Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2019 Oct 8;4(4):67.
doi: 10.3390/biomimetics4040067.

Experimental Study of Body-Fin Interaction and Vortex Dynamics Generated by a Two Degree-Of-Freedom Fish Model

Affiliations
Free PMC article

Experimental Study of Body-Fin Interaction and Vortex Dynamics Generated by a Two Degree-Of-Freedom Fish Model

Seth A Brooks et al. Biomimetics (Basel). .
Free PMC article

Abstract

Oscillatory modes of swimming are used by a majority of aquatic swimmers to generate thrust. This work seeks to understand the phenomenological relationship between the body and caudal fin for fast and efficient thunniform swimming. Phase-averaged velocity data was collected and analyzed in order to understand the effects of body-fin kinematics on the wake behind a two degree-of-freedom fish model. The model is based on the yellowfin tuna (Thunnus albacares) which is known to be both fast and efficient. Velocity data was obtained along the side of the tail and caudal fin region as well as in the wake downstream of the caudal fin. Body-generated vortices were found to be small and have an insignificant effect on the caudal fin wake. The evolution of leading edge vortices formed on the caudal fin varied depending on the body-fin kinematics. The circulation produced at the trailing edge during each half-cycle was found to be relatively insensitive to the freestream velocity, but also varied with body-fin kinematics. Overall, the generation of vorticity in the wake was found to dependent on the trailing edge motion profile and velocity. Even relatively minor deviations from the commonly used model of sinusoidal motion is shown to change the strength and organization of coherent structures in the wake, which have been shown in the literature to be related to performance metrics such as thrust and efficiency.

Keywords: bio-propulsion; biological fluid dynamics; body-fin interaction; circulation production; fish; leading edge vortices; nonsinusoidal motion; swimming; vortex dynamics.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
(A) Exploded view of the model showing the drive system. (B) Front view of model showing dimensions. (C) Side view of model showing dimensions and main components.
Figure 2
Figure 2
(A) Image of the model. (B) Schematic depicting the kinematic parameters.
Figure 3
Figure 3
Tail and caudal fin angle for two representative cases. Circles represent the measured angles; the black curve is a fitted sinusoidal curve for comparison; the dotted line is at zero; and the dot-dashed line is the angular misalignment, ΔθT in (A) and ΔθC in (B). (A) Tail angle, θT, for case 4. (B) Caudal fin angle, θC, for case 1.
Figure 4
Figure 4
(A) Schematic of the water tunnel and experimental setup. (B) Top view of the domain relative to the model. (C) Five planes where data was collected.
Figure 5
Figure 5
Five planes of spanwise vorticity data for the second kinematic group (cases 5, 6, 7, and 8). Positive spanwise vorticity is shown in red and negative in blue. The top row is at t/T=0.32 where the TE is moving out of the page and highlights the trailing edge vortex. The bottom row is at t/T=0.80 where the TE is moving into the page and highlights the leading edge vortex.
Figure 6
Figure 6
Three planes for case 8, where θT,o=3.63 and θC,o0, are shown here. Body (and sting) generated vortices between the body and the caudal fin are visualized using two-dimensional Q-criterion (Q) contours (Q=[1,5,20,50]s2). (A) midspan plane (0 mm). (B) +20 mm plane. (C) +40 mm plane.
Figure 7
Figure 7
Two-dimensional Q-criterion (Q) contours (Q=[1,5,20,50] s2) are used to identify leading edge vortices during the second half-cycle. These plots show the typical life-cycle of a caudal fin LEV for case 7 at the 40 mm plane between t/T=0.48 and 1.40.
Figure 8
Figure 8
Two-dimensional Q-criterion (Q) contours (Q=[1,5,20,50] s2) are used to identify leading edge vortices during the second half-cycle. These plots show the typical life-cycle of a caudal fin LEV for case 7 at the 20 mm plane between t/T=0.48 and 1.40.
Figure 9
Figure 9
Two-dimensional Q-criterion (Q) contours (Q=[1,5,20,50] s2) are used to identify leading edge vortices during the second half-cycle. Cases 5 through 8 are shown when t/T=0.88. The 40 mm plane is shown in (AD) and the 20 mm plane is shown in (EH). The size and strength of the LEV increases with increasing maximum tail amplitude.
Figure 10
Figure 10
Rectangular region used for calculating positive circulation for case 5. Vorticity contours of ωz=±[1,4,9,16] s1 where positive values are shown in red and negative values in blue. The time history for this case can be seen in Figure 11B as the solid red curve. (A) t/T=0.12. (B) t/T=0.32 (peak positive circulation). (C) t/T=0.64.
Figure 11
Figure 11
Circulation magnitude of both positive (red) and negative (blue) circulation versus nondimensional time over a pitching half-cycle. (A) Total same-sign circulation shed per half-cycle by kinematic group. (B) Kinematic Group 1 (θT,o0 and θC,o11). (C) Kinematic Group 2 (θT,o2 and θC,o9). (D) Kinematic Group 3 (θT,o3 and θC,o5). (E) Kinematic Group 4 (θT,o3.6 and θC,o0).
Figure 12
Figure 12
Sample sinusoid summation showing the phase offset between the trailing edge excursion (A) and the caudal fin (C) motion: (A) Motion mainly due to the tail (T). (B) Motion mainly due to the caudal fin (C).
Figure 13
Figure 13
Motion Profiles for cases 1 through 4 where the solid curve represents the trailing edge amplitude and the dashed line represents the trailing edge velocity. The background colors represent time periods of acceleration (red) and deceleration (blue) the yellow circles represent the approximate timing of primary vortex shedding. (A) Case 1. (B) Case 2. (C) Case 3. (D) Case 4.
Figure 14
Figure 14
Spanwise vorticity (ωz=±[1,4,9,16] s1) contours are shown here for cases 1 through 4 when t/T=1.00. Positive spanwise vorticity is shown in red and negative in blue: (A) Case 1. (B) Case 2. (C) Case 3. (D) Case 4.
Figure 15
Figure 15
(Case 1: SG1, KG1) Spanwise vorticity (ωz=±[1,4,9,16] s1) contours are shown here for case 1 which has θT,o0.00, θC,o=12.90, and St=0.31. Positive spanwise vorticity is shown in red and negative in blue. The dashed arrow highlights the linear trajectory of the secondary vortex. The trailing edge motion profile can be found in Figure 13A: (A) t/T=0.40. (B) t/T=0.52. (C) t/T=0.64. (D) t/T=0.76. (E) t/T=0.84. (F) t/T=1.00.
Figure 16
Figure 16
(Case 4: SG1, KG4) Spanwise vorticity (ωz=±[1,4,9,16] s1) contours are shown here for case 4 which has θT,o3.44, θC,o0, and St=0.27. Positive spanwise vorticity is shown in red and negative in blue. The trailing edge motion profile can be found in Figure 13A: (A) t/T=0.40. (B) t/T=0.52. (C) t/T=0.64. (D) t/T=0.76. (E) t/T=0.84. (F) t/T=1.00.
Figure 17
Figure 17
Time averaged x-direction velocity (U/U1=±[0.05,0.10,0.15,0.20,0.30]) contours are shown here for cases 1 through 4 where velocity surplus is red and velocity deficit is blue: (A) Case 1. (B) Case 2. (C) Case 3. (D) Case 4.

Similar articles

See all similar articles

References

    1. Lighthill M.J. Hydromechanics of Aquatic Animal Propulsion. Annu. Rev. Fluid Mech. 1969;1:413–446. doi: 10.1146/annurev.fl.01.010169.002213. - DOI
    1. Magnuson J.J. Locomotion by Scombrid Fishes: Hydromechanics, Morphology, and Behavior. In: Hoar W.S., Randall D.J., editors. Fish Physiology. Volume 7. Locomotion; Shildon, UK: Academic Press; Cambridge, MA, USA: 1978. pp. 239–313.
    1. Bernal D., Dickson K.A., Shadwick R.E., Graham J.B. Review: Analysis of the evolutionary convergence for high performance swimming in lamnid sharks and tunas. Comp. Biochem. Physiol. Part A Mol. Integr. Physiol. 2001;129:695–726. doi: 10.1016/S1095-6433(01)00333-6. - DOI - PubMed
    1. Koochesfahani M.M. Vortical patterns in the wake of an oscillating airfoil. AIAA J. 1989;27:1200–1205. doi: 10.2514/3.10246. - DOI
    1. Triantafyllou G.S., Triantafyllou M.S., Grosenbaugh M.A. Optimal Thrust Development in Oscillating Foils with Application to Fish Propulsion. J. Fluids Struct. 1993;7:205–224. doi: 10.1006/jfls.1993.1012. - DOI
Feedback