Flow patterns and turbulence effects in large cylinder arrays

Studies on flow-induced vibrations in large tube bundles are usually focused solely on frequency analysis, without considering the flow patterns which are responsible for the fluid forces. Furthermore, investigations which involve variations in the spacing ratios do not separate transversal and longitudinal proximity effects. The purpose of this article is to separately analyze the influence of the transversal (T/D) and longitudinal (L/D) spacing ratios of a confined in-line cylinder array with five rows on the flow characteristics and to identify flow patterns. The laser Doppler anemometry technique was employed to acquire the mean velocity and its fluctuations in the transversal and longitudinal directions between the cylinder rows. Strouhal numbers and regimes reported in the literature were identified in the experiments. The same regime did not always persist along all cylinder rows for a given spacing ratio, as a result of the combined longitudinal and transversal proximity effects and also of the generation of turbulence by the array. For the smallest T/D ratio, a quasi-steady behavior associated with the biased flow pattern was noted in the experimental set-up and flip-flopping was observed in one case. Additionally, the flow characteristics in these arrays diverged from tube bundle classifications described in the literature. The behavior of the fluid forces and susceptibility to vibrations in the array were predicted based on the turbulence intensity of the incident flow of the cylinders. The results reinforced the need to extend flow pattern investigations to arrays with more cylinder rows and to consider both transversal and longitudinal proximity effects, when studying flow-induced vibrations.     

Effects of aspect ratio on the drag of a wall-mounted finite-length cylinder in subcritical and critical regimes

The effect of cylinder aspect ratio (??H/d, where H is the cylinder height or length, and d is the cylinder diameter) on the drag of a wall-mounted finite-length circular cylinder in both subcritical and critical regimes is experimentally investigated. Two cases are considered: a smooth cylinder submerged in a turbulent boundary layer and a roughened cylinder immersed in a laminar uniform flow. In the former case, the Reynolds number Re _d (??U _?? d/??, with U _?? being the free-stream velocity and ?? the fluid viscosity) was varied from 2.61?×?10⁴ to 2.87?×?10⁵, and two values of H/d (2.65 and 5) were examined; in the latter case, Re _d ?=?1.24?×?10⁴?C1.73?×?10⁵ and H/d?=?3, 5 and 7. In the subcritical regime, both the drag coefficient C _D and the Strouhal number St are smaller than their counterparts for a two-dimensional cylinder and reduce monotonously with decreasing H/d. The presence of a turbulent boundary layer causes an early transition from the subcritical to critical regime and considerably enlarges the Re _d range of the critical regime. No laminar separation bubble occurs on the finite-length cylinder immersed in the turbulent boundary layer, and consequently, the discontinuity is not observed in the C _D?CRe _d and St?CRe _d curves. In the roughened cylinder case, the Re _d range of the critical regime grows gradually with decreasing H/d, while the C _D crisis becomes less obvious. In both cases, H/d has a negligible effect on the critical value of Re _d at which transition occurs from the subcritical to critical regime.     

Wakes of elliptical cylinders at low Reynolds number

The wakes of elliptical cylinders are numerically investigated at a Reynolds number Re_D = 150. ANSYS-Fluent, based on the finite volume method, is used to simulate two-dimensional Newtonian fluid flow. The cylinder cross-sectional aspect ratio (AR) is varied from 0.25 to 1.0 (circular cylinder), and the angle of attack (α) of the cylinder is changed as α = 0° – 90°. With the changes in AR and α, three distinct wake patterns (patterns I, II, III) are observed, associated with different characteristics of fluid forces. Steady wake (pattern I) is characterised by two steady bubbles forming behind the cylinder, occurring at AR < 0.37 and α < 2.5°. Time-mean drag and fluctuating lift coefficients are small. Pattern II refers to Karman wake followed by steady wake (AR ≥ 0.37 – 0.67, depending on α) with the Karman street transitioning to two steady shear layers downstream. An inflection angle α_i is identified where the time-mean drag of the elliptical cylinder is identical to that of a circular cylinder. Pattern III is the Karman wake followed by secondary wake (AR ≤ 0.67, α > 52°), where the Karman street forming behind the cylinder is modified to a secondary vortex street with a low frequency. The Time-mean drag coefficient is maximum for this pattern.     

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.     

The aerodynamics of a cylinder submerged in the wake of another

Flow-induced fluctuating lift (C_Lf) and drag (C_Df) forces and Strouhal numbers (St) of a cylinder submerged in the wake of another cylinder are investigated experimentally for Reynolds number (Re)=9.7×10³–6.5×10⁴. The spacing ratio L^⁎ (=L/D) between the cylinders is varied from 1.1 to 4.5, where L is the spacing between the cylinders and D is the cylinder diameter. The results show that C_Lf, C_Df and St are highly sensitive to Re due to change in the inherent nature of the flow structure. How the flow structure is dependent on Re and L^⁎ is presented in a flow structure map. Zdravkovich and Pridden (1977) observed a ‘kink’ in time-mean drag distribution at L^⁎≈2.5 for Re>3.1×10⁴, but not for Re≤3.1×10⁴. The physics is provided here behind the presence and absence of the ‘kink’ that was left unexplained since then.     

Flow around a cylinder surrounded by a permeable cylinder in shallow water

The change in flow characteristics downstream of a circular cylinder (inner cylinder) surrounded by an outer permeable cylinder was investigated in shallow water using particle image velocimetry technique. The diameter of the inner cylinder and the water height were kept constant during the experiments as d?=?50?mm and h _w ?=?25?mm, respectively. The depth-averaged free-stream velocity was also kept constant as U?=?170?mm/s which corresponded to a Reynolds number of Re_d?=?8,500 based on the inner cylinder diameter. In order to examine the effect of diameter and porosity of the outer cylinder on flow characteristics of the inner cylinder, five different outer cylinder diameters (D?=?60, 70, 80, 90 and 100?mm) and four different porosities (???=?0.4, 0.5, 0.6 and 0.7) were used. It was shown that both porosity and outer cylinder diameter had a substantial effect on the flow characteristics downstream of the circular cylinder. Turbulent statistics clearly demonstrated that in comparison with the bare cylinder (natural case), turbulent kinetic energy and Reynolds stresses decreased remarkably when an outer cylinder was placed around the inner cylinder. Thereby, the interaction of shear layers of the inner cylinder has been successfully prevented by the presence of outer cylinder. It was suggested by referring to the results that the outer cylinder having 1.6????D/d????2.0 and 0.4????D/d????0.6 should be preferred to have a better flow control in the near wake since the peak magnitude of turbulent kinetic energy was considerably low in comparison with the natural case and it was nearly constant for these mentioned porosities ??, and outer cylinder to inner cylinder diameter ratios D/d.     

Forced convection heat transfer on a heated bottom surface of cavity with different wall-height

Experiments to obtain the heat transfer characteristics of cavity, in which the downstream wall-heightD ₂ was changed from zero toD ₁ of upstream wall-height, have been performed. The vortex flow inside cavity was varied complicatedly depending on aspect-ratio of cavity and main flow velocity, and the flow pattern for cavity ofD ₂/D ₁=0.8 was altered entirely at theRe _H of about 1.5×10⁴. Three heat transfer regions ofNu _m versusRe _H were recognized for the cavity of large aspect-ratio. A close relation between those heat transfer behavior and approaching boundary layer flow was found. Heat transfer correlation was partially obtained for every cavities.     

A numerical study of laminar heat transfer at bottom surface of a cavity submerged in separated flow region of duct

For the two cavity models whose upward and downward wall heights are different from each other, laminar heat transfer is studied numerically in a finite difference method. The effects of cavity configuration, free-stream velocity and buoyancy force on flow and temperature fields as well as heat transfer at the bottom surface are discussed. The flow pattern of DOF (Downward-Facing cavity)-model is more intricated than that of UPF (Upward-Facing cavity)-model, depending on the aspect ratio of cavity or main flow velocity. The mean Nusselt numberNu _m at the bottom surface of both cavity models tends generally to increase with increasing Re_HorGr _w/Re _H ² . However, in the flow region ofRe _H & 500 for DOF-cavity, theNu _m for 0.4 ≦ D₂/D₁ ≦ 0.6 is somewhat lower than that obtained from the other cavities and does not always increase with increasingRe _H.     

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.     

Characteristics and suppression of flow-induced vibrations of two side-by-side circular cylinders

A free-vibration experiment was conducted to examine flow-induced vibration (FIV) characteristics of two identical circular cylinders in side-by-side arrangements at spacing ratio T^⁎ (=T/D)=0.1–3.2, covering all possible flow regimes, where T is the gap spacing between the cylinders and D is the cylinder diameter. Each of the cylinders was two-dimensional, spring mounted, and allowed to vibrate independently in the cross-flow direction. Furthermore, an attempt to suppress flow-induced vibrations was undertaken by attaching flexible sheets at the rear stagnation lines of the cylinders. Based on the vibration responses of the two cylinders, four vibration patterns I, II, III and IV are identified at 0.1≤T^⁎<0.2, 0.2≤T^⁎≤0.9, 0.9<T^⁎<2.1 and 2.1≤T^⁎≤3.2, respectively. Pattern I is characterized by the two cylinders vibrating inphase^, with the maximum amplitudes occurring at the same reduced velocity Ur=10.47 almost two times that (Ur=5.25) for an isolated cylinder. Pattern II features no vibration generated for either cylinder. Pattern III exemplifies the occurrence of the maximum vibration amplitude of a cylinder at a smaller Ur and that of the other cylinder at a higher Ur compared to its counterpart in an isolated cylinder. Pattern IV represents each cylinder response resembling an isolated cylinder response; the vibrations of the two cylinders are, however, coupled inphase or antiphase. Linking maximum vibration amplitudes to fluctuating lift forces acting on fixed cylinders reveals that fluid–structure interactions between two fixed cylinders and between two elastic cylinders are not the same, even though vibration is not significant. As such, while two fixed cylinders generate narrow and wide wakes at 0.2≤T^⁎<1.7, two elastic cylinders do the same for a longer range of T^⁎ (0.2≤T^⁎<2.1). The flexible sheets effectively suppress FIV of the two cylinders in patterns III and IV, and reduce the vibration amplitude in pattern I. For the effectively controlled cases (patterns III and IV), the flexible sheet of each cylinder folds into a semicircle at the base, forming two free edges.     

Flow past a circular cylinder over a free surface: Interaction between the near wake and the free surface deformation

Air-flow around a circular cylinder placed above a free surface and liquid flow under the free surface were investigated experimentally in a wind/wave tunnel. The cylinder spanned the tunnel test-section and was oriented normal to the freestream direction. The main objective of this study was to investigate the interaction of the cylinder wake with the free surface. The flow structure was analyzed for various gap widths, H, between the cylinder and the free surface using a digital particle image velocimetry (PIV) system with a spatial resolution of 2048×2048 pixels. The Reynolds number based on the cylinder diameter was 3.3×10³. For each experimental condition, 400 instantaneous velocity fields were measured and ensemble-averaged to obtain spatial distributions of the mean velocity and turbulence statistics. The results showed that the cylinder near-wake inclined upward due to the influence of the free surface elevation. Vortices were shed, even at a small gap ratio of H/D=0.25, where D is the cylinder diameter. Strong jet-like flow appeared in the gap beneath the cylinder. At a gap ratio of H/D=0.50, the jet flow exhibited a quasi-periodic vibration with a period of 2–3 s. The free surface deformation was caused by the pressure difference in the air-flow immediately above it. As the gap ratio increased, the inclination angle of the wake and the height of the free surface elevation decreased gradually. The liquid flow under the free surface followed a convective flow motion, and the range of the convection depended on the gap width between the cylinder and the free surface.     

Effects of large spanwise wavelength on the wake of a sinusoidal wavy cylinder

The wake of a sinusoidal wavy cylinder with a large spanwise wavelength λ/D_m (=3.79–7.57) and a constant wave amplitude a/D_m=0.152, where D_m is the mean diameter of the cylinder, is investigated using three dimensional (3D) large eddy simulation (LES) at a subcritical Reynolds number Re=3×10³, based on incoming free-stream velocity (U_∞) and D_m. Attention is paid to assimilating the effects of λ/D_m on the cylinder wake, including vortex shedding frequency, spanwise vortex formation length, streamwise velocity distribution, flow separation angle, 3D vortex structure, and turbulent kinetic energy (TKE) distribution. Based on the predominant role of λ/D_m in the near wake modification, three regimes are identified, i.e., regime I at λ/D_m<6.0, regime II at λ/D_m≈6.0 and regime III at λ/D_m>6.0. A dramatic decrease in fluid forces is observed at λ/D_m=6.06, about 16% and 93% reduction in time-averaged drag and fluctuating lift, respectively, compared to those of a smooth cylinder. We identified, for the first time, an optimum λ/D_m (=6.06) for the wavy cylinder with relatively large λ/D_m (>3.5) in the subcritical flow regime. The underlying mechanisms of force reduction are discussed, including the flow characteristics at the three λ/D_m regimes. A comparison is also made between the results of λ/D_m effects on the near wakes of a circular and a square cylinder.     

The near wake of sinusoidal wavy cylinders: Three-dimensional POD analyses

Three-dimensional (3D) proper orthogonal decomposition (POD) analyses are conducted to investigate the near wake of sinusoidal wavy cylinders. For a wave amplitude a/D_m = 0.152, three typical spanwise wavelengths (λ_z) of the wavy cylinder are taken into account, i.e., λ_z/D_m = 1.89, 3.79 and 6.06, where D_m is the mean diameter of the wavy cylinder, among which λ_z/D_m = 1.89 and 6.06 are the optimum wavelengths corresponding to the largest reduction/suppression of fluid forces acting on the wavy cylinder. Time- and space-resolved three-component velocities of the near wake flow, obtained from large eddy simulation (LES) at a subcritical Reynolds number Re = 3 × 10³, are used in the 3D POD analyses. Comparison is made among the wavy cylinders of the three λ_z/D_m values as well as between them and a smooth cylinder, in terms of POD modes, mode energy, mode coefficients, as well as reconstructed flow structures by lower modes. For the optimum λ_z/D_m = 1.89 and 6.06, energy associated with the first two POD modes is significantly reduced compared with that for λ_z/D_m = 3.79 and the smooth cylinder. Distinct characteristics are observed on the lower POD modes for the wavy cylinders. It is found that the first two POD modes for λ_z/D_m = 1.89 and 6.06 are linked to large-scale streamwise vortices that are additionally introduced into the near wake due to the wavy geometry. Meanwhile, POD mode 3 suggests that the wavy cylinder with the larger optimum λ_z/D_m (= 6.06) generates dominant hairpin-like and spanwise coherent structures (CSs) shedding from the saddle at a different frequency from those shedding from the node. Evolutionary development of these CSs is discussed based on reconstructed flows.     

Flow patterns of n-hexadecane–CO2 liquid–liquid two-phase flow in vertical pipes under high pressure

To promote a better understanding of liquid–liquid two-phase flow behavior, particularly under high pressure, flow patterns of n-hexadecane–CO₂ liquid–liquid two-phase upward flow in vertical stainless steel pipes were experimentally investigated. Observations were made in two 0.0015 m I.D. pipes of different lengths (0.068 m and 0.5 m) under high pressure varying from 10.3 to 29.6 MPa using a high pressure visualization system. The total flow rate was fixed at 2.0 × 10⁻⁶ m³/min, while the flow rate ratio (φ) varied from 0.05 to 19. Bubbly flow, plug flow, slug flow, annular flow, and near-one-phase flow regions were found in both pipes, while stratified flow was observed only in the 0.068 m pipe. Flow pattern maps were constructed in the flow rate ratio versus pressure graph, which demonstrates significant impacts of flow rate ratio, pipe length, and pressure on flow patterns. These impacts are discussed in detail. To the authors’ best knowledge, this work is the first attempt to observe complex liquid–liquid two-phase flow behavior with flow pattern transitions under high pressure, and contributes to a better understanding of liquid–liquid two-phase flow behavior.     

Flow characteristics and flow-induced forces of a stationary and rotating triangular cylinder with different incidence angles at low Reynolds numbers

In this paper, the problem of two-dimensional fluid flow past a stationary and rotationally oscillating equilateral triangular cylinder with a variable incident angle, Reynolds number, oscillating amplitude, and oscillating frequency is numerically investigated. The computations are carried out by using a two-step Taylor-characteristic-based Galerkin (TCBG) algorithm. For the stationary cases, simulations are conducted at various incident angles of α=0.0–60.0° and Reynolds numbers of Re=50–160. For the oscillation cases, the investigations are done at various oscillating amplitudes of θ_max=7.5–30.0° and oscillating frequencies of F_s/F_o=0.5–3.0 considering two different incidence angles (α=0.0°, 60.0°) and three different Reynolds numbers (Re=50, 100, 150). The results show that the influences of key parameters (incidence angle, Reynolds number, oscillating amplitude, and oscillating frequency) are significant on the flow pattern and hydrodynamic forces. For the stationary cases, at smaller angle of incidence (α≤30.0°), Reynolds number has a large impact on the position of the separation points. When α is between 30.0° and 60.0°, it was found that the separation points are located at the rear corners. From a topological point of view, the diagram of flow pattern is summarized, including two distinct patterns, namely, main separation and vortex merging. A deep analysis of the influence of Reynolds number and incidence angles on the mean pressure coefficient along the triangular cylinder surface is presented. Additionally, for the oscillating cases, the lock-on phenomenon is captured. The dominant flow patterns are 2S mode and P+S mode in lock-on region at α=0.0°. It is found at α=60.0°, however, that the flow pattern is predominantly 2S mode. Furthermore, except for the case of F_s/F_o=2.0, the mean drag decreases as the oscillating amplitude increases for each Reynolds number at α=0.0°. At α=60.0°, the minimum mean drag for F_s/F_o=1.5 is lower than that for stationary case, and occurs at θ_max=15.0° (Re=100) and θ_max=22.5° (Re=150), respectively. Finally, the effect of Reynolds number on a rotational oscillation cylinder is elucidated.     

Effect of flow diverters on free convection heat transfer from a pair of vertical arrays of isothermal cylinders

Laminar free convection heat transfer from two vertical arrays of five isothermal cylinders separated by flow diverters is studied experimentally using a Mach-Zehnder interferometer. The width of flow diverters is kept constant to two-cylinder diameters and the cylinders vertical center-to-center spacing is equal to three-cylinder diameter. Effect of the ratio of the horizontal spacing between two cylinder arrays to their diameter (S_h/D) on heat transfer from the cylinders is investigated for various Rayleigh numbers. The experiments are performed for S_h/D = 2-4, and the Rayleigh number based on the cylinder diameter ranging from 10³ to 3 × 10³. It is observed that for small S_h/D ratios, the flow diverters have a negative effect on the total rate of heat transfer from the arrays; while by increasing the horizontal center to center spacing, they tend to enhance the overall cooling rate of the array. Moreover, increasing Ra and S_h/D generally results in a higher average Nusselt number for each cylinder in the array.     

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.     

Surface flow pattern and local mass transfer on the free-end surface of a finite circular cylinder

 Relation between the surface flow pattern and the local mass transfer characteristic on the free end surface of a finite circular cylinder mounted on a flat plate was investigated using the oil surface flow visualization and the naphthalene sublimation technique. The aspect ratio [the ratio of the cylinder length to the cylinder diameter (H/D)] was 1.25 and the Reynolds number based on the diameter was 1.48 × 10⁵. Several kinds of critical points on the free-end surface were identified by the visualization and the mass transfer measurement around those critical points through the naphthalene sublimation technique was then performed to investigate the relation between the flow and mass transfer. The free-end surface flow was topologically characterized by the presence of a saddle point and two focal points in the fore-half portion of the surface and two nodes and a saddle point in the rear-half portion. It was found that the rate of mass transfer was largest in the vicinity of the nodes in the rear-half of the free-end surface. Received on 26 April 2000     

Analysis of fluid–structure interaction by an arbitrary Lagrangian–Eulerian finite element formulation

In this paper, the interaction fluid–rigid body is analysed by a finite element procedure that incorporates the arbitrary Lagrangian–Eulerian (ALE) method into a well‐known two‐step projection scheme. The flow is assumed to be two‐dimensional, incompressible and viscous, with no turbulence models being included. The flow past a circular cylinder at ℛℯ=200 is first analysed, for fixed and oscillating conditions. The dependence of lock‐in upon the shift between the mechanical and the Strouhal frequencies, for a given amplitude of forced vibration, is illustrated. The aerodynamic forces and the wake geometry are compared for locked‐in conditions with different driving frequencies. The behaviour of a rectangular cylinder (B/D=4) at ℛℯ=500 (based on height D) is also analysed. The flutter derivatives associated with aerodynamic damping (H₁* and A₂* in Scanlan's notation) are evaluated by the free oscillation method for several values of reduced flow speed above the Strouhal one (namely for 3≤U*≤8). Torsional flutter was attained at U*≥5, with all the other situations showing stable characteristics. Copyright © 1999 John Wiley & Sons, Ltd.     

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.