Plunging airfoil; Transition to chaos; Immersed Boundary Method
Abstract :
[en] The present work investigates the underlying flow physics behind dynamical transitions that take place in the flow-field around a plunging foil as the nondimensional plunge velocity (kh) is increased. The unsteady flow-field is seen to undergo a transition from periodicity to chaos through a quasi-periodic route. Numerical simulations have been performed at different parametric regimes associated with the different dynamical states, using an in-house flow solver developed based on discrete forcing type Immersed Boundary Method (IBM). Results obtained using the IBM methodology are compared both qualitatively and quantitatively with those from a well-validated body-fitted Arbitrary Lagrangian-Eulerian (ALE) approach. This study explores the scope of body non-conformal mesh methods in comparison to body fitted approaches in capturing complex flow topologies, especially, during aperiodic flow regimes. In the discrete direct forcing type IBM solver developed in the present study, application of the momentum forcing and mass/source sink terms at all the grid points inside the solid domain is seen to capture various unsteady flow-mechanisms accurately. These mechanisms are crucial in dictating the dynamics and they play key roles in triggering the aperiodic onsets and sustaining them.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Majumdar, Dipanjan; Indian Institute of Technology Madras, Chennai 600036, India > Department of Aerospace Engineering
Bose, Chandan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Interactions Fluide-Structure - Aérodynamique expérimentale
Sarkar, Sunetra; Indian Institute of Technology Madras, Chennai 600036, India > Department of Aerospace Engineering
Language :
English
Title :
Capturing the dynamical transitions in the flow-field of a flapping foil using Immersed Boundary Method
Ashraf, M.A., Young, J., Lai, J.C.S., Oscillation frequency and amplitude effects on plunging airfoil propulsion and flow periodicity. AIAA J. 50:11 (2012), 2308–2324.
Badrinath, S., Bose, C., Sarkar, S., Identifying the route to chaos in the flow past a flapping airfoil. Eur. J. Mech. B Fluids 66 (2017), 38–59.
Balaras, E., Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations. Comput. Fluids 33:3 (2004), 375–404.
Blondeaux, P., Guglielmini, L., Triantafyllou, M.S., Chaotic flow generated by an oscillating foil. AIAA J. 43:4 (2005), 918–921.
Bos, F.M., Numerical simulations of flapping foil and wing aerodynamics: Mesh deformation using radial basis functions. (Ph.D. thesis), 2010, Delft University of Technology, Delft, Netherlands.
Bos, F.M., van Oudheusden, B.W., Bijl, H., Radial basis function based mesh deformation applied to simulation of flow around flapping wings. Comput. Fluids 79 (2013), 167–177.
Bose, C., Sarkar, S., Investigating chaotic wake dynamics past a flapping airfoil and the role of vortex interactions behind the chaotic transition. Phys. Fluids, 30(4), 2018, 047101.
Choi, H., Moin, P., Effects of the computational time step on numerical solutions of turbulent flow. J. Comput. Phys. 113:1 (1994), 1–4.
Choi, J.-I., Oberoi, R.C., Edwards, J.R., Rosati, J.A., An immersed boundary method for complex incompressible flows. J. Comput. Phys. 224:2 (2007), 757–784.
Couder, Y., Basdevant, C., Experimental and numerical study of vortex couples in two-dimensional flows. J. Fluid Mech. 173 (1986), 225–251.
Deng, J., Sun, L., Teng, L., Pan, D., Shao, X., The correlation between wake transition and propulsive efficiency of a flapping foil: A numerical study. Phys. Fluids, 28(9), 2016, 094101.
Fadlun, E.A., Verzicco, R., Orlandi, P., Mohd-Yusof, J., Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161:1 (2000), 35–60.
Fraser, A.M., Swinney, H.L., Independent coordinates for strange attractors from mutual information. Phys. Rev. A, 33(2), 1986, 1134.
Ghias, R., Mittal, R., Dong, H., A sharp interface immersed boundary method for compressible viscous flows. J. Comput. Phys. 225:1 (2007), 528–553.
Godoy-Diana, R., Marais, C., Aider, J.-L., Wesfreid, J.E., A model for the symmetry breaking of the reverse Bénard-von Kármán vortex street produced by a flapping foil. J. Fluid Mech. 622 (2009), 23–32.
Goldstein, D., Handler, R., Sirovich, L., Modeling a no-slip flow boundary with an external force field. J. Comput. Phys. 105:2 (1993), 354–366.
Grassberger, P., Procaccia, I., Characterization of strange attractors. Phys. Rev. Lett., 50(5), 1983, 346.
Grossmann, A., Kronland-Martinet, R., Morlet, J., Reading and understanding continuous wavelet transforms. Wavelets, 1990, Springer, Berlin, Heidelberg, 2–20.
Gustafson, K., Leben, R.R., 1988. Robust multigrid computation and visualization of separation and vortex evolution in aerodynamic flows. In: 1st National Fluid Dynamics Conference, p. 3604.
Heathcote, S., Gursul, I., Jet switching phenomenon for a periodically plunging airfoil. Phys. Fluids, 19(2), 2007, 027104.
Hou, G., Wang, J., Layton, A., Numerical methods for fluid-structure interaction—a review. Commun. Comput. Phys. 12:2 (2012), 337–377.
Huang, W.-X., Sung, H.J., Improvement of mass source/sink for an immersed boundary method. Internat. J. Numer. Methods Fluids 53:11 (2007), 1659–1671.
Huang, W.-X., Tian, F.-B., Recent trends and progress in the immersed boundary method. Proc. Inst. Mech. Eng. Pt. C J. Mechan. Eng. Sci. 233:23–24 (2019), 7617–7636.
Jasak, H., Jemcov, A., Tukovic, Z., et al. OpenFOAM: A C++ library for complex physics simulations. International Workshop on Coupled Methods in Numerical Dynamics, vol. 1000, 2007, IUC Dubrovnik Croatia, 1–20.
Jones, K.D., Dohring, C.M., Platzer, M.F., Experimental and computational investigation of the Knoller-Betz effect. AIAA J. 36:7 (1998), 1240–1246.
Kennel, M.B., Brown, R., Abarbanel, H.D.I., Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A, 45(6), 1992, 3403.
Khalid, M.S.U., Akhtar, I., Dong, H., Ahsan, N., Jiang, X., Wu, B., Bifurcations and route to chaos for flow over an oscillating airfoil. J. Fluid Struct. 80 (2018), 262–274.
Kim, J., Kim, D., Choi, H., An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 171:1 (2001), 132–150.
Kim, W., Lee, I., Choi, H., A weak-coupling immersed boundary method for fluid–structure interaction with low density ratio of solid to fluid. J. Comput. Phys. 359 (2018), 296–311.
Koochesfahani, M.M., Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27:9 (1989), 1200–1205.
Lai, M.-C., Peskin, C.S., An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J. Comput. Phys. 160:2 (2000), 705–719.
Lai, J.C.S., Platzer, M.F., Jet characteristics of a plunging airfoil. AIAA J. 37:12 (1999), 1529–1537.
Lee, I., Choi, H., A discrete-forcing immersed boundary method for the fluid–structure interaction of an elastic slender body. J. Comput. Phys. 280 (2015), 529–546.
Lee, J., Kim, J., Choi, H., Yang, K.-S., Sources of spurious force oscillations from an immersed boundary method for moving-body problems. J. Comput. Phys. 230:7 (2011), 2677–2695.
Lee, J., You, D., An implicit ghost-cell immersed boundary method for simulations of moving body problems with control of spurious force oscillations. J. Comput. Phys. 233 (2013), 295–314.
Lentink, D., Gerritsma, M., 2003. Influence of airfoil shape on performance in insect flight. In: 33rd AIAA Fluid Dynamics Conference and Exhibit, Orlando Florida, pp. 3447.
Lentink, D., Muijres, F.T., Donker-Duyvis, F.J., van Leeuwen, J.L., Vortex-wake interactions of a flapping foil that models animal swimming and flight. J. Exp. Biol. 211:2 (2008), 267–273.
Leveque, R.J., Li, Z., The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31:4 (1994), 1019–1044.
Leweke, T., Le Dizes, S., Williamson, C.H.K., Dynamics and instabilities of vortex pairs. Annu. Rev. Fluid Mech. 48 (2016), 507–541.
Lewin, G.C., Haj-Hariri, H., Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow. J. Fluid Mech. 492 (2003), 339–362.
Mohd-Yusof, J., Combined immersed-boundary/b-spline methods for simulations of flow in complex geometries. CTR Annu. Res. Brief, NASA Ames/Stanford University, 1997, 317–327.
Nicolaou, L., Jung, S.Y., Zaki, T.A., A robust direct-forcing immersed boundary method with enhanced stability for moving body problems in curvilinear coordinates. Comput. Fluids 119 (2015), 101–114.
Noack, B.R., Obermeier, F., A chaos-theoretical investigation of the wake behind a cylinder. ZAMM Z. Angew. Math. Mech. 71 (1991), T428–T430.
Peskin, C.S., Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10:2 (1972), 252–271.
Platzer, M.F., Jones, K.D., Young, J., Lai, J.C.S., Flapping wing aerodynamics: progress and challenges. AIAA J. 46:9 (2008), 2136–2149.
Saiki, E.M., Biringen, S., Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method. J. Comput. Phys. 123:2 (1996), 450–465.
Schnipper, T., Exotic wakes of flapping fins. (Ph.D. thesis), 2011, Technical University of Denmark, Denmark.
Shyy, W., Aono, H., Chimakurthi, S.K., Trizila, P., Kang, C.-K., Cesnik, C.E.S., Liu, H., Recent progress in flapping wing aerodynamics and aeroelasticity. Prog. Aerosp. Sci. 46:7 (2010), 284–327.
Taira, K., Colonius, T., The immersed boundary method: a projection approach. J. Comput. Phys. 225:2 (2007), 2118–2137.
Takens, F., Detecting strange attractors in turbulence. Dynamical Systems and Turbulence, Warwick 1980, 1981, Springer, Berlin, Heidelberg, 366–381.
von Ellenrieder, K.D., Pothos, S., PIV measurements of the asymmetric wake of a two dimensional heaving hydrofoil. Exp. Fluids 44:5 (2008), 733–745.
Yang, J., Balaras, E., An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries. J. Comput. Phys. 215:1 (2006), 12–40.
Yang, J., Stern, F., A simple and efficient direct forcing immersed boundary framework for fluid–structure interactions. J. Comput. Phys. 231:15 (2012), 5029–5061.
Ye, T., Mittal, R., Udaykumar, H.S., Shyy, W., An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J. Comput. Phys. 156:2 (1999), 209–240.
Young, J., Lai, J.C.S., Oscillation frequency and amplitude effects on the wake of a plunging airfoil. AIAA J. 42:10 (2004), 2042–2052.
Young, J., Lai, J.C.S., Mechanisms influencing the efficiency of oscillating airfoil propulsion. AIAA J. 45:7 (2007), 1695–1702.