square prism

Different flow models have been proposed for the flow around surface-mounted finite-height square prisms, but there is still a lack of consensus about the origin and connection of the streamwise tip vortices with the other elements of the wake. This numerical study was performed to address this gap, in addition to clarifying the relationship of the near-wake structures with the far wake and the near-wall flow, which is associated with the fluid forces. A large-eddy simulation approach was adopted to solve the flow around a surface-mounted finite-height square prism with an aspect ratio of AR = 3 and a Reynolds number Re = 500. The mean drag and normal forces and the bending moment for the prism were quantitatively compared in terms of skin-friction and pressure contributions, and related to the near-wall flow. Both three-dimensional visualizations and planar projections of the time-averaged flow field were used to identify, qualitatively, the main structures of the wake, including the horseshoe vortex, corner vortices and regions of high streamwise vorticity in the upper part of the wake. These features showed the same qualitative behavior as reported in high Reynolds number studies. It was found that some regions of high streamwise vorticity magnitude, like the tip vortices, are associated with the three-dimensional bending of the flow, and the tip vortices did not continuously extend to the free end of the prism. The three-dimensional flow analysis, which integrated different observations of the flow field around surface-mounted finite-height square prisms, also revealed that the mean near-wake structure is composed of two sections of different origin and location of dominance.     

Measurements in the vicinity of a stagnation point

This paper presents measurements of a plane jet impinging onto a normal flat plate placed up to five jet widths from the jet outlet. The small spacing ensured that the stagnation streamline remained in the potential core of the jet. The plate shear stress distribution compared well to that from an analytical solution for the laminar development of the plate boundary layer whose external velocity was determined from the measured pressure. By comparing the shear stress measured under the present low level of free stream turbulence (0.35%) at the jet exit with that of Tu and Wood [Exp. Thermal Fluid Sci. 13 (1996) 364–373] made at about 4%, it is concluded that the turbulence level at the nozzle exit has only a second-order influence on the surface shear stress around the stagnation point. Some spanwise non-uniformity was observed in the plate shear stress, but this was confined largely to the transition region. The mean velocity, Reynolds stresses, and fluctuating pressure were measured along the stagnation streamline using a fast-response pressure probe. A significant increase in the streamwise normal stress and the mean square of the pressure fluctuations occurred before they were eventually attenuated by the plate. This increase occurred in the region where the streamwise velocity was decreasing close to the plate causing extra energy production through the normal stresses. Spectra of the velocity and pressure fluctuations showed that the increase in level was mainly due to the low frequency motion, whereas the subsequent decrease occurred at higher frequencies.     

Cinematographic system for high-image-density particle image velocimetry

A cinematographic system, which integrates the concepts of high-image-density PIV, laser scanning, and framing photography, allows temporal resolution of the order of one percent of the time scale of the largest vortical structures in the turbulent wake from a cylinder at a Reynolds number of 10,000. With this resolution in time, it is possible to track, in a continuous fashion, the patterns of streamwise vorticity in the near-wake. The authors are pleased to acknowledge the financial support of the National Science Foundation, the Office of Naval Research, and the Air Force Office of Scientific Research.     

Quantitative interpretation of vortices from a cylinder oscillating in quiescent fluid

 The instantaneous, quantitative patterns of vortices arising from sinusoidal oscillation of a cylinder in quiescent fluid are experimentally characterized for the first time using high-image-density particle image velocimetry. The near-wake does not indicate a separated layer of distributed vorticity leading to a single, large-scale vortex. Rather, for sufficiently high Reynolds number, a sequence of small-scale vorticity concentrations is formed. Agglomeration of only a fraction of the adjacent concentrations forms a larger-scale vortex. Simultaneously, vorticity concentrations of opposite sense are formed along the base (rear) of the cylinder. Streamline patterns typically indicate, however, only the larger-scale vortex; it has a circulation smaller than the total circulation of all vorticity concentrations that are not revealed by the streamlines. These observations are interpreted in the context of the effective resolution of the flow images. Received: 27 October 1995 / Accepted: 27 August 1996     

Reynolds number dependence of Reynolds and dispersive stresses in turbulent channel flow past irregular near-Gaussian roughness

Direct numerical simulations of fully-developed turbulent channel flow with irregular rough walls have been performed at four friction Reynolds numbers, namely, 180, 240, 360 and 540, yielding data in both the transitionally- and fully-rough regime. The same roughness topography, which was synthesised with an irregular, isotropic and near-Gaussian height distribution, is used in each simulation. Particular attention is directed towards the wall-normal variation of flow statistics in the near-roughness region and the fluid-occupied region beneath the crests, i.e. within the roughness canopy itself. The goal of this study is twofold. (i) Provide a detailed account of first- and second-order double-averaged velocity statistics (including profiles of mean velocity, dispersive stresses, Reynolds stresses, shear stress gradients and an analysis of the mean force balance) with the overall aim of understanding the relative importance of “form-induced” and “turbulence-induced” quantities as a function of the friction Reynolds number. (ii) Investigate the possibility of predicting the levels of streamwise dispersive stress using a phenomenological closure model. Such an approach has been applied successfully in the context of idealised vegetation canopies (Moltchanov & Shavit, 2013, Water Resour. Res., vol. 49, pp. 8222-8233) and is extended here, for the first time, to an irregular rough surface. Overall, the results reveal that strong levels of dispersive stress occur beneath the roughness crests and, for the highest friction Reynolds number considered in this study, show that the magnitude (and gradient) of these “form-induced” stresses exceed their Reynolds stress counterparts. In addition, this study emphasises that the dominant source of spatial heterogeneity within the irregular roughness canopy are “wake-occupied” regions and that a suitable parameterisation of the wake-occupied area is required to obtain an accurate prediction of streamwise dispersive stress.     

Reynolds stress modelling of rectangular open‐channel flow

A Reynolds stress model for the numerical simulation of uniform 3D turbulent open‐channel flows is described. The finite volume method is used for the numerical solution of the flow equations and transport equations of the Reynolds stress components. The overall solution strategy is the SIMPLER algorithm, and the power‐law scheme is used to discretize the convection and diffusion terms in the governing equations. The developed model is applied to a flow at a Reynolds number of 77000 in a rectangular channel with a width to depth ratio of 2. The simulated mean flow and turbulence structures are compared with measured and computed data from the literature. The computed flow vectors in the plane normal to the streamwise direction show a small vortex, called inner secondary currents, located at the juncture of the sidewall and the free surface as well as the free surface and bottom vortices. This small vortex causes a significant increase in the wall shear stress in the vicinity of the free surface. A budget analysis of the streamwise vorticity is carried out. It is found that both production terms by anisotropy of Reynolds normal stress and by Reynolds shear stress contribute to the generation of secondary currents. Copyright © 2006 John Wiley & Sons, Ltd.     

Adverse pressure gradient turbulent flows over rough walls

An experimental study of a fully developed turbulent channel flow and an adverse pressure gradient (APG) turbulent channel flow over smooth and rough walls has been performed using a particle image velocimetry (PIV) technique. The rough walls comprised two-dimensional square ribs of nominal height, k = 3 mm and pitch, p = 2k, 4k and 8k. It was observed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. Similarly, rib roughness significantly increased the level of turbulence production, Reynolds stresses and wall-normal transport of turbulence kinetic energy and Reynolds shear stress well beyond the roughness sublayer. On the contrary, the distributions of the eddy viscosity, mixing length and streamwise transport of turbulence kinetic energy and Reynolds shear stress were reduced by wall roughness, especially in the outer layer. Adverse pressure gradient produced a further reduction in the mean velocity (in comparison to the results obtained in the parallel section) but increased the wall-normal extent across which the mean flow above the ribs is spatially inhomogeneous in the streamwise direction. APG also reinforced wall roughness in augmenting the equivalent sand grain roughness height. The combination of wall roughness and APG significantly increased turbulence production and Reynolds stresses except in the immediate vicinity of the rough walls. The transport velocities of the turbulence kinetic energy and Reynolds shear stress were also augmented by APG across most part of the rough-wall boundary layer. Further, APG enhanced the distributions of the eddy viscosity across most of the boundary layer but reduced the mixing length outside the roughness sublayer.