Investigation of turbulent flow past a yawed wavy cylinder

A large eddy simulation (LES) study was conducted to investigate the three-dimensional characteristics of the turbulent flow past wavy cylinders with yaw angles from 0° to 60° at a subcritical Reynolds number of 3900. The relationships between force coefficients and vortex shedding frequency with yaw angles for both wavy cylinders and circular cylinders were investigated. Experimental measurements were also performed for the validation of the present LES results. Comparing with corresponding yawed circular cylinders at similar Reynolds number, significant differences in wake vortex patterns between wavy cylinder and circular cylinder were observed at small yaw angles. The difference in wake pattern becomes insignificant at large yaw angles. The mean drag coefficient and the Strouhal number obey the independence principle for circular cylinders at yaw angle less than 45°, while the independence principle was found to be unsuitable for yawed wavy cylinders. In general, the mean drag coefficients and the fluctuating lift coefficients of a yawed wavy cylinder are less than those of a corresponding yawed circular cylinder at the same flow condition. However, with the increase of the yaw angle, the advantageous effect of wavy cylinder on force and vibration control becomes insignificant.     

Force coefficients and Strouhal numbers of three circular cylinders subjected to a cross-flow

In this paper, wind tunnel experiments were conducted to measure the mean force coefficients and Strouhal numbers for three circular cylinders of equal diameters in an equilateral-triangular arrangement when subjected to a cross-flow. These experiments were carried out at five subcritical Reynolds numbers ranging from 1.26 × 10⁴ to 6.08 × 10⁴. The pressure distributions on the surface of the cylinders were measured using pressure transducers. Furthermore, the hot-wire anemometer was employed to measure the vortex shedding frequencies behind each cylinder. Six spacing ratios (l/d) varying from 1.5 to 4 were investigated. It is observed that for l/d > 2, the upstream cylinder experiences a lower mean drag coefficient compared with the downstream cylinders. The minimum values of the drag coefficient for the downstream cylinders occur at l/d = 1.5 and l/d = 2, because there is no vortex shedding from the foregoing cylinders. Also, the value of the pressure coefficient behind the upstream cylinder reduces by increasing l/d. Moreover, by decreasing the value of l/d, the Strouhal number for the upstream cylinder increases. It can be concluded that the flow pattern and aerodynamic coefficients are basically dependent on l/d; in other words, decreasing l/d results in an increase in the effects of the flow interference between the cylinders.     

Experimental study on aerodynamic coefficients of yawed cylinders

This paper presents wind tunnel tests on a stationary cylinder inclined with the flow. The cylinder was positioned at different sets of yaw and vertical angles. The flow regime of the tests remained in the subcritical state. Two load cells were designed and installed to measure the aerodynamic forces, with enough sensitivity to measure vortex shedding frequencies. In this paper, the three aerodynamic force coefficients are normalized using the free stream velocity instead of its normal component. The results show that the drag coefficient and the resultant of the lift and side forces coefficients can be described by an empirical function of the incidence angle. The lift and side force coefficients remain however functions of both the horizontal yaw and vertical angles and cannot be expressed as functions of the incidence angle only. The Independence Principle was observed to become inaccurate for yaw angles larger than 40°. However, the measured Strouhal numbers indicate that the vortex shedding frequencies of a yawed cylinder can be predicted using the Independence Principle.     

Effects of an asymmetrical confined flow on a rectangular cylinder

The effects of an asymmetric confined flow on a cylinder of rectangular cross-section are investigated and discussed. Experiments are performed in a wind tunnel by placing cylinders of different cross-sections at various elevations from the floor of the test-section. The Reynolds number is varied within the range 6×10³–4×10⁴. Forces exciting the cylinder are measured by built-in dynamometers placed inside the cylinder structure. The flow is characterized by mean and fluctuating local velocity components to define the inflow distribution and the ensuing wake region. The mean dimensionless force coefficients are then calculated and analyzed. The frequency analysis of the force components acting on the cylinder provides the dynamic characterization of the loading and of the wake shedding. The experimental results highlight that the presence of the wall strongly influences the system dynamics also when the cylinder is placed at a relatively large elevation from the wall itself. The cylinder aspect ratio governs effects of the wall condition on the force coefficients and the Strouhal number.     

Interactions between a rectangular cylinder and a free-surface flow

The salient features of the interaction between a free-surface flow and a cylinder of rectangular cross-section are investigated and discussed. Laboratory-scale experiments are performed in a water channel under various flow conditions and elevations of the cylinder above the channel floor. The flow field is characterized on the basis of time-averaged and fluctuating local velocity measurements. Dynamic loadings on the cylinder are measured by two water-insulated dynamometers placed inside the cylinder structure. Starting from frequency and spectral analyses of the force signals, insights on the relationship between force dominant frequencies and the Strouhal number of the vortex shedding phenomenon are provided. Experimental results highlight the strong influence of the asymmetric configuration imposed by the two different boundary conditions (free surface and channel floor) on (i) the mean force coefficients and (ii) the vortex shedding frequencies. We provide an analysis of the nature of the dependence of average force coefficients on relevant dimensionless groups, i.e., the Reynolds number, normalized flow depth and cylinder submersion.     

Time-averaged topological flow patterns and their influence on vortex shedding of a square cylinder in crossflow at incidence

Flow characteristics around the square cylinder and their influence on the wake properties are studied. Time-averaged flow patterns on the surfaces of square cylinder in a cross-stream at incidence are experimentally probed by surface-oil flow technique and analyzed by flow topology for Reynolds numbers between 3.9×10⁴ and 9.4×10⁴ as the incidence angle changes from 0° to 45°. Vortex shedding characteristics are measured by a single-wire hot-wire anemometer for Reynolds numbers between 5×10³ and 1.2×10⁵. The effects of topological flow patterns on the wake properties then are revealed and discussed. Flows around the square cylinder are identified as three categories: the subcritical, supercritical, and wedge flows according to the prominently different features of the topological flow patterns. The Strouhal number of vortex shedding, turbulence in the wake, and wake width present drastically different behaviors in different characteristic flow regimes. A critical incidence angle of 15° separates the subcritical and supercritical regimes. At the critical incidence angle the wake width and shear-layer turbulence present minimum values. The minimum wake width appearing at the critical incidence angle, which leads to the maximum Strouhal number, is due to the reattachment of one of the separated boundary layer to the lateral face of the square cylinder. If the Strouhal numbers are calculated based on the wake width instead of the cross-stream projection width of cylinder, the data in the subcritical and supercritical regimes are well correlated into two groups, which would approach constants at high Reynolds numbers.     

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 simulation of shear effect on vortex shedding behind a square cylinder

This paper is concerned with the numerical simulation of the flow structure around a square cylinder in a uniform shear flow. The calculations were conducted by solving the unsteady 2D Navier–Stokes equations with a finite difference method. The effect of the shear parameter K of the approaching flow on the vortex-shedding Strouhal number and the force coefficients acting on the square cylinder is investigated in the range K=0·0–0·25 at various Reynolds numbers from 500 to 1500. The computational results are compared with some existing experimental data and previous studies. The effect of shear rate on the Strouhal number and the force acting on the cylinder has a tendency to reduce the oscillation. The Strouhal number, mean drag and amplitude of the fluctuating force tend to decrease as the shear rate increases, but show no significant change at low shear rate. Increasing the Reynolds number decreases the Strouhal number and increases the force acting on the cylinder. At high shear rate the shedding frequencies of the fluctuating drag and lift coefficients are identical. © 1997 John Wiley & Sons, Ltd.     

Numerical modelling of confined flow past a cylinder of square cross-section at various orientations

Results are presented for the unsteady, two-dimensional flow and heat transfer due to a square obstruction of diameter d located asymmetrically between the parallel sliding walls of a channel with length-to-height ratio W/H = 6·44. Analysis is based on the numerical solution of spatially and temporally second-order accurate finite difference approximations of the transport equations expressed in curvilinear co-ordinates. Laminar, constant property flow is assumed for obstruction configurations in which the blockage ratio is d/H = 0·192, the nearest-wall distances are g/d = 0·2, 0·5 and 1, the orientation angles are α=0°, 10° and 20° and the Reynolds numbers are Re=100, 500, and 1000. Preparatory testing of the numerical procedure was performed for a variety of documented flows to verify its physiconumerical accuracy and obtain estimates of the residual grid-dependent uncertainties in the variables calculated. Heat transfer, drag and lift coefficients and Strouhal numbers for the present flow were finally calculated to within 4%–7% of their grid-dependent values using non-uniformly spaced grids consisting of (x=99, y=55) nodes. Above a critical value of the Reynolds number, which depends on the geometrical parameters, the flow is characterized by alternate vortex shedding from the obstruction top and bottom surfaces. Streamline, vorticity and particle streakline plots provide qualitative impressions of the unsteady vortical flow. Especially noteworthy are the extremes in the lift coefficient which ranges from large positive values for an obstruction with g/d=0·2 and α=10° to negative values for one with g/d=0·5 and α=0°. Both the drag and lift coefficients as well as the Strouhal number exhibit non-monotonic variations with respect to the parameters explored. Asymmetries in the obstruction location and orientation account for relatively large vortex-induced periodic variations in heat transfer, especially along the wall nearest the obstruction. Notable differences are also predicted for the heat transfer coefficients of the individual obstruction surfaces as a function of the orientation angle.     

Induced parallel vortex shedding from a circular cylinder at Re of O(10) by using the cylinder end suction technique

In the present work, the objective is to attempt to induce parallel vortex shedding at a moderately high Reynolds number (=1.578 × 10⁴) by using the cylinder end suction method, and measure the associated aerodynamic parameters.We first measured the aerodynamic parameters of a single circular cylinder without end suction, and showed that the quantities measured are in good agreement with equivalent data in the published literature. Next, by using different amount of end suction which resulted in increasing the cylinder end velocity by 1%, 2% and 2.5%, we were able to show that the above corresponded to the situation of under suction, optimal suction and over suction, respectively. With optimal suction, we demonstrated that the end suction method works at Re = 1.578 × 10⁴. The shape of the primary vortex shed became straighter than when there is no end suction, and parameters like cylinder surface pressure distribution, drag force per unit span, as well as vortex shedding frequency all showed negligible spanwise variation. Further careful analyses showed that when compared to the naturally existing curved vortex shedding, with parallel vortex shedding the mid-span drag per unit span became slightly smaller, but the drag averaged over the cylinder span became slightly larger. For cylinder surface pressure, it was found that cylinder end effects mainly influenced the surface pressure in the angular ranges −180°  β < −60° and 60° < β  180°. Without end suction, the cylinder surface pressure in the above ranges was found to increase (become less negative) slightly with |z/d|, but such increase disappeared when optimal end suction was applied, and the cylinder surface pressure distribution became spanwise location independent. As for the vortex shedding frequency (Strouhal number), although the Strouhal number showed spanwise variation when there is no end suction and negligible spanwise variation when optimal suction was applied, the difference between the spanwise averaged Strouhal number was quite negligible. With under suction, the spanwise dependence of various aerodynamic parameters existed, but was found to be not as significant as when no end suction was applied at all. With over suction, the flow situation was found to be practically no change from the optimal suction situation.     

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.     

Direct numerical simulation of three-dimensional flow past a yawed circular cylinder of infinite length

Direct numerical simulation of flow past a stationary circular cylinder at yaw angles (α) in the range of 0–60° was conducted at Reynolds number of 1000. The three-dimensional (3-D) Navier–Stokes equations were solved using the Petrov–Galerkin finite element method. The transition of the flow from 2-D to 3-D was studied. The phenomena that were observed in flow visualization, such as the streamwise vortices, the vortex dislocation and the instability of the shear layer, were reproduced numerically. The effects of the yaw angle on wake structures, vortex shedding frequency and hydrodynamic forces of the cylinder were investigated. It was found that the Strouhal number at different yaw angles (α) follows the independence principle. The mean drag coefficient agrees well with the independence principle. It slightly increases with the increase of α and reaches a maximum value at α=60°, which is about 10% larger than that when α=0°. The root-mean-square (r.m.s.) values of the lift coefficient are noticeably dependent on α.     

Vortex shedding from a square cylinder in presence of a moving wall

A numerical study on the flow past a square cylinder placed parallel to a wall, which is moving at the speed of the far field has been made. Flow has been investigated in the laminar Reynolds number (based on the cylinder length) range. We have studied the flow field for different values of the cylinder to wall separation length. The governing unsteady Navier–Stokes equations are discretized through the finite volume method on a staggered grid system. A SIMPLE type of algorithm has been used to compute the discretized equations iteratively. A shear layer of negative vortex generates along the surface of the wall, which influences the vortex shedding behind the cylinder. The flow‐field is distinct from the flow in presence of a stationary wall. An alternate vortex shedding occurs for all values of gap height in the unsteady regime of the flow. The strong positive vortex pushes the negative vortex upwards in the wake. The gap flow in the undersurface of the cylinder is strong and the velocity profile overshoots. The cylinder experiences a downward force for certain values of the Reynolds number and gap height. The drag and lift are higher at lower values of the Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd.     

A numerical investigation of the flow over a pair of identical square cylinders in a tandem arrangement

This paper describes a numerical study of the two‐dimensional and three‐dimensional unsteady flow over two square cylinders arranged in an in‐line configuration for Reynolds numbers from 40 to 1000 and a gap spacing of 4D, where D is the cross‐sectional dimension of the cylinders. The effect of the cylinder spacing, in the range G = 0.3D to 12D, was also studied for selected Reynolds numbers, that is, Re = 130, 150 and 500. An incompressible finite volume code with a collocated grid arrangement was employed to carry out the flow simulations. Instantaneous and time‐averaged and spanwise‐averaged vorticity, pressure, and streamlines are computed and compared for different Reynolds numbers and gap spacings. The time averaged global quantities such as the Strouhal number, the mean and the RMS values of the drag force, the base suction pressure, the lift force and the pressure coefficient are also calculated and compared with the results of a single cylinder. Three major regimes are distinguished according to the normalized gap spacing between cylinders, that is, the single slender‐body regime (G < 0.5), the reattach regime (G < 4) and co‐shedding or binary vortex regime (G ≥4). Hysteresis with different vortex patterns is observed in a certain range of the gap spacings and also for the onset of the vortex shedding. Copyright © 2011 John Wiley & Sons, Ltd.     

Dependence of the wake on inclination of a stationary cylinder

Three-dimensional vorticity in the wake of an inclined stationary circular cylinder was measured simultaneously using a multi-hot wire vorticity probe over a streamwise range of x/d = 10–40. The study aimed to examine the dependence of the wake characteristics on cylinder inclination angle α (=0°–45°). The validity of the independence principle (IP) for vortex shedding was also examined. It was found that the spanwise mean velocity which represents the three-dimensionality of the wake flow, increases monotonically with α. The root-mean-square (rms) values of the streamwise (u) and spanwise (w) velocities and the three vorticity components decrease significantly with the increase of α, whereas the transverse velocity (v) does not follow the same trend. The vortex shedding frequency decreases with the increase of α. The Strouhal number (St _N), obtained by using the velocity component normal to the cylinder axis, remains approximately a constant within the experimental uncertainty (±8%) when α is smaller than about 40°. The autocorrelation coefficients ρ _u and ρ _v of the u and v velocity signals show apparent periodicity for all inclination angles. With increasing α, ρ _u and ρ _v decrease and approach zero quickly. In contrast, the autocorrelation coefficient ρ _w of w increases with α in the near wake, implying an enhanced three-dimensionality of the wake.     

Reduction in drag and vortex shedding frequency through porous sheath around a circular cylinder

A numerical study on the laminar vortex shedding and wake flow due to a porous‐wrapped solid circular cylinder has been made in this paper. The cylinder is horizontally placed, and is subjected to a uniform cross flow. The aim is to control the vortex shedding and drag force through a thin porous wrapper around a solid cylinder. The flow field is investigated for a wide range of Reynolds number in the laminar regime. The flow in the porous zone is governed by the Darcy–Brinkman–Forchheimer extended model and the Navier–Stokes equations in the fluid region. A control volume approach is adopted for computation of the governing equations along with a second‐order upwind scheme, which is used to discretize the convective terms inside the fluid region. The inclusion of a thin porous wrapper produces a significant reduction in drag and damps the oscillation compared with a solid cylinder. Dependence of Strouhal number and drag coefficient on porous layer thickness at different Reynolds number is analyzed. The dependence of Strouhal number and drag on the permeability of the medium is also examined. Copyright © 2009 John Wiley & Sons, Ltd.     

Reynolds-number-effects in flow around a rectangular cylinder with aspect ratio 1:5

The paper reports on experiments carried out over a wide range of Reynolds numbers in a high pressure wind tunnel. The model was a sharp-edged rectangular cylinder with aspect ratio height/width 1:5 (width/span ratio 1:10.8), which was investigated in both basic orientations, lengthwise (4×10³<Re<4×10⁵) and perpendicular to the flow (2.7×10⁴<Re<6.4×10⁵). The Reynolds number is based on the height of the model normal to the flow. Steady and unsteady forces were measured with a piezoelectric balance. Thus along with steady (i.e. time averaged values) including the base pressure coefficient, also power spectra and probability density functions were measured yielding for example Strouhal numbers, higher statistical moments, etc. A response diagram for the vortex resonance phenomenon was taken for the natural bending motion of the slender model. If lift coefficient for constant angle of attack is plotted against Reynolds number, a significant Reynolds number effect is seen. For α=4°, the curve shows an inflection point and the lift varies between 0.3 and 0.6. For α=6° and 2° there are similar variations shifted to lower and higher values of Re, respectively. Probably the shapes of separation bubbles that depend on the Reynolds number are responsible for these effects. No Reynolds number effects were observed when the long side was normal to the flow, an orientation where reattachment at the side walls is not possible. Comparing both basic cases (α=0° and 90°), the interpretation of the probability distributions of lift force leads to the conclusion that the possibility of reattachment (α=0°) seems to enhance the degree of order in the vortex shedding process.     

Wake dynamics of external flow past a curved circular cylinder with the free-stream aligned to the plane of curvature

The fundamental mechanism of vortex shedding past a curved cylinder has been investigated at a Reynolds number of 100 using three-dimensional spectral/hp computations. Two different configurations are presented herein: in both cases the main component of the geometry is a circular cylinder whose centreline is a quarter of a ring and the inflow direction is parallel to the plane of curvature. In the first set of simulations the cylinder is forced to transversely oscillate at a fixed amplitude, while the oscillation frequency has been varied around the Strouhal value. Both geometries exhibit in-phase vortex shedding, with the vortex cores bent according to the body's curvature, although the wake topology is markedly different. In particular, the configuration that was found to suppress the vortex shedding in absence of forced motion exhibits now a primary instability in the near wake. A second set of simulations has been performed imposing an oscillatory roll to the curved cylinder, which is forced to rotate transversely around the axis of its bottom section. This case shows entirely different wake features from the previous one: the vortex shedding appears to be out-of-phase along the body's span, with straight cores that tend to twist after being shed and manifest a secondary spanwise instability. Further, the damping effect stemming from the transverse planar motion of the part of the cylinder parallel to the flow is no longer present, leading to a positive energy transfer from the fluid to the structure.     

The variation in the maximum loading of a circular cylinder impacted by a 2D vortex with time of impact

Direct numerical simulation is used to study the loading of a rigid, circular cylinder impacted by a 2D vortex. The vortex travels within a stream of fluid characterized by Reynolds number of 150. Vortex impact occurs at twenty-five different times within one vortex shedding cycle. Substantial variation is observed in the maximum values of the drag and lift force coefficients. This variation is due to interaction between the impinging vortex and those attached to the cylinder. As the radius of the impinging vortex is increased from one to three times the cylinder’s diameter, the variation in maximum force coefficients with time of impact decreases. The variation decreases because the larger vortex alters the flow field and vortex shedding cycle prior to impacting the cylinder. For structures impacted by a vortex similar in size, significant under-prediction of the maximum loading may occur if variation in loading with vortex impact time is not considered.