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Flow-excited membrane instability at moderate Reynolds numbers

Published online by Cambridge University Press:  02 November 2021

Guojun Li Open the ORCID record for Guojun Li [Opens in a new window] ,
Rajeev Kumar Jaiman Open the ORCID record for Rajeev Kumar Jaiman [Opens in a new window]  and
Boo Cheong Khoo
Guojun Li*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 119077 Singapore, Republic of Singapore
Rajeev Kumar Jaiman
Affiliation:
Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, V6T 1Z4 Canada
Boo Cheong Khoo
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 119077 Singapore, Republic of Singapore
*
†Email address for correspondence: li.guojun@u.nus.edu
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Abstract

In this paper, we study the fluid–structure interaction of a three-dimensional (3-D) flexible membrane immersed in an unsteady separated flow at moderate Reynolds numbers. We employ a body-conforming variational fluid–structure interaction solver based on the recently developed partitioned iterative scheme for the coupling of turbulent fluid flow with nonlinear structural dynamics. Of particular interest is to understand the flow-excited instability of a 3-D flexible membrane as a function of the non-dimensional mass ratio ($m^{*}$), Reynolds number ($Re$) and aeroelastic number ($Ae$). For a wide range of parameters, we examine two distinct stability regimes of the fluid–membrane interaction: deformed steady state (DSS) and dynamic balance state (DBS). We propose stability phase diagrams to demarcate the DSS and DBS regimes for the parameter space of mass ratio versus Reynolds number ($m^{*}$-$Re$) and mass ratio versus aeroelastic number ($m^{*}$-$Ae$). With the aid of the global Fourier mode decomposition technique, the distinct dominant vibrational modes are identified from the intertwined membrane responses in the parameter space of $m^{*}$-$Re$ and $m^{*}$-$Ae$. Compared to the deformed steady membrane, the flow-excited vibration produces relatively longer attached leading-edge vortices which improve the aerodynamic performance when the coupled system is near the flow-excited instability boundary. The optimal aerodynamic performance is achieved for lighter membranes with higher $Re$ and larger flexibility. Based on the global aeroelastic mode analysis, we observe a frequency lock-in phenomenon between the vortex-shedding frequency and the membrane vibration frequency causing self-sustained vibrations in the dynamic balance state. To characterize the origin of the frequency lock-in, we propose an approximate analytical formula for the nonlinear natural frequency by considering the added mass effect and employing a large deflection theory for a simply supported rectangular membrane. Through our systematic high-fidelity numerical investigation, we find that the onset of the membrane vibration and the mode transition has a direct dependence on the frequency lock-in between the natural frequency of the tensioned membrane and the vortex-shedding frequency or its harmonics. These findings on the fluid-elastic instability of membranes have implications for the design and development of control strategies for membrane wing-based unmanned systems and drones.

JFM classification

Biological Fluid Dynamics: Membranes Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 929 , 25 December 2021 , A40
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Amabili, M. 2008 Nonlinear Vibrations and Stability of Shells and Plates. Cambridge University Press.CrossRefGoogle Scholar
Arbós-Torrent, S., Ganapathisubramani, B. & Palacios, R. 2013 Leading-and trailing-edge effects on the aeromechanics of membrane aerofoils. J. Fluids Struct. 38, 107–126.CrossRefGoogle Scholar
Bahlman, J.W., Swartz, S.M. & Breuer, K.S. 2013 Design and characterization of a multi-articulated robotic bat wing. Bioinspir. Biomim. 8 (1), 016009.CrossRefGoogle ScholarPubMed
Bleischwitz, R., de Kat, R. & Ganapathisubramani, B. 2015 Aspect-ratio effects on aeromechanics of membrane wings at moderate Reynolds numbers. AIAA J. 53 (3), 780–788.CrossRefGoogle Scholar
Bleischwitz, R., De Kat, R. & Ganapathisubramani, B. 2016 Aeromechanics of membrane and rigid wings in and out of ground-effect at moderate reynolds numbers. J. Fluids Struct. 62, 318–331.CrossRefGoogle Scholar
Bleischwitz, R., De Kat, R. & Ganapathisubramani, B. 2017 On the fluid-structure interaction of flexible membrane wings for MAVs in and out of ground-effect. J. Fluids Struct. 70, 214–234.CrossRefGoogle Scholar
Bleischwitz, R., De Kat, R. & Ganapathisubramani, B. 2018 Near-wake characteristics of rigid and membrane wings in ground effect. J. Fluids Struct. 80, 199–216.CrossRefGoogle Scholar
Buoso, S. & Palacios, R. 2017 On-demand aerodynamics in integrally actuated membranes with feedback control. AIAA J. 55 (2), 377–388.CrossRefGoogle Scholar
Chen, Z., Wu, Y. & Sun, X. 2015 Research on the added mass of open-type one-way tensioned membrane structure in uniform flow. J. Wind Engng Ind. Aerodyn. 137, 69–77.CrossRefGoogle Scholar
Drazin, P.G. & Drazin, P.D. 1992 Nonlinear Systems, vol. 10. Cambridge University Press.CrossRefGoogle Scholar
Gordnier, R.E. 2009 High fidelity computational simulation of a membrane wing airfoil. J. Fluids Struct. 25 (5), 897–917.CrossRefGoogle Scholar
Gordnier, R.E. & Attar, P.J. 2014 Impact of flexibility on the aerodynamics of an aspect ratio two membrane wing. J. Fluids Struct. 45, 138–152.CrossRefGoogle Scholar
Gursul, I., Cleaver, D. & Wang, Z. 2014 Control of low Reynolds number flows by means of fluid–structure interactions. Prog. Aerosp. Sci. 64, 17–55.CrossRefGoogle Scholar
Jaiman, R., Pillalamarri, N. & Guan, M. 2016 A stable second-order partitioned iterative scheme for freely vibrating low-mass bluff bodies in a uniform flow. Comput. Meth. Appl. Mech. Engng 301, 187–215.CrossRefGoogle Scholar
Jaiman, R.K., Parmar, M.K. & Gurugubelli, P.S. 2014 Added mass and aeroelastic stability of a flexible plate interacting with mean flow in a confined channel. Trans. ASME J. Appl. Mech. 81 (4), 041006.CrossRefGoogle Scholar
Joshi, V. & Jaiman, R.K. 2017 A variationally bounded scheme for delayed detached eddy simulation: application to vortex-induced vibration of offshore riser. Comput. fluids 157, 84–111.CrossRefGoogle Scholar
Joshi, V., Jaiman, R.K. & Ollivier-Gooch, C. 2020 A variational flexible multibody formulation for partitioned fluid–structure interaction: application to bat-inspired drones and unmanned air-vehicles. Comput. Maths Applics. 80 (12), 2707–2737.CrossRefGoogle Scholar
Kamm, R. & Grodzinsky, A. 2015 Molecular, Cellular, and Tissue Biomechanics. Massachusetts Institute of Technology.Google Scholar
Katopodes, N.D. 2018 Free-surface Flow: Environmental Fluid Mechanics. Butterworth-Heinemann.Google Scholar
Kinsler, L.E., Frey, A.R., Coppens, A.B. & Sanders, J.V. 1999 Fundamentals of Acoustics, 4th edn (ed. L.E. Kinsler, A.R. Frey, A.B. Coppens, & J.V. Sanders), p. 560. Wiley-VCH.Google Scholar
Li, G., Jaiman, R.K. & Khoo, B.C. 2020 a Aeroelastic mode decomposition and mode selection mechanism in fluid-membrane interaction. arXiv e-prints arXiv–2006.Google Scholar
Li, G., Khoo, B.C. & Jaiman, R.K. 2020 b Computational aeroelasticity of flexible membrane wings at moderate Reynolds numbers. In AIAA Scitech 2020 Forum, AIAA Paper 2020-2036. AIAA.CrossRefGoogle Scholar
Li, G., Law, Y.Z. & Jaiman, R.K. 2019 A novel 3d variational aeroelastic framework for flexible multibody dynamics: application to bat-like flapping dynamics. Comput. Fluids. 180, 96–116.CrossRefGoogle Scholar
Liu, X., Cai, G., Peng, F., Zhang, H. & Lv, L. 2018 Nonlinear vibration analysis of a membrane based on large deflection theory. J. Vib. Control 24 (12), 2418–2429.CrossRefGoogle Scholar
Newman, B.G. 1987 Aerodynamic theory for membranes and sails. Prog. Aerosp. Sci. 24 (1), 1–27.CrossRefGoogle Scholar
Rojratsirikul, P., Genc, M., Wang, Z. & Gursul, I. 2011 Flow-induced vibrations of low aspect ratio rectangular membrane wings. J. Fluids Struct. 27 (8), 1296–1309.CrossRefGoogle Scholar
Rojratsirikul, P., Wang, Z. & Gursul, I. 2009 Unsteady fluid–structure interactions of membrane airfoils at low Reynolds numbers. Exp. Fluids 46 (5), 859–872.CrossRefGoogle Scholar
Rojratsirikul, P., Wang, Z. & Gursul, I. 2010 a Effect of pre-strain and excess length on unsteady fluid–structure interactions of membrane airfoils. J. Fluids Struct. 26 (3), 359–376.CrossRefGoogle Scholar
Rojratsirikul, P., Wang, Z. & Gursul, I. 2010 b Unsteady aerodynamics of low aspect ratio membrane wings. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA Paper 2010-729. AIAA.CrossRefGoogle Scholar
Serrano Galiano, S. & Sandberg, R.D. 2016 Effect of the leading and trailing edge geometry on the fluid-structural coupling of membrane aerofoils. In 54th AIAA Aerospace Sciences Meeting, AIAA Paper 2016-0853. AIAA.CrossRefGoogle Scholar
Serrano-Galiano, S., Sandham, N.D. & Sandberg, R.D. 2018 Fluid–structure coupling mechanism and its aerodynamic effect on membrane aerofoils. J. Fluid Mech. 848, 1127–1156.CrossRefGoogle Scholar
Shyy, W., Berg, M. & Ljungqvist, D. 1999 Flapping and flexible wings for biological and micro air vehicles. Prog. Aerosp. Sci. 35 (5), 455–505.CrossRefGoogle Scholar
Smith, R. & Shyy, W. 1995 Computational model of flexible membrane wings in steady laminar flow. AIAA J. 33 (10), 1769–1777.CrossRefGoogle Scholar
Song, A., Tian, X., Israeli, E., Galvao, R., Bishop, K., Swartz, S. & Breuer, K. 2008 Aeromechanics of membrane wings with implications for animal flight. AIAA J. 46 (8), 2096–2106.CrossRefGoogle Scholar
Sun, X., Ren, X. & Zhang, J. 2017 Nonlinear dynamic responses of a perimeter-reinforced membrane wing in laminar flows. Nonlinear Dyn. 88 (1), 749–776.CrossRefGoogle Scholar
Sun, X. & Zhang, J. 2016 Nonlinear vibrations of a flexible membrane under periodic load. Nonlinear Dyn. 85 (4), 2467–2486.CrossRefGoogle Scholar
Sun, X. & Zhang, J. 2017 Effect of the reinforced leading or trailing edge on the aerodynamic performance of a perimeter-reinforced membrane wing. J. Fluids Struct. 68, 90–112.CrossRefGoogle Scholar
Tiomkin, S. & Raveh, D.E. 2019 On membrane-wing stability in laminar flow. J. Fluids Struct. 91, 102694.CrossRefGoogle Scholar
Tregidgo, L., Wang, Z. & Gursul, I. 2011 Fluid-structure interactions for a low aspect-ratio membrane wing at low reynolds numbers. In 41st AIAA Fluid Dynamics Conference and Exhibit, AIAA Paper 2011-3436. AIAA.CrossRefGoogle Scholar
Tregidgo, L., Wang, Z. & Gursul, I. 2012 Frequency lock-in phenomenon for self-sustained roll oscillations of rectangular wings undergoing a forced periodic pitching motion. Phys. Fluids 24 (11), 117101.CrossRefGoogle Scholar
Tregidgo, L., Wang, Z. & Gursul, I. 2013 Unsteady fluid–structure interactions of a pitching membrane wing. Aerosp. Sci. Technol. 28 (1), 79–90.CrossRefGoogle Scholar
Waldman, R.M. & Breuer, K.S. 2017 Camber and aerodynamic performance of compliant membrane wings. J. Fluids Struct. 68, 390–402.CrossRefGoogle Scholar
Webster, F.A. & Griffin, D.R. 1962 The role of the flight membranes in insect capture by bats. Anim. Behav. 10 (3–4), 332–340.CrossRefGoogle Scholar
Yang, H., Dudley, J. & Harris, R. 2018 Aeroelasticity validation study for a three-dimensional membrane wing. AIAA J. 56 (6), 2361–2371.CrossRefGoogle Scholar