Features of flow-induced forces deduced from wavelet analysis

In the present study, the effect of Reynolds number (Re) on flow interference between two side-by-side stationary cylinders and the associated flow-induced forces are investigated using finite element method and wavelet analysis. The pitch ratio chosen is T/D=1.7, where T is the separation distance measured between cylinder centers and D is the diameter, and Re, based on the free-stream velocity and the diameter of the cylinder, is varied within the laminar flow regime, i.e., 60<Re<200. The method of continuous wavelet transform is used to analyze time-variant features of flow-induced forces in the time–frequency domain. Flow patterns in the form of vorticity plots are presented to demonstrate the underlying physics. It is found that flow interference initially occurs in the inner vortices shed from the two cylinders, and extends to the outer vortices with increasing Re. The flow behind two cylinders undergoes three regimes: Regime I—unbiased gap flow, Regime II—stable biased gap flow, and Regime III—unstable gap flow. Flow-induced forces show significant variations when the flow transits from one regime to another. In particular, during the transition from Regimes II to III, the forces not only increase by amplitude, but also change their nature from deterministic to random, and show some nonstationary features. This is shown to be caused by the amalgamation of inner and outer vortices behind the two cylinders when the flow interference extends from inner vortices to outer vortices. Whenever possible, the present results are compared with experimental measurements and theoretical predictions. The numerical simulations are consistent with these other results.     

Cross-flow past a pair of nearly in-line cylinders with the upstream cylinder subjected to a transverse harmonic oscillation

An experimental investigation is presented for the cross-flow past a pair of staggered circular cylinders, with the upstream cylinder subject to forced harmonic oscillation transverse to the flow direction. Experiments were conducted in a water tunnel with Reynolds numbers, based on upstream velocity, U, and cylinder diameter, D, in the range 1440⩽Re⩽1680. The longitudinal separation between cylinder centres is L/D=2.0, with a transverse separation (for the mean position of the upstream cylinder) of T/D=0.17; the magnitude of the harmonic oscillation is 0.44D peak-to-peak and the nondimensional frequency range of the excitation is 0.05⩽f_eD/U⩽0.44. Flow visualization of the wake-formation region and hot-film measurements of the wake spectra are used to investigate the wake-formation process. An earlier study showed that stationary cylinders in this nearly in-line configuration straddle two very different flow regimes, the so-called shear-layer reattachment (SLR) and induced separation (IS) regimes. The present study, demonstrates that oscillation of the upstream cylinder causes considerable modification of the flow patterns around the cylinders. In particular, the wake experiences strong periodicities at the frequency of the oscillating cylinder; in addition to the usual fundamental lock-in, both sub- and superharmonic resonances are obtained. It is also observed that, although the flow exhibits regions of SLR and IS for excitation frequencies below the fundamental lock-in, for frequencies above the lock-in range the flow no longer resembles either of these flow regimes and vortices are formed in the gap between the cylinders.     

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

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

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

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

Dependence of flow classification on the Reynolds number for a two-cylinder wake

This work aims to investigate the dependence of flow classification on the Reynolds number (Re) for the wake of two staggered cylinders. The Re examined ranges from 1.5×10³ to 2.0×10⁴. The pitch ratio, P^⁎=P/d examined is 1.2–6.0 (d is the cylinder diameter), and angle (α) is 0–90°, where P is the center-to-center spacing between two cylinders and α is the angle between the incident flow and the line through the cylinder centers. Two single hotwires were used to measure simultaneously the fluctuating streamwise velocities (u) in the vortex streets generated by the two cylinders. The power spectral density functions and the Strouhal numbers were then obtained from the u signals, based on which the flow structure pattern or mode could be determined. Over two hundred configurations of two staggered cylinders have been examined for each Re. It is found that Re has an appreciable effect on the dependence of the flow mode on P^⁎ and α. The observation is connected to the Re effect on the generic features of a two-cylinder wake such as flow separation, boundary layer thickness, gap flow deflection and vortex formation length.     

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.     

Vortex dynamics of a cylinder wake in proximity to a wall

Large-eddy simulations (LES) are used to investigate the modifications of wake dynamics and turbulence characteristics behind a circular cylinder placed near a wall for varying gap-to-diameter (G/D) ratios (where G signifies the gap between the wall and the cylinder, and D the cylinder diameter). The three-dimensional (3-D), time-dependent, incompressible Navier–Stokes equations with a dynamic subgrid-scale model are solved using a symmetry-preserving finite-difference scheme of second-order spatial and temporal accuracy. The immersed boundary (IB) method is employed to impose the no-slip boundary condition on the cylinder surface. Flow visualizations along with turbulence statistics are presented to gain insight into the flow structures that are due to interaction between the shear layers and the approaching boundary layer. Apart from the vortex shedding mechanism, the paper illustrates the physics involving the shear layer transition, stretching, breakdown and turbulence generation, either qualitatively or quantitatively, in the presence of a wall for a Reynolds number of Re=1440 (based on D and the inlet free-stream velocity U_∞).     

Experimental Investigation of the Transverse Self-Oscillations of Circular Cylinders Mounted with a Narrow Clearance in a Plane Channel

The results of an investigation of the flow past and the behavior of free bluff bodies mounted in pipes and channels with a narrow clearance, conducted in the Institute of Mechanics of Moscow State University, are presented. The drag of circular cylinders of different size and mass in a circulation-free water flow in a plane channel of rectangular cross-section was studied in the transverse self-oscillation regime. The experiments were conducted for Reynolds numbers based on the cylinder diameter 1.7 ? 10⁴ ≤ Re ≤ 7.2 ? 10⁴, relative clearances \(\bar S\) based on a cross-sectional area ranging from 0.76 to 0.9, and cylinder-to-water density ratios ρ _c /ρ ranging from 1.29 to 8.2. Only the case of intense transverse self-oscillations accompanied by impact interaction with the channel wall was considered. The dependence of the period-average cylinder drag coefficient C _x on the basic dimensionless relevant parameters is obtained. The dependence of the dimensionless self-oscillation frequency determined in [1] is refined. The kinematic and dynamic features of the flows past spheres in cylindrical pipes and cylinders in plane channels are compared in the transverse self-oscillation regime.     

ONSET OF ASYMMETRY: FLOW PAST CIRCULAR AND ELLIPTIC CYLINDERS

A computational study of the development of two- dimensional unsteady viscous incompressible flow around a circular cylinder and elliptic cylinders is undertaken at a Reynolds number of 10,000. A higher- order upwind scheme is used to solve the Navier–Stokes equations by the finite difference method in order to study the onset of computed asymmetry around bluff bodies. For the computed cases the ellipses develop asymmetry much earlier than the circular cylinder. The receptivity of the computed flows in the presence of discrete roughness and surface vibration is studied. Finally, the role of discrete roughness in triggering asymmetry for flow past a circular cylinder is studied and compared with flow visualization experiments at Re=10,000     

Flow structure around two finite circular cylinders located in an atmospheric boundary layer: side-by-side arrangement

The flow structure around the free-end region of two adjacent finite circular cylinders embedded in an atmospheric boundary layer (ABL) was investigated experimentally. The experiments were carried out in a closed-return-type subsonic wind tunnel, in which two finite cylinders with an aspect ratio of 6 were mounted vertically on a flat plate in a side-by-side arrangement. The Reynolds number based on the cylinder diameter was about Re=2×10⁴. Systems with gap ratios (i.e., center-to-center distance/cylinder diameter) in the range 1.0–2.0 were investigated. A hot-wire anemometer was employed to measure the wake velocity, and the mean pressure distribution on the cylinder surface was also measured. The flow past two finite cylinders was found to have a complicated three-dimensional wake structure in the region near the free ends. As the gap ratio increases, regular vortex-shedding becomes dominant, but the length of the vortex formation region decreases. The pressure distribution and flow structure around two cylinders were found to differ substantially from the behavior of a two-dimensional circular cylinder due to mutual interference. The three-dimensional flow structure seems to originate from the strong entrainment of irrotational fluids caused by the downwash counter-rotating vortices separated from the finite cylinder (FC) free ends.     

Orbital flow past a cylinder: A numerical approach

Orbital flow past a cylinder is relevant to offshore structures. The numerical scheme presented here is based on a finite-difference solution of the Navier–Stokes equations. Alternating-directional-implicit (ADI) and successive-over-relaxation (SOR) techniques are used to solve the vorticity-transport and stream-function equations. Theoretical simulations to low Reynolds number flows (up to 1000) are discussed for cases involving uniform flow past stationary and rotating cylinders and orbital flow past a cylinder. The separation points for cylinders that are rotating or immersed in an orbital flow are deduced from velocity profiles through the boundary layer using a hybrid mesh scheme. During the initial development of orbital flow surface vorticity on the impulsively started cylinder dominates the flow. A vortex then detaches from behind the cylinder and establishes the flow pattern of the orbit. After some time a collection of vortices circles the orbit and distorts its shape a great deal. These vortices gradually spiral outward as others detach from the cylinder and join the orbital path.     

Strouhal numbers,forces and flow structures around two tandem cylinders of different diameters

This paper presents a detailed investigation of Strouhal numbers, forces and flow structures in the wake of two tandem cylinders of different diameters. While the downstream cylinder diameter, D, was fixed at 25 mm, the upstream cylinder diameter, d, was varied from 0.24D to D. The spacing between the cylinders was 5.5d, at which vortices were shed from both cylinders. Two distinct vortex frequencies were detected behind the downstream cylinder for the first time for two tandem cylinders of the same diameter. The two vortex frequencies remained for d/D=1.0–0.4. One was the same as detected in the gap of the cylinders, and the other was of relatively low frequency and was ascribed to vortex shedding from the downstream cylinder. While the former, if normalized, declined progressively from 0.196 to 0.173, the latter increased from 0.12 to 0.203 with decreasing d/D from 1 to 0.24. The flow structure around the two cylinders is examined in the context of the observed Strouhal numbers. The time-averaged drag on the downstream cylinder also climbed with decreasing d/D, though the fluctuating forces dropped because vortices impinging upon the downstream cylinder decreased in scale with decreasing d/D.     

Large eddy simulations of flow interference between two unequal sized square cylinders

A uniform flow past two unequal sized square cylinders arranged in a side-by-side pattern and at a Reynolds number of 50,000 has been investigated using large eddy simulation (LES) technique. The modelling of sub-grid scales of turbulence is done using the Smagorinsky model. The effect of the transverse gap ratio (T/D) on the flow characteristics has been studied. Numerical simulations are carried out for five different transverse gap ratios (T/D), namely 1.120, 1.250, 1.375, 1.750 and 2.500. Results in terms of the aerodynamic forces, Strouhal number, mean base pressure coefficient, streamlines, vorticity, surface pressure distribution, normal and shear stresses are presented. A shift in the stagnation point for the small square cylinder from the centre of its front face towards its gap side is seen at smaller T/D ratios. The presence of a jet-like flow seen in the gap side is more pronounced at T/D = 1.12. A biased gap side flow towards the near wake of the small square cylinder is seen at smaller T/D ratios. No interference effect is seen at T/D = 2.5. The flow behaviour is similar to that of the isolated square cylinder at this gap ratio.     

URANS vs. experiments of flow induced motions of multiple circular cylinders with passive turbulence control

Two-dimensional Unsteady Reynolds-Average Navier–Stokes equations with the Spalart–Allmaras turbulence model are used to simulate the flow induced motions of multiple circular cylinders with passive turbulence control (PTC) in steady uniform flow. Four configurations with 1, 2, 3, and 4 cylinders in tandem are simulated and studied at a series of Reynolds numbers in the range of 30 000<Re<120 000. Simulation results are verified by experimental data measured in the Marine Renewable Energy Laboratory. Good agreement was observed between the values of vorticity, amplitude ratio, and frequency ratio predicted by numerical simulations and experimental measurements. The amplitude and frequency response show the initial and upper branches in vortex induced vibration (VIV), transition from VIV to galloping, and galloping branch for all PTC-cylinders. The maximum amplitude of 2.9 diameters for the first cylinder is achieved at Re=104 356 in the numerical results. Compared with the first cylinder, the VIV initial branch starts at higher Re for the downstream cylinders due to the presence of the upstream cylinder(s). 2P and 2P+2S vortex patterns are observed at Re=62 049 and Re=90 254 for the single PTC-cylinder. Furthermore, the shed vortices of the downstream cylinders are strongly disrupted and modified by the vortices shed from the upstream one in the cases of multiple PTC-cylinders.     

Wake flow pattern modified by small control cylinders at low Reynolds number

Passive wake control behind a circular cylinder in uniform flow is studied by numerical simulation for Re_D ranging from 80 to 300. Two small control cylinders, with diameter d/D=1/8, are placed at x/D=0.5 and y/D=±0.6. Unlike the 1990 results of Strykowski and Sreenivasan, in the present study, the vortex street behind the main cylinder still exists but the fluctuating lift and the form drag on the main cylinder reduces significantly and monotonously as the Reynolds number increases from 80 to 300. Obstruction of the control cylinders to the incoming flow deflects part of the fluid to pass through the gap between the main and control cylinders, forming two symmetric streams. These streams not only eliminate the flow separation along the rear surface of the main cylinder, they also merge toward the wake centerline to create an advancing momentum in the immediate near-wake region. These two effects significantly reduce the wake width behind the main cylinder and lead to monotonous decrease of the form drag as the Reynolds number increases. As the Reynolds number gets higher, a large amount of the downstream advancing momentum significantly delays the vortex formation farther downstream, leading to a more symmetric flow structure in the near-wake region of the main cylinder. As the Reynolds number increases from 80 to 300, both increasing symmetry of the flow structure in the near-wake and significant delay of the vortex formation are the main reasons for the fluctuating lift to decrease monotonously.     

Flow-induced vibration of a circular cylinder subjected to wake interference at low Reynolds number

Two- and three-dimensional numerical simulations of the flow around two circular cylinders in tandem arrangements are performed. The upstream cylinder is fixed and the downstream cylinder is free to oscillate in the transverse direction, in response to the fluid loads. The Reynolds number is kept constant at 150 for the two-dimensional simulations and at 300 for the three-dimensional simulations, and the reduced velocity is varied by changing the structural stiffness. The in-line centre-to-centre distance is varied from 1.5 to 8.0 diameters, and the results are compared to that of a single isolated flexible cylinder with the same structural characteristics, m^?=2.0 and ζ=0.007. The calculations show that significant changes occur in the dynamic behaviour of the cylinders, when comparing the flow around the tandem arrangements to that around an isolated cylinder: for the tandem arrangements, the lock-in boundaries are wider, the maximum displacement amplitudes are greater and the amplitudes of vibration for high reduced velocities, outside the lock-in, are very significant. The main responsible for these changes appears to be the oscillatory flow in the gap between the cylinders.     

Fluid trapping by two partially shrouded rotating cylinders

In this paper we examine the prospect of using localized flow control for biomimetic fluid trapping. The problem is of interest for applications that call for guided transport of fluid volumes.The study shows that trapping can be achieved with the help of two partially shrouded rotating cylinders in a side-by-side arrangement. Secondary flows that manifest successful trapping resemble recirculation zones forming under the crests of peristaltic deformation waves, in particular with respect to their response to increasing incident flow velocity. Varying the rotation speed of the cylinders provides means to control the amount of trapped fluid.Numerical calculations to support these conclusions are presented in the paper for 0≤Re≤100 and h≈2, where Re and h are, respectively, the Reynolds number and the center-to-center distance between two cylinders divided by the cylinder diameter. Experimental validation of numerical results is performed for 0≤Re≤4.     

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 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.     

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

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