Flow around four cylinders arranged in a square configuration

This paper presents an experimental study of the flow around four circular cylinders arranged in a square configuration. The Reynolds number was fixed at Re=8000, the pitch-to-diameter ratio between adjacent cylinders was varied from P/D=2 to 5 and the incidence angle was changed from α=0° (in-line square configuration) to 45° (diamond configuration) at an interval of 7.5°. The flow field was measured using digital Particle Image Velocimetry (PIV) to examine the vortex shedding characteristics of the cylinders, together with direct measurement of fluid dynamic forces (lift and drag) on each cylinder using a piezoelectric load cell. Depending on the pitch ratio, the flow could be broadly classified as shielding regime (P/D≤2), shear layer reattachment regime (2.5≤P/D≤3.5) and vortex impinging regime (P/D≥4). However, this classification is valid only in the case that the cylinder array is arranged nearly in-line with the free stream (α≈0°), because the flow is also sensitive to α. As α increases from 0° to 45°, each cylinder experiences a transition of vortex shedding pattern from a one-frequency mode to a two-frequency mode. The flow interference among the cylinders is complicated, which could be non-synchronous, quasi-periodic or synchronized with a definite phase relationship with other cylinders depending on the combined value of α and P/D. The change in vortex pattern is also reflected by some integral parameters of the flow such as force coefficients, power spectra and Strouhal numbers.     

TANDEM CYLINDERS IN IMPULSIVELY STARTED FLOW

The impulsively started flow field for circular cylinders of equal diameter arranged in tandem was investigated using flow visualization and particle image velocimetry (PIV), over a longitudinal pitch ratio range ofL /D=1·0–3·0, and for Reynolds numbers from Re=1200–3800. The PIV technique was used to obtain a time history of the instantaneous in-plane vorticity field from the moment of impulsive start, from which the spatial and temporal development of the flow was studied. Measurements of vortex strength and vortex position relative to the cylinders were obtained from these data. Three types of fluid behaviour were identified based on L/D: single bluff-body behaviour when the cylinders are in contact, constrained streamwise growth and lateral expansion of the gap recirculation zones at small and intermediate L/D, and independent formation of recirculation zones similar to a single impulsively started circular cylinder at larger L/D.     

Vortex shedding from two finite circular cylinders in a staggered configuration

Wind tunnel experiments were conducted to measure the vortex shedding frequencies for two circular cylinders of finite height arranged in a staggered configuration. The cylinders were mounted normal to a ground plane and were partially immersed in a flat-plate turbulent boundary layer. The Reynolds number based on the cylinder diameter was Re_D=2.4×10⁴, the cylinder aspect ratio was AR=9, the boundary layer thickness relative to the cylinder height was δ/H=0.4, the centre-to-centre pitch ratio was varied from P/D=1.125 to 5, and the incidence angle was incremented in small steps from α=0° to 90°. The Strouhal numbers were obtained behind the upstream and downstream cylinders using hot-wire anemometry. From the behaviour of the Strouhal number data obtained at the mid-height position, the staggered configuration could be broadly classified by the pitch ratio as closely spaced (P/D<1.5), moderately spaced (1.5?P/D?3), or widely spaced (P/D>3). The closely spaced staggered finite cylinders were characterized by the same Strouhal number measured behind both cylinders, an indication of single bluff-body behaviour. Moderately spaced staggered finite cylinders were characterized by two Strouhal numbers at most incidence angles. Widely spaced staggered cylinders were characterized by a single Strouhal number for both cylinders, indicative of synchronized vortex shedding from both cylinders at all incidence angles. For selected staggered configurations representative of closely spaced, moderately spaced, or widely spaced behaviour, Strouhal number measurements were also made along the vertical lengths of the cylinders, from the ground plane to the free end. The power spectra showed that for certain cylinder arrangements, because of the influences of the cylinder–wall junction and free-end flow fields, the Strouhal numbers and flow patterns change along the cylinder.     

Numerical and experimental investigation of flow-acoustic resonance of side-by-side cylinders in a duct

The phenomenon of flow-excited acoustic resonance is a design concern in many engineering applications, especially when wakes of bluff bodies are encountered in ducts, piping systems, heat exchangers, and other confined systems. In this paper, the case of self-excited acoustic resonance of two side-by-side cylinders in a duct with cross-flow is investigated both numerically and experimentally for a single spacing ratio of T/D=2.5, where D is the diameter of the cylinders and T is the centre-to-centre distance between them. The numerical investigation is performed using a finite-volume method at a Reynolds number of 3.0×10⁴ to simulate the unsteady flow field, which is then coupled with an imposed resonant sound field of the first acoustic cross-mode of the duct calculated through the use of Finite Element Analysis (FEA). The experimental investigation has been performed using phase-locked Particle Image Velocimetry (PIV) of the flow field during the occurrence of a self-excited acoustic resonance condition in the duct. The results of both methods reveal that the flow-excited acoustic resonance produces a strong oscillatory flow pattern in the cylinder wakes, with strong in-phase vortex shedding being synchronized by the acoustic resonance. The distribution and strength of the aeroacoustic sources and sinks within the flow field have been computed by means of Howe׳s theory of aerodynamic sound for both the experimental and numerical cases, with the results of the two methods comparing favourably, showing comparable trends in the oscillating flow fields, and very similar trends in the distribution of net acoustic power.     

Vortex shedding flow behind a slowly rotating circular cylinder

This paper investigates flow past a rotating circular cylinder at 3600?Re?5000 and α?2.5. The flow parameter α is the circumferential speed at the cylinder surface normalized by the free-stream velocity of the uniform cross-flow. With particle image velocimetry (PIV), vortex shedding from the cylinder is clearly observed at α<1.9. The vortex pattern is very similar to the vortex street behind a stationary circular cylinder; but with increasing cylinder rotation speed, the wake is observed to become increasing narrower and deflected sideways. Properties of large-scale vortices developed from the shear layers and shed into the wake are investigated with the vorticity field derived from the PIV data. The vortex formation length is found to decrease with increasing α. This leads to a slow increase in vortex shedding frequency with α. At α=0.65, vortex shedding is found to synchronize with cylinder rotation, with one vortex being shed every rotation cycle of the cylinder. Vortex dynamics are studied at this value of α with the phase-locked eduction technique. It is found that although the shear layers at two different sides of the cylinder possess unequal vorticity levels, alternating vortices subsequently shed from the cylinder to join the two trains of vortices in the vortex street pattern exhibit very little difference in vortex strength.     

Numerical simulation of cross-flow around four cylinders in an in-line square configuration

Successful numerical simulations can reveal important flow characteristics and information which are extremely difficult to obtain experimentally. Two- and three-dimensional (3-D) numerical simulations of cross-flow around four cylinders in an in-line square configuration are performed using a finite-volume method. For 2-D studies, the Reynolds numbers (Re) are chosen to be Re=100 and 200 and the spacing ratio L/D is set at 1.6, 2.5, 3.5, 4.0 and 5.0. For the 3-D investigation, the simulation is only performed at a Re=200, a spacing ratio L/D=4.0 and an aspect ratio H/D=16. The 2-D studies reveal three distinct flow patterns: (I) a stable shielding flow; (II) a wiggling shielding flow and (III) a vortex shedding flow. A transformation of the flow pattern from (I) to (II) at Re=100 will increase the amplitude of the maximum fluctuating pressure on the downstream cylinder surface by 4–12 times, while a transformation of the flow pattern from (II) to (III) will enhance the maximum fluctuating pressure amplitude by 2–3 times. There is a large discrepancy between 2-D simulation and flow visualization results at L/D=4.0 and Re=200. A probable cause could be the strong 3-D effect at the ends of the cylinder at low H/D. It was found that, for an in-line square configuration at critical L/D and when H/D is lower than a certain value, 3-D effects are very significant at the ends of the cylinders. In such cases, a time-consuming 3-D numerical simulation will have to be performed if full replication of the flow phenomenon were to be achieved.     

Flow-excited acoustic resonance of two side-by-side cylinders in cross-flow

The aeroacoustic response of two side-by-side circular cylinders in cross-flow is investigated experimentally. In order to investigate the effect of the gap between the cylinders on the acoustic resonance mechanism, six spacing ratios between the cylinders, in the range of T/D=1.25–3, have been investigated, where D is the diameter of the cylinders and T the centre-to-centre distance between them. Special attention is given to the intermediate spacing ratio range, which exhibits bistable flow regimes in the absence of resonance. During the tests, the acoustic cross-modes of the duct housing the cylinders are self-excited. For the intermediate spacing ratios, T/D=1.25, 1.35, 1.46 and 1.75, two distinct vortex-shedding frequencies at the off-resonance conditions are observed. These are associated with the wide and narrow wakes of the cylinders, as described in the literature. In this case, acoustic resonances occur at a Strouhal number, which is between those observed before the onset of resonance. The acoustic resonance synchronizes vortex shedding in the two wakes and thereby eliminates the bistable flow phenomenon. For large spacing ratios, T/D=2.5 and 3, vortex shedding occurs at a single Strouhal number at which the acoustic resonance is excited.     

Asymmetric vortex shedding flow past an inclined flat plate at high incidence

This paper reports an experimental investigation of the vortex shedding wake behind a long flat plate inclined at a small angle of attack to a main flow stream. Detailed velocity fields are obtained with particle-image velocimetry (PIV) at successive phases in a vortex shedding cycle at three angles of attack, α=20°, 25° and 30°, at a Reynolds number Re≈5,300. Coherent patterns and dynamics of the vortices in the wake are revealed by the phase-averaged PIV vectors and derived turbulent properties. A vortex street pattern comprising a train of leading edge vortices alternating with a train of trailing edge vortices is found in the wake. The trailing edge vortex is shed directly from the sharp trailing edge while there are evidences that the formation and shedding of the leading edge vortex involve a more complicated mechanism. The leading edge vortex seems to be shed into the wake from an axial location near the trailing edge. After shedding, the vortices are convected downstream in the wake with a convection speed roughly equal to 0.8 the free-stream velocity. On reaching the same axial location, the trailing edge vortex, as compared to the leading edge vortex, is found to possess a higher peak vorticity level at its centre and induce more intense fluid circulation and Reynolds stresses production around it. It is found that the results at the three angles of attack can be collapsed into similar trends by using the projected plate width as the characteristic length of the flow.     

Influence of wall proximity on characteristics of wake behind a square cylinder: PIV measurements and POD analysis

Influence of wall proximity on characteristics of the wake behind a two-dimensional square cylinder was experimentally studied in the present work. A low-speed recirculation water channel was established for the experiment; the Reynolds number based on the free-stream velocity and cylinder width (D) was kept at Re_D = 2250. Four cases with different gap width, e.g., G/D = 0.1, 0.2, 0.4 and 0.8, were chosen for comparison. Two experimental techniques, e.g., the standard PIV with high image-density CCD camera and TR-PIV with a high-speed camera were employed in measuring the wake field, enabling a comprehensive view of the time-averaged wake pattern at high spatial resolution and the instantaneous flow field at high temporal resolution, respectively. For the four cases, the difference in spatial characteristics of the wake in the vicinity of the plane wall was analyzed in terms of the time-averaged quantities measured by the standard PIV, e.g., the streamline pattern, the vector field, the streamwise velocity fluctuation intensity and the reverse-flow intermittency. The proper orthogonal decomposition (POD) method was extensively used to decompose the TR-PIV measurements, giving a close-up view of the energetic POD modes buried in the wake. The low-order flow model of the wake at G/D = 0.8 and 0.4 was constructed by using the linear combination of the first two POD modes and the time-mean flow field, which reflected well the vortex shedding process in the sense of the phase-dependent patterns. The intermittent appearance of the weakly separated region near the wall was found at G/D = 0.4. On going from G/D = 0.8 to 0.4, the remarkable variation of the instantaneous wake in the longitudinal direction confirmed that the wall constraint stretches the vortices in the plane of the wall and transfers the energy to the longitudinal component at the expense of the lateral one.     

The effect of a splitter plate on the flow around a finite prism

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height square prism was investigated experimentally in a low-speed wind tunnel. Measurements of the mean drag force and vortex shedding frequency were made at Re=7.4×10⁴ for square prisms of aspect ratios AR=9, 7, 5 and 3. Measurements of the mean wake velocity field were made with a seven-hole pressure probe at Re=3.7×10⁴ for square prisms of AR=9 and 5. The relative thickness of the boundary layer on the ground plane was δ/D=1.5–1.6 (where D is the side length of the prism). The splitter plates were mounted vertically from the ground plane on the wake centreline, with a negligible gap between the leading edge of the plate and rear of the prism. The splitter plate heights were always the same as the heights of prisms, while the splitter plate lengths ranged from L/D=1 to 7. Compared to previously published results for an “infinite” square prism, a splitter plate is less effective at drag reduction, but more effective at vortex shedding suppression, when used with a finite-height square prism. Significant reduction in drag was realized only for short prisms (of AR≤5) when long splitter plates (of L/D≥5) were used. In contrast, a splitter plate of length L/D=3 was sufficient to suppress vortex shedding for all aspect ratios tested. Compared to previous results for finite-height circular cylinders, finite-height square prisms typically need longer splitter plates for vortex shedding suppression. The effect of the splitter plate on the mean wake was to narrow the wake width close to the ground plane, stretch and weaken the streamwise vortex structures, and increase the lateral entrainment of ambient fluid towards the wake centreline. The splitter plate has little effect on the mean downwash. Long splitter plates resulted in the formation of additional streamwise vortex structures in the upper part of the wake.     

Numerical simulation of flow around a square cylinder in uniform-shear flow

This paper presents results obtained from a numerical simulation of a two-dimensional (2-D) incompressible linear shear flow over a square cylinder. Numerical simulations are performed, using the lattice Boltzmann method, in the ranges of 50⩽Re⩽200 and 0⩽K⩽0.5, where Re and K are the Reynolds number and the shear rate, respectively. The effect of the shear rate on the frequency of vortex shedding from the cylinder, and the lift and drag forces exerted on the cylinder are quantified together with the flow patterns around the cylinder. The present results show that vortex structure behind the cylinder is strongly dependant on both the shear rate and Reynolds number. When Re=50, a small K can disturb the steady state and cause an alternative vortex shedding with uneven intensity. In contrast, a large value of K will suppress the vortex shedding from the cylinder. When Re>50, the differences in the strength and size of vortices shed from the upper and lower sides of the cylinder become more pronounced as K increases. Vortex shedding disappears when K is larger than a critical value, which depends on Re. The flow patterns around the cylinder for different Re tend towards self-similarity with increasing K. The lift and drag forces exerted on the cylinder, in general, decrease with increasing K. Unlike a shear flow past a circular cylinder, the vortex shedding frequency past a square cylinder decreases with increasing the shear rate. A significant reduction of the drag force occurs in the range 0.15<K<0.3.     

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height circular cylinder

The influence of a wake-mounted splitter plate on the flow around a surface-mounted circular cylinder of finite height was investigated experimentally using a low-speed wind tunnel. The experiments were conducted at a Reynolds number of Re=7.4×10⁴ for cylinder aspect ratios of AR=9, 7, 5 and 3. The thickness of the boundary layer on the ground plane relative to the cylinder diameter was δ/D=1.5. The splitter plates were mounted on the wake centreline with negligible gap between the base of the cylinder and the leading edge of the plate. The lengths of the splitter plates, relative to the cylinder diameter, ranged from L/D=1 to 7, and the plate height was always equal to the cylinder height. Measurements of the mean drag force coefficient were obtained with a force balance, and measurements of the vortex shedding frequency were obtained with a single-component hot-wire probe situated in the wake of the cylinder–plate combination. Compared to the well-studied case involving an infinite circular cylinder, the splitter plate was found to be a less effective drag-reduction device for finite circular cylinders. Significant reduction in the mean drag coefficient was realized only for the finite circular cylinder of AR=9 with intermediate-length splitter plates of L/D=1–3. The mean drag coefficients of the other cylinders were almost unchanged. In terms of its effect on vortex shedding, a splitter plate of sufficient length was able to suppress Kármán vortex shedding for all of the finite circular cylinders tested. For AR=9, vortex shedding suppression occurred for L/D≥5, which is similar to the case of the infinite circular cylinder. For the smaller-aspect-ratio cylinders, however, the splitter plate was more effective than what occurs for the infinite circular cylinder: for AR=3, vortex shedding suppression occurred for all of the splitter plates tested (L/D≥1); for AR=5 and 7, vortex shedding suppression occurred for L/D≥1.5.     

Identification of flow regimes around two staggered square cylinders by a numerical study

The flow over two square cylinders in staggered arrangement is simulated numerically at a fixed Reynolds number (\(Re =150\)) for different gap spacing between cylinders from 0.1 to 6 times a cylinder side to understand the flow structures. The non-inclined square cylinders are located on a line with a staggered angle of \(45^{\circ }\) to the oncoming velocity vector. All numerical simulations are carried out with a finite-volume code based on a collocated grid arrangement. The effects of vortex shedding on the various features of the flow field are numerically visualized using different flow contours such as \(\lambda _{2}\) criterion, vorticity, pressure and magnitudes of velocity to distinguish the distinctive flow patterns. By changing the gap spacing between cylinders, five different flow regimes are identified and classified as single body, periodic gap flow, aperiodic, modulated periodic and synchronized vortex shedding regimes. This study revealed that the observed multiple frequencies in global forces of the downstream cylinder in the modulated periodic regime are more properly associated with differences in vortex shedding frequencies of individual cylinders than individual shear layers reported in some previous works; particularly, both shear layers from the downstream cylinder often shed vortices at the same multiple frequencies. The maximum Strouhal number for the upstream cylinder is also identified at \({G}^{*}=1\) for aperiodic flow pattern. Furthermore, for most cases studied, the downstream cylinder experiences larger drag force than the upstream cylinder.     

FLOW VISUALIZATION AROUND A CIRCULAR CYLINDER NEAR TO A PLANE WALL

Flow visualization, particle image velocimetry and hot-film anemometry have been employed to study the fluid flow around a circular cylinder near to a plane wall for Reynolds numbers, based on cylinder diameter, between 1200 and 4960. The effect of changing the gap between the cylinder and the wall, G, from G=0 (cylinder touching the wall) to G/D=2, was investigated. It is shown that the flow may be characterized by four distinct regions. (a) For very small gaps, G/D≤0·125, the gap flow is suppressed or extremely weak, and separation of the boundary layer occurs both upstream and downstream of the cylinder. Although there is no regular vortex shedding, there is a periodicity associated with the outer shear-layer. (b) In the “small gap ratio” region, 0·125<G/D<0·5, the flow is very similar to that for very small gaps, except that there is now a pronounced pairing between the inner shear-layer shed from the cylinder and the wall boundary layer. (c) Intermediate gap ratios, 0·5<G/D<0·75, are characterized by the onset of vortex shedding from the cylinder. (d) For the fourth region, characterized by the largest gap ratios considered, G/D>1·0, there is no separation of the wall boundary layer, either upstream or downstream of the cylinder.     

Flow structures around an equilateral triangle arrangement of three spheres

This paper represents the results of an experimental study on the flow structure around a single sphere and three spheres in an equilateral-triangular arrangement. Flow field measurements were performed using a Particle Image Velocimetry (PIV) technique and dye visualization in an open water channel for a Reynolds number of Re = 5 × 10³ based on the sphere diameter. The distributions and flow features at the critical locations of the contours of the velocity fluctuations, the patterns of sectional streamlines, the vorticity contours, the turbulent kinetic energy, the Reynolds stress correlations and shedding frequency are discussed. The gap ratios (G/D) of the three spheres were varied in the range of 1.0 ⩽ G/D ⩽ 2.5 where G was the distance between the sphere centers, and D was the sphere diameter which was taken as 30 mm. Due to the interference of the shedding shear layers and the wakes, more complex features of the flow patterns can be found in the wake region of the two downstream spheres behind the leading sphere. For G/D = 1.25, a jet-like flow around the leading sphere through the gap between the two downstream spheres occurred, which significantly enhanced the wake region. It was observed that a continuous flow development involving shearing phenomena and the interactions of shedding vortices caused a high rate of fluctuations over the whole flow field although most of the time-averaged flow patterns were almost symmetric about the two downstream spheres.     

Uncovering large-scale coherent structures in natural and forced turbulent wakes by combining PIV,POD, and FTLE

Planar velocity data of the unsteady separated flow in the turbulent wake of a circular cylinder obtained by particle image velocimetry (PIV) are analyzed in order to visualize the large-scale coherent structures associated with alternating vortex shedding at a Reynolds number of 2,150. Two different cases are examined: unforced vortex shedding in the natural wake and vortex lock-on incited by forced perturbations superimposed in the inflow velocity. Proper orthogonal decomposition (POD) is employed to reconstruct the low-order wake dynamics from randomly sampled snapshots of the velocity field. The reconstructed flow is subsequently used to determine the evolution of the finite-time Lyapunov exponent (FTLE) fields which identify the Lagrangian coherent structures. The results demonstrate that the combination of methods employed offers a powerful visualization tool to uncover large-scale coherent structures and to exemplify vortex dynamics in natural and forced bluff-body wakes.     

On vortex shedding from low aspect ratio dual step cylinders

A dual-step cylinder is comprised of two cylinders of different diameters. A large diameter cylinder (D) with low aspect ratio (L/D) is attached to the mid-span of a small diameter cylinder (d). The present study investigates the effect of Reynolds number (Re_D) and L/D on dual step cylinder wake development for D/d=2, 0.2≤L/D≤3, and two Reynolds numbers, Re_D=1050 and 2100. Experiments have been performed in a water flume facility utilizing flow visualization, Laser Doppler Velocimetry (LDV), and Particle Image Velocimetry (PIV). The results show that vortex shedding occurs from both the large and small diameter cylinders for 1≤L/D≤3 at Re_D=2100 and 2≤L/D≤3 at Re_D=1050. At these conditions, large cylinder vortices predominantly form vortex loops in the wake and small cylinder vortices form half-loop vortex connections. At lower aspect ratios, vortex shedding from the large cylinder ceases, with the dominant frequency in the large cylinder wake attributed to the passage of vortex filaments connecting small cylinder vortices. At these lower aspect ratios, the presence of the large cylinder induces periodic vortex dislocations. Increasing L/D increases the frequency of occurrence of vortex dislocations and decreases the dominant frequency in the large cylinder wake. The identified changes in wake topology are related to substantial variations in the location of boundary layer separation on the large cylinder, and, consequently, changes in the size of the vortex formation region. The results also show that the Reynolds number has a substantial effect on wake vortex shedding frequency, which is more profound than that expected for a uniform cylinder.     

Three-dimensional simulations of flow past two circular cylinders in side-by-side arrangements at right and oblique attacks

The flow past two identical circular cylinders in side-by-side arrangements at right and oblique attack angles is numerically investigated by solving the three-dimensional Navier–Stokes equations using the Petrov–Galerkin finite element method. The study is focused on the effect of flow attack angle and gap ratio between the two cylinders on the vortex shedding flow and the hydrodynamic forces of the cylinders. For an oblique flow attack angle, the Reynolds number based on the velocity component perpendicular to the cylinder span is defined as the normal Reynolds number Re_N and that based on the total velocity is defined as the total Reynolds number Re_T. Simulations are conducted for two Reynolds numbers of Re_N=500 and Re_T=500, two flow attack angles of α=0° and 45° and four gap ratios of G/D=0.5, 1, 3 and 5. The biased gap flow for G/D=0.5 and 1 and the flip-flopping bistable gap flow for G/D=1 are observed for both α=0° and 45°. For a constant normal Reynolds number of Re_N=500, the mean drag and lift coefficients at α=0° are very close to those at α=45°. The difference between the root mean square (RMS) lift coefficient at α=0° and that at α=45° is about 20% for large gap ratios of 3 and 5. From small gap ratios of 0.5 and 1, the RMS lift coefficients at α=0° and 45° are similar to each other. The present simulations show that the agreement in the force coefficients between the 0° and 45° flow attack angles for a constant normal Reynolds number is better than that for a constant total Reynolds number. This indicates that the normal Reynolds number should be used in the implementation of the independence principle (i.e., the independence of the force coefficients on the flow attack angle). The effect of Reynolds number on the bistable gap flow is investigated by simulating the flow for Re_N=100–600, α=0° and 45° and G/D=1. Flow for G/D=1 is found to be two-dimensional at Re_N=100 and weak three-dimensional at Re_N=200. While well defined biased flow can be identified for Re_N=300–600, the gap flow for Re_N=100 and 200 changes its biased direction too frequently to allow stable biased flow to develop.     

Unsteady near wake of a flat disk normal to a wall

The unsteady wake of a flat disk (diameter D) located at a distance of H from a flat plate has been experimentally investigated at a Reynolds number Re _D  = 1.3 × 10⁵. Tests have been performed for a range of gap ratio (H/D), spanning from 0.3 to 1.75. The leading edge of the flat plate is either streamlined (elliptical) or blunt (square). These configurations have been studied with PIV, high speed PIV and multi-arrayed off-set fluctuating pressure measurements. The results show a progressive increase of the complexity of the flow and of the interaction as the gap ratio decreases. For large values of H/D (1.75), the interaction is weak and the power spectral densities (PSD) exhibit a strong peak associated with the vortex shedding events (St = 0.131) – St = fD/U _∞ is the Strouhal number. For lower values of H/D (0.75), the magnitude of the wall fluctuating pressure increases significantly. A large band contribution is associated with the unsteady wake structure and turbulence. A slight increase of the shedding frequency (St = 0.145) is observed. A critical value of the gap ratio (about 0.35) has been determined. Below this critical value, a three-dimensional separated region is observed and the natural vortex shedding process is very strongly altered. These changes induce a great modification of the fluctuating pressure at the wall. Each interaction reacts in a different way to perturbed upstream conditions. In particular, the disk is an overwhelming perturbation for the lowest H/D value studied here and the relative influence of the upstream turbulence on the wall fluctuating pressure below the near wake region is moderate.     

Three-dimensional numerical simulations of cross-flow around four cylinders in an in-line square configuration

This paper presents a numerical study of three-dimensional (3-D) laminar flow around four circular cylinders in an in-line square configuration. The investigation focuses on effects of spacing ratio (L/D) and aspect ratio (H/D) on 3-D flow characteristics, and the force and pressure coefficients of the cylinders. Extensive 3-D numerical simulations were performed at Reynolds number of 200 for L/D from 1.6 to 5.0 at H/D=16 and H/D from 6 to 20 at L/D=3.5. The results show that the 3-D numerical simulations have remedied the inadequacy of 2-D simulations and the results are in excellent agreement with the experimental results. The relation between 3-D flow patterns and pressure characteristics around the four cylinders is examined and discussed. The critical spacing ratio for flow pattern transformation was found to be L/D=3.5 for H/D=16, while a bistable wake pattern was observed at L/D=1.6 for the same aspect ratio. Moreover, a transformation of flow pattern from a stable shielding flow pattern to a vortex shedding flow pattern near the middle spanwise positions of the cylinders was observed and was found to be dependent on the aspect ratio, spacing ratio, and end wall conditions. Due to the highly 3-D nature of the flows, different flow patterns coexist over different spanwise positions of the cylinders even for the same aspect ratio. It is concluded that spacing ratio, aspect ratio, and the no-slip end wall condition have important combined effects on free shear layer development of the cylinders and hence have significant effects on the pressure field and force characteristics of the four cylinders with different spacing ratios and aspect ratios.