Vortex Shedding Patterns Research Articles

Kármán Vortex Street in Bose-Einstein Condensate with PT Symmetric Potential

Abstract Kármán vortex street not only exists in nature, but also widely appears in engineering practice, which is of great significance for understanding superfluid. And parity-time (PT) symmetric potential provides a good platform for the study of Kármán vortex street. In this paper, different patterns of vortex shedding formed behind PT symmetric potential in Bose-Einstein condensate (BEC) are
simulated numerically. Kármán vortex street and others are discovered to emerge in the wake of a moving obstacle with appropriate parameters. Compared with BEC without PT symmetric potential, the frequency and amplitude of the drag force are more complex. The parametric regions of the combined modes are scattered around the Kármán vortex street. Numerical simulations indicate that the imaginary part of the PT symmetric potential affects the vortex structure patterns. Finally, we proposed an experimental protocol that may observe Kármán vortex street.

Numerical investigation of cavity dynamics and cavitation-induced vibrations of a flexible hydrofoil

This work investigates the cavitation and fluid–structure interaction characteristics of a flexible NACA0015 hydrofoil. The simulation incorporates the Zwart–Gerber–Belamri cavitation model and two-way fluid–structure interactions. The detached eddy simulation method is employed to analyze the impact of cavitation and elastic deformation on hydrodynamic performance. The vibrational response and cavitating flow field around the hydrofoil are investigated. The results show that the vibrational mode of the elastic hydrofoil shifts with increasing flow speed. Furthermore, the vertical vibrational displacement of the hydrofoil aligns with the variations in cavitation volume in the flow field. The structural vibrational deformation of an elastic hydrofoil notably affects the evolution of cavitation. Additionally, fluid–structure interaction in the presence of cavitation influences the pattern of vortex shedding wakes in the flow field. The results of this study can serve as a reference for the design of hydrofoils constructed from composite elastic materials.

Effects of aspect ratio on flow characteristics on free surface-mounted rectangular cylinders

Turbulent flow characteristics around free surface-mounted rectangular cylinders of different streamwise aspect ratios (AR=1, 2, 2.5, 3, 4, 5, and 8 denoted as AR1, AR2, AR2.5, AR3, AR4, AR5, and AR8, respectively) at a Reynolds number based on the freestream velocity and cylinder height, Reh = 11100, were investigated experimentally using a time-resolved particle image velocimetry system. The results reveal distinct flow behaviors for different aspect ratios. The separated shear layer is shed directly into the wake for AR1, while AR2 and AR2.5 exhibits intermittent reattachment on the cylinder and direct shedding into the wake. However, for AR≥3 cylinders, the separated shear layer reattaches onto the cylinder and is later shed into the wake after subsequent separation from the trailing edge of the cylinder. Comparative analysis with previous studies on rectangular cylinders in uniform flow and wall-mounted conditions demonstrates similarities in reattachment behavior on the cylinder to uniform flow cases and wake reattachment mechanism akin to wall-mounted cylinders subjected to a thin turbulent boundary layer. The Reynolds stresses, turbulence production, and vortex shedding patterns examined with frequency spectra and proper orthogonal decomposition of velocity fluctuations exhibit significant dependence on streamwise aspect ratio.

Large-eddy simulation of vortex-induced vibration of a circular cylinder at Reynolds number 10 000

The canonical scenario of cross-flow vortex-induced vibration (VIV) of a circular cylinder in the turbulent regime, which has been studied by several physical experiments in the literature, is reexamined in this study through high-fidelity large-eddy simulations (LES) at a Reynolds number 104. The VIV response (including vibration amplitude and frequency) and hydrodynamic coefficients predicted by the present LES agree with the experimental results better than previous numerical attempts. In addition, several phenomena reported by previous experimental studies are confirmed numerically for the first time. After validating against the experiments, new VIV characteristics and physical mechanisms are explored with confidence. First, a collective analysis on the frequency spectra of the displacement, lift, and velocity signals provides a complete picture of the frequency response of the system. In contrast, the use of a single signal may miss certain aspects of the frequency response, so that caution should be exercised. Second, spanwise correlation of primary vortex shedding is examined, where relatively low correlations in the upper and lower branches are likely because the vortex shedding patterns involve complex vortex generation and interaction. Third, the effect of mass ratio (m*) of the cylinder on the VIV response is analyzed with a range of m* (=1.4–3.4) relevant to cylindrical structures used in offshore engineering (such as subsea pipelines). The variations in the amplitude response, frequency response, and hydrodynamic coefficients with m* and reduced velocity are examined in detail. The present results suggest that a lighter pipeline is more susceptible to the onset of VIV.

Harnessing flow-induced vibrations for energy harvesting: Experimental and numerical insights using piezoelectric transducer.

Flow-induced vibrations (FIV) were considered as unwanted vibrations analogous to noise. However, in a recent trend, the energy of these vibrations can be harvested and converted to electrical power. In this study, the potential of FIV as a source of renewable energy is highlighted through experimental and numerical analyses. The experimental study was conducted on an elastically mounted circular cylinder using helical and leaf springs in the wind tunnel. The Reynolds number (Re) varied between 2300-16000. The motion of the cylinder was restricted in all directions except the transverse direction. The micro-electromechanical system (MEMS) was mounted on the leaf spring to harvest the mechanical energy. Numerical simulations were also performed with SST k-ω turbulence model to supplement the experiments and were found to be in good agreement with the experimental results. The flow separation and vortex shedding induce aerodynamic forces in the cylinder causing it to vibrate. 2S vortex shedding pattern was observed in all of the cases in this study. The maximum dimensionless amplitude of vibration (A/D) obtained was 0.084 and 0.068 experimentally and numerically, respectively. The results showed that the region of interest is the lock-in region where maximum amplitude of vibration is observed and, therefore, the maximum power output. The piezoelectric voltage and power output were recorded for different reduced velocities (Ur = 1-10) at different resistance values in the circuit. It was observed that as the amplitude of oscillation of the cylinder increases, the voltage and power output of the MEMS increases due to high strain in piezoelectric transducer. The maximum output voltage of 0.6V was observed at Ur = 4.95 for an open circuit, i.e., for a circuit with the resistance value of infinity. As the resistance value reduced, a drop in voltage output was observed. Maximum power of 10.5μW was recorded at Ur = 4.95 for a circuit resistance of 100Ω.

Vortex shedding behind porous flat plates normal to the flow

This work examines the influence of body porosity on the wake past nominally two-dimensional rectangular plates of fixed width $D$ in the moderate range of Reynolds numbers $Re = UD/\nu$ (with $U$ the incoming velocity and $\nu$ the kinematic viscosity) between 15 000 and 70 000. With porosity $\beta$ defined as the ratio of open to total area of the plate, it is well established that as porosity increases, the wake shifts from the periodic von Kármán shedding behaviour to a regime where this vortex shedding is absent. This change impacts the fluid forces acting on the plate, especially the drag, which is significantly lower for a wake without vortex shedding. We analyse experimentally the transition between these two regimes using hot-wire anemometry, particle-image velocimetry and force measurements. Coherence and phase measurements are used to determine the existence of regular, periodic vortex shedding based on the velocity fluctuations in the two main shear layers on either side of the wake. Results show that, independent of $Re$ , the wake exhibits the classical Kármán vortex shedding pattern for $\beta <0.2$ but this is absent for $\beta >0.3$ . In the intermediate range, $0.2<\beta <0.3$ , there is a transitional regime that has not previously been identified; it is characterised by intermittent shedding. The flow alternates randomly between a vortex shedding and a non-shedding pattern and the total proportion of time during which vortex shedding is observed (the intermittency) decreases with increasing porosity.

Aerodynamic characteristics and wake formation behind a pair of side-by-side rectangular cylinders using the lattice Boltzmann method

In this work, the lattice Boltzmann method is used to numerically analyze the interactions of flowing fluid with two side-by-side rectangular cylinders at a fixed Reynolds number of 150. The gap ratios between the cylinders are varied from 0.5 to 5 while the aspect ratios of both cylinders are varied from 0.25 to 4. The deflected, bistable, flip-flopping, chaotic, single bluff body, two pairs’ street of anti-phase vortex shedding, anti-phase synchronized, and in-phase non-synchronized wake patterns are observed upon varying the aspect ratios as well as the gap ratios. The observed results show that the mean drag coefficients of both side-by-side rectangular cylinders, as well as that of the single cylinder, exhibit decreasing trends till the aspect ratio = 2 and become almost constant afterward. The Strouhal number varies abruptly at the gap ratio of 0.5 and becomes steady for gap ratios = 2 and 5. The root-mean-square values of lift coefficients of two side-by-side rectangular cylinders exhibit variations till the aspect ratio equal to 1.5 and then becomes constant afterward. This study also reveals that an increment in aspect ratios results in the minimization of the drag force and controls the wake, while the increment in gap ratio results in stabilizing the chaos produced in the flow structure due to jet flow influence. The wake patterns in this study are found to be consistent with the numerical and experimental work of other researchers.

Effect of topographical pattern on vortex shedding and heat transfer phenomena in power-law fluid flow around a rotating cylinder

The present numerical investigation studies the momentum and heat transfer phenomena from a heated rotating patterned cylinder in the vortex shedding regime. In particular, the effect of surface patterns ( ω , δ ), fluid behavior ( 0.4 ≤ n ≤ 1.6 ), cylinder rotation speed ( 0.5 ≤ α ≤ 2 ), and Prandtl number ( 1 ≤ Pr ≤ 100 ) at Reynolds number 100 on the force coefficients and Nusselt number are studied. Vorticity and isotherm profiles demonstrate the flow dynamics and heat transfer characteristics. According to the findings of this study, the formation of the vortex (including its size, shape, and number of vortices) and the time period during which the vortex shedding pattern repeats itself demonstrates a dependency on the shape of the cylinder, fluid behavior, and rotating speed. It has been noted that a significant decrease in the frequency of vortex shedding occurs on adding topographical patterns. Additionally, it has been noticed that on increasing rotational speed, vortex shedding can be suppressed for all fluid behaviors. Numerical simulation results reveal that the average drag coefficient ( C ¯ D ) for a rotating patterned cylinder decreases with increasing rotational speed ( α ), and it further reduces on increase in pattern frequency ( ω ) and amplitude ( δ ) compared to a smooth circular cylinder. The shear-thinning fluid behavior helps to dissipate the heat from the cylinder to the surrounding fluid. Conversely, shear-thickening fluid behavior exhibits the opposite trend.

Turbulent transports in the flow around a rectangular cylinder with different aspect ratios

The flow around a rectangular cylinder exhibits intricate features, encompassing phenomena such as separation, reattachment, boundary layer transition, and relaminarization. This study explores the intense transport of turbulent fluctuations in these complex flow phenomena, including momentum and turbulent kinetic energy (TKE) transport, for three aspect ratios (L/D=5,10 and 15) at a medium Reynolds number (Re=1000). The connection between these transports and crucial vortical structures is elucidated for the first time. On the lateral side of the cylinder, strong momentum transport occurs, dominated by ejection and sweep events associated with the hairpin vortex. The generation of the LE vortex also leads to active TKE production. The existence of the LE separation bubble, as well as the relaminarization of the downstream boundary layer at L/D=10 and 15, affects the distribution of production terms. This perspective offers an effective yet novel approach that has not been previously addressed in prior researches. The redistribution of TKE results in a disturbance growth, linked to boundary layer transition. The source term reveals that streamwise TKE carried into the recirculating region is closely related to the frequency prior amplified by the LE shear layer. In the wake behind TE, turbulent transports are influenced by vortex shedding patterns.

Coupling of the immersed boundary and Fourier pseudo-spectral methods applied to solve fluid–structure interaction problems

The current manuscript addresses fluid–structure interaction (FSI) problems to the analysis of vortex-induced vibration (VIV), employing the methodology designated as IMERSPEC2D. The approach seamlessly integrates the Fourier pseudo-spectral method (FPSM) and the immersed boundary method (IBM) to solve the Navier–Stokes (NS) and continuity equations. Simultaneously, the effects of cylindrical structure, involving 1 and 2 degrees of freedom (d.o.f.) are simulated, by incorporating structural motion equations into NS via the IBM source term and implementing a two-way FSI algorithm. In the paper are presented the comparison of low and high-order temporal integration methods applied to solve the dynamic behavior of the structure and the dimensionless of the cylinder’s structural motion equations, resulting in an increase in computational time step from 1E(-9\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-9$$\\end{document}) to 1E(-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-3$$\\end{document}). Validation results to refined mesh simulations include the accurate representation of the lock-in phenomenon to simulations of 1 d.o.f. obtaining the range between reduced velocity 5.456 and 5.568 and the maximal amplitude is 0.352. Notably, the eight-shape pattern of the 2 d.o.f. cylinder displacement is obtained and the formation of C2S wake patterns is achieved, as presented by other authors. In conclusion, the dimensionless approach reduces computational time, while the high-order both of IMERSPEC methodology and time advancement integration to FSI improve the results of the cylinder’s motion and alters distinct vortex shedding patterns in fluid dynamics.

Kármán vortex street in a spin–orbit-coupled Bose–Einstein condensate with PT symmetry

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street’ is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately 0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.

Cross-flow vortex-induced vibrations of a circular cylinder under stochastic inflow at low Reynolds number

The vortex-induced vibrations of an elastically mounted circular cylinder (with mass ratio = 2) in stochastically fluctuating inflow are numerically studied at a Reynolds number of 150. Numerical simulations are carried out on a discrete forcing immersed boundary method (IBM) based in-house fluid–structure interactions (FSI) solver. The existence of gust in the incoming flow causes substantial qualitative and quantitative changes in the vibrating system’s flow and response properties. The oscillation amplitude and extent of lock-in have been found to increase. In the noisy inflow, the vibrating system experiences higher fluid forces than the uniform inflow. A comparison with the vibration characteristics under uniform flow has been conducted to understand the noise’s influence better. Standard vortex-shedding patterns are not detected in the wake. Instead, rich vortex interaction behavior like vortex-merging, vortex-pairing, and formation of mushroom-shaped vortical structures are documented.

Effects of splitter plate and mass ratio on flow-induced vibration and heat transfer characteristics of a circular cylinder in turbulent flow: A numerical study

The two-degree-of-freedom (2DOF) flow-induced vibration (FIV) of a circular cylinder with heat transfer in turbulent flow is numerically investigated. The cylinder with an attached splitter plate is elastically supported and allowed to vibrate in both in-line and transverse directions. The unsteady RANS and energy equations along with the SST k-ω turbulent model are coupled with the equation of vibration to study the FIV of the cylinder. The effects of the attached plate length (L/D = 0.5, 1.0, and 1.5) and the mass ratio (mr=2 and 6.76) on the heat transfer rate, vortex shedding patterns, vibration trajectories, FFT, and cylinder displacements are studied in a wide range of Reynolds number (1156–9246) and reduced velocity (2–16). The results indicate that FIV can have either a positive or negative effect on heat transfer enhancement, depending on the splitter plate length and the type of cylinder vibration response. At high Reynolds numbers, the cylinder vibration response is observed in the galloping region, accompanied by a significant vibration amplitude. In this region, for L = 0.5D, vibration has a positive effect on heat transfer, while for other lengths, this effect is negative. For L = 1.5D and a reduced velocity of 5.5, contributions of vortex-induced vibration (VIV) and surface area in the heat transfer enhancement are 23.5 % and 44.3 %, respectively. By reducing the mass ratio from 6.76 to 2.6 for L = 0.5D, the heat transfer rate increases by approximately 40 % compared to a stationary cylinder.

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.

Spanwise phase transition between pure modes A and B in a circular cylinder’s wake. Part II: spatiotemporal evolution of vorticity

Through direct numerical simulation, the transition from pure mode A to mode B in the near wake of a circular cylinder is studied without consideration of vortex dislocations. The Reynolds number is calculated from 100 to 330 with a computational spanwise length of 4 diameters. In the present section, the spatiotemporal evolution of the vorticity and its sign are analyzed. The results show that mode B, as a kind of weak disturbed vorticity with opposite signs, actually appears partially on the rear surface of the cylinder and in the shear layers once Re exceeds 193. With increasing , the vortex-shedding patterns in the near wake undergo the initial generation stage of mode B coupling with the fully developed pure mode A (), the mode swapping or coexistence stage between modes A and B (), the self-adjustment stage of the nondimensional spanwise wavelength from 0.8 to 1 in dominant mode B (), and the full development stage of mode B (). In particular, the spanwise phase transition initially occurs at a certain spanwise position in the initial generation stage where a part of mode A and a part of mode B with specific vorticity signs appear, e.g. the vortex in mode A and the vortex in mode B, in which and vortices are vortices with three vorticity components satisfying the vorticity sign law and shed from the upper and lower shear layers, respectively.

How vortex dynamics affects the structural load in step cylinder flow

The vortex dynamics and the structural load in a step cylinder (consisting of a small, d, and a large, D, cylinder) flow are investigated numerically at Reynolds number ( $Re_D$ ) 150 for diameter ratios $D/d=2.0, 2.4$ and 2.8. First, the formation mechanism of a non-uniform oblique vortex shedding (the vortex shedding frequency remains unchanged as the oblique shedding angle varies) behind the small cylinder is explained: an increase in the production rate of the vortex strength and a farther downstream movement of the vortex formation position occur simultaneously as the vicinity of the step is approached along the small cylinder. Second, the structural load (the drag and lift) along the step cylinder is investigated, where four local extremes (two local minima and two local maxima) are observed. An in-depth investigation of the vortex dislocation effects on the structural load is provided, showing that the decreased circulation in the near wake and the weakened staggered Kármán vortex shedding pattern cause a major reduction (90 %) of the sectional lift amplitude and a relatively modest reduction (5.7 %) of the sectional drag amplitude, compared with the corresponding sectional force when no vortex dislocation occurs. This new knowledge combined with the three-dimensional effect of the step cylinder wake (caused by the blending of the small and larger cylinder wakes around the step) explain the formation of the four local extremes and the distribution of the structural load between them. Finally, it is found that the increasing $D/d$ amplifies the structural load variation along the step cylinder.

Reduction in drag and vortex-induced vibration of a circular cylinder covered by a porous layer in the laminar regime

The reduction in drag and vortex-induced vibration (VIV) of a circular cylinder covered by a porous layer is numerically studied in the laminar regime. The mass ratio and damping ratio of the system are fixed at mr = 2 and ξ = 0.01, respectively. The effects of the Darcy number (Da = 10−4, 10−3 and 10−2), the relative layer thickness (b = 0.25, 0.5 and 1), the Reynolds number (Re = 100, 150 and 200), and reduced velocity (2 ≤ Ur ≤ 10) on the vortex shedding pattern, vibration amplitude, and dynamic forces on the system are investigated. Both the one and two degrees of freedom of motion are considered. Results show that the porous layer with Da = 10−2 is effective in drag reduction and VIV suppression for various Reynolds numbers. A porous layer with Da = 10−3 could also suppress VIV while enlarging the drag force on the system.

Two-degrees of freedom flow-induced vibration of circular cylinder with nonlinear stiffness

Nonlinear stiffness is widespread in engineering field, which normally caused by deformation of anisotropic structures or support gaps between structures. In this work, two-degrees of freedom flow-induced vibration (FIV) of a circular cylinder with nonlinear stiffness supporting is numerically investigated in a wide reduced velocity range (3≤U*≤20). The amplitude and frequency responses, force acting on the cylinder, and the near-wake structures are analyzed to understand the influence of nonlinear stiffness on the FIV behavior. Results show that the FIV responses of cylinder can be divided into two parts according nonlinear strength: low nonlinear strength range (0≤λ ≤ 4) range and high nonlinear strength range (4 < λ ≤ 10). Low value of λ can amplify the amplitudes in two vibration directions when compared with that of λ = 0. The maximum amplitudes of 0.34D (λ = 4, U* = 14) and 1.12D (λ = 0.25, U* = 7) are obtained in flow and cross flow directions, respectively. Typical trajectories of “8” shape are observed for all cases, which means that the vibrate frequency in flow direction is double to that of cross flow direction for a given reduced velocity and nonlinear strength. In addition, bending trajectory can be captured with the rise of λ. The vortex shedding patterns of 2 S, P + S, and 2 P are obtained under low nonlinear strength (0≤λ ≤ 4) and only the 2 S pattern can be observed under high nonlinear strength (4 < λ ≤ 10).

Numerical investigation of horizontal flow film boiling of saturated liquid over two inline cylinders in the mixed convection regime

Mixed convection film boiling in a system of two cylinders positioned in an in-line configuration is numerically studied. The relative importance of inertia over buoyancy is given by Froude number. The direction of the incoming saturated liquid is perpendicular to the direction of gravity. Simulations are performed for the Reynolds number values of 50, 100, and 150; non-dimensional wall superheat values of 0.3, 0.6, and 0.9; and non-dimensional spacing between cylinders values of 2.0, 4.0, and 6.0. Three modes of vortex shedding from the cylinders are identified. An increase in the Reynolds number increases the heat transfer for the upstream cylinder and decreases heat transfer for the downstream cylinder. Increasing the non-dimensional wall superheat leads to decrease in the heat transfer rate from both the cylinders. Changing the non-dimensional spacing between the cylinders does not significantly alter the heat transfer from the upstream cylinder. However, heat transfer rate from the downstream cylinder increases significantly with increase in the non-dimensional spacing between the cylinders. The dynamic interface is affected by the shear layer instability and the vortex shedding pattern, which in turn affects the vapor film thickness around the cylinders and the rates of heat transfer from the cylinders.

Three-dimensional numerical investigation of a transversely oscillating slotted cylinder and its applications in energy harvesting

The present paper numerically investigates the fluid dynamics associated with the flow over an elastically mounted circular cylinder at a Reynolds number of 500. A slit normal to the flow direction is placed at the cylinder's centre. The study covers the large parametric set of calculations for the combined mass-damping ratio $m^{*}\zeta = 0.2$ , including the slit offset for six different offset angles ( $-30^\circ \leq \alpha \leq +30^\circ$ ) measured from the vertical axis at the centre point of the cylinder and the effect of slit widths ( $0.1 \leq s/D \leq 0.3$ ) on the aerodynamic loading, vibration response and associated flow characteristics. Furthermore, a wide range of reduced velocities ( $3\leq U_r \leq 7$ ) are examined for the complete closure of studying the effect on the vortex-induced vibration response. The results demonstrate that adding the normal slit increases the periodic suction-blowing phenomena, strengthening the vortex shedding. The results suggest that the normal slit can suppress or increase vortex-induced vibration depending on the slit-offset angle. Placing it toward the front stagnation point results in the increased oscillation amplitude (with a wider wake behind the cylinder) while shifting it toward the rear stagnation point diminishes the cylinder's oscillations. The paper reveals that this dual behaviour of the normal slit (based on its offset placement) is closely related to the phase difference between the lift force and the oscillation amplitude. Various vortex-shedding patterns associated with the different slit-offset angles are duly reported in the paper. Furthermore, a magnet is attached to the slit cylinder, and its effect on the energy harvesting capability via a coil-magnet arrangement is explored in detail for a wide range of reduced velocities.