There are various propulsion, maneuvering, and stabilization mechanisms in nature, which can provide inspiration for similar mechanisms in man-made vehicles. This study aims to elucidate and compare the propulsive vortical signature and performance of a foil in two important natural mechanisms of pure pitching and undulatory oscillations. Governing equations are solved with a pressure-based finite volume method solver, in an arbitrary Lagrangian–Eulerian framework domain containing a NACA 0012 foil moving with prescribed kinematics. The results show that in a given Reynolds number (Re), the undulating mechanism produces thrust at a higher Strouhal number (St) and with smaller growth slope, but mostly higher efficiency, versus St, than pitching mechanism. In addition, vortical structures of these mechanisms have significant differences and also vary considerably with St. One of the distinguishable features of vortical signatures is the presence of the leading-edge vortices for the pitching foil, which are not appearing in the undulating foil’s vortical pattern.
TangorraJLEspositoCJLauderGV. Biorobotic fins for investigations of fish locomotion. In: Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, 2009 (IROS 2009), St. Louis, MO, 10–15 October 2009, pp.2120–2125. New York: IEEE.
2.
TangorraJLDavidsonSNMaddenPG. A biorobotic pectoral fin for autonomous undersea vehicles. In: Proceedings of the 28th annual international conference of the IEEE engineering in medicine and biology society, 2006 (EMBS 2006), New York, 30 August–3 September 2006, vol. 1, pp.2726–2729. New York: IEEE.
3.
TanXKimDUsherN. An autonomous robotic fish for mobile sensing. In: Proceedings of the 2006 IEEE/RSJ international conference on intelligent robots and systems, Beijing, China, 9–15 October 2006, pp.5424–5429. New York: IEEE.
4.
KodatiPHinkleJWinnA. Hydrodynamics, design, and fabrication. IEEE T Robot2008; 24: 105–117.
5.
KodatiPDengX. Experimental studies on the hydrodynamics of a robotic ostraciiform tail fin. In: Proceedings of the 2006 IEEE/RSJ international conference on intelligent robots and systems, Beijing, China, 9–15 October 2006, pp.5418–5423. New York: IEEE.
6.
PalmisanoJRamamurtiRLuK-J. Design of a biomimetic controlled-curvature robotic pectoral fin. In: Proceedings of the 2007 IEEE international conference on robotics and automation, Rome, 10–14 April 2007, pp.966–973. New York: IEEE.
7.
EllingtonCP. The novel aerodynamics of insect flight: applications to micro-air vehicles. J Exp Biol1999; 202: 3439–3448.
8.
KhuranaMChahlJ. Bioinspired corrugated airfoils for micro air vehicles. In: SPIE smart structures and materials + nondestructive evaluation and health monitoring. International Society for Optics and Photonics, 2013, p.86860X-X-11. March 10–14, 2013 – Town & Country Resort and Convention Center, San Diego, Canada; SPIE (The International Society for Optical Engineering).
9.
YuhJMaraniGBlidbergDR. Applications of marine robotic vehicles. In: YuhJMaraniGBlidbergDR (eds) Intelligent service robotics, vol. 4. Springer Berlin Heidelberg, 2011, pp.221–231.
10.
AndersonJM. Vorticity control for efficient propulsion (DTIC Document). PhD Dissertation, MIT, Cambridge, MA, 1996.
11.
AmiralaeiM. Computational fluid dynamic simulation of airfoils in unsteady low Reynolds number flows. PhD Dissertation, Ryerson University, Toronto, ON, Canada, 2012.
12.
Okong’oNKnightDD. Implicit unstructured Navier-Stokes simulation of leading edge separation over a pitching airfoil. Appl Numer Math1998; 27: 269–308.
13.
TriantafyllouMSTriantafyllouGSGopalkrishnanR. Wake mechanics for thrust generation in oscillating foils. Phys Fluids A: Fluid1991; 3: 2835–2837.
14.
YoungJSLaiJC. Oscillation frequency and amplitude effects on the wake of a plunging airfoil. AIAA J2004; 42: 2042–2052.
15.
MittalR. Computational modeling in biohydrodynamics: trends, challenges, and recent advances. IEEE J Oceanic Eng2004; 29: 595–604.
16.
CarrLMcCroskeyW. A review of recent advances in computational and experimental analysis of dynamic stall. In: IUTAM symposium on fluid dynamics of high angle of attack, 1992. Tokyo, Japan, September 13–17, 1992; SpringerBerlin Heidelberg.
17.
CarrLW. Progress in analysis and prediction of dynamic stall. J Aircraft1988; 25: 6–17.
18.
LighthillJ. Mathematica biofluiddynamics. Society for Industrial & Applied Mathematics, U.S.1975.
19.
WuTBrokawCBrennenC. Swimming and flying in nature, vols 1 and 2. New York: Plenum Press, 1975.
20.
RaynerJ. A vortex theory of animal flight. Part 1. The vortex wake of a hovering animal. J Fluid Mech1979; 91: 697–730.
21.
BrattJ. Flow patterns in the wake of an oscillating aerofoil. HM Stationery Office, 1953. Issue 2773 of Reports and memoranda [Aeronautical Research Council. Reports and Memoranda. no. 2773.]; H.M. Stationery Office, UK; October1953.
22.
FuchiwakiM.TanakaK.TanakaH.KamemotoK.BaysalO., 1999. Flow patterns behind pitching airfoil and unsteady fluid forces. In: Proceedings of the 3rd ASME/JSME Joint Fluids Engineering Conference, San Francisco, CA, USA.
23.
KoochesfahaniMM. Vortical patterns in the wake of an oscillating airfoil. AIAA J1989; 27: 1200–1205.
24.
AkbariMPriceS. Simulation of dynamic stall for a NACA 0012 airfoil using a vortex method. J Fluid Struct2003; 17: 855–874.
25.
HamdaniHSunM. Aerodynamic forces and flow structures of an airfoil in some unsteady motions at small Reynolds number. Acta Mech2000; 145: 173–187.
26.
VisbalMRShangJ. Investigation of the flow structure around a rapidly pitching airfoil. AIAA J1989; 27: 1044–1051.
27.
BozkurttasMDongHMittalR. Hydrodynamic performance of deformable fish fins and flapping foils. In: Proceedings of the 44rd AIAA aerospace sciences meeting and exhibit, Reno, NV, 9–12 January, 2006, pp.16743–16753. Reno, NV: AIAA.
28.
BozkurttasMMittalRDongH. Low-dimensional models and performance scaling of a highly deformable fish pectoral fin. J Fluid Mech2009; 631: 311–342.
29.
DongHBozkurttasMMittalR. Computational modelling and analysis of the hydrodynamics of a highly deformable fish pectoral fin. J Fluid Mech2010; 645: 345–373.
30.
DongHMittalRBozkurttasMNajjarF (2005) Wake structure and performance of finite aspect-ratio flapping foils. In: 43rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2005-81, Reno, 10–13Jan2005.
31.
MittalRDongHBozkurttasM. Hydrodynamic performance of a flexible fish pectoral fin. B Am Phys Soc2006. 59th Annual Meeting of the APS Division of Fluid Dynamics; Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida.
32.
MittalRDongHBozkurttasM. Locomotion with flexible propulsors: II. Computational modeling of pectoral fin swimming in sunfish. Bioinspir Biomim2006; 1: S35–S41.
33.
AkhtarIMittalRLauderGV. Hydrodynamics of a biologically inspired tandem flapping foil configuration. Theor Comp Fluid Dyn2007; 21: 155–170.
34.
FlammangBELauderGVTroolinDR. Volumetric imaging of fish locomotion. Biol Letters2011; 7: 695–698.
35.
ShadwickRELauderGV. Fish biomechanics. Amsterdam; Boston, MA: Academic Press, 2006, p.xiii, 542 pp.
36.
LauderGVTytellED. Hydrodynamics of undulatory propulsion. Fish Physiol2005; 23: 425–468.
37.
TytellEDLauderGV. The hydrodynamics of eel swimming: I. Wake structure. J Exp Biol2004; 207: 1825–1841.
38.
DruckerEGLauderGV. Experimental hydrodynamics of fish locomotion: functional insights from wake visualization. Integr Comp Biol2002; 42: 243–257.
39.
BorazjaniI. (2008). Numerical simulations of fluid-structure interaction problems in biological flows. PhD Thesis, Mechanical Engineering Department, University of Minnesota, Minneapolis, MN, USA.
40.
HirtCAmsdenAACookJ. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J Comput Phys1974; 14: 227–253.
41.
DoneaJHuertaAPonthotJ-P. Arbitrary Lagrangian-Eulerian methods. In: SteinEDe BorstRHughesTJR (eds) Encyclopedia of computational mechanics, vol. 1: fundamentals, ch. 14. John Wiley & Sons, Ltd, New York City, New York, United States. 2004: Volume 1, Chapter 14, Pages 413–437.
42.
FerzigerJHPericM. Computational methods for fluid dynamics. Berlin: Springer-Verlag, 1996.
43.
SfakiotakisMLaneDMDaviesJBC. Review of fish swimming modes for aquatic locomotion. IEEE J Oceanic Eng1999; 24: 237–252.
44.
BarthTJespersenD. The design and application of upwind schemes on unstructured meshes. In: Proceedings of the 27th aerospace sciences meeting, Reno, NV, 9–12 January 1989. Reston, VA: AIAA.
45.
DarwishMMoukalledF. TVD schemes for unstructured grids. Int J Heat Mass Tran2003; 46: 599–611.
46.
ShyyWThakurSOuyangH. Computational techniques for complex transport phenomena. Cambridge University Press: Cambridge, United Kingdom, 2005.
47.
IssaRIGosmanAWatkinsA. The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme. J Comput Phys1986; 62: 66–82.
48.
BlasiusH. Grenzschichten in Flüssigkeiten mit kleiner Reibung. Inaugural-Dissertation. von H. Blasius. Druck von B. G. Teubner: Leipzig, Germany, 1907.
49.
ZhangLChangXDuanX. A block LU-SGS implicit unsteady incompressible flow solver on hybrid dynamic grids for 2D external bio-fluid simulations. Comput Fluid2009; 38: 290–308.
ArneyDCFlahertyJE. An adaptive method with mesh moving and local mesh refinement for time-dependent partial differential equations (DTIC Document). Defense Technical Information Center (DTIC); United States Department of Defense. 1988.
52.
AdjeridSFlahertyJE. A local refinement finite-element method for two-dimensional parabolic systems. SIAM J Sci Stat Comp1988; 9: 792–811.
53.
Mohan RaiM. A conservative treatment of zonal boundaries for Euler equation calculations. J Comput Phys1986; 62: 472–503.
54.
VidelerJHessF. Fast continuous swimming of two pelagic predators, saithe (Pollachius virens) and mackerel (Scomber scombrus): a kinematic analysis. J Exp Biol1984; 109: 209–228.
55.
BorazjaniISotiropoulosF. Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J Exp Biol2008; 211: 1541–1558.
56.
HuntJCWrayAMoinP. Eddies, streams, and convergence zones in turbulent flows. Studying Turbulence Using Numerical Simulation Databases 2, National Aeronautics and Space Administration. Ames Research Center, Moffett Field, CA. 1988, pp.193–208.
57.
AndersonJStreitlienKBarrettD. Oscillating foils of high propulsive efficiency. J Fluid Mech1998; 360: 41–72.
58.
XiaoQLiaoW. Numerical investigation of angle of attack profile on propulsion performance of an oscillating foil. Comput Fluids2010; 39: 1366–1380.
