Abstract
The wake characteristics of a custom-designed airfoil performing pitching oscillations, heaving oscillations, and a combination of pitch and heave oscillations are compared in this study. The influence of flapping parameters are investigated at a constant Reynolds number Re\(_{c} = 2640\) and is presented for the Strouhal numbers based on the oscillation amplitude, StA, varying in the \(0.1 \leqslant {\text{S}}{{{\text{t}}}_{A}} \leqslant 0.4\) range. The generation of vorticity above and below the airfoil depends on the airfoil’s initial direction of motion and remains the same for all types of flapping oscillations investigated. The evolution of the leading-edge and trailing-edge vortices is presented. The heaving oscillations of the airfoil are found to have a greater influence on the characteristics of the leading edge vortex. The wake behind the combined pitch-heave oscillations appears to be governed by pitching oscillations below \({\text{S}}{{{\text{t}}}_{A}} = 0.24\), whereas it is driven by heaving oscillations above \({\text{S}}{{{\text{t}}}_{A}} = 0.24\). The force computations indicate that the mere existence of the reverse von Kármán street is not sufficient to develop the thrust on the airfoil. The periodic component of velocity fluctuations significantly influences the wake characteristics. The anisotropic stress field developed around the airfoil due to the periodic fluctuations of the velocity is presented. The coherent structures developed in the wake are identified using the proper orthogonal decomposition and a qualitative comparison of the structures for different flapping oscillations is presented. The energy transfer from the flapping airfoil to the fluid for different flapping oscillations is highest for heaving oscillations followed by combined pitch-heave oscillations and pitching oscillations.
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REFERENCES
Oshima, H. and Ramaprian, B., Velocity measurements over a pitching airfoil, AIAA J, 1997, vol. 35, no. 1, pp. 119–126.
Sarkar, S. and Venkatraman, K., Numerical simulation of thrust generating flow past a pitching airfoil, Computers Fluids, 2006, vol. 35, no. 1, pp. 16–42.
Deng, J., Sun, L., and Shao, X., Dynamical features of the wake behind a pitching foil, Phys. Rev. E, 2015, vol. 92, no. 6, p. 063013.
Ashraf, I., Agrawal, A., Khan, M.H., Srivastava, A., Sharma, A., et al., Thrust generation and wake structure for flow across a pitching airfoil at low Reynolds number, Sadhana, 2015, vol. 40, no. 8, pp. 2367–2379.
Lai, J. and Platzer, M., Jet characteristics of a plunging airfoil, AIAA J., 1997, vol. 37, no. 12, pp. 1529–1537.
Lewin, G.C. and Haj-Hariri, H., Modeling thrust generation of a two-dimensional heaving airfoil in a viscous flow, J. Fluid Mech., 2003, vol. 492, pp. 339–362.
Ashraf, M., Young, J., and Lai, J., Oscillation frequency and amplitude effects on plunging airfoil propulsion and flow periodicity, AIAA J., 2012, vol. 50, no. 11, pp. 2308–2324.
Martín-Alcántara, A., Fernandez-Feria, R., and Sanmiguel-Rojas, E., Vortex flow structures and interactions for the optimum thrust efficiency of a heaving airfoil at different mean angles of attack, Phys. Fluids, 2015, vol. 27, no. 7, p. 073602.
Guglielmini, L. and Blondeaux, P., Propulsive efficiency of oscillating foils, Europ. J. Mech-B/Fluids, 2004, vol. 23, no. 2, p. 255–278.
Moriche, M., Flores, O., and Garcia-Villalba, M., On the aerodynamic forces on heaving and pitching airfoils at low Reynolds number, J. Fluid Mech., 2017, vol. 828, pp. 395–423.
Floryan, D., Van Buren, T., Rowley, C.W., and Smits, A.J., Scaling the propulsive performance of heaving and pitching foils, J. Fluid Mech., 2017, vol. 822, pp. 386–397.
Zheng, H., Xie, F., Zheng, Y., Ji, T., and Zhu, Z., Propulsion performance of a two-dimensional flapping airfoil with wake map and dynamic mode decomposition analysis, Phys. Rev. E, 2019, vol. 99, no. 6, p. 063109.
Triantafyllou, M., Triantafyllou, G., and Gopalkrishnan, R., Wake mechanics for thrust generation in oscillating foils, Phys. Fluids A: Fluid Dyn., 1991, vol. 3, no. 12, pp. 2835–2837.
Jones, K., Dohring, C., and Platzer, M., Experimental and computational investigation of the Knoller–Betz effect, AIAA J., 1998, vol. 36, no. 7, pp. 1240–1246.
Vandenberghe, N., Zhang, J., and Childress, S., Symmetry breaking leads to forward flapping flight, J. Fluid Mech., 2004, vol. 506, pp. 147–155.
Schnipper, T., Andersen, A., and Bohr, T., Vortex wakes of a flapping foil, J. Fluid Mech., 2009, vol. 633, pp. 411–423.
Jones, K. and Platzer, M., Numerical computation of flapping-wing propulsion and power extraction . In: 35th Aerospace Sciences Meeting and Exhibit, 1997, p. 826.
Godoy-Diana, R., Aider, J.L., and Wesfreid, J.E., Transitions in the wake of a flapping foil, Phys. Rev. E, 2008, vol. 77, no. 1, p. 016308.
Badrinath, S., Bose, C., and Sarkar, S., Identifying the route to chaos in the flow past a flapping airfoil, Europ. J. Mech.-B/Fluids, 2017, vol. 66, pp. 38–59.
Bose, C. and Sarkar, S., Investigating chaotic wake dynamics past a flapping airfoil and the role of vortex interactions behind the chaotic transition, Phys. Fluids, 2018, vol. 30, no. 4, p. 047101.
Godoy-Diana, R., Marais, C., Aider, J.L., and 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., 2009, vol. 622, pp. 23–32.
Cleaver, D.J., Wang, Z., and Gursul, I., Bifurcating flows of plunging airfoils at high Strouhal numbers, J. Fluid Mech., 2012, vol. 708, pp. 349–376.
Medjroubi, W., Stoevesandt, B., and Peinke, J., Wake classification of heaving airfoils using the spectral/hp element method, J. Comput. Appl. Math., 2012, vol. 236, no. 15, pp. 3774–3782.
Andersen, A., Bohr, T., Schnipper, T., and Walther, J.H., Wake structure and thrust generation of a flapping foil in two-dimensional flow, J. Fluid Mech., 2017, vol. 812.
Mackowski, A. and Williamson, C., Direct measurement of thrust and efficiency of an airfoil undergoing pure pitching, J. Fluid Mech., 2015, vol. 765, pp. 524–543.
Anderson, J., Streitlien, K., Barrett, D., and Triantafyllou, M., Oscillating foils of high propulsive efficiency, J. Fluid Mech., 1998, vol. 360, pp. 41–72.
Huq, A.A., Sankar, R.A., Lakshmanan, C., Rukesh, C., Kulkarni, D., Subramanya, M., and Rajani, B., Numerical prediction of aerofoil aerodynamics at low Reynolds number for MAV application, NAL PD CF 910.
Ferziger, J.H. and Peric, M., Computational Methods for Fluid Dynamics, Vol. 3, Springer, 2002.
OpenFOAM, The Open Source CFD Toolbox User Guide (2017).
Zheng, Z.C. and Wei, Z., Study of mechanisms and factors that influence the formation of vortical wake of a heaving airfoil, Phys. Fluids, 2012, vol. 24, no. 10, p. 103601.
Wei, Z. and Zheng, Z.C., Mechanisms of deflection angle change in the near and far vortex wakes behind a heaving airfoil. In: 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2013, p. 840.
Koochesfahani, M.M., Vortical patterns in the wake of an oscillating airfoil, AIAA J., 1989, vol. 27, no. 9, pp. 1200–1205.
Van Buren, T., Floryan, D., and Smits, A.J., Scaling and performance of simultaneously heaving and pitching foils, AIAA J., 2019, vol. 57, no. 9, pp. 3666–3677.
Bose, C., Gupta, S., and Sarkar, S., Dynamic interlinking between near- and far-field wakes behind a pitching–heaving airfoil, J. Fluid Mech., 2021, vol. 911, p. A31.
Vineeth, V.K., Patel, D.K., Roy, S., Goli, S., and Roy, A., Investigations into transient wakes behind a custom airfoil undergoing pitching motion, Europ. J. Mech.-B/Fluids, 2019, vol. 85. pp. 193–213.
Ohmi, K., Coutanceau, M., Loc, T.P., and Dulieu, A., Vortex formation around an oscillating and translating airfoil at large incidences, J. Fluid Mech., 1990, vol. 211, pp. 37–60.
Heathcote, S. and Gursul, I., Jet switching phenomenon for a periodically plunging airfoil, Phys. Fluids, 2007, vol. 19, no. 2, p. 027104.
Williamson, C.H. and Roshko, A., Vortex formation in the wake of an oscillating cylinder, J. Fluids Struct., 1988, vol. 2, no. 4, pp. 355–381.
Dynnikova, G.Y., Dynnikov, Y.A., and Guvernyuk, S., Mechanism underlying Kármán vortex street breakdown preceding secondary vortex street formation, Phys. Fluids, 2016, vol. 28, no. 5, p. 054101.
Dynnikova, G.Y., Dynnikov, Y.A., Guvernyuk, S., and Malakhova, T., Stability of a reverse Kármán vortex street, Phys. Fluids, 2021, vol. 33, no. 2, p. 024102.
Saha, A.K., Muralidhar, K., and Biswas, G., Vortex structures and kinetic energy budget in two dimensional flow past a square cylinder, Computers Fluids, 2000, vol. 29, no. 6, pp. 669–694.
Sirovich, L., Turbulence and the dynamics of coherent structures. I. Coherent structures, Quart. Appl. Math., 1987, vol. 45, no. 3, pp. 561–571.
Vineeth, V.K. and Patel, D.K., Propulsion performance and wake transitions of a customized heaving airfoil, Intern. J. Modern Phys. C, 2021, vol. 32, no. 9, pp. 1–28.
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The authors like to acknowledge the support provided by the Council of Scientific and Industrial Research (CSIR), Government of India, in the form of Senior Research Fellowship (SRF).
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Vineeth, V.K., Patel, D.K. Comparative Analysis of the Characteristics of the Vortex Wake behind a Flapping Wing Performing Oscillations of Different Types. Fluid Dyn 56 (Suppl 1), S101–S125 (2021). https://doi.org/10.1134/S0015462822020124
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DOI: https://doi.org/10.1134/S0015462822020124