Effect of blockage on the strouhal number of two-dimensional bluff bodies

From considerations of the vortex flow equations, it is deduced that the Strouhal number $\text{S′}$ for two-dimensional bluff bodies under wall confinement (blockage) is linearly dependent upon the shear-layer velocity parameter $\text{k′}$. This is substantiated by experimental data for a circular cylinder and reactangular prisms. It is also found that, for rectangular prisms, the value of the base pressure gives a good estimate of the drag and the Strouhal number irrespective of the blockage ratio.     

Vortex shedding from bluff cylinders in strongly sheared turbulent streams

Vortex shedding frequencies across circular and rectangular cylinders in uniformly sheared turbulent flow have been measured at high subcritical Reynolds numbers and large shear parameters and turbulence intensities. The results confirm the occurence of spanwise cells with nearly constant shedding frequency. The presence of strong shear and turbulence appears, in general, to cause a strong spanwise variation of the local base pressure coefficient and an appreciable decrease of the average Strouhal number.     

Flow interference between three equispaced cylinders when subjected to a cross flow

The drag and lift coefficients occurring on one cylinder in a group of three lying with their axes perpendicular to a uniform stream flow have been measured at a flow Reynolds number of 3 × 10⁴ at various inclination angles to the free stream. The cylinders were arranged with their centres equidistant from each other (an equilateral triangle), the spacing ratio of their centres being in the range 1.25 < S/D < 5.From the force coefficients for the individual cylinders, total force coefficients for the group as a whole and the direction in which the resultant force acts were determined. It was found that at certain inclination angles the force coefficients were similar to those pertaining to two-cylinder flow, but that in general the effect of the third cylinder was significant. The results presented should aid in the establishment of standard design codes for flow interference around groups of cylinders.     

Aerodynamic forces on structures of circular cross-section. Part 2. The influence of turbulence and three-dimensional effects

The review discusses the influence of turbulence and certain three-dimensional effects on the mean drag coefficient, the Strouhal Number and the root-mean-square lift coefficient. The data show that the nature of the effects of turbulence depends on the ratio of the scale of turbulence and the diameter of the cylinder. The effects of large scale turbulence are adequately predicted by quasi-steady theory. Small scale turbulence is better able to penetrate the shear layers around the cylinders and thus influence the mean and fluctuating pressure distributions, and also to cause premature transitions from one Reynolds number regime to another. Small scale turbulence can cause dramatic increases in fluctuating lift. The strength of pressure fluctuations due to vortex shedding is shown to be closely related to angle of separation.The data on the spanwise correlation of fluctuating lift display considerable scatter. While the data suggest that this parameter is sensitive to the effects of turbulence, aspect ratio etc. it is difficult to quantify the influences because of the limited data, particularly for high Reynolds numbers. The same is true of the data on the effects of finite aspect ratio. The latter subject is discussed in detail.     

Across-wind vibrations of structures of circular cross-section. Part I. Development of a mathematical model for two-dimensional conditions

A model is presented for predicting the across-wind response of constant-diameter circular cylinders vibrating in a mode of uniform amplitude and subject to uniform flow. A key feature of the model is the representation of all motion-dependent phenomena by a nonlinear aerodynamic damping force. This force coexists with the fluctuating force which arises from vortex shedding on a stationary cylinder, and the two forces are assumed to be uncorrelated.The ability of the device used in representing the motion-induced force to model certain aeroelastic characteristics associated with vibrating cylinders is demonstrated. The device is shown to be capable of successfully reproducing two effects; namely, the increase of the spanwise correlation of forces with increasing amplitude, and the phenomenon of “lock in” where the shedding frequency is apparently dictated by the vibration frequency.The model is developed within the framework of random-vibration theory, and a number of simplifying assumptions are necessary to incorporate the nonlinear aerodynamic damping force and also to account for the influence of turbulence. Numerical experiments, undertaken to examine the nature of the approximations involved in the assumptions adopted, are described. The results of the numerical experiments are very encouraging and justify the simplifications made in the modelling process.     

An examination of the effect of boundary layer thickness on vortex shedding from a square cylinder near a wall

A computational study has been undertaken to examine the effect of boundary layer thickness δ/D on vortex shedding from a square cylinder in proximity to a solid wall. The computations were carried out in a second-moment turbulence modeling framework using a finite-volume technique. The computed results show that, in general, thickening of the wall boundary layer causes wake periodicity to persist for increasingly smaller cylinder-to-wall gap widths, S/D. The nature of the periodic motion changes as S/D approaches the critical value for complete suppression of vortex shedding. Similar to experimental observations, the location at which coupled shear layer motion is first observed shifts downstream of the base region. This shift is characterized by a rise in the shedding frequency and a drop in the time-averaged drag and lift on the cylinder. In addition, the pressure distribution along the lower wall is seen to change significantly due to the reduced size of the recirculation region in the cylinder wake.     

Wind-tunnel-wall constraint on two-dimensional rectangular-section prisms

The effect of wall constraint on rectangular-section prisms is investigated experimentally in a low-turbulence wind tunnel up to a blockage ratio of 0.25. The depth to width ratio ($\text{d}\text{h}$) of the sections varies from 0.5 to 5.0.It is shown that the effect of confinement on the mean surface pressure on the models is not uniform in the streamwise direction and therefore cannot be regarded as an increase in the effective dynamic pressure estimated from drag or base pressure measurements as assumed by some investigators. The current bluff-body blockage correction formulae are found to be inadequate for correcting the drag and base pressure for these sections, particularly at large blockage ratios. A new equation, which is a modification of Maskell's equation and includes a shape factor to allow for the depth of the rectangular section, yields satisfactorily corrected drag and base pressure. Due to the large depth of the sections in the stream direction, corrections to the pressure distribution around them for blockage using this equation, are not very satisfactory. The correction for the Strouhal number using the new equation is valid up to $\text{d}\text{h}\text{= 3.0}$.     

串列双方柱气动干扰效应试验研究

为了进一步澄清串列方柱的气动干扰效应,以串列双方柱为研究对象,在雷诺数Re=8.0×104、间距比P/B为1.25~5(其中P为方柱中心间距、B为方柱边长)条件下,通过风洞试验同步测得上下游方柱沿周向和展向的表面风压,研究了上下游方柱的风压和气动力特性、两方柱之间气动力的柱间相关性、各方柱气动力沿展向的柱内相关性等随方柱间距的变化情况,分析并给出了干扰条件下非高斯风压沿方柱周向的分布区域。研究结果表明：串列双方柱的临界间距比P/B处在3和3.5之间,在临界间距前后,两个方柱的气动性能均会发生突变;气动力的柱间相关性和柱内相关性随方柱间距变化剧烈,间距比P/B=1.25的串列方柱的气动力柱内相关性远强于单方柱;串列双方柱的风压非高斯区域随间距比的变化较大,下游方柱表面风压的非高斯特性较单方柱更为显著。     

Re-examination of the effect of a plane boundary on force and vortex shedding of a circular cylinder

The hydrodynamic forces and vortex shedding of a smooth circular cylinder immersed in different boundary layers were experimentally investigated at Reynolds numbers from 1.30×10⁴ to 1.45×10⁴. The effects of the bed proximity, the thickness of the boundary layer, and the velocity gradient in the boundary layer on the pressure distribution, the hydrodynamic forces and the vortex shedding behavior were examined. The experimental results show that both the drag and lift coefficients strongly depend on the gap ratio, and are affected by the boundary layer. A downward lift is observed at certain gap ratios in rod-generated boundary layers, and an explanation of this downward lift is given. Two different criteria for calculating the Strouhal number in the literature are discussed in this paper. It is found that the variation of the root-mean-square (RMS) lift coefficient reveals the onset or suppression of the vortex shedding. A quantitative method for identifying the vortex shedding suppression point is proposed. The observations show that the vortex shedding is suppressed at a gap ratio of about 0.2–0.3, depending on the thickness of the boundary layer. This critical gap ratio decreases as the thickness of the boundary layer increases.     

Experimental study of the interaction between a pair of circular cylinders normal to a uniform shear flow

The flow about two cylinders of diameter D, displaced in a plane normal to a uniformly sheared free stream with a centreline separation H, has been investigated experimentally. The freestream shear parameter (D/U_c)dU/dy was 1.48 × 10^?2, and the Reynolds number based on the freestream central velocity was 4.3 × 10⁴. Three distinct flow regions were observed: for 1.1<H/D<1.8 the flow through the gap between the cylinders is biased and unstable; for 1.8?H/D<2.0 the flow through the gap is biased and stable; and for 2?H/D the gap flow is not biased. The present paper describes the effects of mutual interference on the pressure distributions, the vortex-shedding frequencies and the interaction of the vortex streets for these three regions.     

Large-eddy simulation of flows past complex truss structures

Numerical simulation of turbulent flows past typical truss structures that are common in bridges and towers has been conducted. Large-eddy simulation (LES) method is used that has been verified in computing flows past simple bodies at moderate Reynolds numbers. Truss structures consist of thin members that are too small to be accurately resolved by numerical grids that can be handled by most computer systems. It has been found that when the individual members are long angular bars, the overall flow can be reproduced fairly well by approximating the members with rectangular cylinders whose cross sections are resolved by more than 2×2 computational cells and by taking computational regions extending at least four structure heights downstream and about three heights across the vertical and spanwise directions. The drag coefficient and the vortex shedding characteristics along with the complex wake structures associated with the truss structures are reproduced reasonably well.     

The effect of surface strands,angle of attack,and ice accretion on the flow field around electrical power cables

The influence of surface strands, angle of attack, and ice accumulation on the flow field around electrical power cables of various geometries is not clearly understood. The purpose of this study was to examine the effect of these factors on the near wake flow field of three stationary wind tunnel models, namely, Model 1 (smooth and heavily iced), Model 2 (stranded and lightly iced), and Model 3 (stranded and heavily iced). Some angles of attack, θ, significantly altered the flow field by encouraging a rise in Strouhal number for all models at θ=0°, for Model 2 at θ=150–160°, and for Model 3 at θ=180°. Under certain conditions (θ=0°, U >22 m/s, Re>42,000) for Model 3, dual vortex shedding frequency peaks were present. These changes in Strouhal number may potentially predispose models to low drag and high lift forces.     

A note on two-dimensional fence flows,with emphasis on wall constraint

An experimental investigation of the effects of wind tunnel blockage on the flow over two-dimensional surface mounted flat plates is reported. The blockage ratio was varied for a range of boundary layer thickness to fence height ratio ($\text{δ}\text{h}$) and wall friction to free stream velocity ratios ($\text{U}{}_{\mathrm{\tau }}\text{U}{}_1$). Measurements of fence surface pressures and the length of the downstream recirculation zone indicated that the effect of wall constraint was, in general, inseparable from the effects of the upstream flow characteristics. In contrast to the case of plates normal to a uniform free stream, blockage had a significant effect on the maximum front face pressures. This effect, like that on the base pressure, seemed to correlate with $\text{U}{}_{\mathrm{\tau }}\text{h}\text{ν}$ whereas the resultant variations of drag with blockage were dependent on $\text{δ}\text{h}$. Both the normalised length, $\text{R}{}_{\mathrm{<mtext>L</mtext>}}\text{h}$, of the recirculating region at zero blockage and its variation with blockage were also determined by $\text{δ}\text{h}$ only, but there was clearly no simple qualitative connection between $\text{R}{}_{\mathrm{<mtext>L</mtext>}}\text{h}$ and the base pressure, C_pp, as their often is for bluff bodies away from a boundary.Despite previous attempts in the literature to look for a correlation between fence drag and a single boundary layer parameter (Plate [1]; Good and Joubert [2]; Raju et al. [3], it is argued that any such correlation is probably marginal. The implications of these results for bluff body experiments of the ‘environmental’ kind are briefly discussed.     

Characterization of flow oblique to a circular cylinder with low aspect ratio using 3-D detached eddy simulation

Large-amplitude vibrations of stay cables in cable-stayed bridges can threaten the safety and serviceability of the structures. Understanding of the excitation mechanism is necessary to mitigate such vibrations effectively and efficiently. Experimental research has investigated the mechanism of oscillation using flow oblique to a cylinder; however, since the aspect ratio of the cylinder is much lower than that of a real stay cable in bridges, the results might not reliably describe the real phenomenon. The aim of this study is (1) to provide better understanding of aspect ratio effects of a circular cylinder on aerodynamic characteristics of the cylinder oblique to flow associated with the large-amplitude cable vibrations and (2) to provide the experimentalists suggestions of a requisite aspect ratio and appropriate pressure-measuring positions of a cylinder for fully developed flow around the cylinder. To this end, the current work applied three-dimensional detached eddy simulations (DES) to flow around a yawed and inclined cylinder to investigate the importance of the aspect ratio of the cylinder when flow oblique to the cylinder develops fully along its spanwise axis. The Reynolds number is 1.4 × 10⁵ based on the incoming flow velocity and the diameter of the cylinder. Three aspect ratios (L/D=10, 20, and 30; L: a cylinder length; D: a cylinder diameter) and two numerical conditions (slip and periodic) on spanwise boundaries were employed. Results showed that three-dimensional flow and the associated forces on a yawed and inclined cylinder are significantly influenced by the spanwise aspect ratios and spanwise boundary conditions. This study suggests that when a wind tunnel experiment investigates flow oblique to a very slender cylinder, such as attempting to model a stay cable, experimentalists should use a sufficiently high spanwise aspect ratio of the cylinder. For the case of the 30° yaw and 45° inclined cylinder, the requisite ratio would be approximately 60 or higher and appropriate pressure-measuring positions of a half to two-thirds of the cylinder length from its upper/upstream end in order to accurately model inherently three-dimensional characteristics of the flow.     

Effects of the vibration regime on the spanwise correlation of the aerodynamic forces on a 5:1 rectangular cylinder

It is well known that the spanwise correlation of aerodynamic pressures and forces on vibrating cylinders increases with the amplitude of oscillation. Little knowledge, however, exists on how the nature of the motion, i.e. the degree of freedom in which the body vibrates and the reduced wind velocity, affects such correlation. In this paper, some results are presented of a wind tunnel study aimed at investigating the spanwise correlation of aerodynamic pressure and force fluctuations on a rectangular cylinder with an aspect ratio of 5:1. Measurements were carried out on the stationary cylinder and in four dynamic configurations, each characterised by different values of the heaving and pitching natural frequencies. With varying reduced wind velocity, in each dynamic configuration the three vibration regimes of vortex shedding lock-in, forced motion and flutter were observed in the tests. In the paper only two dynamic configurations are presented, one being that in which the heaving and pitching natural frequencies in still air coincide. This is an interesting case, in which the dynamic response is very much affected by the possibility that the motion has of switching from one degree of freedom to another.     

On the wake with and without vortex shedding suppression behind a two-dimensional square cylinder in proximity to a plane wall

A comparative study of the wake characteristics behind a two-dimensional square cylinder in proximity to a plane wall was made on two systems, i.e. G/D=0.25 and 0.5, which corresponds to the wakes with and without suppression of the vortex shedding, respectively. Here, G is the gap distance and D is the width of the square cylinder. Synchronized measurements of wall-pressure fluctuations and velocity fluctuations were made using a microphone array and a split-fiber film, respectively. For the system G/D=0.5, a regular Karman-like vortex shedding at fD/U₀=0.13 was found by inspection of the streamwise velocity spectra. When the gap width is reduced to G/D=0.25, a low-speed separation bubble was formed in the region 4.25<x/D<9.25, while the intermittent existence of large-scale vortices at the reduced frequency fD/U₀=0.116 was identified in the upper shear layer. The convective vortex dynamics were analyzed in terms of the cross-correlation of the wall-pressure fluctuation, coherence and cross-correlation of wall-pressure fluctuations with velocity fluctuations at various positions located at the lower edge of the cylinder (y/D=G/D) and the outer edge of the upper shear layer. The convection velocities of the Karman-like vortices in the system G/D=0.5 was determined to be U_c/U₀=0.64. However, in the system G/D=0.25 the convection velocities before and behind x/D=3.25 were determined to be U_c/U₀=0.32 and 0.64, respectively.     

Drag reduction on a circular cylinder using dual detached splitter plates

Drag reduction on a circular cylinder using dual detached splitter plates is numerically studied. Two splitter plates with the same length as the cylinder diameter (d) are placed along the horizontal centerline; one is upstream of the cylinder and the other is in the near-wake region, respectively. Their positions are described by the gap ratios G₁/d, G₂/d, where G₁ represents the gap between the cylinder stagnation point and the rear edge of the upstream splitter plate, and G₂ denotes the gap between the cylinder base point and the leading edge of the downstream splitter plate. The drag varies with the two gap ratios; it has the minimum value at a certain set of gap ratios for each Reynolds number. The upstream splitter plate reduces the stagnation pressure by friction, while the downstream one increases the base pressure by suppressing vortex shedding. This combined effect causes a significant drag reduction on the cylinder. In particular, the drag sharply increases past the optimum G₂/d; this is related to the restarted vortex shedding in the wake region.