Session G28: Swimming Efficiency

For free swimming the efficiency and economy optima are the same

Most computational and experimental studies into the ``optimality'' of fins or wings are based on the placement of a model in a uniform stream and finding an optimum of either efficiency or economy. This approach is easy, but inherently inconsistent: any efficiency other than zero implies the presence of thrust, which is then incompatible with uniform speed. The proper way to reconcile the two is to assume the presence of sufficient parasitic drag to balance the thrust. But then different wings are implicitly attached to different bodies, and the optima are over a range of unrelated bodies. The consistent way to address optimization is in the context of free swimming. In this work a simple theoretical model based on a heaving and pitching plate is used to investigate the implications of free swimming. In particular, performance is optimized over the manifold of constant average thrust. Once constrained to this manifold, then the efficiency and economy optima are collocated. This simple model can predict the results of our prior computations for flexible wings. More importantly, the model details the interplay between the circulatory and non-circulatory lift/thrust, and can predict the motion of whale tails. The phase of pitch and heave work themselves out so as to keep the motion on the aforementioned manifold. These results have significance to swimming and to insect flapping in air where added mass has considerable effect.   

Hydrodynamic Wake Resonance as an Underlying Principle of Efficient Unsteady Propulsion

In this study, three dimensional wake structures are generated by an actively flexible robotic elliptical fin. Particle image velocimetry is used to characterize and quantify the wake and to extract time averaged velocity profiles. A linear spatial stability analysis is performed on the velocity profiles to find the frequency of maximum spatial growth, i.e. the resonant frequency of the time averaged jet. It is found that (1) optima in propulsive efficiency occur when the driving frequency of a flapping fin matches the resonant frequency of the jet profile, (2) there can be multiple wake resonant frequencies and modes corresponding to observed multiple peaks in efficiency, (3) observed wake structures are largely linear phenomena and (4) wake patterns are strongly influenced by the nearest resonant mode. Multiple peaks in efficiency and transitions in the wake structure can be explained by this theoretical framework. Surprisingly, the analysis, although one-dimensional, captures the performance exhibited by a three-dimensional propulsor, showing the robustness and broad applicability of the technique.   

Identifying optimal vortex spacing for swimming and flying animals

Swimming and flying animals generate thrust by creating an unsteady vortex wake through the oscillation of their appendages. To determine the vortex spacing that maximizes propulsive efficiency, a finite core vortex array model was developed to compute the unsteady velocity field generated by vortex streets representative of bio- inspired propulsion. The model systematically varies the streamwise and transverse spacing between vortex cores to determine the time averaged velocity field induced by a reverse von Karman vortex street and a uniform freestream velocity. Experimental particle image velocimetry was conducted in the wake of a rigid pitching panel to determine the size and strength of the vortex cores to input to the model. Viscosity is accounted for by assuming a Gaussian vorticity distribution around the vortex core. A linear spatial stability analysis was performed on the computed velocity profiles to determine which vortex configuration leads to efficient propulsion. Here it is assumed that efficient propulsion proceeds when the driving frequency of the vortex street matches the resonant frequency of velocity jet.   

Propulsive performance of a flapping foil in a hydrodynamic tunnel: direct force measurements

The study of simplified flapping wings has received much attention in the past two decades because of the renewed interest in biomimetic locomotion at intermediate Reynolds numbers ($10-10^4$). Recent works from our group have been devoted to the study of a pitching foil system in a hydrodynamic tunnel, exploiting particle image velocimetry first to characterize the transitions in the flow around the foil as a function of the flapping parameters (amplitude and frequency), and second to investigate the effect of flexibility. Here we report on our first results with an improved experimental setup where the pitching foil mechanism is mounted on a mechanical balance that allows us to have a time-resolved direct force measurement using an LVDT displacement sensor. We compare the performance of two different foils, one rigid and one flexible that have been previously characterized. We analyze the time-correlation of the thrust measurement with the instantaneous angular position of the foil, as well as the mean values of the force signals.   

Optimal shapes for self-propelled swimmers

We optimize swimming shapes of three-dimensional self-propelled swimmers by combining the CMA- Evolution Strategy with a remeshed vortex method. We analyze the robustness of optimal shapes and discuss the near wake vortex dynamics for optimal speed and efficiency at Re=550. We also report preliminary results of optimal shapes and arrangements for multiple coordinated swimmers.   

Effect of Vehicle Configuration on the Performance of a Submersible Pulsed-Jet Vehicle at Intermediate Reynolds Number

Recent results have demonstrated that pulsed jet propulsion can achieve propulsive efficiency greater than that for steady jets when short, high frequency pulses are used, and the pulsed-jet advantage increases as Reynolds number decreases into the intermediate range ($\sim $50). An important aspect of propulsive performance, however, is the vehicle configuration. The nozzle configuration influences the jet speed and, in the case of pulsed-jets, the formation of vortex rings with each jet pulse, which have important effects on thrust. Likewise, the hull configuration influences the vehicle speed through its effect on drag. To investigate these effects, several flow inlet, nozzle, and hull tail configurations were tested on a submersible, self-propelled pulsed-jet vehicle (`Robosquid' for short). In terms of propulsive efficiency, changing between forward and aft-facing inlets had little effect, but changing from a smoothly tapered aft hull section to a blunt tail increased propulsive efficiency slightly due to reduced drag for the blunt tail configuration at intermediate Re. Sharp edged orifices also showed an advantage over smooth nozzles.   

The Effect of Caudal Fin Shape on the Hydrodynamics of Swimming

The caudal fin is thought to be the main thrust generator in body/caudal fin swimmers because the largest undulations occur at the caudal fin. The shape of the fin could possibly be one of the most important factors in thrust generation for such swimmers. However, investigating this experimentally is quite challenging due to the issues in controlling and measuring forces on different appendages of live fish. We can investigate the effect of caudal fin shape through controlled numerical simulations. We construct virtual swimmers with different caudal fin shapes but with the same projected area. We attach trapezoidal and heterocercal shapes of caudal fins (e.g. observed in trouts and sharks, respectively) to a mackerel body and test these swimmers beside the original mackerel with a hemocercal tail. We prescribe the same carangiform kinematics to all virtual swimmers and carry out self-propelled simulations under similar conditions, i.e., the undulations are prescribed while motion of the center of mass is calculated. The simulations are continued until the quasi-steady state is reached, in which the swimmers are compared in terms of different performance measures.   

Effects of shape on the thrust performance and vortical structure of flapping plates

Three-dimensional unsteady hydrodynamics of flapping plates with different shapes are numerically investigated using the lattice Boltzmann and immersed boundary method. The plate shape is quantitatively described by the area moments. The thrust exhibits a monotonous increase with the area moments. Two typical regimes are identified. One is un-linear relation between the thrust and the area moment for lower area moment and the other is linear relation for larger area moment. Moreover, the vortical structures in the wake are usually composed of two rows of vortex rings formed by the vortices shed from the leading and trailing edges as well as the two tip sides. As the strength of the vortices changes with the plate shape, the topology of the vortical structures is closely related to the plate shape. Further, the intrinsic relationship between the hydrodynamics and the vortical structures in the wake is analyzed using some unconventional force expressions and simplified vortex ring models.