We investigate numerically vortex-induced vibrations (VIV) of two identical two-dimensional elastically mounted cylinders in tandem in the proximity–wake interference regime at Reynolds number Re = 200 for systems having both one (transverse vibrations) and two (transverse and in-line) degrees of freedom (1-DOF and 2-DOF, respectively). For the 1-DOF system the computed results are in good qualitative agreement with available experiments at higher Reynolds numbers. Similar to these experiments our simulations reveal: (1) larger amplitudes of motion and a wider lock-in region for the tandem arrangement when compared with an isolated cylinder; (2) that at low reduced velocities the vibration amplitude of the front cylinder exceeds that of the rear cylinder; and (3) that above a threshold reduced velocity, large-amplitude VIV are excited for the rear cylinder with amplitudes significantly larger than those of the front cylinder. By analysing the simulated flow patterns we identify the VIV excitation mechanisms that lead to such complex responses and elucidate the near-wake vorticity dynamics and vortex-shedding modes excited in each case. We show that at low reduced velocities vortex shedding provides the initial excitation mechanism, which gives rise to a vertical separation between the two cylinders. When this vertical separation exceeds one cylinder diameter, however, a significant portion of the incoming flow is able to pass through the gap between the two cylinders and the gap-flow mechanism starts to dominate the VIV dynamics. The gap flow is able to periodically force either the top or the bottom shear layer of the front cylinder into the gap region, setting off a series of very complex vortex-to-vortex and vortex-to-cylinder interactions, which induces pressure gradients that result in a large oscillatory force in phase with the vortex shedding and lead to the experimentally observed larger vibration amplitudes. When the vortex shedding is the dominant mechanism the front cylinder vibration amplitude is larger than that of the rear cylinder. The reversing of this trend above a threshold reduced velocity is associated with the onset of the gap flow. The important role of the gap flow is further illustrated via a series of simulations for the 2-DOF system. We show that when the gap-flow mechanism is triggered, the 2-DOF system can develop and sustain large VIV amplitudes comparable to those observed in the corresponding (same reduced velocity) 1-DOF system. For sufficiently high reduced velocities, however, the two cylinders in the 2-DOF system approach each other, thus significantly reducing the size of the gap region. In such cases the gap flow is entirely eliminated, and the two cylinders vibrate together as a single body with vibration amplitudes up to 50% lower than the amplitudes of the corresponding 1-DOF in which the gap flow is active. Three-dimensional simulations are also carried out to examine the adequacy of two-dimensional simulations for describing the dynamic response of the tandem system at Re = 200. It is shown that even though the wake transitions to a weakly three-dimensional state when the gap flow is active, the three-dimensional modes are too weak to affect the dynamic response of the system, which is found to be identical to that obtained from the two-dimensional computations.

We carry out fluid–structure interaction simulations of self-propelled virtual swimmers to investigate the effects of body shape (form) and kinematics on the hydrodynamics of undulatory swimming. To separate the effects of form and kinematics, we employ four different virtual swimmers: a carangiform swimmer (i.e. a mackerel swimming like mackerel do in nature); an anguilliform swimmer (i.e. a lamprey swimming like lampreys do in nature); a hybrid swimmer with anguilliform kinematics but carangiform body shape (a mackerel swimming like a lamprey); and another hybrid swimmer with carangiform kinematics but anguilliform body shape (a lamprey swimming like a mackerel). By comparing the performance of swimmers with different kinematics but similar body shapes we study the effects of kinematics whereas by comparing swimmers with similar kinematics but different body shapes we study the effects of form. We show that the anguilliform kinematics not only reaches higher velocities but is also more efficient in the viscous ( Re ∼102) and transitional ( Re ∼103) regimes. However, in the inertial regime ( Re =∞) carangiform kinematics achieves higher velocities and is also more efficient than the anguilliform kinematics. The mackerel body achieves higher swimming speeds in all cases but is more efficient in the inertial regime only whereas the lamprey body is more efficient in the transitional regime. We also show that form and kinematics have little overall effect on the 3-D structure of the wake (i.e. single vs double row vortex streets), which mainly depends on the Strouhal number. Nevertheless, body shape is found to somewhat affect the small-scale features and complexity of the vortex rings shed by the various swimmers. * a max : tail-beat amplitude a ( z ) : amplitude envelope A : width of the wake A m : oscillation amplitude BCF : body/caudal fin c : damping factor c cr : critical damping factor CF∗ : mean force coefficient CFo : mean non-dimensional force in the axial direction CP∗ : mean power coefficient CPo : mean non-dimensional power CT∗ : mean thrust coefficient CTo : mean non-dimensional thrust CT : computed tomography D : cylinder diameter D ( t ) : drag EBT : elongated body theory f : tail-beat frequency f c : oscillation frequency fn : natural frequency fo : non-dimensional tail-beat frequency F : force F : force vector exerted on the virtual swimmer's body by the fluid FSI : fluid–structure interaction h : lateral displacement of fish body ![Graphic][1] : lateral velocity of fish body h max : maximum displacement of the tail h ( z,t ) : lateral excursion of the body at time t and location z HCIB : hybrid Cartesian immersed-boundary IB : immersed boundary k : wave number KC : Kuelegan–Carpenter number L : total body length LC–FSI : loose coupling fluid–structure interaction LL : lamprey swimming like a lamprey LM : lamprey swimming like mackerel m : mass of the virtual swimmer ML : mackerel swimming like a lamprey MM : mackerel swimming like a mackerel MPG : miles per gallon M red : reduced mass n : normal vector the surface nj : j th component of the normal vector p : non-dimensional pressure PIV : particle image velocimetry P side : power losss due to lateral undulations of the fish body Q T : rotation matrix of the non-inertial frame relative to the inertial frame ra : non-dimensional position in the inertial frame rr : non-dimensional position relative to the non-inertial frame r.m.s. : root mean squared Re * : mean Reynolds number based on swimming speed U* Reo : non-dimensional viscosity or Reynolds number based on characteristic velocity Uo S : symmetrical parts of the velocity gradient SC–FSI : strong coupling fluid–structure interaction St * : mean Strouhal number based on swimming speed U * Sto : Strouhal number based on the characteristic velocity Uo t : time T : mean thrust T : period of a tail-beat cycle ua : non-dimensional Cartesian absolute velocity vector of the fluid in the inertial reference frame uc : velocity of the non-inertial frame or the center of mass u m : maximum oscillation velocity un : fluid velocity normal to the body ur : non-dimensional Cartesian relative velocity vector of the fluid in the non-inertial reference frame ut : fluid velocity vector tangential to the body U : mean swimming speed U * : mean non-dimensional swimming speed Uo : characteristic (tether) velocity U red : reduced velocity VIV : vortex-induced vibration x c : position vector of center of mass non-dimensionalized by L x c : location of the center of the cylinder z : axial direction measured along the fish axis from the tip of the fish's head α : under-relaxation coefficient Γ( t ) : a dynamically evolving surface η* : mean efficiency (velocity over power) ηf : Froude efficiency λ : wavelength ν : kinematic viscosity ρ : fluid density τij : viscous stress tensor ω : angular frequency ξ : damping coefficient Ω : angular velocity [1]: /embed/inline-graphic-3.gif

A laboratory experiment was performed to study the dynamically rich interaction of a turbulent open channel flow with a bed-mounted axial-flow hydrokinetic turbine. An acoustic Doppler velocimeter and a torque transducer were used to simultaneously measure at high temporal resolution the three velocity components of the flow at various locations upstream of the turbine and in the wake region and turbine power, respectively. Results show that for sufficiently low frequencies the instantaneous power generated by the turbine is modulated by the turbulent structure of the approach flow. The critical frequency above which the response of the turbine is decoupled from the turbulent flow structure is shown to vary linearly with the angular frequency of the rotor. The measurements elucidate the structure of the turbulent turbine wake, which is shown to persist for at least fifteen rotor diameters downstream of the rotor, and a new approach is proposed to quantify the wake recovery, based on the growth of the largest scale motions in the flow. Spectral analysis is employed to demonstrate the dominant effect of the tip vortices in the energy distribution in the near-wake region and uncover meandering motions.

Laboratory experiments have yielded evidence suggestive of large-scale meandering motions in the wake of an axial flow hydrokinetic turbine in a turbulent open channel flow (Chamorro et al., J. Fluid Mech., vol. 716, 2013, pp. 658–670). We carry out a large-eddy simulation (LES) of the experimental flow to investigate the structure of turbulence in the wake of the turbine and elucidate the mechanism that gives rise to wake meandering. All geometrical details of the turbine structure are taken into account in the simulation using the curvilinear immersed boundary LES method with wall modelling (Kang et al., Adv. Water Resour., vol. 34(1), 2011, pp. 98–113). The simulated flow fields are in good agreement with the experimental measurements and confirm the theoretical model of turbine wakes (Joukowski, Tr. Otdel. Fizich. Nauk Obshch. Lyub. Estestv., vol. 16, 1912, no. 1), yielding a near-turbine wake that consists of two layers: the tip vortex (or outer) shear layer that rotates in the same direction as the rotor; and the inner layer counter-rotating hub vortex. Analysis of the calculated instantaneous flow fields reveals that the hub vortex undergoes spiral vortex breakdown and precesses slowly in the direction opposite to the turbine rotation. The precessing vortex core remains coherent for three to four rotor diameters, expands radially outwards, and intercepts the outer shear layer at approximately the location where wake meandering is initiated. The wake meandering manifests itself in terms of an elongated region of increased turbulence kinetic energy and Reynolds shear stress across the top tip wake boundary. The interaction of the outer region of the flow with the precessing hub vortex also causes the rotational component of the wake to decay completely at approximately the location where the wake begins to meander (four rotor diameters downstream of the turbine). To further investigate the importance of turbine geometry on far-wake dynamics, we carry out LES under the same flow conditions but using actuator disk and actuator line parametrizations of the turbine. While both actuator approaches yield a meandering wake, the actuator line model yields results that are in better overall agreement with the measurements. However, comparisons between the actuator line and the turbine-resolving LES reveal significant differences. Namely, in the actuator line LES model: (i) the hub vortex does not develop spiral instability and remains stable and columnar without ever intercepting the outer shear layer; (ii) wake rotation persists for much longer distance downstream than in the turbine-resolving LES; and (iii) the level of turbulence kinetic energy within and the overall size of the far-wake meandering region are considerably smaller (this discrepancy is even more pronounced for the actuator disk LES case) compared with the turbine-resolving LES. Our results identify for the first time the instability mechanism that amplified wake meandering in the experiment of Chamorro et al., show that computational models that do not take into account the geometrical details of the turbine cannot capture such phenomena, and point to the potential significance of the near-hub rotor design as a means for suppressing the instability of the hub vortex and diminishing the extent and intensity of the far-wake meandering region.

The turbulent boundary layer approaching a wall-mounted obstacle experiences a strong adverse pressure gradient and undergoes three-dimensional separation leading to the formation of a dynamically rich horseshoe vortex (HSV) system. In a pioneering experimental study, Devenport and Simpson [J. Fluid Mech. 210, 23 (1990)] showed that the HSV system forming at the leading edge region of a wing mounted on a flat plate at Re=1.15×105 exhibits bimodal, low-frequency oscillations, which away from the wall produce turbulent energy and stresses one order of magnitude higher than those produced by the conventional shear mechanism in the approaching turbulent boundary layer. We carry out numerical simulations for the experimental configuration of Devenport and Simpson using the detached-eddy-simulation (DES) approach. The DES length scale is adjusted for this flow to alleviate the well known shortcoming of DES; namely that of premature, laminar-like flow separation. The numerical simulations reproduce with good accuracy most experimental observations, including both the distributions of the mean flow and turbulence quantities and the bimodal dynamics of the velocity field in the HSV region. The only remaining discrepancy between experiments and simulations is the predicted location of the HSV, which is somewhat further upstream from the wing than the measured one. Proper orthogonal decomposition (POD) of the resolved flow field is employed to gain insights into the coherent dynamics of the flow. The POD analysis shows that 85% of the energy in the vortex region is accounted for by the first two POD modes whose dynamics is quasiperiodic. To elucidate the physical mechanisms that lead to the onset of the bimodal dynamics, we employ probability-density-function-based conditional averaging and visualization of the instantaneous three-dimensional structure of the HSV using the q criterion. We show that the bimodal dynamics is due to the continuous and aperiodic interplay of two basic states: an organized state with a coherent necklace-like HSV, and a disorganized state with hairpin vortices wrapping around the HSV. We argue that the emergence of hairpin vortices is the result of centrifugal instability.

As the pulsatile cardiac blood flow drives the heart valve leaflets to open and close, the flow in the vicinity of the valve resembles a pulsed jet through a nonaxisymmetric orifice with a dynamically changing area. As a result, three-dimensional vortex rings with intricate topology emerge that interact with the complex cardiac anatomy and give rise to shear layers, regions of recirculation, and flow instabilities that could ultimately lead to transition to turbulence. Such complex flow patterns, which are inherently valve- and patient-specific, lead to mechanical forces at scales that can cause blood cell damage and thrombosis, increasing the likelihood of stroke, and can trigger the pathogenesis of various life-threatening valvular heart diseases. We summarize the current understanding of flow phenomena induced by heart valves, discuss their linkage with disease pathways, and emphasize the research advances required to translate in-depth understanding of valvular hemodynamics into effective patient ther...