The sharp-interface CURVIB approach of Ge and Sotiropoulos [L. Ge, F. Sotiropoulos, A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries, Journal of Computational Physics 225 (2007) 1782-1809] is extended to simulate fluid structure interaction (FSI) problems involving complex 3D rigid bodies undergoing large structural displacements. The FSI solver adopts the partitioned FSI solution approach and both loose and strong coupling strategies are implemented. The interfaces between immersed bodies and the fluid are discretized with a Lagrangian grid and tracked with an explicit front-tracking approach. An efficient ray-tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies. Numerical experiments are carried out for two FSI problems: vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions. For both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements. The numerical experiments suggest that both the properties of the structure (mass, geometry) and the local flow conditions can play an important role in determining the stability of the FSI algorithm. Under certain conditions unconditionally unstable iteration schemes result even when strong coupling FSI is employed. For such cases, however, combining the strong-coupling iteration with under-relaxation in conjunction with the Aitken's acceleration technique is shown to effectively resolve the stability problems. A theoretical analysis is presented to explain the findings of the numerical experiments. It is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the FSI algorithm. The stabilizing role of under-relaxation is also clarified and an upper bound of the required for stability under-relaxation coefficient is derived.

SUMMARYFor all Re, however, the swimming power is shown to be significantly greater than that required to tow the rigid body at the same speed. We also show that the variation of the total drag and its viscous and form components with St depend on the Re. For Re=300, body undulations increase the drag over the rigid body level, while significant drag reduction is observed for Re=4000. This difference is shown to be due to the fact that at sufficiently high Re the drag force variation with St is dominated by its form component variation, which is reduced by undulatory swimming for St>0.2. Finally, our simulations clarify the 3D structure of various wake patterns observed in experiments -single and double row vortices -and suggest that the wake structure depends primarily on the St. Our numerical findings help elucidate the results of previous experiments with live fish, underscore the importance of scale (Re) effects on the hydrodynamic performance of carangiform swimming, and help explain why in nature this mode of swimming is typically preferred by fast swimmers.

SUMMARYWe 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~10 2 ) and transitional (Re~10 3 ) regimes. However, in the inertial regime (Reϱ) 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.

SUMMARYWe employ numerical simulation to investigate the hydrodynamic performance of anguilliform locomotion and compare it with that of carangiform swimming as the Reynolds number (Re) and the tail-beat frequency (Strouhal number, St) are systematically varied. The virtual swimmer is a 3-D lamprey-like flexible body undulating with prescribed experimental kinematics of anguilliform type. Simulations are carried out for three Reynolds numbers spanning the transitional and inertial flow regimes, Re=300, 4000 (viscous flow), and ϱ (inviscid flow). The net mean force is found to be mainly dependent on the tail-beat frequency rather than the tail-beat amplitude. The critical Strouhal number, St*, at which the net mean force becomes zero (constant-speed selfpropulsion) is, similar to carangiform swimming, a decreasing function of Re and approaches the range of St numbers at which most anguilliform swimmers swim in nature (St~0.45) only as Re increases. The anguilliform swimmerʼs force time series is characterized by significantly smaller fluctuations above the mean than that for carangiform swimmers. In stark contrast with carangiform swimmers, the propulsive efficiency of anguilliform swimmers at St* is not an increasing function of Re but instead is maximized in the transitional regime. Furthermore, the power required for anguilliform swimming is less than that for the carangiform swimmer at the same Re. We also show that the form drag decreases while viscous drag increases as St increases. Finally, our simulations reinforce our previous finding for carangiform swimmers that the 3-D wake structure depends primarily on the Strouhal number.

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 inline) 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 syst...

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The tail (caudal fin) is one of the most prominent characteristics of fishes, and the analysis of the flow pattern it creates is fundamental to understanding how its motion generates locomotor forces. A mechanism that is known to greatly enhance locomotor forces in insect and bird flight is the leading edge vortex (LEV) reattachment, i.e. a vortex (separation bubble) that stays attached at the leading edge of a wing. However, this mechanism has not been reported in fish-like swimming probably owing to the overemphasis on the trailing wake, and the fact that the flow does not separate along the body of undulating swimmers. We provide, to our knowledge, the first evidence of the vortex reattachment at the leading edge of the fish tail using three-dimensional highresolution numerical simulations of self-propelled virtual swimmers with different tail shapes. We show that at Strouhal numbers (a measure of lateral velocity to the axial velocity) at which most fish swim in nature (approx. 0.25) an attached LEV is formed, whereas at a higher Strouhal number of approximately 0.6 the LEV does not reattach. We show that the evolution of the LEV drastically alters the pressure distribution on the tail and the force it generates. We also show that the tail's delta shape is not necessary for the LEV reattachment and fish-like kinematics is capable of stabilising the LEV. Our results suggest the need for a paradigm shift in fish-like swimming research to turn the focus from the trailing edge to the leading edge of the tail.

Fish schooling is a remarkable biological behavior that is thought to provide hydrodynamic advantages. Theoretical models have predicted significant reduction in swimming cost due to two physical mechanisms: vortex hypothesis, which reduces the relative velocity between fish and the flow through the induced velocity of the organized vortex structure of the incoming wake; and the channeling effect, which reduces the relative velocity by enhancing the flow between the swimmers in the direction of swimming. Although experimental observations confirm hydrodynamic advantages, there is still debate regarding the two mechanisms. We provide, to our knowledge, the first three-dimensional simulations at realistic Reynolds numbers to investigate these physical mechanisms. Using large-eddy simulations of self-propelled synchronized swimmers in various rectangular patterns, we find evidence in support of the channeling effect, which enhances the flow velocity between swimmers in the direction of swimming as the lateral distance between swimmers decreases. Our simulations show that the coherent structures, in contrast to the wake of a single swimmer, break down into small, disorganized vortical structures, which have a low chance for constructive vortex interaction. Therefore, the vortex hypothesis, which is relevant for diamond patterns, was not found for rectangular patterns, but needs to be further studied for diamond patterns in the future. Exploiting the channeling mechanism, a fish in a rectangular school swims faster as the lateral distance decreases, while consuming similar amounts of energy. The fish in the rectangular school with the smallest lateral distance (0.3 fish lengths) swims 20% faster than a solitary swimmer while consuming similar amount of energy.