Hydrodynamics of Dolphin s Swimming

Transcription

1 Hydrodynamics of Dolphin s Swimming Author Name Keshu Priyadarshi, Aastha Dhiman, Ankita singh, Antriksh Johri Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi , India Abstract Research into dolphin swimming has historically been guided by false assumptions of effortless, high-speed swimming. These assumptions have instigated the development of drag-reduction hypotheses but tests of these hypotheses have generally had little success. The autecological approach has dominated recent efforts and has been more successful. In this review we summarize results of decades of research efforts to study these creatures. (1) Drag is minimized primarily by the streamlined shape of the body and appendages, with no known contributions from compliant dampening, dermal ridges, secretions, boundary layer heating, or skin folds. All indications are that the boundary layer is turbulent. (2) Muscles for the upstroke and downstroke of swimming dolphins provide approximately equal power. (3) Output force is enhanced by insertions occurring on the long processes of the vertebrae and on the subdermal connective tissue sheath. (4) Measured swimming speeds are lower than previously believed, with maximum reported routine speeds being approximately 3 m/s. (5) Porpoising behaviour appears to be the most energetically conservative manner in which to breathe when swimming at high speed. (6) Riding surf and wind waves involves the balance between the wave slope and the weight of the animal whereas riding the bow wave involves the interaction of the pressure wave in front of a ship and the drag of the dolphin.

2 Declaration The term-paper is of mainly of review type and it presents a thorough review of literature on the topic. No computational work or analytical calculations were performed in the term-paper. All authors have made equal contributions in preparation of this term-paper

3 Key words: Dolphins, Hydrodynamics, Gray s Paradox, Streamlined Body, Aerodynamics Introduction The swimming of Dolphins, whose well-authenticated maximum speed is 15 knots or more, is of interest not only to the biologist but also to those who would emulate this performance by artificial means. Fundamental to such a study is a knowledge of the swimming movement, which is not easily observed and has long been disputed. It has been a longstanding impression both within as well as outside of the scientific community that dolphins swim with a low energy expenditure (Fish and Hui, 1991; Fish and Rohr, 1999). As movement through water is difficult because of the higher density and viscosity of the medium compared with air (Denny, 1993; Vogel, 1994), the mechanics. To discuss the dynamics of swimming

4 we have to take in consideration the drag force that in turn leads to a discussion of Gray's Paradox: the big discrepancy which showed to exist between the power apparently needed to overcome this drag at high speed, and the maximum power to be expected from the swimming.james Gray thought that the power needed for the dolphin to swim at such speeds exceeded its available power nearly 10 times over.the challenge to date has been the inability either to directly measure the thrust generated by a swimming dolphin or to measure the associated flow field. 1. Literature review 1.1 Early review of Dolphins The earliest account of the swimming ability of dolphins came from Aristotle who considered dolphins the fastest of all animals. A description of the dolphin swimming mechanism was given by Borelli (De Motu Animalium; 1680), who noted the up and down movements of the cetacean tail. Observations on dolphins indicated that propulsion was accomplished by tail movement. Direct observations of dolphin swimming motions were difficult because of the high stroke frequency and distortion of viewing through water. In one case, a device was mounted on the back and tail stock of a free-swimming dolphin to record lateral and vertical movements of the tail. Thrust performance of dolphin tails was considered superior to screw propellers (Pettigrew, 1893; Petersen, 1925; Triantafyllou and Triantafyllou, 1995). Screw propellers could not vary speed because of their inelastic nature. This was believed that it limited the effective speed range of propellers whereas the oscillatory motions of flexible dolphin tails could adjust to velocity changes and maintain effective thrust production.(pettigrew, 1893; Petersen, 1925; Saunders, 1951).

5 The dolphin shape came under scrutiny by engineers in the 1800s. Cayley (circa 1800) considered the dolphin body as a solid of least-resistance design (Gibbs-Smith, 1962). The streamlined, fusiform shape of the dolphin closely matches modern low-drag airfoils. 1.2 Gray s Paradox Gray's Paradox is a paradox posed in 1936 by British zoologist Sir James Gray. The paradox was to figure out how dolphins can obtain such high speeds and accelerations with what appears to be a small muscle mass. He used a simple hydrodynamic model based on a rigid body to calculate drag power and applied it to a dolphin and a porpoise swimming at speeds of 10.1 and 7.6 m/s, respectively. The results indicated that the estimated drag power could not be reconciled with the available power generated by the muscles. In the words of Sir James Gray (1936): "If the resistance of an actively swimming dolphin is equal to that of a rigid model towed at the same speed, the muscles must be capable of generating energy at a rate at least seven times greater than that of other types of mammalian muscle." For his calculations, Gray initially assumed that turbulent boundary flow conditions existed because of the speed and size of the animals. But considering the high velocity of dolphins, the drag force on them had to be lower. This could be achieved through maintenance of a fully laminar boundary layer. Gray proposed a mechanism whereby the dolphins' oscillating flukes would laminarize the boundary layer by accelerating the flow over the posterior half of the body. However, it turned out that there were potential errors in estimation of dolphin swimming speed and inconsistencies between dolphin swimming performance and data on muscle power outputs. Gray used a shipboard observation by E. F. Thompson, who timed a

6 dolphin with a stopwatch as it swam along the side of the ship (length = 41.5 m) from stern to bow in 7 s (10.1 m/s). If the dolphin was swimming close enough to use the wave system of the ship, its speed may have been artificially enhanced and energetic effort reduced because of free-riding behaviours. 1.3 Kramer Max Kramer, a German scientist claimed to have solved the puzzle of Gray s paradox in 1960s. Kramer claimed that a laminar boundary layer without separation could be achieved at high Reynolds number through their soft compliant skin that dampens incipient turbulence. To prove this, Kramer coated a torpedo with an artificial skin based on a dolphin's skin. The dolphin integument is composed of a smooth, hairless epidermal surface forming an elastic membrane and is anchored to the underlying dermis with its blubber layer by longitudinal dermal crest with rows of papillae, which penetrate the lower epidermis. By covering a torpedo with simulated dolphin skin made of a rubber membrane underlain with viscous fluid, he demonstrated that a dolphin could modify the flow of water in precisely the way that Gray had imagined in order for the animals to reach their observed speeds. A 59% reduction in drag was achieved at Re = 15x10 6 compared to a rigid reference model with fully turbulent flow. Kramer claimed to have exposed the "dolphin's secret" and provided a resolution to Gray's Paradox. 1.4 Naval Research Naval interest in swimming by dolphins and other marine life began nearly 50 years ago. The main reason for the naval interest was to

7 design and improve watercrafts by gaining knowledge about the propulsion systems of fish and marine mammals to learn how to increase speed and manoeuvrability. Particular interest was focused on properties associated with (1) silence, (2) speed, (3) endurance or range, (4) wakelessness, and (5) mechanical efficiency. Stealth was associated with both silence and wakelessness. The U.S. Navy's Marine Mammal Program originated in 1960 when a Pacific white-sided dolphin (Lagenorhynchus obliquidens) was acquired for hydrodynamic studies. This purchase was largely motivated by accounts of extraordinary swimming speeds of dolphins and the desire to reduce the hydrodynamic resistance of torpedoes and submarines. If the work of Sir James Gray and Dr. Max Kramer was true, then this strategy could be applied to torpedoes, for example, 10-fold reductions in drag seemed possible

8 The studies were conducted on Lagenorhynchus obliquidens, which was trained to glide through a series of submerged hoops. Collars were attached to the body of the dolphin which induced turbulent flow. It was found that the boundary layer over the dolphin was primarily turbulent and there were no unusual physiological or hydrodynamic phenomena. Throughout the 1980s, dolphin hydrodynamic research focused on metabolic effort and on various hypothesized turbulent drag reduction techniques employed by dolphins. Although it was found that dolphins seem to be physiologically efficient as swimmers, it did not appear that unusual metabolic changes take place. The studies

9 did not reach a conclusion and the Americans were unable to duplicate Kramer s work and while the Soviets made claim, no solid evidence has surfaced of their work. 1.5 Frank E. Fish And Timothy Wei The Gray s Paradox finally still persisted even after a lot of research work and experimentation on this topic. This was until a scientist named Frank E. Fish pronounced an answer in Frank E. Fish was Fish, a marine biologist at West Chester University and the lead author on the new study in the Journal of Experimental Biology, had long been searching for a way to directly measure the thrust, and thus power, of a swimming dolphin. According to Fish, A dolphin propels itself forward by moving its tail with its lateral flukes, while its flippers steer. The flukes push on the surrounding water, and the water pushes back, creating thrust. The initial experiments were often based on dragging a static body through water, and thus did not fully capture the forces at work when an object actively moves through the water, as a dolphin does while swimming. Fish focused on improved hydrodynamic models that took into account the flexibility of the flukes in an attempt to more directly measure thrust. He specifically studied routine and maximum swimming speeds, morphological design related to hydrodynamic performance, drag reduction, swimming kinematics, thrust production and efficiency, behavioural strategies employed for energy economy when swimming, and manoeuvrability. Despite the effectiveness of engineered mechanisms for drag reduction, there was no direct supporting evidence for special drag reduction mechanisms (i.e., maintenance of laminar flow) associated with the dolphin skin. The propulsive mechanism relies on symmetrical dorsoventral oscillations of flukes with controlled pitch. Oscillation frequency increases nearly linearly with velocity whereas peak-to-peak amplitude remains constant at approximately 20% of

10 body length. Vorticity control is an important mechanism in the generation of thrust at high propulsive efficiency. But it wasn t till the development of a technique called Particle Image Velocimetry (PIV) that Fish had found a final solution to this issue. In this technique, used to measure the forces exerted by swimming fish, a high-speed video camera follows the movement of tiny glass beads dropped into a tank and illuminated by a laser. By tracking the movement of the beads through the water as the fish beats its fins or tail, researchers could calculate the speed of the beads and then back-calculate the thrust exerted by the fish. With the help of Timothy Wei, a professor at Rensselaer School of Engineering they designed a modification of PIV to help the U.S. swim coaches break down the individual strokes and movements of their athletes. By using bubbles and natural light, instead of glass beads and lasers, Wei could humanely test on humans. Using 2 bottlenose dolphins as their subjects, Primo and Puka The team bought a soaker hose, in which water seeps out of several tiny pores, and placed it at the bottom of a pool. They pumped compressed air through the hose, creating a curtain of tiny bubbles. Trainers then directed Primo and Puka to swim through the curtain while a video camera taped the location and movement of the bubbles. From there, the thrust exerted by the dolphins could be calculated. Thus, from the findings of Fish it could be concluded that Gray s Paradox is wrong and the high speed of dolphins can be explained from the high thrust they produce and their musculature. 2. Problem formulation / Experimental set-up Particle image velocimetry (PIV) was used to solve Gray s Paradox.

11 This technique was used to measure the forces exerted by Dolphins. In this a high-speed video camera follows the movement of tiny glass beads dropped into a tank and illuminated by a laser. By tracking the movement of the beads through the water as the Dolphins beats its fins or tail, we could calculate the speed of the beads and then back-calculate the thrust exerted by the fish. Use of glass beads and laser beam was harmful for dolphins so Wei designed a new technique where he used bubbles and natural light,instead of glass beads and lasers. 2.1Bubble DPIV DPIV method use illuminated micro-bubbles that were generated in a narrow sheet from a finely porous hose and a compressed air source. The movement of the bubbles was tracked with a high-speed video camera. Dolphins swam at speeds of 0.7 to 3.4 m s(-1) within the bubble sheet oriented along the mid sagittal plane of the animal. The wake of the dolphin was visualized as the micro-bubbles were displaced because of the action of the propulsive flukes and jet flow. The oscillations of the dolphin flukes were shown to generate strong vortices in the wake. Thrust production was measured from the vortex strength through the Kutta-Joukowski theorem of aerodynamics. The dolphins generated up to 700 N during small amplitude swimming and up to 1468 N during large amplitude starts. The results of this study demonstrated that bubble DPIV can be used effectively to measure the thrust produced by large-bodied dolphins. 2.2Thrust Due to Vortex Oscillations of the dolphin s flukes, like an oscillating hydrofoil, produce strong trailing vortices with rotation determined by the direction of motion of the fluke. By defining and integrating along a closed contour around the core of each vortex generated by the dolphin s tail, the circulation, Γ, which is proportional to the lift, was calculated using the formula Γ = V ds (1)

12 where V is the velocity around the contour and ds is the corresponding differential tangent vector on the contour. For these measurements, a nonzero value of Γ implies there exits a non zero thrust.this thrust is produced by the vortex formation.vortex strength through the two-dimensional airfoil Kutta Joukowski theorem of aerodynamics. The thrust, T, is proportional to the circulation of the shed vortex, Γ T = ργvb, (2) Where, v is the vertical velocity of the tail, perpendicular to the direction of swimming, ρ is the fluid density (1024 kg m 3 for seawater) and b is the span of the dolphin s flukes. The important thing to recognize is that the tail motion is perpendicular to the axis of the body, and that the lift vector generated by the tail therefore points along the body axis toward the head. When the dolphin is swimming, then, the tail motion is vertical, and the lift generated by the tail is oriented horizontally which is the thrust provided by dolphins. The thrust which is produced due to the formation of vortices can be compared with the drag force and a coefficient similar to coefficient of drag can be calculated. Let us call this coefficient as coefficient of lift,. T = ργvb = ( ) (3) Where, S c is the area of the fin. u is the velocity of dolphin and v is the velocity of fin.

13 2.3DRAG FORCE: A streamlined shape has much less drag than a non-streamlined shape. Whatever drag exists for a streamlined shape is composed primarily of skin-friction drag with the pressure drag being very small. The increase in skin-friction drag occurs because the streamlined body has more area exposed to the airflow and thus has a greater area over which the boundary layer may act. A streamlined shape also experiences almost no boundary-layer separation.

14 However, the shape of a body or different airspeeds encountered cannot explain all aerodynamic results relating to the amount of drag. A better measure of performance is needed. This measure is the non-dimensional drag coefficient. C D - Coefficient of drag The drag force experienced by the body is given by, (4) A- Wetted area - Density of fluid u- velocity of body

15 2.4BALANCE OF FORCES Let us say the length of the whale is l and it is moving with a constant velocity u in a fluid of density. The caudal fin has an area S c and It oscillates laterally with an amplitude h. In terms of length distance, the amplitude is. (5) The frequency of the fin is f and it is moving with a lateral velocity v. There are in total three forces acting on the dolphin. There are two drag forces acting on the dolphin, one on the fin(d), (Drag coefficient C D ), parallel to the fin and the other on the body(d b ), (Drag coefficient C Db ), in direction of u. Also there is one lift force acting on the body (Lift coefficient C L ) perpendicular to the fin. Now, ( ) (6) ( ) (7) (8) Now let us say,

16 (9) (10) Where T is time period of the fin. So (11) Also, (12) (13) Similarly, (14) Hence, (15) For constant speed swimming, The forward thrust produces by the life force of the fin, should balance the drag on the body and the fin. By taking the horizontal component of D as and (16) ( ) ( ) (17) By solving this equation we get the relationship between lift and drag coefficients as:- ( ) (18) 3. Results and discussion

17 The result of the Gray s paradox is that there was no paradox and we can abolish Gray's paradox.first off, we can stop looking for a magic mechanism to reduce drag.there may be ways to reduce drag, but the dolphin s skin isn t going to show us those. The results showed that a dolphin's tail, or fluke, is more than capable of producing enough thrust to speed the mammal through the water. The flukes are essentially wings.they generate a lift force that is directed forward, on both the upstroke and downstroke.this produces the thrust that pushes the dolphin through the water. The flukes are also flexible, which is key to enabling the dolphin to maintain a highly efficient way of swimming over a broad range of speeds. Minimization of aerodynamic drag force in racing cars and planes Any physical body being propelled through the air has drag associated with it. In aerodynamics, drag is defined as the force that opposes forward motion through the atmosphere and is parallel to the direction of the free-stream velocity of the airflow. Drag must be overcome by thrust in order to achieve forward motion. There are several types of drag: pressure, skin friction, parasite, induced, and wave.now, we will try to analyse if the aerodynamic drag force can be reduced employing the mechanism of how dolphins swim fast. The idea that new technologies can be developed from observation of nature has been long standing. Indeed, nature has served as the inspiration for various technological developments.it is no accident that the shape of modern submarines, fish, and marine mammals are so closely matched. Parallels between natural and engineered designs occur because both are selected for a range of performance constrained by the same physical forces.

18 The realization of new and superior designs to reduce drag based on animal systems has been tantalizing, although elusive.aquatic animals are considered superior in their capabilities to technologies produced from nautical engineering. Speeds over 11 m/s have been attained by dolphins.such high levels of performance are assumed to be dependent on adaptations which reduced drag. Both machines and animals must contend with the same physical laws that regulate their design and behavior.animals, like dolphins, demonstrate high levels of performance with respect to movement through water, and therefore, may be useful as model systems to analyse novel mechanisms for drag reduction. Every moving body having relative motion with other fluid must associated with drag force which should be overcome by thrust in order to achieve forward motion. Air particles over the aircraft makes different types of drag i.e. pressure, skin friction, parasite, induced, and wave.various methods to generate downforce such as inverted wings, diffusers, and vortex generators are employed in order to reduce these drag forces.of all these vortex generators is the one which is our topic of discussion because it is the one of the main reasons which cause dolphins to move so fast. Vortex Generators(VGs) A vortex generator is an aerodynamic surface, consisting of a small vane or bump that creates a vortex.vortex generators delay flow separation and aerodynamic stalling; they improve the effectiveness of control surfaces. The boundary layer normally thickens as it moves along the aircraft surface, reducing the effectiveness of trailing-edge control surfaces, vortex generators can be used to remedy this problem. The goal is to delay flow separation on the downstream side on the roof of the car on account of decreasing pressure difference between the upstream and downstream sides by creating vortex at the rear end

19 of the car roof. So vortex generators are commonly used on aircrafts to prevent downstream flow separation and improve their overall performance by reducing drag. The flow gets separated at its rear end when no vortex generators are used at its rear end. On the other hand the separation of flow is controlled when the Vortex generators are installed at its rear end. Carrying out experiments it can be seencd(drag coefficient) is decreasing with the increase of Re(Reynold s number) for both with and without vortex generator but for a fixed Re, Cd with vortex generator is less than, Cd without vortex generator. This indicates reduction of drag because of the vortex generator.

20 The Vortex Generators placed just before the separation points, supply the loss in momentum by generating streamwise vortices. Thus separation point will be shifted further into the downstream and allows the expanded airflow topersist proportionally longer and hence the velocity of flow at the separation point reduces with an increase in staticpressure. This static pressure reduces the control of overall pressure in the entire flow separation region. As a result of increased back pressure, the drag force is reduced. Thus shifting the separation points provides advantage in dragreduction first is to narrow the separation region in which low pressure constitutes the cause of drag; another is toraise the pressure of the flow separation region. A combination of these two effects reduces the drag acting on thevehicle. But the Vortex Generators itself produces the drag. So the total effect is calculated by subtracting the dragproduced by itself from the reduction in drag caused by shifting of the separation point downstream. Larger the size of Vortex Generators larger is the effect. But the effect will be optimized for a certain size of the Vortex Generator. 4. Future scope / un-resolved issues 4.1Future Scope: When we contemplate the F1 cars of the future you imagine their shape and that is all about aerodynamics. F1 cars haven t changed much in looks over the past 30 years and there is no reason why they

21 should we cannot un-invent aerodynamics. But there is always a scope for improvement and hence people do believe that the future of F1 cars does hold something good. F1 cars have always been open wheeled, apart from the 1954 W196 Mercedes, known as the Streamliner (in 1955 the same car appeared in single-seater format). According to veteran aerodynamics engineer Frank Dernie, it is inconceivable that the F1 car of the future will have covered wheels. Almost all surfaces of a covered wheel racing car produce lift and it takes only a small upset to make them take off. An F1 car, when upset, very rarely takes off and if it does it comes back to earth very quickly. So from a safety point of view it has to be open wheel. The challenge for F1 aerodynamicists of working with open wheels is the sophistication of modelling the way the air is disturbed by the spinning wheels and how to channel the disturbed air around and over and under the bodywork. This provides a vital part of the engineering challenge of F1 and the engineers say it probably still will in 20 years time, so complex is the problem. As well as work in the wind tunnel, teams use computer simulator programmes like computational fluid dynamics, which divide the car into billions of tiny squares and perform many billions of calculations based on adding in variables based on car movement. 4.2Un-resolved issues The flukes of dolphins are flexible, which is key to enabling the dolphin to maintain a highly efficient way of swimming over a broad range of speeds.the dolphins may have the ability to control that flexibility. It could be that the fluke becomes stiffer the faster the dolphin swims, increasing its swimming efficiency at high speeds.or maybe the dolphins can actively control fluke stiffness by changing the tension of tendons in their tail.but we are not sure how they're doing it.the marine biologist are in the midst of trying to figure that out.

22 5. Conclusion Gray s paradox was based on the false assumption of considering the flow to be laminar.in reality flow is turbulent which increases the drag coefficient and that results in increasing the drag force.all fishes have streamlined body which decreases the vortex formation that results in decreasing the drag force. Even after giant body Dolphins still can swim very fast because their fluke tail can produce the power they need by using their powerful tails.their fluke tail oscillate at a very high frequency and amplitude that generates vortices which produces thrust and it helps to overcome the drag force. Dolphin's tail, or fluke, is more than capable of producing enough thrust to speed the mammal through the water. The flukes generate a lift force that is directed forward, on both the upstroke and down-stroke.this produces the thrust that pushes the dolphin through the water. REFERENCES Research article The hydrodynamics of dolphin drafting Daniel Weihs Au, D. and Weihs, D. (1980). At high speeds dolphins save energy by leaping. Nature 284, Weihs D: Dynamics of dolphin porpoising revisited. Integr Comp Biol 2002, 42: Hui CA: Surfacing behavior and ventilation in free-ranging dolphins. J Mammal 1989, 70: Peterson, C. G. J "The Motion of Whales During Swimming," Nature 116: Pershin, S. V "Hydrodynamic Analysis of Dolphin and Whale Fin Profiles," Bionika 9:26-32 (translated from Russian).

23 Parry, D. A. 1949a. "The Swimming of Whales and a Discussion of Gray's Paradox," J. Exp. Biol. 26: Links: l phins-swimming-speeds/#.vti8efmuf5m -dolphins-swimming-paradox-ocean-animals-science/ Aerodynamics_of_a_Car_CFD_Analysis phins-swimming-speeds/#.vti_r2eqqkp ng-vortex-generator.pd