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.     

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.     

Turbulent winds and pressure effects around a rough cylinder at high Reynolds number

Time histories of the fluctuating wind pressure differential across the shell of a full-scale cooling tower were measured in 1974 by Princeton University personnel. Data were recorded around a single level, at the throat, at a height of ～100 m. A set of simultaneous three-minute records from these data is examined statistically in the present paper. The methods employed include spectral and correlation analyses, plus parametric time-series characterization of the data.Aside from its direct engineering interest as an aid in defining dynamic wind-loading conditions, the fluctuating flow activity around the tower throat may be interpreted as a fair example of turbulent flow about a rough circular cylinder at a Reynolds number approaching 10⁸. This aspect is emphasized in the present paper. In this situation the relation of the spectrum of the incident wind to pressure spectra about the cylindrical section may be of interest in connection with theories of the deformation of turbulence by bluff bodies. Further, the spatial distribution of the “parsimonious” parameters obtained from an autoregressive time-series analysis of the data reveals strong correlations with clearly identifiable flow phenomena around the perimeter, such as key points of the pressure distribution, flow separation, etc.The study, although limited to a single wind record, sixteen peripherally spaced pressure records, and only three minutes of selected time-history data, develops a coherent picture of a turbulent flow phenomenon at high Reynolds number.     

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

This paper presents the results of experiments carried out in an open jet wind tunnel on a group of four equispaced cylinders to determine the lift and drag coefficients for a single cylinder in a group and for the group as a whole. The spacing ratio of their centres was in the range 1.1<S/ D<5 while the angle of inclination or stagger angle of the group varied over the range 0° < α < 180°. In all cases the flow Reynolds number was in the subcritical zone at Re=3×10⁴ based on the diameter of a single cylinder. The results are compared with those obtained for flow interference between a group of three cylinders and it is suggested that these results be included with similarly determined data to form a basic code of design.     

Fluctuating surface shear stresses on bluff bodies

A pulsed wall gauge has been used to obtain measurements of the mean and fluctuating skin friction on the top surface of bluff bodies mounted in thick turbulent boundary layers. The mean flow results presented in our earlier paper [2] are complemented here by further mean surface shear stress data and by fluctuating data, which include some measurements of the probability density function of the instantaneous surface shear stress. By suitable combinations of body geometry and upstream flow properties three different “types” of flow, characterised by very different mean flow behaviour in the vicinity of the body, have been investigated. It is argued that the practically important effects of the flow around such bodies often depend much less on the mean flow structure than on the nature of the fluctuating flow.     

Flow patterns and vortex shedding behavior behind a square cylinder

The flow structures, wake-flow characteristics and drag coefficients of a square cylinder at various Reynolds numbers (Re) and incidence angles (θ) were experimentally studied in an open-loop wind tunnel. The cross section of square cylinder is characterized by the aspect ratio (AR) and blockage ratio (BR) of 25% and 4%, respectively. The Reynolds number is changed from 4000 to 36,000 and the incidence angle is adjusted from 0° to 45°. The flow patterns near/behind the square cylinder were determined using the smoke-wire scheme. The global velocity fields and streamline patterns were analyzed using the particle image velocimetry (PIV). Additionally, the flow-topology method was applied to analyze the flow patterns by calculating the separatrices, alleyways and critical points. Experimental results showed that the flow structures around the square cylinder exhibit three modes—leading-edge separation, separation bubble and attached flow. The surface-pressure profile, drag coefficient (C_D), lift coefficient (C_L) and vortex shedding frequency were detected/calculated using a pressure transducer and hot-wire anemometer. The lift coefficient did not significantly vary with Re. The minimum C_D occurs at θ=12°, whereas the minimum C_L occurs at θ=13°. The minimum projected-Strouhal-number (St_d) occurs at θ=0° while the maximum St_d occurs at θ=15°.     

Aerodynamic stability of the downstream of two tandem square-section cylinders

The work reported in the present paper consists of three parts. In part one, the velocity distribution in the wake of a square cylinder at different distances from it (2⩽x/D⩽12) are measured and reported. Analytical expressions for the wake velocity distribution and for the correlation between wake half-width and downstream distance are obtained. The above expressions make it possible to estimate the wake velocity distribution without the availability of the actual experimental data. In part two, the lift and drag acting on the downstream of two cylinders are measured. The results are found to be in reasonable agreement (except in the range L/D=3–4 and T/D=2–3) with previous measurements, and are presented as contours of constant quantities, which make them useful to other researchers for quick information retrieval or estimation. Based on these steady flow results, the region where the downstream cylinder will become unstable to transverse galloping (static instability) are estimated and reported. In the next part, data are acquired with the downstream cylinder undergoing transverse oscillation. From the measurement of the phase angle between the body frequency component of the lift force and the cylinder displacement, the region where the downstream cylinder will be (dynamically) unstable to transverse galloping is estimated, and is found to be in good agreement with the estimation based on the steady flow results in the range L/D⩽4. The variations of the mean drag as well as the Strouhal number and fluctuating lift and drag of the downstream cylinder with reduced velocity are also measured at different L/D and A/D, and possible explanations for the behaviour of the data are offered.     

Applicability of LES to the turbulent wake of a rectangular cylinder—Comparison with PIV data

The applicability of the large eddy simulation (LES) technique to wake flows past a bluff body should be clarified in order to improve numerical accuracy for the estimation of aerodynamic forces and pressures acting on a bluff body. Here, we conduct both LES and particle image velocimetry (PIV) measurement for turbulent flows past rectangular cylinders with a depth/breadth ratio ranging from D/B=2.00 to 3.00 at Re=2000 and 20,000, which sensitively change turbulence structures due to flow separation and reattachment. For LES, we use the dynamic Smagorinsky-type SGS (sub-grid scale) model. First, at Re=2000 where pure turbulent viscosity without numerical viscosity is realized, the accuracy of the SGS modeling for the prediction of not only aerodynamic characteristics but also turbulence statistics in the wake of rectangular cylinders is examined in comparison with PIV data. Furthermore, at Re=20,000 where the numerical dissipation must be incorporated, we clarify the unfavorable effects of the numerical dissipation on the turbulence structures in the wake.     

Numerical investigation on the three-dimensional unsteady flow past a 5:1 rectangular cylinder

This paper deals with the three-dimensional simulation of the unsteady flow around a stationary 5:1 rectangular cylinder at zero-degree angle of attack, low Mach number (M_∞=0.1) and high Reynolds number (Re=26,400, based on the plate thickness). Detached-Eddy Simulation (DES) was adopted as strategy of turbulence modeling. Results obtained with a hybrid mesh show satisfactory agreement when validated against experimental data and other computational results from the literature. Particular attention is devoted to the effects of the spanwise extension of the computational domain. Results show that the common choice of a spanwise period equal to the chord of the cylinder might not be enough to allow the natural loss of correlation of the pressure fluctuations and the free development of large-scale turbulent structures. The key role played by the amount of numerical dissipation, which is introduced by the second-order central difference scheme used to discretize the inviscid fluxes in the governing equations, is highlighted. The promising results obtained with DES for this benchmark test case suggest that this hybrid method is well suited for complex problems of high-Reynolds number bluff body aerodynamics and fluid-structure coupling.     

Experimental investigation of the aerodynamic stability of the “Endless Column”, Romania

Wind tunnel tests have been performed on several models of the “Endless Column”, a 30 m tall sculpture, created by C. Brancusi in 1938. In spite of its slenderness, the Column, located in Targul Jiu, Romania, has shown a great stability against wind. In order to clarify if the symmetric, original shape has influence upon its stability, we have carried out tests on section models of “Endless Column” shape (EC models) and square shape (SQ models), of various Sc numbers. Across-wind response was determined in smooth flow for wind speeds in wind tunnel of 1–10 m/s (Re=4000–46,000) for angles of attack 0°, 10° and 45°. Furthermore, an aerolastic full model was created and tests under smooth and turbulent flow conditions were performed for angles of attack between 0° and 45°. For low wind speeds, in the area of vortex-induced vibrations, the EC models had similar response with the SQ models; however, for higher wind speeds the EC models proved to be more stable. Based on measurements of aerodynamic drag and lift coefficients and by a verification of Glauert den Hartog criterion, it could be concluded that is a very low possibility for EC model to encounter galloping; for extremely high wind speeds though, this might not be impossible.     

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.     

The effect of nonharmonic forcing on bluff-body aerodynamics at a low Reynolds number

The aerodynamic response of a circular cylinder to nonharmonic forcing of the inflow velocity is studied by numerically solving the equations of two-dimensional fluid motion on an orthogonal curvilinear mesh. The effect of varying the inflow velocity waveform while maintaining other forcing parameters constant at a Reynolds number of 180 is considered in this study. The forcing frequency is 84% of the natural vortex shedding frequency in the unforced wake while the peak-to-peak amplitude of velocity oscillation is 65% of the reference velocity. Results are reported for the drag and lift coefficients and the flow field in terms of streamline patterns and vorticity distributions. It is shown that the wake is locked-on to the forcing frequency for all cases tested but the aerodynamic response is systematically modified by the imposed changes in the velocity waveform. The magnitude and the phase of the fluctuating drag and lift forces and the mean drag force are affected. These effects are associated with changes in the mechanism of vortex formation and shedding in the wake of the cylinder; it is found that the rolling up of the individual shear layers on both sides can be manipulated to promote shedding of single vortices or vortex pairs.     

Air entrainment and turbulent fluctuations in hydraulic jumps

A hydraulic jump is the sudden transition from a high-velocity impinging flow into a turbulent roller in an open channel. Substantial amounts of air are entrapped at the impingement point, and significant free-surface fluctuations take place above the roller. In the present study, some physical modelling was conducted in a relatively large sized facility. The flow conditions included a wide ranges of inflow Froude numbers and Reynolds numbers (3.8 < Fr₁ < 10.0, 2.1 × 10⁴ < Re < 1.6 × 10⁵). The fluctuating features of free-surface and roller position were investigated non-intrusively with a series of acoustic displacement meters. The characteristic frequencies of the fluctuating motions were documented, and some major roller surface deformation patterns were revealed. The air-water flow properties were investigated with an intrusive phase-detection probe. The void fraction and bubble count rate data were documented in the jump roller, together with the interfacial velocity distributions. The rate of air entrainment was estimated based upon the void fraction and interfacial velocity distribution data. Some simultaneous measurements of instantaneous void fraction and free-surface fluctuations as well as longitudinal jump front oscillations were conducted. The relationship between the rate of air entrainment and turbulent fluctuations is discussed. Both the turbulent fluctuation and aeration properties are basic design parameters in urban water systems in which a hydraulic jump may take place. The present work provides relevant information for water systems including covered channels and partially-filled pipes.     

Regular drag fluctuations due to air flow normal to a plate-type structure

A model structure resembling a flat plate (or a tall prestige building) was tested in a low-turbulence wind tunnel. With flow normal to the façade the model oscillated vigorously in the flow direction when passing through a “critical” velocity range. A sufficient minimum of experimental circumstances are reported to facilitate future search for this “Big Foot” phenomenon that should interest all those who assume that the dynamic drag forces of bluff structures are soley due to the turbulent wind field.     

A comparative study of three aerodynamic devices for suppressing vortex-induced oscillation

Three main types of aerodynamic damping devices, namely, a perforated shroud, helical strakes, and longitudinal slats, have been fitted on a circular cylinder for study in the same wind tunnel and under similar conditions. The drag coefficient of each device has also been determined at Reynolds numbers up to 1.5 × 10⁵.     

Aerodynamic forces acting on a rectangular prism placed vertically in a turbulent boundary layer

An experimental investigation was carried out into the aerodynamic forces acting on a rectangular prism with a square cross-section, placed vertically in a turbulent boundary layer. Experimental data were collected to examine the effects on the aerodynamic forces due to variations of (1) the parameters characterizing the boundary layer, (2) the aspect ratio of the prism, and (3) the angle of attack of approaching flow. For flow with zero angle of attack, the pressure drag coefficient of the prism defined by $\text{C}{}_{\mathrm{<mtext>D</mtext><mtext>\tau </mtext>}}\text{= D/(}\text{1}\text{2}\text{?u}{}_{\mathrm{\tau }}{}^2\text{hw)}$ was found to be expressed by a power function hu_τ/ν in the range h/δ < 1.2?;1.4 for each aspect ratio $\text{h}\text{w}$, where D is the time-mean drag, u_τ is the shear velocity, ? is the density of fluid, h and w are the height and width of the prism, respectively, ν is the kinematic viscosity, and δ is the thickness of the boundary layer. It was also found that the drag coefficient is uniquely related to h/δ in the range of h/δ larger than 1.2–1.4, and the characteristics of the mean and fluctuating aerodynamic forces varying with the angle of attack are similar to those obtained from a two-dimensional rectangular prism. However, the magnitudes of the mean and fluctuating forces were found to be considerably smaller than those of the two-dimensional rectangular prism.     

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。     

Effect of rotational oscillation upon fluid forces about a circular cylinder

The present work aims at a computational study of the effect of various parameters that influence fluid-force behavior when a circular cylinder is subjected to rotational oscillations. A numerical simulation is conducted using the unsteady form of Reynolds-averaged Navier-Stokes equations combined with the k-ε model of turbulence. The study is carried out to examine the influence of various flow parameters, such as oscillation non-dimensional frequencies (0.1-2), rotational non-dimensional amplitudes (0.25-3) and Reynolds numbers (2000-30,000). Special attention is focused on the resonance condition at lower frequency and the subsequent drag reduction at higher frequency. It is found that the peak value of fluid forces on the circular cylinder increases abruptly when the forcing frequency is closer to the vortex shedding frequency. This is followed by a drag reduction at higher forcing frequencies, which becomes very strong at a non-dimensional oscillation frequency around 1 and at rotational amplitudes larger than 1. The former phenomenon is found to intensify with an increase in Reynolds numbers, but the latter almost preserves its strength in the range of Reynolds numbers considered here.     

Spanwise pressure coherence on prisms using wavelet transform and spectral proper orthogonal decomposition based tools

This paper presents new approaches to clarifying spanwise pressure coherence on typical prisms using some advanced tools based on continuous wavelet transform and spectral-branched proper orthogonal decomposition. Wavelet coherence and coherence modes have been developed for mapping characteristics of spanwise coherence of pressure and turbulence. Temporal-spectral spanwise coherence maps have been represented in the time-frequency plane and spatial-spectral spanwise coherence maps have been expressed in the space-frequency plane. Some new findings are that spanwise pressure coherence not only depends on spanwise separation, frequency and turbulent conditions, but is also influenced by bluff body flow and time. Intermittent and time-dependent pressure coherence in the time domain has been investigated as the nature of pressure coherence. Furthermore, distribution and intermittency of pressure coherence are significantly influenced by analyzed time-frequency resolutions and parameters of the analyzed wavelet function. The coherence mode has been proposed for better understanding of the effect of bluff body flow on pressure coherence. Physical measurements of surface fluctuating pressure and turbulence have been carried out on typical prisms with slenderness ratios of B/D=1 and 5 in turbulent flow.     

Study of the vortex shedding flow around a body near a moving ground

The two-dimensional viscous incompressible fluid flow around a circular cylinder near a moving ground is numerically simulated. In a moving ground one eliminates the influence of the ground boundary layer, which is a crucial factor in the numerical simulation of the flow around a body moving in a close vicinity to a flat ground. A Lagrangian mesh-free vortex method is used to calculate global and local quantities of high Reynolds number flow of 1.0×10⁵. This method is modified to take into account the sub-grid scale phenomena through a second-order velocity structure function model adapted to the Lagrangian scheme. In the present algorithm vortices with a Lamb core are generated only on the circular cylinder surface to ensure that the no-slip condition is satisfied and that the circulation is conserved. On the ground it is only sufficient to ensure the impermeability condition. Based on the experimental results available in the literature, the critical drag behaviour was found to be directly related to a global change in the near wake structure of the cylinder.