Aeroelastic behavior of a flag in ground effect

Abstract The aeroelastic behavior of a flexible plate subjected to a uniform axial flow is investigated in the presence of a rigid plane set parallel to the plate. It is shown that the ground effect reduces the flutter inflow velocity and strengthens the possibility of using the flag for extracting energy from winds and currents. The numerical analysis is carried out assuming that both the unsteady potential incompressible flow and the plate can be described with 2D models, i.e., a lumped vortex panel method and a nonlinear Euler–Bernoulli beam model, respectively, without losing the essential features of the fluid–structure interaction. Asymmetry of post-critical behavior (limit-cycle oscillations) and sensitivity of the results to the main flag parameters (distance from the ground, mass ratio and damping) are also considered, including also the energy distribution over the identified proper orthogonal modes. The investigated reduction of the flutter velocity in ground effect has been also confirmed with experimental tests relative to a polypropylene flag with and without the rigid panel mimicking the presence of the ground.

[1]  Michael P. Païdoussis,et al.  The dynamics of variants of two-dimensional cantilevered flexible plates in axial flow , 2009 .

[2]  Aerodynamic optimization of the flat-plate leading edge for experimental studies of laminar and transitional boundary layers , 2012 .

[3]  M. Sugihara,et al.  AN EXPERIMENTAL STUDY OF PAPER FLUTTER , 2002 .

[4]  Earl H. Dowell,et al.  Flutter and limit cycle oscillations of two-dimensional panels in three-dimensional axial flow , 2003 .

[5]  Earl H. Dowell,et al.  Theory and experiment for flutter of a rectangular plate with a fixed leading edge in three-dimensional axial flow , 2012 .

[6]  Abdullah O. Nuhait,et al.  Aeroelastic Behavior of Flat Plates Moving Near the Ground , 2010 .

[7]  M. P. Paı¨doussis,et al.  On the instability and the post-critical behaviour of two-dimensional cantilevered flexible plates in axial flow , 2007 .

[8]  B. Feeny,et al.  On the physical interpretation of proper orthogonal modes in vibrations , 1998 .

[9]  E. D. Langre Methodological advances in predicting flow-induced dynamics of plants using mechanical-engineering theory. , 2012 .

[10]  G. Kerschen,et al.  The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview , 2005 .

[11]  T. Theodorsen General Theory of Aerodynamic Instability and the Mechanism of Flutter , 1934 .

[12]  M. P. Païdoussis,et al.  Time-marching analysis of fluid-coupled systems with large added mass , 1995 .

[13]  Brian F. Feeny,et al.  On the Proper Orthogonal Modes and Normal Modes of Continuous Vibration Systems , 2002 .

[14]  Lixi Huang,et al.  Flutter of Cantilevered Plates in Axial Flow , 1995 .

[15]  G. X. Li,et al.  The Non-linear Equations of Motion of Pipes Conveying Fluid , 1994 .

[16]  Michael P. Païdoussis,et al.  Cantilevered flexible plates in axial flow: Energy transfer and the concept of flutter-mill , 2009 .

[17]  D. Dessì,et al.  Analytical formulation of 2-D aeroelastic model in weak ground effect , 2013 .

[18]  K. Zaman,et al.  Nonlinear oscillations of a fluttering plate. , 1966 .

[19]  Michel Loève,et al.  Probability Theory I , 1977 .

[20]  Olivier Doare,et al.  Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency , 2011, 1104.3732.

[21]  Franco Mastroddi,et al.  Limit-cycle stability reversal via singular perturbation and wing-flap flutter , 2004 .

[22]  C. Eloy,et al.  Flutter of an elastic plate in a channel flow: confinement and finite-size effects , 2011 .

[23]  C. Eloy,et al.  The origin of hysteresis in the flag instability , 2011, Journal of Fluid Mechanics.

[24]  I. Ward,et al.  Mechanical and acoustic frequency responses in flat hot-compacted polyethylene and polypropylene panels , 2006 .

[25]  C. Eloy,et al.  Flutter of a rectangular plate , 2007 .

[26]  S. Alben,et al.  Flapping states of a flag in an inviscid fluid: bistability and the transition to chaos. , 2008, Physical review letters.

[27]  J. Katz,et al.  Low-Speed Aerodynamics , 1991 .

[28]  Daniele Dessi,et al.  Analysis of the global bending modes of a floating structure using the proper orthogonal decomposition , 2012 .

[29]  E. Dowell Nonlinear oscillations of a fluttering plate. II. , 1966 .

[30]  K. Isogai,et al.  A THEORETICAL STUDY OF PAPER FLUTTER , 2002 .

[31]  B. Feeny,et al.  Interpreting proper orthogonal modes of randomly excited vibration systems , 2003 .

[32]  Kari Karhunen,et al.  Über lineare Methoden in der Wahrscheinlichkeitsrechnung , 1947 .