Shedding Modes Research Articles

Evaluation of combustion stability of single and multi-protrusion inserted hybrid rocket motor

The present study explores the influence of protrusions on the combustion stability of a hybrid rocket motor. The primary aim is to analyze single, double, and triple-protrusion configurations taking into account variables such as their location, material, and spacing between them. Protrusions used were made of Nylon (regress during combustion) and graphite (non-regress during combustion). For the base-case (without protrusion), significant pressure oscillations were observed, arising from the interaction between vortex shedding and fundamental longitudinal acoustic modes of the chamber at the fuel grain exit. A protrusion at 0.8X/L (X-protrusion insertion point from head-end, L-fuel grain length) disrupted the interaction between acoustic modes and vortex shedding, substantially dampened its amplitude (around 96% reduction). In case of double (0.2–0.8X/L, 0.5–0.8X/L) and triple-protrusions (0.2–0.5-0.8X/L), the distance between protrusions is playing a key role in inducing the pressure oscillations. When protrusions are kept close (0.5–0.8X/L and 0.2–0.5-0.8X/L), the excitation of third mode acoustics were observed. This was attributed to the continuous increase in protrusion height. If protrusion height exceeds 6–7 mm, the flow over the front protrusion separated and impinges on the subsequent protrusion. This causes pressure oscillations in double and triple-protrusion cases. These pressure oscillations were mitigated using regressable protrusions made of nylon, as they keep the height within the range of 6–7 mm. The results of this research provide valuable perspectives on the significance of protrusions in controlling combustion instability in hybrid rockets.

Simulation of Vortex-Induced Vibration for a Cylinder with Different Rounded Corners under Re = 150

A comprehensive 2D numerical model was conscientiously developed to investigate the vortex-induced vibration phenomena in a cylindrical structure with rounded corners. The Navier-Stokes equation was adeptly solved under the specific condition of a Reynolds number (Re) of 150. The investigation reveals intricate details of the phenomena. The study aimed to systematically analyze the interaction between drag and lift force coefficients, cylinder vibration amplitude, and the patterns of vortex shedding modes under various conditions. This study systematically altered the radius of the cylinder’s rounded corners to evaluate their effects on both structural and hydrodynamic responses. This variation was crucial in comprehending how slight alterations in the cylinder’s geometry impact significant changes in the flow dynamics and correlated vibration behavior. The model’s numerical results revealed the significant impact of the curved edge ratio on both the hydrodynamic forces acting on the cylinder and its vibration response. The variation in edge curvature resulted in changes in drag and lift coefficients, leading to a significant impact on the amplitude of vibration. This elucidates the crucial role of geometric design in controlling and optimizing the structural behavior of cylindrical structures under fluid flow conditions.

Vibration characteristics of a downstream cylinder with rounded corners in an equilateral triangular arrangement at Reynolds number of 180

In this study, we numerically investigate the vibration response of a cylinder arranged in an equilateral triangle with two stationary upstream cylinders at a low Reynolds number of Re = 180. We concentrate on three different rounded corner arrangements: four rounded corners (FRCs), upwind rounded corners (URCs), and leeward rounded corners (LRCs). In addition, we examine three dimensionless rounded corner radii: 0.1, 0.3, and 0.5. The results indicate that as the dimensionless radius increases, the influence of the corner position on the dimensionless amplitude and frequency becomes more pronounced. Furthermore, the dimensionless amplitude and dimensionless frequency curves exhibit significant variations under the different corner arrangements. Within the reduced velocity range (Vr) of 2–5, rounded corners are observed to reduce both the lift and drag coefficients. An increase in the dimensionless radius for a given corner configuration acts to decrease both the lift and drag coefficients. Frequency-domain analysis of the lift coefficient and dimensionless displacement indicates that the observed frequency peaks caused by mutual interference are produced by irregular vortex shedding due to the mutual extrusion and merging of shear layers. At Vr = 4, the FRC, URC, and LRC configurations with a corner radius of 0.5 all exhibit the 2S vortex shedding mode. As Vr increases, the vortex shedding mode for LRCs with a corner radius of 0.5 progressively becomes irregular. At Vr = 16, the vortex shedding mode for LRCs with a corner radius of 0.5 is the regular 2P + 2S mode.

A numerical study on dynamic flows past three tandem inclined elliptic cylinders near moving wall

This numerical study focuses on the dynamic flows past three tandem inclined elliptic cylinders of equal spacing parallel to a moving wall using a lattice Boltzmann method. The gap ratio (G/D=0.6–2.5, where G and D are the gap between the wall surface and cylinder center and major axis, respectively), spacing ratio (L/D=1.5–10, where L is the distance of two adjacent cylinder centers), and inclination angle (α=±15°,±30°,±45°—the angle between normal vector and cylinder's major-axis) are explored at Reynolds number Re = 150 (based on D). The intended analysis links hydrodynamic coefficients, wake structures, and spectral analysis in parameter space of α−G/D−L/D to fluid mechanics. The flow is highly adjustable in this space, dividing into seven regimes: overshoot, continuous reattachment, alternative reattachment, wavy, meandering, quasi-coshedding, and coshedding, which are spatially classified into four modes due to flow interference: shear layer, primary, two-layered, and secondary vortex shedding modes. Transitions between adjacent modes determine three boundaries; and hydrodynamic coefficients differ substantially in parameter space. Due to shadowing, the upstream cylinder has a larger drag coefficient than the middle and downstream cylinders, reducing the drag coefficient of upstream cylinder and the lift coefficient of middle and downstream cylinders. α=±45° has the highest lift oscillation among the three cylinders and a small drag coefficient of the upstream cylinder. The moving wall's proximity effect increases the upstream cylinder's lift coefficient for α<0°, being negligible for high G/D across the full L/D range and stabilizing the lift oscillation of three cylinders.

Experimental investigation of flow-induced vibration and flow field characteristics of a flexible triangular cylinder

Flow-induced vibration (FIV) of a flexible cylinder with a triangular cross-section, allowed to oscillate in the cross-flow, inline and torsional direction, is studied experimentally through water tunnel tests. The dynamic response of the cylinder was studied for three different angles of attack ( $0^\circ, 30^\circ, 60^\circ$ ), at reduced velocities of 0.9–16.27, corresponding to Reynolds numbers of 364–3600. At the angle of attack of $0^\circ$ , vortex-induced vibration at low reduced velocity was observed, which transitioned to galloping at higher reduced velocities. At the angles of attack of $30^\circ$ and $60^\circ$ , galloping-type response was observed over the range of the reduced velocities tested. Our results show that the cylinder's torsional oscillation breaks the system's symmetry and affects the structural response at higher reduced velocities regardless of the angle of attack. The FIV response of the flexible triangular cylinder is distinct from that of a rigid flexibly mounted triangular cylinder due to torsional oscillation, spanwise flexibility and the two fixed boundary conditions limiting the amplitude of oscillation. Flow field analysis in the wake of the cylinder was done qualitatively and quantitatively using hydrogen bubble flow visualisation and time-resolved volumetric particle tracking velocimetry techniques, respectively. Our results show the existence of highly three-dimensional vortex structures in the wake of the cylinder. We studied the coupling between the vortex shedding modes in the wake of the cylinder and the structural vibration modes through the spatiotemporal mode analysis using the proper orthogonal decomposition technique to distinguish between different types of the FIV response observed.

Experimental study on Q-learning control of airfoil trailing-edge flow separation using plasma synthetic jets

In this paper, a continuous Q-learning algorithm is deployed to optimize the control strategy of a trailing-edge airfoil flow separation at a chord-based Reynolds number of 2×105. With plasma synthetic jets issued at the middle chord and a hot wire placed in the separated shear layer acting as the actuator and sensor, respectively, a high-speed reinforcement learning control at an interaction frequency of 500 Hz is realized by a field-programmable gate array. The results show that in the Q-learning control, the controller only needs several seconds to elevate the instantaneous reward to a level close to the final mean reward, and convergence of the control law typically takes less than 100 s. Although the relative drag reduction achieved by Q-learning control (10.2%) is only slightly higher than the best open-loop periodical control at F∗=4 (9.6%), the maximum power saving ratio is improved noticeably by 62.5%. Physically, Q-learning control creates more turbulent fluctuations, earning more rewards by increasing the transition possibilities toward high-value states. With increasing penalty strength of plasma actuation, the final control laws obtained from Q-learning exhibit a decreasing number of active states. Detailed comparisons between the open-loop and Q-learning control strategies show that the statistics of the controlled velocity fields remain similar, yet the turbulent fluctuations contributed by the vortex shedding mode are reduced by constant-frequency plasma actuation.

Effects of a detached splitter on the vortex-induced vibration of a 5:1 rectangular cylinder

The present paper examines the vortex-induced vibration (VIV) of a 5:1 rectangular cylinder with a detached splitter in its near wake. The tested gap ratio between the cylinder and the splitter (g/D, where g is the gap between the cylinder rear and the splitter and D is the depth of the rectangular cylinder) ranges from 0.5 to 2.0, with an increment of 0.5. To serve as a reference case, the rectangular cylinder without the splitter is also tested under the same conditions. The test Reynolds number ranges from 32 320 to 56 507. This study delves into the vibration response, pressure distributions, and power spectral densities (PSD) of the cylinder under varying gap ratios. Based on qualitative and quantitative analyses between the cylinder and the splitter using phase average techniques, smoke-wire visualization, and numerical simulation, the different vortex shedding modes according to different gap ratios were identified. Experimental and numerical results show that the detached splitter and its gap ratio play important roles in determining the cylinder VIV properties. For g/D = 0.5, the detached splitter has a sensible mitigation on the cylinder VIV. However, as the gap ratio increases, the VIV response initially recovers to the reference case at g/D = 1.0 and subsequently enlarges at g/D = 1.5 and 2.0. The pressure distribution results showed that the detached splitter demonstrates its effects primarily through fluctuations in the pressure field rather than the mean field. In addition, at g/D = 0.5, a sensibly decayed PSD is observed, while at g/D = 1.0–2.0, an intensified PSD is detected. The underlying mechanism of the detached splitter on the VIV of the 5:1 rectangular cylinder should be attributed to the von Kármán vortex street compared to the reference case.

Wall effect on the wake characteristics of a transversely rotating sphere

In the present work, the flow over a transversely rotating sphere placed at varying separation from a plane wall at a Reynolds number Re=U∞Dν of 300 is numerically investigated using Open Source Field Operation and Manipulation, where Re is defined based on the free stream velocity (U∞) and the diameter (D) of the sphere. Three values of the non-dimensional rotational speed ω*=ωD2U∞, viz., −1, 0 and 1, have been chosen with ω being the dimensional rotation rate with anticlockwise rotation being positive. The non-dimensional separation gap G=gD between the sphere and the wall is varied from 0.25 to 3.0. Here, g is the dimensional gap between the sphere and the wall. At ω*=0 and G = 0.25, the wall completely suppresses vortex shedding from the sphere, whereas flow is found to be unsteady for other values of ω* and G. As compared to the case in the absence of the wall, the presence of the wall causes an increase in vortex shedding frequency for ω*=0 and 1 and decrease for ω*=−1. Hilbert spectrum reveals that the wake nonlinearity remains unchanged with an increase in G for ω*=0. On the other hand, it increases for ω*=−1 and decreases for ω*=1. Similar to the observation made for vortex shedding, the presence of wall increases drag force on the sphere for ω*=0 and 1 and decreases for ω*=−1. In order to reveal the spatial and temporal behavior of the coherent structures in the unsteady wake, dynamic mode decomposition (DMD) has been performed. For all the values of G, DMD mode 1 is found to be the primary vortex shedding mode.

Asynchronous quantum Kármán vortex street in two-component Bose-Einstein condensate with PT symmetric potential

The dynamics of a miscible two-component Bose-Einstein condensate (BEC) with PT (parity-time) symmetric potential are investigated numerically. The dynamical behaviors of the system is described by Gross-Pitaevskii (GP) equations under the mean-field theory. Firstly, the ground state of the system is obtained by the imaginary-time propagation method. Then dynamical behaviors are numerically simulated by the time-splitting Fourier pseudo-spectral approach under periodic boundary conditions. By adjusting the width and velocity of the obstacle potential, various patterns such as no vortex, oblique drifting vortex dipole, V-shaped vortex pairs, irregular quantum turbulence and combined modes are studied. It is noted that the shedding vortex pairs in components 1 and 2 are staggered, which is called “the asynchronous quantum Kármán vortex street”. Here, the ratio of the distance between two vortex pairs in one row to the distance between vortex rows is approximately 0.18, which is less than the stability criterion 0.28 of classical fluid. We calculated the drag force acting on the obstacle potential during generation of the asynchronous quantum Kármán vortex street. It is found that periodical oscillation of the drag force is generated via drifting up or down of the vortex pairs. Meanwhile, we analyzed the influence of the imaginary part of the PT symmetric potential with gain-loss for wake. The trajectory and frequency of the vortex are changed, due to the imaginary part breaks the local symmetry of the system. In addition, the imaginary part affects the stability of the asynchronous quantum Kármán vortex street. Lots of numerical simulations are carried out to determine the parameter regions of various vortex shedding modes. We also proposed an experimental protocol to realize the asynchronous quantum Kármán vortex street in the miscible two-component BEC with PT symmetric potential.

Near-moving-wall flows past three tandem elliptical cylinders at low Reynolds number of 150

Dynamic flows past three tandem elliptic cylinders of equal spacing in parallel arrangement with a moving wall are numerically conducted by the lattice Boltzmann method. The gap ratio (G/D, where G and D are the gap between the wall surface and cylinder center and major axis, respectively) from 0.6 to 2.5 and spacing ratio (L/D, where L is the distance of two adjacent cylinder centers) from 1.5 to 10 are examined at Reynolds number of Re = 150 (based on D). The desired analysis correlates variations of hydrodynamic coefficients, wake structures, and spectral analysis in wide space of G/D and L/D with underlying fluid mechanics. The flow is highly adjustable in G/D−L/D space, dividing into six distinct regimes: overshoot, continuous reattachment, alternative reattachment, wavy, meandering, and coshedding, which are spatially classified into four modes because of flow interference, namely, shear layer, primary, two-layered, and secondary vortex shedding modes. The transition between adjacent modes defines three boundaries. The first boundary always occurs behind the middle or downstream cylinder, whereas the second and third boundaries occur between the upstream and middle cylinders and the downstream cylinder wake. Due to the near-wall flow interference, the hydrodynamic coefficients are highly changeable in L/D−G/D space, signifying the crucially lower drag coefficient of the middle and downstream cylinders than that of a single cylinder. A small G/D determines the increase in lift coefficient of the upstream cylinder as a result of the ground effect, while the shadowing effect of the upstream cylinder induces identical Strouhal numbers of the middle and downstream cylinders.

Numerical study on the hydrodynamic performance and wake dynamics of propulsive wing propulsors with different cross-flow fans

The propulsive wing propulsor (PWP), which means an underwater thruster equipped with a wing, a cross-flow fan (CFF), and a deflector, is capable of generating both horizontal thrust and vertical lift, thus enhancing the maneuverability of underwater vehicles and serving as a propulsion device. The hydrodynamic performance of the PWP is significantly influenced by the blade number it possesses. An unsteady numerical method based on the Reynolds-averaged Navier–Stokes equations was developed to examine the impact mechanism of blade number on the hydrodynamic performance, load fluctuation, and wake evolution of the PWP. The results indicate that as the blade number increases, the hydrodynamic forces, power, and propulsive efficiency of the PWP gradually increase. When the blade number exceeds 26, the performance of the PWP tends to stabilize. Insufficient blades can lead to turbulence in the internal flow of the CFF, intensifying interference between blade vortices, resulting in secondary peaks and frequency-domain bifurcations in hydrodynamics. With an increasing blade number, disturbances to the blade vortices decrease, enhancing the periodicity of PWP hydrodynamic fluctuations, but there may be an increase in high-frequency noise levels. The wake modes of the PWP undergo four transitions: double vortex pair mode, single vortex pair mode, single vortex pair + single vortex mode, and vortex strip mode. Disturbed blade vortices promote the transition of vortex pair shedding modes in the PWP wake, thereby causing variations in the periodicity of PWP hydrodynamics. Excessive amplitude and frequency may lead to structural fatigue damage in the PWP.

Vibration characteristic of free-to-rotate elliptical cylinder at low Reynolds number

Investigating the vibration characteristics of elliptical cylinders is important to harvest useful energy or suppress harmful vibration, but there still exist insufficiently understood in freely rotating elliptical cylinders. Herein, this paper investigates the transverse vibration characteristics of a freely rotating elliptical cylinder at Re = 150. The incompressible Navier-Stokes equation and structural dynamics equation are solved separately, and the two-way fluid-structure interaction is performed by exchanging fluid forces and structural displacements. The elliptical cylinder, with varying axial ratios (AR = 1.0–2.5) and mass ratios (m* = 10 or 5), can vibrate transversely and rotate around its center freely. The established numerical model is verified by the published results, and the numerical values are in good agreement with the experimental results. The vibration response and flow field characteristics over a range of reduced velocities (2 ≤ Ur ≤ 14) are explored. The results demonstrate that both the axial ratio and mass ratio significantly affect the vibration characteristics. Increasing the axial ratio or decreasing the mass ratio lead to a wider synchronization region. Within the synchronization region, the elliptical cylinder undergoes significant and unstable rotation, and P + S mode can be observed. Outside the synchronization region, only a small amplitude rotation takes place near the initial position, the transverse vibration amplitude is consistent with that of a non-rotatable elliptical cylinder, and the vortex shedding mode demonstrates 2S. This work provides important guidance in investigating the vibration characteristics of the elliptical cylinder.

Multiple regimes of lock-in and hysteresis in free vibration of a rotating cylinder

Flow-induced vibration of a rotating cylinder that is free to oscillate in the stream-wise and cross stream directions is studied in the laminar flow regime via linear stability analysis (LSA) and direct time integration (DTI). LSA reveals that the instability can arise from fluid-, elastic-, or coupled fluid-elastic modes depending on the rotation rate of the cylinder, α, and reduced speed, U*. Beyond α=2, the U*-range of lock-in increases exponentially with an increase in α. DTI brings out the multiple regimes of lock-in at various α. Each lock-in regime extends for a certain range of U* and is associated with a different mode of vortex shedding. The modes differ in terms of the number of pair of vortices shed during each cycle of cylinder oscillation. The amplitude of cylinder oscillation increases with an increase in the number of shed vortices. With an increase in Re, the number of vortex shedding modes increase. Vortices are generally shed during the upstream movement of cylinder, while the shear layer wraps around it resulting in large lift during the downstream motion. The flow as well as the oscillation amplitude is found to be sensitive to the initial condition for a certain range of α and U*. A flow regime is discovered where three distinct response states can be realized depending on the initial condition. Hysteresis in response to the cylinder and flow, with respect to increase and decrease in U*, occurs near the transition between lock-in and desynchronization and during the switch in the mode of vortex shedding.

Experimental study on the wave-induced fluid resonance and suppression scheme in the narrow gap of two floating rectangular structures

An experimental study on the wave-induced gap resonance and resonant suppression scheme for two floating rectangular structures (TFRSs) is systematically presented. The instantaneous velocity fields for the present problem are measured using an enhanced underwater particle image velocimetry measurement system. Detailed experimental results have been presented to study the influences of the wave and structural parameters on the gap resonant characteristics. The resonant wave height and wave frequency were sensitive to the variation of the gap width but not very sensitive to the variation of the surface roughness on the rounded corner of TFRSs. The nonlinear effects of harmonic components on resonant free surface elevation are estimated. To analyze the vortex structures, different vortex identification methods in literature are analyzed and their merits and demerits are summarized based on a comparative analysis of the measured velocity data. The Ω-criterion vortex identification approach is then selected to evaluate the vortex intensity and capture the main vortex cores. Thanks to the adopted technique, the subsequent separation of the two quasi-symmetric vortex structures is considered to be a significant contribution to energy dissipation. The vortex shedding and dissipation modes of different TFRSs are very similar and exhibit slight variations in resonant responses. A formula of the modified Reynolds number for the gap resonance problem of TFRSs is proposed. The non-dimensional vortex strengths are nonlinearly dependent on the newly modified Reynolds number and linearly dependent on the Keulegan–Carpenter (KC) number. Finally, an optimal suppression scheme for the gap resonance problem of TFRSs is suggested.

Flow-induced response and wake characteristics of a flexible splitter plate attached to a circular cylinder in laminar flow

This paper reported the numerical results of the flow past a flexible splitter plate attached to the rear of a rigid circular cylinder at a low Reynolds number of 160. The finite-volume method (FVM) in OpenFOAM-9 and the finite-element method (FEM) in deal.ii are utilized to solve the fluid and solid domains of the fluid–structure interaction (FSI) issue, respectively. The effects of the plate length L/D and normalized Young's modulus E* are examined. According to the equilibrium position and bending deformation order, five response modes are identified, including the symmetry-I, symmetry-II, symmetry-III, bifurcation-I, and bifurcation-II. The amplitude of the plate-tip is enhanced as the vortex shedding frequency approaches the natural frequency. Nevertheless, the bifurcation is observed between the symmetry-I and symmetry-II modes, where the vibration amplitude sharply drops. The number of local vortices occurring along the surface of flexible plate increases with the plate length, leading to more local negative pressure regions. Consequently, the higher mode response is excited. The greater shear stress occurs at the position of small curvature radius during the plate deformation. The 2S (a pair of vortices is alternately shed per cycle) vortex shedding mode is recognized in most cases. In contrast, the P + S (a pair of vortices shedding from one side and a single vortex shedding from the other side) mode is observed in the bifurcation-II mode with a relatively large amplitude. Due to the deflection, the wake flow becomes asymmetrical with a significant elongation of the recirculation region. Four interaction behaviors between the boundary layers and the plate are identified. The significant reduction of hydrodynamic forces is achieved when the flexible plate experiences the bifurcation.

Vortex-induced vibration characteristics of three cylinders with isosceles-triangle arrangements at low Reynolds number

The geometric factors of multi-cylinders are one of the factors affecting the efficient energy capture of vortex-induced vibration aquatic clean energy. Based on the computational fluid dynamics numerical simulation method and overset mesh technology, an efficient dynamic model of VIV (vortex-induced vibration) of two-dimensional elastic-supported cylinders was established. The influence of different vertex angles on the VIV characteristics in the isosceles-triangle arrangement was investigated. The results show that the upstream cylinder is less affected by the vertex-angle, and the peak value moves to the left in the α-A*y curve of the downstream cylinders. As α increases, the upstream cylinder moves in an 8 shape and moves in the negative direction of the flow direction, while the downstream cylinders move in an O shape and gradually become narrow. The vortex shedding mode of downstream cylinders is mostly the P + S mode, and its amplitude is related to the position of the upstream cylinder's wake vortex effect. The lift and drag coefficients of the downstream cylinders are affected by α, while the dominant frequency of vibration is independent of the change in α and is greatly affected by Re. With the increase in Re, the positive correlation between the lift coefficient and transverse displacement gradually weakens.

Flow past rotating cylinders using deterministic vortex method

This study examines the performance of an in-house code based on a deterministic vortex method on circular and square cylinders rotating with constant velocity. Subjecting a bluff body to rotary about its axis effectively reduces drag forces, suppresses the fluctuating forces, and increases the lift forces (known as the Magnus effect). Rotating cylinders are well known for their use in rotor ships, rotor aircrafts, and wind turbines. This study aims to establish the accuracy of the in-house code for the rotating circle cylinders based on the results from the literature and examine the behavior of the rotating square cylinders (a less-studied case). A square section, as a many-sided shape, can be considered when the behavior of more complex geometries is of interest, such as trajectories of the sediments, or replacing circular sections when autorotation is of importance. Both cylinders are exposed to a uniform flow of Re = 200 and an imposed rotation rate range of 0 ≤ α ≤ 5.5 for the circular, and 0 ≤ α ≤ 5 for the square cylinder. The present numerical tool is able to predict the vortex shedding suppression as a result of forced rotation. For both cases, a systematic increase in the time-averaged lift coefficient (≈25.5 for the circular and ≈26 for the square case when α = 5) and a general descending trend in the time-averaged drag coefficient (≈0.03 for the circular and ≈0 for the square case when α = 5) are detected. The second mode of vortex shedding for the circular cylinder is captured within a narrow range of rotation rates. A noticeable feature of the flow over rotating square cylinders is the emergence of near-field wakes in the near-body region, which develop independently from the wake behind the body. To the best of the authors’ knowledge, this is the first comprehensive study of a rotating body carried out using a deterministic vortex method-based numerical tool.

Numerical study of flow regimes and force characteristics for cruciform cylinder in oscillatory flow

Oscillatory flow past cruciform cylinder is numerically investigated using the Large-eddy simulation (LES) technique. The flow regimes and force characteristics of the cruciform cylinder are analyzed in detail for β (frequency parameter) numbers ranging from 200 to 500 and KC (Keulegan–Carpenter) number equals 10. Three vortex shedding modes are observed at different β values, which affect the torques exerted on the cruciform cylinder. At sections far from the node, two vortices shed within each cycle. The transverse force curve exhibits a regular pattern and a significant dominant frequency is observed in the transverse force spectra. However, as the node is approached, the vortex shedding becomes increasingly complex, leading to significant changes in the amplitudes and shapes of the transverse forces. Additionally, the sectional force coefficients agree well with those on the isolated cylinder at sections far from the node, whereas they exhibit significant increases at the sections near the node. Finally, the force coefficients of the cruciform cylinder are compared with those of the isolated cylinder for 2 < KC < 30 at β = 500. The results indicate that the cruciform cylinder experiences an increase in force coefficients, attributed to the influence of the node in cruciform cylinder.

Forced oscillations of a cylinder in the flow of viscoelastic fluids

We investigate the effects of fluid elasticity on the flow forces and the wake structure when a rigid cylinder is placed in a viscoelastic flow and is forced to oscillate sinusoidally in the transverse direction. We consider a two-dimensional, uniform, incompressible flow of viscoelastic fluid at $Re=100$ , and use the FENE-P model to represent the viscoelastic fluid. We study how the flow forces and the wake patterns change as the amplitude of oscillations, $A^*$ , the frequency of oscillations (inversely proportional to a reduced velocity, $U^*$ ), the Weissenberg number, $Wi$ , the square of maximum polymer extensibility, $L^2$ , and the viscosity ratio, $\beta$ , change individually. We calculate the lift coefficient in phase with cylinder velocity to determine the range of different system parameters where self-excited oscillations might occur if the cylinder is allowed to oscillate freely. We also study the effect of fluid elasticity on the added mass coefficient as these parameters change. The maximum elastic stress of the fluid occurs in between the vortices that are observed in the wake. We observe a new mode of shedding in the wake of the cylinder: in addition to the primary vortices that are also observed in the Newtonian flows, secondary vortices that are caused entirely by the viscoelasticity of the fluid are observed in between the primary vortices. We also show that, for a constant $Wi$ , the strength of the polymeric stresses increases with increasing reduced velocity or with decreasing amplitude of oscillations.

Large-scale streaks in a turbulent bluff body wake

A turbulent circular disk wake database (Chongsiripinyo &amp; Sarkar, J. Fluid Mech., vol. 885, 2020) at Reynolds number $Re = U_\infty D/\nu = 5 \times 10^{4}$ is interrogated to identify the presence of large-scale streaks – coherent elongated regions of streamwise velocity. The unprecedented streamwise length – until $x/D \approx 120$ – of the simulation enables investigation of the near and far wakes. The near wake is dominated by the vortex shedding (VS) mode residing at azimuthal wavenumber $m=1$ and Strouhal number $St = 0.135$ . After filtering out the VS structure, conclusive evidence of large-scale streaks with frequency $St \rightarrow 0$ , equivalently streamwise wavenumber $k_x \rightarrow 0$ in the wake, becomes apparent in visualizations and spectra. These streaky structures are found throughout the simulation domain beyond $x/D \approx 10$ . Conditionally averaged streamwise vorticity fields reveal that the lift-up mechanism is active in the near as well as the far wake, and that ejections contribute more than sweeps to events of intense $-u'_xu'_r$ . Spectral proper orthogonal decomposition is employed to extract the energy and the spatiotemporal features of the large-scale streaks. The streak energy is concentrated in the $m=2$ azimuthal mode over the entire domain. Finally, bispectral mode decomposition is conducted to reveal strong interaction between $m=1$ and $St = \pm 0.135$ modes to give the $m=2$ , $St \rightarrow 0$ streak mode. Our results indicate that the self-interaction of the VS mode generates the $m=2$ , $St \rightarrow 0$ streamwise vortices, which leads to streak formation through the lift-up process. To the authors’ knowledge, this is the first study that reports and characterizes large-scale low-frequency streaks and the associated lift-up mechanism in a turbulent wake.