David N. Beal

Biorobotic insights into how animals swim

SUMMARY Many animals maneuver superbly underwater using their pectoral appendages. These animals range from sunfish, which have flexible, low aspect ratio fins, to penguins, which have relatively stiff, high aspect ratio wings. Biorobotics is a means of gaining insight into the mechanisms these animals use for maneuvering. In this study, experiments were carried out with models of abstracted penguin wings, and hydrodynamic characteristics – in particular, efficiency – were measured directly. A cross-flow vortex model of the unsteady force mechanism was developed that can compute instantaneous lift and drag forces accurately. This makes use of the steady characteristics of the fin and proposes that cross-flow drag vortices of bluff bodies in steady flow are analogous to dynamic stall vortices and that fin oscillation is a means for keeping the vortices attached to the fin. From what has been reported for sunfish with pectoral fins to our current measurements for single abstracted penguin wings, we infer that the maximum hydrodynamic efficiency has remained largely unchanged. A selection algorithm was used to rapidly find the fin oscillation parameters for optimum efficiency. Finally, we compared the measurements on the penguin-like relatively stiff fins and the reported flow visualization of flexible sunfish pectoral fins. The flexible pectoral fins of station-keeping sunfish exhibit a rich repertoire of capability such as the formation of dynamic stall vortices simultaneously on two leading edges during part of the cycle, changes in projected area in different planes, and the vectoring of jets. However, such fins may not be scalable to larger biorobotic vehicles and relatively stiff fins appear to be better suited instead, albeit with somewhat limited station-keeping ability.

Open-Loop Control of a Multifin Biorobotic Rigid Underwater Vehicle

This paper presents an open-loop control system for a new experimental vehicle, named the biorobotic autonomous underwater vehicle (BAUV). The rigid cylindrical hull of the vehicle is attached with six strategically located fins to produce forces and moments in all orthogonal directions and axes with minimal redundancy. The fins are penguin-wing inspired and they implement the unsteady high-lift principle found widely in swimming and flying animals. The goal has been to design an underwater vehicle that is highly maneuverable by taking the inspiration from nature where unsteady hydrodynamic principles of lift generation and the phase synchronization of fins are common. We use cycle-averaged experimental data to analyze the hydrodynamic forces and moments produced by a single foil as a function of its kinematic motion parameters. Given this analysis, we describe a method for synthesizing and coordinating the sinusoidal motion of all six foils to produce any desired resultant mean force and moment vectors on the vehicle. The mathematics behind the resulting algorithm is elegant and effective, yielding compact and efficient implementation code. The solution method also considers and accommodates the inherent physical constraints of the foil actuators. We present laboratory experimental results that demonstrate the solution method and the vehicles resulting high maneuverability.

Synchronization of Animal-Inspired Multiple High-Lift Fins in an Underwater Vehicle Using Olivo–Cerebellar Dynamics

The development of neuroscience-based control methodologies and their integration with the high-lift unsteady hydrodynamics of control surfaces inspired by swimming and flying animals are the subjects of this paper. A biology-inspired rigid autonomous undersea vehicle called the biorobotic autonomous undersea vehicle (BAUV) has been developed at the Naval Undersea Warfare Center (NUWC), Newport, RI. The BAUV is equipped with six simultaneously rolling and pitching fins for generating large unsteady control forces for performing agile maneuvers. First, as an exploratory example, we introduce the van der Pol oscillator as an oscillatory controller for the BAUV and we describe experiments performed to examine the fin forces (thrust and lift) and electric power requirement, and to demonstrate the effectiveness of the oscillators limit cycle property for disturbance rejection effectiveness. We then describe a BAUV control system that includes six inferior-olive (IO) neuron models for control of the pitch and roll motion of the six foils. These IO neurons exhibit limit cycle oscillation (LCO). For control of the BAUV, these IO neurons must oscillate in synchronism with specific relative phases. We present here four feedback linearizing control systems of varying complexity for control of the relative phases of the IO neurons. It is shown that each of the IO control systems accomplishes asymptotic regulation of the phases and thus enables the foils to produce the required control forces. The first controller has a global synchronization property, but the remaining controllers accomplish local synchronization. We present simulation results for tracking piecewise, time-varying phase angle commands as well as experimental results for control of the BAUV by IO neurons. The results show that with appropriate phasing of the fins, an optimal graceful gait of the BAUV is achieved where no untoward force or moment is present. An analog hardware version of the local controller with a cluster of six IO neurons has also been built, which allows five of the signals to rapidly synchronize to the reference, with or without prescribed phase shift, much like in the simulations. The designed controllers can be used in any platform or multivariate BAUV-like system requiring fast, accurate phase control. Laboratory test results for the phase synchronization of two servomotors (roll and pitch) using the designed analog hardware controller are also shown.

Unified Scaling for Flapping Fins

Conventional scaling for steady-fin or flapping-fin forces in a uniform flow is by definition incompatible with the scaling that has been developed for hovering flapping fins. Most flapping-fin-based vehicles will need to operate in all three operating regimes: fixed fin in cruise, flapping in cruise, and flapping in hover. A unified normalization scheme is proposed to enable smooth and optimal transition of the scaling rules between these regimes. A rigid flapping foil was experimentally tested in a towing tank. The generated side force was found to be a function only of the fin bias angle and the vector magnitude of the inflow and flapping speeds. The thrust was found to be a function of the ratio of fin flapping speed to total speed magnitude in addition to bias and speed magnitude. As an application of this scaling, an algorithm to synthesize the foil motion parameters for a desired thrust and side force regardless of vehicle speed was tested experimentally on a single foil in real time.

Pre-swirl Maneuvering Propulsor: Part 1 Computations

Recent concept studies have demonstrated the potential to utilize a pre-swirl propulsor configuration with adjustable upstream stators to generate propulsor side forces. These studies led to a set of experiments and corresponding computations to validate this concept. Ducted and open pre-swirl propulsors were configured with an upstream stator row and downstream rotor. During normal operation, the upstream stator blades are all situated at the same pitch angle and pre-swirl the flow into the propulsor when generating a roll moment to counter the moment produced by the rotor. By varying the pitch angles of the stator blade about the circumference, it is possible to both generate a mean stator side force and subsequently vary the axial velocity and swirl that is ingested into the inflow. The rotor then generates side forces in response to the inflow. Wind tunnel experiments were conducted to measure the steady, spatially varying stator wake flows for various stator geometric configurations using stereo particle image velocimetry. Computations utilized both potential flow and fully viscous 3-D (Reynolds Averaged Navier-Stokes, RANS) computations to predict the stator forces, velocity field and rotor response. Rotor design space investigations varied blade parameters including blade number, rake, skew and a combination of the two. RANS was used to then validate the final propulsor design with experimental data used to validate the computations. Computational data demonstrated that total side force coefficients on the order of 0.2 could be generated by the propulsor alone with results consistent with recent water tunnel measurements. This amount of control authority exceeds current control surface capabilities at 3 knots for Navy 21” unmanned undersea vehicles.

Unsteady Vortex Flows Produced by Trailing Edge Articulation

The unsteady vortex flows produced by biologically inspired tail articulation are investigated. The application is to provide active means of reducing tonal noise due to upstream wake interaction with downstream propellers on underwater vehicles. By reducing the wake velocity defect, the periodic unsteady propeller blade pressure fluctuations that are the source of the noise should be reduced. Accordingly, experiments to measure the flows produced by an upstream stator fitted with a movable trailing edge were carried out in a water tunnel for Reynolds numbers in the range 75,000 <Re <300,000. A stator model with a hinged flapping trailing edge section operated at frequencies up to 21 Hz corresponding to a range of Strouhal number 0.0<St<0.18. Velocity measurements of the articulating stator wake were carried out by laser Doppler velocimetry (LDV) and particle image velocimetry (PIV). Reduced mean and rms LDV data show that trailing edge articulation generates vortex structures with dependence on both Strouhal number and articulation amplitude. Estimates of the time mean stator drag that were obtained by integrating the mean wake profiles were used to estimate optimal Strouhal numbers in terms of wake elimination. Instantaneous phase-averaged measurements via PIV show a transition in the unsteady stator wake flow regimes as St is increased, from a deflected vortex sheet to a series of rolled up, discrete vortices. Measurements of the wake high-light the characteristics of the vortex structures and provide a means to estimate the impact on downstream propellers.

Noise Control Due to the Stator Wake Blade Interaction via Tail Articulation

The biologically inspired method of tail articulation is investigated as a means of reducing tonal noise due to wake deficit blade interaction in underwater vehicles. Experiments are carried out in a water tunnel under typical operating conditions for underwater vehicles. Tail articulation is implemented using a life scale stator model with a hinged flapping tail operating both in free-stream velocities corresponding to Reynolds number in the range 75000 < Re < 300000 and at frequencies up to 30 Hz to investigate the range of Strouhal number 0.0 < St < 0.35. Velocity measurements of the active stator wake are carried out by laser Doppler velocimetry (LDV) and particle image velocimetry (PIV) to investigate the effects of tail articulation on the stator wake. Time-averaged measurements of the stator wake by LDV show that of the tail articulation has a dominant effect on the time mean stator drag. Instantaneous phase-averaged measurements of the stator wake by PIV show a transition in the unsteady stator wake as is increased, from a deflected vortex sheet to a series of rolled up, discrete vortices. Measurements are made of the wake due to both sinusoidal and nonsinusoidal tail motion profiles, which show that significant wake alteration is achieved with tail articulation. A low-order model describing the creation and convection of vorticity by tail articulation is developed which describes wake phenomena observed in LDV and PIV measurements. Finally, a 3-D unsteady propeller simulation using both experimental wake velocity data by PIV and simulated wake velocity data generated with the reduced-order model are used to predict the effect of sinusoidal tail articulation on radiated noise. Results using simulated data indicate that a significant noise alteration is achieved in all cases, and noise reduction of 5-8 dB is achieved in some cases.

Blade Tonal Noise Reduction Using Stator Trailing-Edge Articulation

The biologically-inspired method of trailing-edge articulation is investigated as a means of reducing tonal noise due to the stator wake / rotor blade interaction in underwater vehicles. This work is experimental in nature and conducted in the closed channel water tunnel at Naval Undersea Warfare Center in Newport, Rhode Island. Tail articulation is carried out with a life scale stator model with hinged flapping tail designed to (i) operate in freestream velocities corresponding to Reynolds number in the range 75,000 < Re < 300,000 and (ii) operate at frequencies up to 30 Hz in order to investigate the range of Strouhal number 0.0 < St < 0.35. Velocity measurements in the active stator wake are carried out by Laser Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV) in order to investigate the effects of tail articulation on the stator wake. Time averaged measurements of the stator wake by LDV show that Strouhal number of the tail articulation has a dominant effect on the time mean stator drag. Instantaneous phase-averaged measurements of the stator wake by PIV show three regimes of the stator wake as Strouhal number is increased; quasi-steady wake spreading, vortex roll up, and strong vortex wake. Ongoing experiments with an instrumented propeller will demonstrate the efficacy of stator trailing-edge articulation on reducing unsteady blade forces.Copyright