Hydrodynamic study of freely swimming shark fish propulsion for marine vehicles using 2D particle image velocimetry
© Babu et al. 2016
Received: 29 October 2015
Accepted: 21 March 2016
Published: 6 April 2016
Two-dimensional velocity fields around a freely swimming freshwater black shark fish in longitudinal (XZ) plane and transverse (YZ) plane are measured using digital particle image velocimetry (DPIV). By transferring momentum to the fluid, fishes generate thrust. Thrust is generated not only by its caudal fin, but also using pectoral and anal fins, the contribution of which depends on the fish’s morphology and swimming movements. These fins also act as roll and pitch stabilizers for the swimming fish. In this paper, studies are performed on the flow induced by fins of freely swimming undulatory carangiform swimming fish (freshwater black shark, L = 26 cm) by an experimental hydrodynamic approach based on quantitative flow visualization technique. We used 2D PIV to visualize water flow pattern in the wake of the caudal, pectoral and anal fins of swimming fish at a speed of 0.5–1.5 times of body length per second. The kinematic analysis and pressure distribution of carangiform fish are presented here. The fish body and fin undulations create circular flow patterns (vortices) that travel along with the body waves and change the flow around its tail to increase the swimming efficiency. The wake of different fins of the swimming fish consists of two counter-rotating vortices about the mean path of fish motion. These wakes resemble like reverse von Karman vortex street which is nothing but a thrust-producing wake. The velocity vectors around a C-start (a straight swimming fish bends into C-shape) maneuvering fish are also discussed in this paper. Studying flows around flapping fins will contribute to design of bioinspired propulsors for marine vehicles.
KeywordsCarangiform swimming Caudal fin locomotion Flow visualization Propulsor hydrodynamics Particle image velocimetry Pectoral fins Reverse von Karman vortex street Wake
In the present study, flow visualization experiments are carried out to visualize the flow pattern around the caudal, pectoral, anal and dorsal fins of a freely swimming fish using two-dimensional (2D) particle Image velocimetry (PIV) system.
Freshwater black shark (Labeo chrysophekadion) with a body length of 26 cm is used for the present experimental study. The fish is placed inside a glass tank of size L × B × D = 75 cm × 29 cm × 37 cm, with water level at 28 cm, and it is allowed to swim freely in the tank. The fish swims across the tank length, and the PIV measurement is taken at the steady phase of its movement, which is observed to be in the middle one-third portion of the tank. In this experiment, the laser pulse is operated continuously and fish will always cross this laser plane in multiple times with same time interval. Then, a range of images is selected for processing velocity fields. From the visual observations, based on the recorded video, the Strouhal number of the freely swimming shark fish used in this experiment is approximately 0.23, where the tail fin oscillation frequency is 0.6 Hz, amplitude is 0.1 m and the fish swimming speed is 0.26 m/s.
Two-dimensional PIV technique is used to study the flow around a swimming fish. This helps in clearly understanding the instantaneous velocity vector fields of the flow field around the fish. It is a non-intrusive experimental technique which can measure the whole flow field with high spatial and temporal resolution at any instant.
The PIV technique involves the introduction of tiny particles called ‘seeder particles’ into the fluid path. The size and density of seeder particles are chosen such that they follow the flow path faithfully at all operating conditions. Hollow glass spheres with a mean diameter of 10 µm are used as the tracer particles. The seeding particles in the plane of interest are illuminated by a laser sheet of appropriate thickness 0.5–2.5 mm. Two images (an image pair) of the illuminated flow field are obtained within a separation time ‘∆t’ by means of high-resolution camera. The displacement of the tracer particles during the time interval ‘∆t’ gives velocity of the fluid particle. The experiments are performed at three different time intervals, Δt = 300, 620 and 900 ms. If the Δt is less than 300 ms, no swirl of velocity vectors is observed. Then, the Δt gradually increases from 300 to 900 ms, and velocity fields around the fish body are observed. The Reynolds number (Re) of swimming fish is in the range of 105, and at low Re number, the 2D velocity fields do not affect.
In PIV measurement scheme, the images are divided into a number of small sections called interrogation windows or regions. The corresponding interrogation regions in frame 1 and 2 are correlated using cross-correlation method. The maximum of the correlation corresponds to the displacement of the particles in interrogation window. The displacement gives the vector length and direction in interrogation zones. Small interrogation windows give more vectors but contain less particles. The main advantage of the cross-correlation approach is displacement that can be obtained with directional ambiguity.
The velocity fields obtained by PIV are used to determine the pressure fields. The pressure and velocity are linked by the Navier–Stokes (NS) equations, and the pressure can be measured indirectly by measuring the velocity field. There exist two methods to measure the pressure field indirectly. The first method is direct spatial integration of the momentum equations [21, 22]. The second method is solving a Poisson equation for the pressure field . The present study does not include the comparison aspects of velocity field to pressure field.
PIV results and discussion
Fishes generate propulsive forces, are able to maneuver rapidly and stabilize its body motions using its fins such as pectoral, dorsal, pelvic, anal and caudal fins (see Fig. 1). By using its fins, fishes can control roll, pitch and yaw motions. The paired pectoral fins (one on each side) are used for maneuvering as well as for instantaneous stopping (braking) . The median dorsal fins act as keels, used for directional stability and to prevent from spinning or rolling. Pelvic fins and anal fins are used as stabilizers. Caudal fin is used for propulsion, maneuvering and braking. The flow visualization experiments are carried out on a freely swimming sub-carangiform mode shark fish in longitudinal vertical (XZ) plane and transverse (YZ) plane by using two-dimensional particle image velocimetry.
Figure 10 shows CCD image and velocity vector field around adipose and anal fins at Δt = 300 ms. Orientation of the caudal fin in this figure shows the flexibility present in its movements. The jets produced by adipose fin and anal fins are observed in the peduncle region (region containing the tail and the body). At the posterior end of the fish, a pair of counter-rotating vortices is observed. Figure 11 shows CCD image and velocity vector field around anterior portion of fish. At low amplitudes and frequencies of caudal fin, when Strouhal number (st) is less than 0.2, the vortices become inward and thus the fish experiences drag due to these vortices. This wake resembles like a von Karman vortex street shown in Fig. 11. Figure 12 shows CCD image and velocity vector field around pectoral fins. These paired pectoral fins undergo deformation during their flapping cycle. It undergoes chordwise and spanwise deformations as well as twisting. During power stroke and return stroke, the effective angle of attack of flow with fin increases, thereby producing thrust in both the strokes. Figure 13 shows CCD image and velocity vector field around dorsal fins. Dorsal fins generate strong vortices. Flow leaving the dorsal and anal fins rolls up and then interacts with caudal fin vortices. Figures 14 and 15 show CCD image and velocity vector fields around caudal fin in starboard stroke in YZ plane at Δt = 900 ms. A pair of counter-rotating vortices is generated around the caudal fin in the YZ plane. Figure 16 shows CCD image and velocity vector field around caudal fin stroke in YZ plane at Δt = 900 ms, while the fin is at the center plane. A jet with high velocity flow is observed at the top of the caudal fin. Figure 17 shows CCD image and velocity vector field around caudal fins, during portside stroke, in YZ plane at Δt = 900 ms. Figure 18 shows flow around a maneuvering fish. During maneuvering of a fish, jets are observed at the side of fish causing a turning moment instantaneously.
Summary and conclusions
The flow visualization experiments are carried out on a freely swimming freshwater black shark using two-dimensional particle image velocimetry in longitudinal vertical (XZ) and transverse (YZ) planes. The velocity vector fields show that both paired fins (pectoral fins) and median fins (dorsal, anal and caudal fins) produce reverse von Karman vortices resulting in the flow jets and consequent thrust (propulsive force). It is also observed that the fin flexibility in chordwise and spanwise direction substantially improves the thrust generation and direction control of the fish. The fish anal fin and caudal fin vortices are also presented here and show that they also contribute to the fish propulsive force. By studying the nature flow velocity distribution around fish fins propulsion systems, one can design flapping foil propulsion systems for ships and underwater vehicles.
All authors were equally involved in the study and preparation of the manuscript. All authors read and approved the final manuscript.
The authors would like to thank Department of Ocean Engineering, IIT Madras, India, for providing support for doing this project.
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
- Politis GK, Belibasakis KA (1999) High propulsive efficiency by a system of oscillating wing tails. In: CMEM, WIT conference.
- Anderson JM, et al. Oscillating foils of high propulsive efficiency. J Fluid Mech. 1998;360:41–72.MathSciNetView ArticleMATHGoogle Scholar
- Müller UK, Van Den Heuvel BLE, Stamhuis EJ, Videler JJ. Fish foot prints: morphology and energetics of the wake behind a continuously swimming mullet (Chelon labrosus Risso). J Exp Biol. 1997;201:2893–906.Google Scholar
- Muller UK, Stamhuis EJ, Videler JJ. Hydrodynamics of unsteady fish swimming and the effects of body size: comparing the flow fields of fish larvae and adults. J Exp Biol. 2000;203(2):193–206.Google Scholar
- Drucker EG, Lauder GV. Locomotor function of the dorsal fin in teleost fishes: experimental analysis of wake forces in sunfish. J Exp Biol. 2001;204(17):2943–58.Google Scholar
- Sakakibara J, Nakagawa M, Yoshida M. Stereo-PIV study of flow around a maneuvering fish. Exp Fluids. 2004;36(2):282–93.View ArticleGoogle Scholar
- Stamhuis E, Videler J. Quantitative flow analysis around aquatic animals using laser sheet particle image velocimetry. J Exp Biol. 1995;198(2):283–94.Google Scholar
- Videler JJ. Fish swimming, vol. 10. Berlin: Springer; 1993.View ArticleGoogle Scholar
- Wakeling JM, Johnston IA. Body bending during fast-starts in fish can be explained in terms of muscle torque and hydrodynamic resistance. J Exp Biol. 1999;202(6):675–82.Google Scholar
- Webb PW. Hydrodynamics and energetics of fish propulsion. Bull Fish Res Board Can. 1975;190:1–159.Google Scholar
- Webb PW, Blake RW. Swimming. In: Hildebrand M, editor. Functional vertebrate morphology. Cambridge: Harvard University Press; 1983.Google Scholar
- Weihs D. A hydrodynamic analysis of fish turning manoeuvres. Proc R Soc Lond B. 1972;182:59–72.View ArticleGoogle Scholar
- Westerweel J. Fundamentals of digital particle image velocimetry. Meas Sci Technol. 1997;8(12):1379.View ArticleGoogle Scholar
- Wolfgang MJ, et al. Near-body flow dynamics in swimming fish. J Exp Biol. 1999;202(17):2303–27.Google Scholar
- Wu YT. Hydromechanics of swimming propulsion part 1: swimming of a two-dimensional flexible plate at variable forward speeds in an in viscid fluid. J Fluid Mech. 1971;46:337–55.View ArticleMATHGoogle Scholar
- Blake RW. Fish locomotion. Cambridge: Cambridge University Press; 1983.Google Scholar
- Breder CM. The locomotion of fishes. New York: New York Zoological Society; 1926.Google Scholar
- Babu MNP, Krishnankutty P, Mallikarjuna JM. Experimental study of flapping foil propulsion system for ships and underwater vehicles and PIV study of caudal fin propulsors. In: Autonomous underwater vehicles (AUV), 2014 IEEE/OES, p. 1, 7, 6–9 Oct 2014.
- Gero DR. The hydrodynamic aspects of fish propulsion. Am Mus Novitates. 1952;1601:1–32.Google Scholar
- http://www.lavision.de/en. Accessed 20 May 2014.
- van Oudheusden B, Scarano F, Roosenboom E, Casimiri E, Souverein L. Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible flows. Exp Fluids. 2007;43:153–62.View ArticleGoogle Scholar
- de Kat R, van Oudheusden B, Scarano F. Instantaneous planar pressure field determination around a square-section cylinder based on time-resolved stereo-PIV. In: 14th international symposium on applications of laser techniques to fluid mechanics; Lisbon, Portugal. 2008.
- Gurka R, Liberzon A, Hefetz D, Rubinstein D, Shavit U. “Computation of pressure distribution using PIV velocity” data. In: 3rd international workshop on PIV. Santa Barbara, CA, US, p. 101–6; 1999.
- Drucker EG, Lauder GV. Wake dynamics and fluid forces of turning maneuvers in sunfish. J Exp Biol. 2001;204:431–42.Google Scholar