It has been established theoretically that self-propulsion of deformable bodies in ideal fluid can occur with a careful specification of the deformation mode shape. With the fluid assumed ideal, vortex shedding, rotational wake, and induced drag would not occur. The implication is that for a real fluid, provided the existence of a thin boundary layer, similarly configured bodies with the same deformation mode shape self-propel without vortex shedding, rotational wake, and induced drag. Only viscous drag effects, due to the existence of the thin boundary layer, are present and unavoidable. The motion mode in question is the little-exploited anguilliform mode exhibited in some aquatic animal swimming. The Anguilla includes the snake, eel, lamprey, and leach, among others.

NEELBOT-1.0 robot design without waterproofing skin. (Photo courtesy of UNO Marketing Dept.)
Region of interest for measuring fluid flow velocities using PIV techniques.

An anguilliform swimming robot (Figure 1) was designed and built to replicate an idealized “wakeless” swimming motion. The idealized swimming motion is a reactive swimming technique that produces thrust by accelerations of the added mass in the vicinity of the body. The net circulation for the unsteady motion is theorized to be eliminated. Particle Image Velocimetry (PIV) equipment then measured the wake field velocities produced by the robot, and these results were compared to the predicted hydrodynamics. Figure 2 shows the final robot prototype, NEELBOT-1.1, swimming on the free surface of the Towing Tank of UNO (University of New Orleans) and a schematic showing the interested wake region behind it. Several assumptions are taken with both the theory and the experiment, but the evidence is still conclusive enough to draw comparisons between the two.

The robot was designed to replicate the desired, theoretical motion by applying control theory methods. Independent joint control was used due to hardware limitations. The fluid velocity vectors in the propulsive wake downstream of the tethered, swimming robot were measured using Stereoscopic Particle Image Velocimetry (SPIV) equipment. Simultaneously, a load cell measured the thrust (or drag) forces of the robot via a hydrodynamic tether. The measured field velocities and thrust forces were compared to the theoretical predictions for each.

The desired, ideal motion was not replicated consistently during SPIV testing, producing off-design scenarios. The thrust-computing method for the ideal motion was applied to the actual, recorded motion and compared to the load cell results. The theoretical field velocities were computed differently by accounting for shed vortices due to a different shape than ideal. The theoretical thrust shows trends similar to the measured thrust over time. Similarly promising comparisons are found between the theoretical and measured flow-field velocities with respect to qualitative trends and velocity magnitudes. The initial thrust coefficient prediction was deemed insufficient, and a new one was determined from an iterative process.

The off-design cases shed flow structures into the downstream wake of the robot. The first is a residual disturbance of the shed boundary layer, which is to be expected for the ideal case, and dissipates within one motion cycle. The second are larger-order vortices that are being shed at two distinct times during a half-cycle.

These qualitative and quantitative comparisons were used to confirm the possibility of the original hypothesis of “wakeless” swimming. While the ideal motion could not be tested consistently, the results of the off-design cases agree significantly with the adjusted theoretical computations. This shows that the boundary conditions derived from slender-body constraints and the assumptions of ideal flow theory are sufficient enough to predict the propulsion characteristics of an anguilliform robot undergoing this specific motion.

This work was done by Brandon M. Taravella of the University of New Orleans for the Office of Naval Research. ONR-0035

This Brief includes a Technical Support Package (TSP).
Experimental Confirmation of an Aquatic Swimming Motion Theoretically of Very Low Drag and High Efficiency

(reference AD1015757) is currently available for download from the TSP library.

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