Cylinders In Tandem Arrangement Research Articles

Numerical study of flow around two teardrop cylinders in tandem arrangement at low Reynolds number

In this paper, the numerical method is used to investigate the flow around two tandem teardrop cylinders for four different arrangements at low Reynolds numbers. The influence of Reynolds number and spacing ratio on the drag, lift coefficient and Strouhal number are calculated and analyzed. The Reynolds number ranges from 50 to 200, while the spacing ratio ranges from 0 to 15. The results indicate that the Reynolds number has a more significant effect than the spacing ratio on the two tandem teardrop cylinders. Moreover, the influence of Reynolds number and spacing ratio on drag and lift coefficients can be divided into three regions. The drag and lift coefficients exhibit regular variations in the front and rear regions, and irregularly in the intermediate region, which are 140~ 170,125 ~ 140,80 ~ 125 and 125 ~ 140 at Reynolds number and concentrated in 2.4-2.8 ?S <6 in spacing ratio for the four arrangements. A sudden increase present in both cylinders in all arrangements, except for the drag coefficient of the upstream cylinder which varies with Reynolds number. For a fixed spacing ratio or Reynolds numbers, constant vortex shedding is observed in cylinders with the various of Re or S. Arrangement A shows the latest onset of vortex shedding, regardless variations in the Reynolds number or the the spacing ratio. Additionally, intermittent vortex shedding is noted in Arrangements A and C before transitioning to a constant state. Overall, compared to the circular cylinders in tandem arrangement, the teardrop cylinders demonstrate superior flow characteristics. The results will provide a certain theoretical foundation for applications in engineering practice.

Examination of forces acting on two circular cylinders in tandem arrangement

Flow-induced vibrations of a two-dimensional circular cylinder in the wake of another stationary equal-sized cylinder under a Reynolds number of 150 are numerically simulated by a well-developed in-house code. The center-to-center distance between two cylinders is 4 diameters, and the downstream cylinder with a mass ratio of 50 is free to oscillate in the transverse direction only. The instantaneous frequencies of lift forces acting on both cylinders are obtained by the combined singular spectrum analysis and Hilbert transform method. The time-varying frequencies are consistent with those obtained by the wavelet transform of the original lift forces and also show very good agreement with the vortex shedding frequencies from both cylinders. The time-varying frequency and envelope of lift forces acting on the downstream cylinder are the result of nonlinear fluid–structure interactions, which is ascribed to the presence of multi-frequency components in the frequency spectrum obtained by harmonic analysis. Vibration of the downstream cylinder is the result of vortex shedding from both cylinders. The vortex shedding frequency from the downstream cylinder is greatly influenced by the wake from the upstream cylinder. On the other hand, the movement of the downstream cylinder slightly affects the vortex shedding frequency from the upstream cylinder. Consequently, the cylinder movement is locked upon the natural frequency when the vortex shedding frequency is close to the value of 0.155 in stationary situation, which results in a small synchronized region of the reduced velocity ranging from 6.2 to 6.4.

Numerical study of wake flow across two circular cylinders in tandem arrangement with high rotation speed

Flow behind a bluff body is marked with unstable wake pattern eventually impacting the forces acting on the body, which can be actively controlled by rotation. When multiple rotating bluff bodies are placed in close proximity, the wake flow and resulting forces are significantly affected by the mutual flow interaction, necessitating detailed analysis for practical applications. In this vein, this study investigates the variation in wake flow across two circular cylinders, placed in a tandem arrangement, for both co-rotation and counter-rotation configurations. Two-dimensional numerical simulations are performed at a low Reynolds number of 100 for three gap ratios of L/D = 1.5, 2, and 4, where L and D are the center-to-center distance between the cylinders and the cylinder diameter, respectively. The non-dimensional rotation rate is varied from 0 to 6 for the co-rotation configuration and the range is extended till 15 for counter-rotation configuration to capture the secondary instability regime of the system. Flow regimes and force coefficients are analyzed to qualitatively and quantitatively map the overall system behavior, respectively. The flow regimes observed for different rotation rates and L/D are noticed to be different combinations of the flow regimes observed for a single rotating cylinder. Irrespective of the co-rotation or counter-rotation configuration, the dominant frequency of secondary vortex shedding for both upstream and downstream cylinder is noticed to be same, indicating that either a single vortex is shed from the system or a synchronized vortex pair is shed with one vortex from each cylinder. Compared to the co-rotating cylinders, counter-rotating cylinders demonstrate predominant inclination toward steady flow behavior over majority of the studied rotation rates.

Turbulent flows past two elliptical cylinders in tandem arrangement: wake dynamics and aerodynamic characteristics

Abstract. This study investigates the aerodynamic phenomena of drafting, a common technique observed in various racing sports, by analyzing the wake dynamics behind two 2D elliptic cylinders placed in tandem. The research explores how the separation distance and the azimuthal angle between the cylinders affect turbulent wake patterns and aerodynamic coefficients. A numerical study was conducted using a RANS-based simulation, with findings validated through physical experiments in a wind tunnel. The study identifies six distinct wake dynamics: Wake states without vortex shedding, Single bluff body wake, Suppressed vortex shedding, Coupled vortex shedding, Anti-phase vortex shedding, and In-phase vortex shedding. These dynamics vary significantly with changes in separation ratio and angle of attack, highlighting the critical influence of these parameters on the wake behavior and aerodynamic performance. The results are presented in a phase diagram, illustrating the evolution of wake patterns across different conditions. This research fills existing knowledge gaps by providing a detailed analysis of the wake dynamics behind elliptic cylinders at high Reynolds numbers, with potential applications in improving aerodynamic strategies in various engineering and sporting contexts.

Global stability analysis of flow-induced-vibration problems using an immersed boundary method

In this work, a numerical framework for global stability analysis of rigid-body-motion fluid–structure-interaction problems is presented. The Jacobian matrices which arise in the linearization procedure are derived numerically via the first-order finite difference scheme. The linearized fluid–structure coupled equations are solved using an immersed boundary method. The linear stability solver is first tested on two canonical cases, i.e., the flow past a stationary cylinder and the flow past an isolated elastically mounted cylinder. An excellent agreement between the results obtained here and those from available published research is achieved. The solver is then used to study the linear stability of the flow past two elastically mounted cylinders in tandem arrangement. The variations in growth rate and frequency of two leading modes with reduced velocity are examined. The mechanisms of lock-in and galloping phenomena observed in nonlinear simulation are elucidated from the perspective of linear instabilities in the leading modes.

Flow past two diamond-section cylinders in tandem arrangement at a low Reynolds number

The unsteady flow surrounding two fixed diamond cylinders is analyzed at Reynolds number 100 over normalized center-to-center spacing ratios 2−15. By analyzing the contours of instantaneous vorticity, variations of recirculation length, surface pressure, and fluid forcing of cylinders, the value of normalized critical spacing is found to be 3.4. In the reattachment zone below critical spacing, vortex-shedding from the upstream (UC) and downstream (DC) cylinders is anti-phase. At the critical spacing, regular vortex-shedding commences also from the UC, and vortex-shedding from the cylinders becomes phase synchronized for the first time. The analysis of a vortex-shedding cycle at the critical spacing reveals that the cylinders shed vortices at the same frequency, but with a time delay. Impingement of vortices shed from the UC on the DC strengthens vorticity around the DC and shifts the instantaneous position of its forward stagnation point from the leading edge. The understanding that locations of stagnation points govern the direction and magnitude of lift force comes from the analysis of flow at the critical gap. When the surface bounded by stagnation points is occupied mostly with negative vorticity, the instantaneous lift is negative and vice versa. At critical spacing, mean streamlines show the emergence of an anti-wake at forward stagnation point of the DC for the first time. Over the entire range of cylinder separation, nine distinct patterns of separation topologies are identified. Below critical spacing, both pressure and viscous drag components, and hence, total drag of the DC are negative or upstream-acting.

Three-dimensional computation for flow-induced vibrations of two circular cylinders in tandem arrangement with narrow spacing

Flow-induced vibrations of two circular cylinders in tandem arrangement which are mounted in a three-dimensional flow field are investigated at a high Reynolds number of 20,000. A third-order upwind finite element scheme and the arbitrary Lagrangian–Eulerian (ALE) formulation are used to solve the three-dimensional incompressible Navier–Stokes equations. Two circular cylinders which are treated as rigid bodies are free to vibrate in both in-line and cross-flow directions. Accordingly, both cylinders are assumed as a two-degree of freedom system. The upstream cylinder is set in a smooth flow and the downstream cylinder lies in the wakes which are shed from the upstream one. Spacing S between center-to-center of the cylinders is 2D and 3D (D is the diameter of the cylinders ) less than the critical spacing. The Scruton number Sc with respect to the flow-induced vibration is given as 0.99. The excitation vibrations to the in-line direction occur in the low range of the reduced velocity because of the low Scruton number. In addition, large cross-flow amplitudes of both cylinders are observed in the high range of the reduced velocity.

Flow-induced vibrations of ten tandem cylinders at low Reynolds number

Flow-induced vibrations of ten cylinders in tandem arrangement are numerically investigated by using the immersed boundary method with a low Reynolds number (Re = 100). Seven spacing ratios L/D (where L = center–center spacing between tandem cylinders and D = diameter of the cylinder) are selected from 1.1 to 4.0, and the reduced velocity Ur ranges from 2.0 to 13.5 with an increment of 0.5. Small (L/D < 2.0) and large (L/D > 2.0) spacing ranges are identified, both including two types of responses: wake-induced vibration (WIV; Ur = 2.0–9.0∼10.5 for a small L/D and Ur = 2.0–6.0∼6.5 for a large L/D) and wake-induced galloping (WIG; Ur > 9.0∼10.5 for a small L/D and Ur > 6.0∼6.5 for a large L/D). The largest vibration amplitude of each cylinder is obtained in the WIG region for the small L/D condition. The presence of downstream cylinders suppresses the vortex shedding of upstream cylinders and thus postpones the vibration of upstream cylinders at a small Ur, whereas the downstream cylinder enhances the vibration at a larger Ur due to the wake interference. For a small L/D, three flow regimes with the extended-body, reattachment, and co-shedding patterns are successively presented as Ur increases. For a large L/D, four types of flow regimes, namely, EB-2S (the extended-body with “2S” pattern), RT-2S (the reattachment with “2S” pattern), TR-2S (two-row vortex street with “2S” pattern), and CS-VS (co-shedding with variation shedding), are classified. Two new vortex shedding patterns, “2G (two counter-rotating vortices shed from each side per vibration cycle)” and “2C (two co-rotating vortices shed from each side per vibration cycle),” have been identified. In the WIV region, there is only one dominant vibration frequency for upstream cylinders (C1–C7), while a sub-harmonic frequency emerges and dominates C8–C10 when L/D is large. The fluctuating lift force spectra show a broad-band frequency distribution due to the irregular positions of the vortex generation and merging, and the dominant frequency in the WIG region decreases consecutively from C1 to C10.

Effect of vortex-induced vibrations on mass transfer enhancement in a channel with two cylinders in tandem arrangement

The vortex-shedding phenomenon leads to a self-sustained vibration named Vortex-Induced Vibration (VIV), an important mass transfer enhancement method. This work studies the VIV effects of two circular cylinders inside a channel in a tandem arrangement on the mixing performance. A comprehensive study is conducted on different modes of cylinder vibrations, i.e., both cylinders vibrate, one cylinder vibrates, another cylinder is stationary, and both cylinders are stationary. The finite volume method is applied to solve the fluid flow equations, and the cylinders' vibration is modeled as a mass-spring-damping system. At low ranges of the reduced velocity, the vibration's amplitude of the cylinder is significant, and the mixing index reaches its highest values. For the case in which the distance between two cylinders is four times their diameter, the best mixing performance is related to two vibrating cylinders. In this mode, the mixing index increased up to 35% and 78% with respect to two stationary cylinders and a single stationary cylinder, respectively. Also, the investigation shows that increasing the distance between the cylinders improves the mixing process. For cylinders' distances of 4.5 and 5, the mixing index reaches 98% and up at the channel outlet.

Flow-Induced vibration and heat transfer enhancement in tandem cylinders: Effects of cylinder shape, corner radii, and spacing ratio

In this work, flow-induced vibration (FIV) of two heated cylinders in the tandem arrangement is numerically investigated at a Reynolds number of 150. The effect of the spacing ratio (L/D) and the corner radius (r*) is investigated by changing L/D from 2 to 4 and r* from 0 to 1, where 0 corresponds to the square cross-section and 1 to the circular cross-section. The cylinders are oriented to maintain a constant angle of attack of 45° and are allowed to vibrate in the transverse direction only. The one degree of freedom (1-DOF) motion of the cylinders is studied with varying reduced velocities (Ur = 2–10). The mass ratio (m*) of the cylinder is taken as 10, while the damping is neglected to obtain the maximum vibrational amplitude. The findings suggest that the maximum vibrational amplitude (A/D) occurs for square-shaped cylinders, while the least occurs for circular shapes. It was found that the lock-in for a single cylinder occurred at Ur = 6, irrespective of the corner radius. For tandem cylinders with L/D = 2, the lock-in region occurred at Ur = 6–8 for circular cylinders and at Ur = 8–10 for square cylinders. However, lock-in occurred at Ur = 6–8 for both square and circular tandem cylinders at L/D = 4. The vorticity patterns observed in this study include 2S, C(2S), 2P, and P + S. The flow topology, the response behavior of the cylinders, and local (Nul) and average (Nuavg) Nusselt numbers were affected by various parameters, including the corner radius, spacing ratio, reduced velocity, and the average drag coefficient. For the single cylinder, changing the shape from square to circular resulted in a 40.4% and 4.71% decrease in the maximum A/D and Nuavg, respectively. Considering the twin square cylinders in tandem with L/D = 2, the upstream and downstream cylinders experienced 3.86% and 58.0% higher A/D as compared to the single cylinder. However, increasing L/D to 4 from 2 decreased the maximum A/D for upstream and downstream square cylinders by 5.41% and 3.07%, respectively. Compared to the square cylinders at L/D = 4, the circular cylinders resulted in a 28.6% and 35.1% decrease in maximum A/D for upstream and downstream cylinders, respectively, whereas at the same time experienced 33.1% and 32.0% higher Nuavg, respectively. In conclusion, the circular cylinders in tandem arrangement give higher rates of heat transfer while experiencing lower vibration as compared to square and filleted cylinders.

Splitter plate-based flow control study for two square cylinders in tandem arrangement

A numerical study is performed to investigate the effectiveness of a splitter plate (SP) for the unsteady wake-regime control of two-dimensional tandem square cylinders (TSC) arranged with large (G/D = 6), intermediate (G/D = 4) and small (G/D = 2) gap-widths. Here, G is the center-to-center distance between the cylinders, and D is their side-length. The numerical simulations are conducted using an in-house developed FFIBLBM (flexible-forcing-immersed-boundary-lattice-Boltzmann-method) solver at Reynolds number (Re) of 100. The TSC arrangement with SP attached to either upstream or downstream cylinders is named TSC-SPU and TSC-SPD, respectively. It is found that the shear-layer characteristics, wake-regime, and flow-induced forces on TSC are highly susceptible to the G/D ratio and SP length. We observed four distinct flow patterns: VS-VS (vortex shedding-vortex shedding), QS-VS (quasi-steady-vortex shedding), S-VS (steady-vortex shedding), and S–S (steady-steady) in the wakes of TSC. Among them, the S–S flow pattern is the controlled wake-regime, with steady and stabilized vortices behind both cylinders, yielding considerably lesser drag on the TSC. Precisely, at large gap-width (G/D = 6), the TSC-SPU configuration only attains the S–S flow type for which the upstream and downstream cylinder experience 11.86% and 97.73% lesser drag, respectively, than the TSC without an attached SP. However, at intermediate gap-width (G/D = 4), both TSC-SPU and TSC-SPD generate the S–S flow type. Still, the TSC-SPU is advantageous in drag reduction, where the drag of the upstream and downstream cylinders is reduced by 1.61% and 7.26%, respectively. On the other hand, the S–S flow type is established for low gap-width (G/D = 2) with TSC-SPD setup for which the drag reduction for upstream and downstream cylinders are 1.85% and 12.76%, respectively.

Cross flow over two heated cylinders in tandem arrangements at subcritical Reynolds number using large eddy simulations

This study analyses the heat transfer and flow characteristics of cross-flow over two heated infinite cylinders in a tandem (in-line) configuration. Non-isothermal Large Eddy Simulations (LES) using the dynamic Smagorinsky model were conducted at a fixed Reynolds number of 3,000 (based on the free stream velocity and the cylinder diameter). A range of cylinder gap ratios (1.0≤L/D≤5.0) was investigated (in increments of 0.25) with two different Prandtl numbers Pr=0.1 and 1.0. Results show that the flow structures vary according to the order of the patterns: (i) Extended body regime: without attachment for low L/D (1.0-1.25) where cylinders behave as a single bluff body with top–bottom vortex shedding, (ii) Shear layer reattachment regime: with reattachment for moderate L/D (1.5-3.75) where the detached shear layer from the upstream cylinder reattaches to the downstream cylinder, and (iii) Co-shedding regime: for high gap ratios (3.75≤L/D≤5.0) a phenomenon called “jumping”, where the two cylinders behave as isolated bluff bodies. Furthermore, it was observed that the average Nusselt number of both cylinders experience a drastic variation at a critical spacing ratio (between 3.75≤L/D≤4.0). For L/D≤3.0, the average Nusselt number of the upstream cylinder was found to be higher than that of the downstream one. However, for spacing ratios L/D>3.0, the average Nusselt number was similar for both cylinders. For the downstream cylinder, the maximum Nusselt number was located at the separation angle and was found to be independent of the spacing ratio.

Investigation of the flow around two tandem rotated square cylinders using the least square moving particle semi-implicit based on the vortex particle method

Characteristics of the flow around two rotated square cylinders in tandem arrangements at low Reynolds numbers (Re) and normalized gap spacings (S) were numerically investigated using a newly proposed least squares moving particle semi-implicit based on vortex particle method. The proposed method removes the background grid dependencies from the late vortex particle method and improves the computational cost using multiresolution particles. It is found that the proposed method captures the flow characteristics well. In this study, five vortex wake patterns are revealed at different Re (Re=3−150) and spacing (S=0.5–6.0). The time history and variations of aerodynamics coefficients, such as drag and lift coefficients, root mean square value of lift coefficient, and Strouhal number, alongside vorticity contours, are discussed to clarify each flow pattern's characteristics. A significant increase in aerodynamics coefficients is observed for both cylinders at the critical spacing, which may range from 1.5 to 3.0, depending on the Re. The Strouhal number has an increasing trend past the critical spacing at all selected Re. Meanwhile, the mean drag coefficient of both cylinders remains mostly the same. Conversely, the root mean square value of the lift coefficient of the downstream cylinder has a decreasing trend and, in specific cases, becomes lower than the upstream cylinder.

Aspect ratio and interference effects on flow over two rectangular cylinders in tandem arrangement

Flow past twin tandem rectangular cylinders for various gap ratios (L* = 1.0–8.0) and aspect ratios (B* = 0.3–4.0) at a Reynolds number of 150 was investigated via 2D direct numerical simulation. Results showed that based on the variation trend of fluid force with B*, three types of gaps spacing are categorized, i.e., narrow gap (L* = 1.0, 2.0), medium gap (L* = 3.0, 4.0), and wide gap (L* = 6.0, 8.0). Higher B* reduces the fluctuating force of downstream cylinder (DC) for narrow gaps, but amplifies that of the DC for wide gaps. For medium gaps, variation of fluid forces with B* < 1 is in line with that of wide gaps, while it resembles that of narrow gap type at B* > 1. Moreover, gap flow is classified into three flow regimes, i.e., extended body, reattachment, and co-shedding. Wake flow structures of DC show 2S vortex type at narrow gaps for all B* cases, whereas they transfer from synchronized C(2S) to 2S type when B* > 0.3 for medium and wide gaps. Proper orthogonal decomposition analysis captures the spatial distribution and temporal evolution of coherent structure hidden in flow field; thus, it well explains the fundamental mechanism that fluid force, gap flow and wake vortex change with B* and L*.

Vortex-Induced Vibrations of Two Cylinders in Tandem Arrangement at Low Reynolds Number

Vortex-Induced Vibrations of Two Cylinders in Tandem Arrangement at Low Reynolds Number

Energy Harvesting from Wake-Induced Vibrations of a Downstream Cylinder in Tandem Arrangement

World energy demand increases every year and energy production from conventional sources, such as fossil fuels leads to environmental degradation and global warming. To counter these adverse effects more efforts are being made to harvest clean energy from renewable energy sources. This work focuses on an energy harvester that operates on flow-induced vibrations. Any structure exposed to fluid flow may experience flow-induced vibrations and the energy from these vibrations can be harvested. This work is a numerical study where the vibrations of a downstream cylinder in the wake of an identical cylinder are studied. The upstream cylinder is held stationary whereas the downstream cylinder is allowed to vibrate in transverse direction only. The spacing ratio between the cylinders is kept fixed at 2.5, and the reduced velocity is varied from 2 to 14. The mass ratio and the damping ratio are taken as 10 and 0.01, respectively. In this analysis, the maximum vibrational amplitude was observed at lock-in condition at reduced velocity of 8, and this is where the maximum efficiency was also observed.

Vortex-induced vibrations of two rigidly coupled circular cylinders in tandem arrangement

In this paper, we study the transverse vortex-induced vibrations (VIV) of two rigidly connected circular cylinders of equal size, arranged in a tandem configuration, by means of two-dimensional numerical computations. Results are examined for Re=250 and a fixed center-to-center separation of 2D. The dynamic response of the two-cylinder system is investigated in detail over a domain of reduced velocities ranging from Ur=2 to 8. The diverse types of branches are identified, on the basis of their distinct characteristics in the amplitude and frequency responses. Among them, the lower branch is of particular interest as it is quasi-periodic in nature, instead of the periodic regime that is well documented for the isolated cylinder case. By scrutinizing the vorticity dynamics, it reveals that this quasi-periodicity arises from the switching between two flow states, which are essentially distinguished by whether an active gap flow is present. The dynamically rich response leads to a rich variety of phase dynamics, involving phase locking, trapping, slipping and drifting; in particular, phase drifting is indicative of a forthcoming phase jump of 180° between the lift force and the displacement. It is also found that in the initial branch, the excitation of the system is driven by the pressure lift force on the rear cylinder; by contrast, in the lower branch, it is the pressure lift force on the front cylinder that acts as a source of excitation.

Numerical investigation of flow around two cylinders in tandem above a scoured bed

Flow mechanisms around two cylinders in tandem arrangement above a scoured bed have been investigated using the three-dimensional unsteady Navier–Stokes equations with the Spalart–Allmaras improved delayed detached-eddy simulation model. A turbulent inlet boundary layer generation method is adopted to obtain more realistic inlet boundary conditions. First, uniform flow over a single cylinder at Re = 3900 and flow over a single cylinder above scoured beds at Re = 6000 were simulated to validate the numerical model, boundary layer generation method, and mesh density effect. Second, two cylinders in the tandem arrangement above scoured beds with six different pitch ratios L/D are investigated numerically in terms of instantaneous vortex characteristics, the hydrodynamic force, and time-averaged flow fields. The simulation results in scoured beds are compared with simulations under the near flat wall and wall-free conditions. The major findings can be summarized as follows. (1) When L/D≤2.0, the wake of two tandem cylinders is dominated by the intermittent shedding, and the downstream sand dune in the scoured bed hinders the Kármán vortex formation at the rear of the downstream cylinder. Lift force fluctuations of the two cylinders have small amplitudes, and their spectra show a multi-peak distribution and no dominant peak frequency in the spectrum of the upstream cylinder. A squarish cavity-like recirculation zone is formed between two cylinders at L/D=2.0. (2) When L/D≥3.0, the periodic vortex shedding is evident in the wake of the upstream cylinder, and the small sand berm between two cylinders has an impact on the bottom shear layer of the upstream cylinder. The downstream cylinder is periodically impacted by the vortices shed from the upstream cylinder. Lift force spectra of the upstream and downstream cylinders have the same peak frequency. (3) Due to the influence of scoured bed and the inlet boundary layer, the time-averaged lift coefficient of the upstream cylinder remains negative when L/D≥1.5, and the critical spacing for drag inversion is relatively smaller compared with under wall-free conditions. The negative pressure coefficient values of the upstream cylinder are smaller than the values in near flat wall and wall-free conditions.

A hybrid Lagrangian–Eulerian flow solver applied to elastically mounted cylinders in tandem arrangement

The fluid–structure interaction of cylinders in tandem arrangement is used as validation basis of a multi-domain Lagrangian–Eulerian hybrid flow solver. The solver is built on a Lagrangian approximation of the entire flow-field using particles, in which grid based Eulerian flow solutions are overlaid, one for every solid body. The Eulerian grids are body fitted but of limited width and may overlap in cases of close proximity of the bodies. The Eulerian and Lagrangian solutions are strongly (implicitly) interconnected in two ways: The Lagrangian solution provides the conditions over the outer boundaries of the Eulerian grids, while the Eulerian solutions update the flow properties of the particles that are within their own domains. Also, implicit is the coupling of the solver with the structural dynamics in case the cylinders are elastically supported. The Lagrangian solver is based on the density–dilatation–vorticity–pressure formulation and makes use of the Particle Mesh method to obtain the flow velocity field while the Eulerian one on the density–velocity–pressure formulation. The hybrid solver is first validated in the case of an isolated rigid cylinder at Re=100. Then the case of a single elastically mounted cylinder at Re=200 is considered, followed by the case of two cylinders in tandem arrangement that are either rigid or elastically mounted. Good agreement with results produced with spectral element and immersed boundary methods is found indicating the capabilities of the hybrid predictions. Also the flexibility of the method in handling complex multi-body fluid–structure interaction problems is demonstrated by allowing grid-overlapping.

Experimental investigation on flow-induced vibration of two high mass-ratio flexible cylinders in tandem arrangement

This paper reports experimental results from flow-induced vibration (FIV) response of two identical flexible circular cylinders in the tandem arrangement. The two flexible cylinders are mounted horizontally in the test section of a subsonic wind tunnel and each cylinder has a mass-ratio of 120 and an aspect ratio of 47. The dynamic response of the system is studied for both the upstream and downstream cylinders for center-to-center separation distances in the range of 3 to 7 times the diameter of the cylinder. Amplitudes and frequencies of oscillation, as well as phase differences between the response of the upstream and downstream cylinders are studied in the reduced velocity range of U∗=4.3−31.7 and the Reynolds number range of Re=2,570−24,536. The dynamic response observed in this study are presumably the result of two combined phenomena of vortex-induced vibration and wake-induced vibration. Despite the high mass-ratio of the cylinders, higher modes of vibrations, both odds and even modes, up to the fourth mode are excited in both the upstream and downstream cylinders, owing to the high-flexibility of the cylinders. While for low separation distance between the cylinders the FIV response of the upstream cylinder is under influence of the downstream cylinder, as the separation distance between the cylinders is increased, the upstream cylinder’s response exhibits mono-frequency oscillations similar to those observed for an isolated cylinder. However, the FIV response of the downstream cylinder is always under influence of the upstream cylinder and as the separation distance between the cylinders is increased the response is dominated by the multi-frequency oscillations. Also, for large separation distance of 7D, as well as cases where multi-frequency oscillations occur, the synchronization between the cylinders, quantified by the phase difference between the oscillations of the cylinders, varies over the duration of oscillations. Standing-wave behavior is observed for most cases at low reduced velocity ranges for which mono-frequency oscillations dominate the response while the traveling-wave behavior is observed at higher reduced velocities at which multi-frequency oscillations dominate the FIV response of the system.