Maneuvering Hydrodynamics of Fish and Small Underwater Vehicles

102

INTEG. AND COMP. BIOL., 42:102117 (2002)

Maneuvering Hydrodynamics of Fish and Small Underwater Vehicles1

PROMODE R. BANDYOPADHYAY2Propulsion, Hydrodynamics and Silencing Division,

Naval Undersea Warfare Center, Newport, Rhode Island 02841

SYNOPSIS. The understanding of fish maneuvering and its application to underwater rigid bodies areconsidered. The goal is to gain insight into stealth. The recent progress made in NUWC is reviewed. Fishmorphology suggests that control fins for maneuverability have unique scalar relationships irrespective oftheir speed type. Maneuvering experiments are carried out with fish that are fast yet maneuverable. Thegap in maneuverability between fish and small underwater vehicles is quantified. The hydrodynamics of adorsal fin based brisk maneuvering device and a dual flapping foil device, as applied to rigid cylindricalbodies, are described. The role of pectoral wings in maneuvering and station keeping near surface waves isdiscussed. A pendulum model of dolphin swimming is presented to show that body length and tail flappingfrequency are related. For nearly neutrally buoyant bodies, Froude number and maneuverability are related.Analysis of measurements indicates that the Strouhal number of dolphins is a constant. The mechanism ofdiscrete and deterministic vortex shedding from oscillating control surfaces has the property of large am-plitude unsteady forcing and an exquisite phase dependence, which makes it inherently amenable to activecontrol for precision maneuvering. Theoretical control studies are carried out to demonstrate the feasibilityof maneuverability of biologically inspired bodies under surface waves. The application of fish hydrodynam-ics to the silencing of propulsors is considered. Two strategies for the reduction of radiated noise are de-veloped. The effects of a reduction of rotational rate are modeled. The active cambering of blades made ofdigitally programmable artificial muscles, and their thrust enhancement, are demonstrated. Next, wakemomentum filling is carried out by artificial muscles at the trailing edge of a stator blade of an upstreamstator propulsor, and articulating them like a fish tail. A reduction of radiated noise, called blade tonals, isdemonstrated theoretically.

FIG. 1. Definition of length scales of a fish. FIG. 2. Morphology of dorsal fins of fish families.

INTRODUCTIONThe engineering community generally believes that

man made vehicles and machines are matured in de-velopment for steady state operation; biology-inspiredfurther improvements might not be cost effective.However, the following two products are recent ex-amples where induced drag of wing-tip vortices hasbeen reduced with devices inspired by winglets ofsoaring eagles: the Spiroid Wing Tip of Gulfstream IIaircraft developed at Boeing, and the propellor with

1 From the Symposium Stability and Maneuverability presented atthe Annual Meeting of the Society for Integrative and ComparativeBiology, 37 January 2001, at Chicago, Illinois.

2 Present address: Code 342 Cognitive & Neural S&T Division,Office of Naval Research, 800 N. Quincy St., Arlington, Virginia22217-5660. E-mail: [email protected]

tip-less round blades, by Bannasch (2000). Moreover,the following developments have opened up opportu-nities in unsteady operations, namely in maneuvering,in addition to, perhaps, in propulsion: our new under-standing of the mechanisms of lift enhancement viaunsteady vortex dynamics, the advances in digital con-trol, control theory and active materials technology(Ellington, 1984; Dickinson et al., 1999; Bandyopa-dhyay, 1999; Bar-Cohen, 2001; Madden et al., 2001).This paper reviews the related progress made atNUWC. The science of maneuvering and stealth inswimming and flight in nature is distilled and appliedto conventional rigid bodied and generic underwatervehicles. To name a few, the present work rests on the

at University of the W

est of England on June 25, 2015http://icb.oxfordjournals.org/

Dow

nloaded from

103MANEUVERING HYDRODYNAMICS OF FISH AND SUVS

FIG. 3. Reciprocal of aspect ratio of dorsal fin.

FIG. 4. The example of a digitized bluefish trajectory in the rectangular tank with pipe and cinder block maze.

theoretical foundations of fish locomotion laid by Tay-lor (1952), Lighthill (1975) and Wu (1971ad, 1972),the numerical studies by Webb (1975) and the scalinglaws of Triantafyllou and Triantafyllou (1995).

LOW-SPEED MANEUVERING DYNAMICS OF FISH ANDSMALL UNDERWATER VEHICLES

Morphology of control surfacesWhile biologists tend to attach importance to vari-

ations of a theme, engineers have a need to simplify,that is to minimize the variations, to arrive at a robustapplication. This probably is a reflection of the fact

that, in general, in a comparable environment, emerg-ing materials, actuators and their control are far frombeing as dynamically competent as those in living an-imals. It is reasonable to assume that even the staticmorphology of a fish can provide clues to its loco-motion, habitat and ecology (see among others, Ligh-thill, 1975; Aleyev, 1977; Bandyopadhyay et al.,1997). As a starting point, the simplified morphologyof various fish families is examined to determine whatmakes some families more maneuverable than others.Maneuverability is defined as the minimum or com-monly observed turning radius at a given normal ac-celeration. As suggested here, internal Froude numbermay be interpreted as a measure of maneuverability.Ability to make a sudden stop or start is also a measureof maneuvering ability although this is not consideredhere.

Length scales of the body and fins of a fish definedin Figure 1 are examined. Twenty-eight species of fishare considered. They are classified into three catego-ries: low-speed highly maneuverable, high speed poor-ly maneuverable, and an overlapping category. The re-lationship between fin morphology and the character-istics of maneuvering is shown in Figures 2 and 3.Several definite trends are observed. The result in Fig-ure 3 agrees with observation that a cylinder, whoselength to diameter ratio is less than 10, tends to beunstable. In the next section, a dorsal fin device forbrisk maneuvering based on the result in Figure 2, isexamined in the context of a rigid cylinder having alarge aspect ratio.



Dow

nloaded from

104 PROMODE R. BANDYOPADHYAY

FIG. 5. (a) Coefficient of normal acceleration. Solid lines: Eq. (1). (b) Reduced coefficient of normal acceleration. Solid lines: Eq. (3).

TABLE 1. Relationship between lengths of dolphins and their natural frequencies. From Bandyopadhyay et al. (2000a).

Author of Data (in Rohr et al., 1998) Lang and Daybell Rohr et al. Fish Rohr et al.Dolphin Specie Lagenorhynchus

ObliquidensTursiopsTruncatus

TursiopsTruncatus

PseudorcaCrassidens

Range of Length L (cm)Average Length L (cm)Natural Frequency n (Hz) due to Pendulum

Model

209209

0.34

182283240

0.32

251270260

0.31

365365

0.26

Gap in maneuverabilityAn experiment was carried out comparing the ma-

neuverability of fish and small underwater vehicles toquantitatively establish the gap. Bluefish and mackerel,which are oceanic fast swimmers and yet are maneu-verable, were selected for an experiment on maneu-verability. Swimming tanks with baffles, as shown inFigure 4, were designed to photograph their trajecto-ries. The turning dynamics were determined from the

digitized trajectories. The results of coefficient of nor-mal acceleration Cg versus turning radius r/L werecompared with two small underwater vehicles as inFigure 5a. Here, Cg 5 (V2/r)/g is acceleration perpen-dicular to the path, V is total velocity, r is the radiusof curvature in trajectory, and g is acceleration due togravity. There is a large gap between the maneuveringcapability of fish and the vehicles. There is a universaltrend, namely,



Dow

nloaded from


FIG. 6. Photograph of cylinder and dorsal fin assembly. The solenoid-cam arrangement inside the cylinder used to deploy the fins is alsovisible in the middle.

FIG. 7. Comparison of side thrust between abruptly cambered (left) and permanently cambered (right) fins at a steady tow speed of 3.6 m/sec. The ordinates are in arbitrary volt scale.

21C 5 (r/L) ,g (1)which is followed but in large turn radii only. Comparedto underwater vehicles, fish can make the same radiusturn at a normal acceleration that is lower by a factorthat can be as large as 10. Lower speed and laminar flowcould allow a fish to make stealthy maneuvers.

Froude number and maneuverabilityThe scaling law in Figure 5a can be improved so

that the wide Reynolds number range between naturaland man-made bodies is covered. Propose that the co-efficient of normal acceleration during a turn is a func-

tion of inertia forces, viscous forces and gravity forces.Define Re 5 VL/y, and an internal Froude number Fr5 V/ , where V is speed, L is length, y is kinematicgLviscosity, and g is acceleration due to gravity. Thesetwo ratios can be combined as:

4 3Fr V y5 . (2)3 2Re L g

This combined parameter can be used to rescale thecoefficient of normal acceleration shown in Figure 5a,and the result is shown in Figure 5b. The solid linesin Figure 5b are:



Dow

nloaded from


FIG. 8. Photograph of an euthynnid (due to Magnuson). The pectoral fins are swept back to change planform area and lift.

FIG. 9. Dimensions of a reference plain cylinder and two sets ofwings used to model the maneuvering ability of winged bodies. Thetail wings are always retained for stability. The dimensions are sim-ilar to the tow tank model described later. FIG. 10. Reduction of required angles of attack in winged bodies.

21C rg ; . (3)3 1 2n V L2 3g L

The inverse power trend (3) is now followed over agreater range of turn radius in both fish and vehicledata. The significance of internal Froude number is asfollows. Rewrite Fr as:

V L V 1 T Fr 5 5 5 . (4) 1 2!g L 2p LgL

V In other words, this internal Froude number is a ratioof the time period of natural oscillation T like a pen-dulum, and the time it takes for the body to travel adistance equal to its length. This is reminiscent ofFroude number that is relevant to wave drag of surfaceships. It is interesting that the jets produced by fish,dolphins or whales for propulsion is similar to the re-cent flow visualization of fluttering of long and lightstrips in a liquid by Belmonte et al. (1998) (also see

Aleyev, 1977; Videler, 1993). (Lightness can be con-sidered equivalent to near neutral buoyancy for sub-merged bodies.) On the other hand, heavy and shortstrips tumble. Note that they also similarly definean (internal) Froude number, which is the reciprocalof the one given above. According to Belmonte et al.(1998), Fr defined as in the present work, have a highvalue for long and light strips which flutter. Thus, fish,dolphins and whales have high Froude numbers. Onthe other hand, short heavy animals like the beetle ofFish (1999) have a low value of Fr. Thus, we reinter-pret the conclusion of Fish that flexibility of a hump-back whale gives it higher maneuverability than thatof a whirligig beetle which is rigid. We conclude thatinternal Froude number is related to maneuverability.

The commonality of the wake pattern and the termsin the Froude number for fluttering objects suggests



Dow

nloaded from


FIG. 11. Compared to their body lengths, winged cylinders makea shorter radii turn.

FIG. 12. Schematic of a surface wave propagating right to left over a submerged body. The velocity field and elliptic particle motion due tofinite depth of water and time signature of horizontal (Fx) and vertical (Fz) forces acting on the body are shown.

that a dolphin can be modeled as a simple pendulum.The dolphin swimming data due to Rohr et al. (1998)was examined (Bandyopadhyay et al., 2000a). Table1 is a summary of the data sets based on lengths. Itwas proposed that the jet responsible for dolphin pro-pulsion is analogous to the jet due to the predomi-nantly side to side motion of fluttering long or lightstrips when dropped freely in air or water. The naturalfrequencies of dolphins calculated based on the fol-lowing pendulum model is shown in Table 1:

Ln 5 1 2p . (5)@1 2!g

When dolphin-swimming data based on their lengthare extrapolated to zero swimming speed, they agree

with the calculated values. This length considerationaccounts for the seeming scatter in the data. Thus,(buoyancy or lightness), length (slenderness) andFroude number appear to play important roles in ma-neuvering.

Strouhal number of dolphinsIt is known indirectly that fish propulsion takes

place predominantly in the Strouhal number range of0.25 , St , 0.35, where St 5 fA/U (Fish and Rohr,1999). Here, f and A are frequency and amplitude oftail oscillation, and U is speed of fish motion. For dol-phins, measurements due to Rohr et al. (1998) indicatethat the amplitude of oscillation is given by A/L 5 0.26 0.02 and it is independent of speed. When speed isexpressed as body length traversed per second, thenfrequency can be expressed as: f 5 1.1(U/L). This issupported by Rohr et al.s (1998) data, the mean trendof Kayan and Pyatetskiy (introducing f 5 0 at U 5 0)and the accounting of natural frequency (see Fig. 5 inBandyopadhyay et al., 2000a). With the above tworelationships, for dolphins, we then have

St 5 0.22. (6)Thus, dolphins also have a similar and constant Strou-hal number as fish, although their Reynolds number ismuch higher. This provides another layer of evidencethat fish, dolphins and whales have similar Froudenumbers and mechanisms of maneuvering and propul-sion, irrespective of their Reynolds numbers.

FISH-INSPIRED CONTROL FOR MANEUVERING:DORSAL FIN DEVICE

The maneuverability of normally, stable cylinders(length/diameter $ 10) is considered here. Their ma-neuverability is a slow process when it involves thepitching of small fins near the boat tails and a subse-quent large-scale separation of the entire cylinder. A



Dow

nloaded from


FIG. 13. Photograph of instrumented laboratory scale model for evaluation of fish inspired control surfaces on a rigid cylinder. This controlsurface is passive and is an euthynnid-inspired offset pectoral winglet for pitch stabilization near surface waves.

FIG. 14. Variation of the absolute values of the maximum or min-imum of the coefficients of axial forces and pitching moments withtowing speed. Note reduction due to hydrofoil.

76 mm diameter and 754 mm long cylinder modelwith a dorsal fin device that is abruptly deployable,and shown in Figure 6, was constructed. The modelwas towed in a tank and a typical result of the pro-duction of side thrust is shown in Figure 7. It is clearthat the dorsal fin when cambered abruptly produceslarge levels of side thrust practically immediately.

The theoretical study of biologically inspired controlsurfaces described later showed that the above resultis of general significance. While man made vehicles,like aircraft, have a moment-based control, biological-ly based maneuvering of engineering bodies would beforce based. One consequence of the latter is the fasterunder water response allowing a greater agility.

FISH-INSPIRED CONTROL FOR MANEUVERING:SMALL AGILE VEHICLES

Pectoral fins and turning. Several species of fast yetagile fish (Fig. 8) have large pectoral fins. They do nothave a gas bladder and retract these fins to control liftforce. A detailed hydrodynamic coefficients basedmodeling was carried out to determine the effective-ness of these pectoral fins in low speed maneuveringin an engineering context. The computational model-ing of cruise and turn was carried out on three config-urations of the cylinder shown in Figure 9: a referenceplain cylinder and two others where pairs of wings, ofthe order of cylinder diameter, are attached. All threecylinders are provided with a pair of tail planes forstability. The results are shown in Figures 10 and 11.The wings allow the cylinder to be sustained at lowerangles of attack. They also allow the cylinder to makelower radii turns.Damping due to pectoral fins near surface waves

The effect of the pectoral wings was examined inpresence of travelling surface waves. This geometryand the forces on a body due to linear theory areshown in Figure 12. The model shown in Figure 13was constructed, where the wing was offset from thecylinderbelow it and not above. The maximum andminimum values of the periodic coefficients of axialforce and pitching moments are compared in Figure14 between the hydrofoil-cylinder and the plain cyl-inder case. Here, coefficient of axial force Cfx 5 Fx/(rgbAf), and coefficient of pitching moment CTy 5 Ty/(rgbAp D), where Fx is axial force, Ty is pitching mo-ment, r is fluid density, g is acceleration due to gravity,b is peak-to-trough wave height, Af is frontal area, Apis planform area, and D is the offset of the hydrofoilleading edge from the model axis (511.43 cm for thehydrofoil-cylinder model and D/2 for the plain cylin-



Dow

nloaded from


FIG. 15. Schematic of the maneuvering devices (Dorsal and CaudalFins) and axisymmetric cylinder. Dorsal fins, shown uncambered,are mounted in the horizontal plane. The caudal fins, mounted inthe horizontal plane, are akin to flukes in whales. XI 2 ZI 5 InertialCoordinate System (Origin at the Calm Surface). 2 5 Trans-X9 Z9I Ilation of Inertial Frame (Origin at Geometrical Center). XB 2 ZB 5Body Fixed Coordinate System.

FIG. 17. Dorsal Fin Control: Sinusoidal Disturbance: (a) Depth er-ror ze 5 z 2 yr; (b) Depth z and reference command yr; (c) Camberd 5 u; (d) Pitch angle.

FIG. 16. Closed-Loop System (Including the Caudal and Dorsal FinControllers).

FIG. 18. Schematic of model for studying the following effects: (1)the precision maneuvering ability of dual flapping foils attached tothe tail of a rigid cylinder, and (2) the interference between simulatedhead motion and tail flapping of a fish on a rigid cylinder. A softwareoperated digital controller is used to select the phase lag of the noseslider actuator relative to the two flap actuators that operate in phase,called waving mode here (as opposed to clapping mode where theyoperate in anti-phase).

der). The pectoral wings have a stabilizing dampingeffect.

Theoretical control study of biologically-inspiredcontrol surfaces. The control system synthesis of asmall cylinder equipped with a pair of dorsal and cau-dal fins, and in the presence of surface waves, asshown in Figure 15, was examined. Closed loop con-trol laws were derived using the dorsal and caudal finsfor depth and pitch control, respectively. The systemis shown in Figure 16. For the typical cylinder ge-ometries considered here, Figure 17 shows an exampleof a simulation where precise depth control and pitchregulation were achieved using the dorsal fin only.

FISH-INSPIRED CONTROL FOR MANEUVERING:DUAL FLAPPING FOILS

Unsteady vortex mechanismThe remaining gap in turning ability depicted in

Figure 5 between fish and rigid bodies can be attri-

buted primarily to the absence of sufficient control sur-faces and perhaps to flexibility of the main body inthe latter category (Fish, 1999). Fish-inspired controlsurfaces can therefore be a partial solution for maneu-verability for rigid bodies. The hydrodynamic mech-anism of maneuvering and stealth of the moving sur-faces of a fish was examined in an engineering exper-iment. The head and tail oscillations of a fish weresimulated on a rigid cylinder that also removed theadded complication of body undulation. Several ex-periments were carried out on the strut mounted float-ing cylinder shown in Figure 18. A six-component dy-namic load cell, three actuators and two displacementsensors for measuring the phase of the tail actuatorswere housed within the model. Dye visualization andphase-matched laser Doppler velocimetry measure-ments of the vortex shedding due to the oscillation ofthe tail flaps, and time histories of the forces and mo-ments on the entire model assembly were carried out



Dow

nloaded from


FIG. 19. Photograph of water tunnel model of the dual flapping foil device. Dual flapping foils and divider plate are shown at the right end;to the left of foils lie the actuators, two phase transducers, and actuator control circuits. The six-component load cell is located at the junctionof the strut and cylinder.

FIG. 20. Photograph of cylinder model for studying the interference effects between head and tail oscillations, and digital controller ofactuators.

for an uniform freestream and various tail oscillationStrouhal numbers. In the first configuration, only thepair of flapping foils attached to the tail was oscillatedand the slider in the nose was absent. In the second,the interaction of both the nose and tail oscillationswas examined. Figures 19 and 20 show the photo-graphs of the instrumented model in these two config-urations, respectively.

Figure 21 shows the measurements of time inte-grated axial (thrust) force coefficient (ca) versus Strou-hal number (St) of tail flap oscillation, They are de-fined as: ca 5 F/(1/2 rU`2D2) and St 5 fA/U`. Here, Fis axial force, r is fluid density, U` is freestream ve-locity, d is length scale of flap, f and A are flap oscil-lation frequency and amplitude, repectively. The dataasymptotes to Lighthills two-dimensional inviscid the-



Dow

nloaded from


FIG. 21. Comparison of measurements of axial force (thrust) components.

FIG. 22. Vorticity-velocity vector maps in the axial plane (x/D versus 6 y/D) in the waving mode for phase t*.

ory at Strouhal numbers that are below the range offish. We believe that Lighthills line indicates the nat-ural shedding symptote. As St is increased, axial forcegenerated becomes oscillation frequency dependent,approaching the forced shedding asymptote of Ban-dyopadhyay (1996).

The pairs of tail flaps (Figs. 18 and 19) were oscil-lated in two modes termed waving and clapping. Their

phase is the same and opposite in them, respectively,mimicking the motion the names indicate. The respec-tive vorticity-velocity vector maps of the vortex shed-ding process in the axial plane are shown in Figures22 and 23, where t* 5 tU`/D is phase and the locationsof the flap trailing edges are indicated by two smallfilled squares on the vertical axis. The large cross-stream forces in waving mode (Fig. 22), which have



Dow

nloaded from


FIG. 23. Vorticity-velocity vector maps in the axial plane (x/D versus 6 y/D) in the clapping mode for phase t*.

FIG. 24. Decay of circulation distribution in the wake of flapping foils: waving mode of flapping. The horizontal axis represents flap phase.

maneuvering and axial components, owe their originto the formation of a staggered vortex train. On theother hand, the clapping mode which produces a pureaxial thrust only (Fig. 23), owes its origin to symmet-ric vortex trains which are mirror images of each other.

The resulting induced velocity between the successivevortices in the waving (maneuvering) mode is inclinedto the streamwise axis. On the other hand, it is a per-fectly aligned streamwise jet in the clapping mode.The general conclusion is that the mechanism of dis-



Dow

nloaded from


FIG. 25. Variation of time-averaged axial thrust with phase lag ofnose slider. Speed, Frequency & Tail Flap Strouhal number St: 16.221.0 cm/sec, 3.77 Hz & 0.60.46.

FIG. 26. A small agile vehicle. The ruler is 30 cm long. The four pairs of flapping foils are arranged in a cross configuration. The horizontaland vertical pairs oscillate in the opposite phase producing high and uniform thrust. The main body is the so-called low drag laminar B1 body.The flap actuators are located inside the main body.

crete and deterministic vortex shedding from oscillat-ing control surfaces has the property of large ampli-tude unsteady forcing and an exquisite phase depen-dence, which makes it inherently amenable to activecontrol for precision maneuvering.

Decay of wake. The vorticity-velocity vector mapswere used to compute the circulation in the shed vor-tices by two methods: velocity line and vorticity areaintegrals. The circulation distributions are comparedimmediately after formation and after a short travel inFigure 24, for the waving mode. The maximum valueof circulation (2G) drops by a factor of 3 within amere distance of half the body diameter or flap width(D). The effect is a rapidly dissipating wake. Such arapid drop is attributed to a transverse-to-freestreamorientation of the vortex, rather than a streamwise ori-entation.

In the second configuration (Fig. 20), a small ob-struction, a maximum of 34 mm, was alternately pro-

truded at the port and starboard sides of the nose togenerate small vortices and simulate the effect of thehead swaying of a fish. The vortices interacted withthose shed from the dual flapping foils in the tail. Thephase between the nose and tail flap motion was variedand the axial force signature on the entire cylinder as-sembly was measured. The time-integrated values areshown in Figure 25. It is remarkable that a fine thrustregulation within 65% can be achieved by phasedseeding of vortices between spatially distributed con-trol surfaces.

A biologically-inspired maneuvering vehicle. Mea-surements with the flapping foil cylinder model shownin Figure 19 indicate the following. At say, 20 cm/secof flow speed, the steady drag levels are 1/100th of thepeak unsteady forces and 1/50th of the time mean val-ues due to the dual flapping foils. Thus, a remarkablefeature of flapping foil locomotion is the productionof large unsteady forces. However, in man-made sys-tems, unsteady mechanisms are rare.

While their peak and mean values are large, theforces produced by flapping foils are inherently peri-odic with large differences between the minimum andmaximum values. To generate large forces practicallyat all phase, pairs of flapping foils may therefore beoperated out of phase. Figure 26 shows such a smallvehicle. The dual flapping foils are arranged in a cru-cifix form. For pure thrust, the horizontal pairs operateout of phase with respect to the vertical pairs. Inde-pendent operation of the dual flapping foils could pro-vide precision maneuvering. The main body has a lam-inar low drag profile. The low-speed swimming of thetethered neutrally buoyant vehicle in Figure 26 hasbeen demonstrated in a small tank (Bandyopadhyay etal., 2000b).

BIOMIMETIC PROPULSOR: ACTIVE NOISE CONTROLIn a predator-prey environment, the ideal underwa-

ter animal or vehicle should produce no noise andleave no wake signature. Thus the primary motivationfor biological studies might be stealth. Maneuvering



Dow

nloaded from


FIG. 27. Modeling of the effects of reduction in rotational speed of a propulsor on radiated noise.

FIG. 28. Details of the Biomimetic Propulsor model: (a) end viewof blade with artificial muscle, (b) plan view of blade in (a), and (c)experimental setup of propulsor assembly in water-filled box, withmotor drive and load cell.

involves operation at off-design condition. Two strat-egies for propulsor noise reduction are examined here:reduction of rotational speed and blade tonals, wherescience distilled from biology may be applicable toengineering problems.

Reduction of rotational speedA modeling was carried out to determine the effect

of reduction of rotational rate of a propulsor on thesesources of radiated noise: blade rate tonal due to wakedeficit; trailing edge singing; and, ingested turbulence.

They are expressed as rotational rate (RPM) to thepower of 4, 5 and 6, respectively. The result is shownin Figure 27. A RPM reduction of 5% can give a 35 dB reduction in noise.

In principle, we can propose that the application ofunsteady lifting mechanisms of fruit fly (Ellington,1984; Dickinson et al., 1999), namely rotation lift, de-layed stall and wake capture, might be an avenue forlift enhancement, leading to reduction of RPM. How-ever, the implementation of these mechanisms to prac-tical propulsors is fraught with difficulties. An impor-tant step in this direction involves the development ofprogrammable cambering of blades using electro-ac-tive polymeric artificial muscles. A small two-bladedpropulsor, shown in Figure 28, was built. A controllerwas built that could power the muscle electrodes bymeans of square waveforms: positive, negative or bi-polar. The peak volts, frequency and duty cycle couldbe varied. Figure 29 shows the types of blade cam-bering achieved. A low frequency pulse (O(1 Hz)) ledto cambering and oscillation, while a high frequencypulse (O(100 Hz)) led to cambering only. Figure 30shows an example of thrust enhancement of about 15%at a RPM of 520 due to blade cambering.

Reduction of blade tonalsA rotor blade traversing the wake of stator blade

experiences a time-dependent load due to vertical gust,which gives rise to radiated noise, called blade tonals.Lighthills equation relating the load derivative to fluc-tuating pressure describes this overall process. Now, ifthe trailing edge of the upstream stator blade is oscil-lated like a fish tail, then the momentum deficit in thewake can be filled. This can be expected to reduce the



Dow

nloaded from


FIG. 29. Cambering of blade muscle. Non-rotating propulsor. Input pulse forms and nature of cambering are as follows. (a) Bipolar: Muscleis Flat, (b) Positive Unipolar: Muscle is Cambered Negatively; Negative Lift; Reversed Thrust, and (c) Negative Unipolar: Muscle is CamberedPositively; Positive Lift; Forward Thrust. Power supply to muscles: 100 Hz and 7 V; High frequency leads to cambering without oscillationand bubbles; 1 cm 3 1 cm Grid.

FIG. 30. Comparison of thrust signature during active cambering. Two-bladed propulsor. RPM 5 520. Negative Fx indicates positive thrust.Muscle: MS-417 cloth backing; Power: 3 V, 1 Hz; No bubbles are produced during these measurements. Pulse: Negative Unipolar producingpositive cambering.

vertical gust on the rotor, and thereby the noise radi-ated. This flow, shown in Figure 31, was modeled hy-drodynamically. The controller, of the dynamic inver-sion type, is shown in Figure 32, which produces thecirculation necessary to cancel the derivative of the

lift. Sears function is used to account for the phasedifference between gust and rotor lift. The result of acontroller canceling the derivative of the lift is shownin Figure 33. The peak-peak amplitude of the radiatednoise is reduced by at least 40 dB.



Dow

nloaded from


FIG. 31. Schematic representation of blade tonal generation: a rotor blade traversing a stator wake. The trailing edge of the stator bladeoscillates like a fish tail to fill the wake momentum deficit and reduce the vertical gust on the rotor blade, which is the source of blade tonalnoise.

FIG. 32. Block diagram of control strategy: choose actuator cir-culation G(t), so that L in rotor blade is reduced.

FIG. 33. Comparison of radiated noise due to gust from statorwake. Upper: control off; lower: control on.

CONCLUDING REMARKSThe progress made at NUWC in bridging biology

and the hydrodynamics of small underwater vehiclesis reviewed. Maneuvering hydrodynamics is exam-ined, the goal being the understanding of mechanismsof noise reduction. The approach is not to build roboticreplicas of swimming or flying animals. Instead, thescientific principle is distilled and applications are con-ceived for retro-fitting to, or for modification of exist-ing engineering vehicles or components.

The general conclusion is that, swimming andflight in nature are characterized by oscillating controlsurfaces, which could sometimes include the mainbody. The mechanism of discrete and deterministicvortex shedding from oscillating control surfaces hasthe property of large amplitude unsteady forcing andan exquisite phase dependence, which makes it suit-able for active control for precision maneuvering,stealth and lift enhancement. The knowledge base isnew but advanced. Several examples of applicationsto rigid cylinders and propulsors are discussed. How-ever, the applications are not widely explored yet.Rich possibilities remain. Advances in actuator tech-nology, like artificial muscles, are required for newand matured application of the recently understood

unsteady vortex dynamics principles of swimmingand flight in nature.

ACKNOWLEDGMENTSThe author gratefully acknowledges the sponsor-

ship of the Office of Naval Research (Codes 342 and333), Program Managers Dr. Teresa McMullen, andMr. James Fein, for early support. Collaborationwith the following are acknowledged: Professor An-uradha Annaswamy of MIT, William P. Krol, Jr.,William H. Nedderman, John Castano, James Dick,James Q. Rice and Daniel P. Thivierge of NUWC,Dr. William Macy of URI, Professor SahjendraSingh of UNLV and Dr. Mehran Mojarrad of BPI ofNew Mexico.



Dow

nloaded from


REFERENCESAleyev, Y. G. 1977. Nekton. Junk, The Hague.Annaswamy, A., W. P. Krol, Jr., and P. R. Bandyopadhyay. 2000. A

biomimetic propulsor for active noise control. Part 2: Theory.Bull. of the American Physical Society, 45, No. 9:95.

Bandyopadhyay, P. R. 1996. A simplified momentum model of amaneuvering device for small underwater vehicles. NUWC-NPT Technical Report 10,552, Naval Undersea Warfare Center,Newport, Rhode Island.

Bandyopadhyay, P. R. 1999. Emerging approaches to flow controlin hydrodynamics. Paper CDC99-INV0134, The 38th IEEEConf. On Decision and Control, Control Systems Society, Dec.710, 1999, Tempe, AZ, Vol. 3 of 5:2,8452,850.

Bandyopadhyay, P. R., J. M. Castano, J. Q. Rice, R. B. Philips, W.H. Nedderman, and W. K. Macy. 1997. Low-speed maneuveringhydrodynamics of fish and small underwater vehicles. ASMEJ. Fluids Eng. 119:136144.

Bandyopadhyay, P. R., J. M. Castano, W. H. Nedderman, and M. J.Donnelly. 2000a. Experimental simulation of fish-inspired un-steady vortex dynamics on a rigid cylinder. ASME J. FluidsEng., 122, No. 2:219238.

Bandyopadhyay, P. R. et al., 2000b. Biomimetics research atNUWC. Video (Edited), 14 Mts., Naval Undersea Warfare Cen-ter, Newport, Rhode Island.

Bandyopadhyay, P. R., W. H. Nedderman, and J. Dick. 1999a. Bi-ologically-inspired bodies under surface waves. Part 1: Loadmeasurements. ASME J. Fluids Eng., 121, No. 2:469478.

Bandyopadhyay, P. R., S. Singh, and F. Chockalingam. 1999b. Bi-ologically-inspired bodies under surface waves. Part 2: Theo-retical control of maneuvering. ASME J. Fluids Eng., 121, No.2:479487.

Bandyopadhyay, P. R., W. P. Krol, Jr., D. P. Thivierge, W. H. Ned-derman, and M. Mojarrad. 2000c. A biomimetic propulsor foractive noise control. Part 1: Experiments. Bull. of the AmericanPhysical Society, 45, No. 9:95.

Bannasch, R. 2001. New wing and propellor constructions inspiredby techniques learned from wing-propelled animals. TechnicalUniversity, Berlin (due to appear).

Bar-Cohen, Y. (ed.) 2001. Electroactive polymer actuators as arti-ficial muscles: Reality, potential and challenges. SPIE Press,Bellingham, Washington.

Belmonte, A., H. Eisenberg, and E. Moses. 1998. From flutter totumble: Inertial drag and Froude similarity in falling paper.Physical Review Letters 81:345348.

Dickinson, M. H., F. Lehmann, and S. P. Sane. 1999. Wing rotationand the aerodynamic basis of insect flight. Science. 284:1,9541,960.

Ellington, C. P. 1984. The aerodynamics of hovering insect flight.IV. Aerodynamic mechanisms. Phil. Trans. R. Soc. London SerB 305:79113.

Fish, F. E. 1999. Performance constraints on the maneuverability offlexible and rigid biological systems. Proceedings of the 11thInternational Symposium on Unmanned Untethered Submers-ible Technology. Autonomous Undersea Systems Institute, Dur-ham, New Hampshire: pp. 394406.

Fish, F. E. and J. Rohr. 1999. Review of dolphin hydrodynamics andswimming performance. SPAWARS System Center TechnicalReport 1801, San Diego, California.

Madden, J. D., P. G. Madden, and I. W. Hunter. 2001. In Proceedingsof SPIE 8th Annual Symposium on Smart Structures and Ma-terials: Electroactive polymer actuators and devices. YosephBar-Cohen, Ed., SPIE, Bellingham, Washington.

Rohr, J. J., E. W. Hendricks, L. Quigley, F. E. Fish, J. W. Gilpatrick,and J. Scardina-Ludwig. 1998. Observations of dolphin swim-ming speed and Strouhal number. Tech. Rept. 1,769, U.S. NavySpace and Naval Warfare Systems Center, San Diego, Califor-nia.

Lighthill, J. 1975. Mathematical biofluiddynamics. Soc. Ind. Appl.Math., Philadelphia.

Taylor, G. I. 1952. Analysis of the swimming of long and narrowanimals. Proc. R. Soc. London. Ser. A Biol. Sci. 214:158183.

Triantafyllou, G. S. and M. S. Triantafyllou. 1995. An efficientswimming machine. Sci. Amer. 272:6470.

Videler, J. J. 1993. Fish swimming. Chapman & Hall, London.Webb, P. W. 1975. Hydrodynamics and energetics of fish propulsion.

Bull. Fish. Res. Bd. Can. 190:1158.Wu, T. Y. 1971a. Hydrodynamics of swimming propulsion. Part 1.

Swimming of a two-dimensional flexible plate at variable for-ward speeds in an inviscid fluid. J. Fluid Mech. 46:337355.

Wu, T. Y. 1971b. Hydrodynamics of swimming propulsion. Part 2.Some optimum shape problems. J. Fluid Mech. 46:521544.

Wu, T. Y. 1971c. Hydrodynamics of swimming propulsion. Part 3.Swimming and optimum movements of a slender fish with sidefins. J. Fluid Mech. 46:545568.

Wu, T. Y. 1971d. Hydromechanics of swimming fishes and ceta-ceans. Adv. Appl. Mech. 11:163.

Wu, T. Y. 1972. Extraction of flow energy by a wing oscillating inwaves. J. Ship Res. 14:6678.



Dow

nloaded from

Maneuvering Hydrodynamics of Fish and Small Underwater Vehicles

Documents

Transcript of Maneuvering Hydrodynamics of Fish and Small Underwater Vehicles