The interaction between flutter and buffet in transonic flow

This paper presents a kind of nodal-shaped oscillation that is caused by the interaction between flutter and buffet in transonic flow. This response differs from the common limit cycle oscillation that appears in transonic aeroelastic problems. The benchmark active controls technology model with the NACA0012 airfoil is used as the research model. First, both buffet and flutter cases are computed through unsteady Reynolds-averaged Navier–Stokes method and are validated by experimental data. Second, the interaction is found to occur beyond the flutter onset velocity at Mach 0.71. When the pitching angle of a fluttering structure exceeds the buffet onset angle, the high-frequency aerodynamic loads induced by transonic buffet destroy the original flutter model, and then the amplitude of the structure motion decays. When the structural pitching angle is less than the buffet onset angle, the buffet disappears and flutter occurs again. As the process repeats itself, the transonic aeroelastic system displays a nodal-shaped oscillation (divergent–damping–divergent–damping oscillation). Finally, the mechanism of the interaction is discussed by analyzing the energy transportation between the flow and the structure in one cycle of nodal-shaped oscillation, and by observing the variation in the phase-angle difference between the plunging and pitching displacements. In this way, this research provides a new approach to understand flutter suppression.

[1]  Andrew Arena,et al.  Accelerating computational fluid dynamics based aeroelastic predictions using system identification , 2001 .

[2]  Xi-yun Lu,et al.  Numerical investigation of the compressible flow past an aerofoil , 2009, Journal of Fluid Mechanics.

[3]  Daniella E. Raveh,et al.  Frequency lock-in phenomenon for oscillating airfoils in buffeting flows , 2011 .

[4]  Weiwei Zhang,et al.  Aeroservoelastic Analysis for Transonic Missile Based on Computational Fluid Dynamics , 2009 .

[5]  Weiwei Zhang,et al.  Two Better Loosely Coupled Solution Algorithms of CFD Based Aeroelastic Simulation , 2007 .

[6]  Earl H. Dowell,et al.  Three-Dimensional Transonic Aeroelasticity Using Proper Orthogonal Decomposition-Based Reduced-Order Models , 2001 .

[7]  Ali H. Nayfeh,et al.  An analytical and experimental investigation into limit-cycle oscillations of an aeroelastic system , 2012, Nonlinear Dynamics.

[8]  M Schuster David,et al.  MAVRIC Flutter Model Transonic Limit Cycle Oscillation Test , 2001 .

[9]  Zhi J. Wang,et al.  A block LU-SGS implicit dual time-stepping algorithm for hybrid dynamic meshes , 2003 .

[10]  Eric Coustols,et al.  NUMERICAL PREDICTION OF SHOCK INDUCED OSCILLATIONS OVER A 2D AIRFOIL: INFLUENCE OF TURBULENCE MODELLING AND TEST SECTION WALLS , 2006, Proceeding of Fourth International Symposium on Turbulence and Shear Flow Phenomena.

[11]  Robert M. Bennett,et al.  NACA 0012 benchmark model experimental flutter results with unsteady pressure distributions , 1992 .

[12]  David J. Lucia,et al.  Reduced-Order Model Development Using Proper Orthogonal Decomposition and Volterra Theory , 2004 .

[13]  L. Eriksson,et al.  Investigation of large scale shock movement in transonic flow , 2010 .

[14]  Daniella E. Raveh,et al.  Reduced-Order Models for Nonlinear Unsteady Aerodynamics , 2001 .

[15]  Weiwei Zhang,et al.  Control law design for transonic aeroservoelasticity , 2007 .

[16]  Robert W. Bunton,et al.  Limit Cycle Oscillation Characteristics of Fighter Aircraft , 2000 .

[17]  Charles M. Denegri,et al.  Limit Cycle Oscillation Prediction Using Artificial Neural Networks , 2001 .

[18]  Oddvar O. Bendiksen Transonic Limit Cycle Flutter of High-Aspect-Ratio Swept Wings , 2008 .

[19]  Jens Nitzsche A NUMERICAL STUDY ON AERODYNAMIC RESONANCE IN TRANSONIC SEPARATED FLOW , 2009 .

[20]  Qing Xiao,et al.  A numerical study of transonic buffet on a supercritical airfoil , 2004 .

[21]  Jeffrey P. Thomas,et al.  Using Automatic Differentiation to Create a Nonlinear Reduced-Order-Model Aerodynamic Solver , 2010 .

[22]  Tapan K. Sengupta,et al.  Direct numerical simulation of 2D transonic flows around airfoils , 2013 .

[23]  P. Sagaut,et al.  Large-eddy simulation of the shock/boundary layer interaction , 2001 .

[24]  Daniella E. Raveh Numerical Study of an Oscillating Airfoil in Transonic Buffeting Flows , 2009 .

[25]  C. Farhat,et al.  Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity , 2008 .

[26]  O. Bendiksen Review of unsteady transonic aerodynamics: Theory and applications , 2011 .

[27]  W. Schröder,et al.  Coupled Airfoil Heave/Pitch Oscillations at Buffet Flow , 2013 .

[28]  Weiwei Zhang,et al.  Efficient Method for Limit Cycle Flutter Analysis Based on Nonlinear Aerodynamic Reduced-Order Models , 2012 .

[29]  P. Beran,et al.  Reduced-order modeling: new approaches for computational physics , 2004 .

[30]  Charbel Farhat,et al.  Adaptation of Aeroelastic Reduced-Order Models and Application to an F-16 Configuration , 2007 .

[31]  Fred Nitzsche,et al.  Application of Multi-Input Volterra Theory to Nonlinear Multi-Degree-of-Freedom Aerodynamic Systems , 2010 .

[32]  Liviu Librescu,et al.  Nonlinear Open-/Closed-Loop Aeroelastic Analysis of Airfoils via Volterra Series , 2004 .

[33]  Azeddine Kourta,et al.  Buffeting in transonic flow prediction using time‐dependent turbulence model , 2005 .

[34]  John W. Edwards,et al.  Transonic Shock Oscillations and Wing Flutter Calculated with an Interactive Boundary Layer Coupling Method , 1996 .

[35]  C. Allen,et al.  Unified fluid–structure interpolation and mesh motion using radial basis functions , 2008 .

[36]  Bingshuang Xu,et al.  Stability and Hopf bifurcation of a two-dimensional supersonic airfoil with a time-delayed feedback control surface , 2014 .

[37]  Earl H. Dowell,et al.  Theoretical Predictions of F-16 Fighter Limit Cycle Oscillations for Flight Flutter Testing , 2009 .

[38]  B. Lee,et al.  Role of Kutta waves on oscillatory shock motion on an airfoil , 1994 .

[39]  Weiwei Zhang,et al.  Reduced-Order-Model-Based Flutter Analysis at High Angle of Attack , 2007 .

[40]  Liviu Librescu,et al.  Open/Closed-Loop Nonlinear Aeroelasticity for Airfoils via Volterra Series Approach , 2002 .

[41]  D. Magidov,et al.  Predicting the onset of flow unsteadiness based on global instability , 2007, J. Comput. Phys..

[42]  Jeffrey P. Thomas,et al.  Nonlinear Inviscid Aerodynamic Effects on Transonic Divergence, Flutter, and Limit-Cycle Oscillations , 2001 .

[43]  Andrey Garbaruk,et al.  Origin of transonic buffet on aerofoils , 2007, Journal of Fluid Mechanics.

[44]  D. Raveh,et al.  Transonic unsteady aerodynamics in the vicinity of shock-buffet instability , 2012 .

[45]  Earl H. Dowell,et al.  Some Recent Advances in Nonlinear Aeroelasticity: Fluid- Structure Interaction in the 21 st Century , 2010 .

[46]  Weiwei Zhang,et al.  ROM Based Aeroservoelastic Analysis in Transonic Flow , 2007 .

[47]  David J. Lucia,et al.  Reduced-order modelling of limit-cycle oscillation for aeroelastic systems , 2004 .

[48]  Earl H. Dowell,et al.  Nonlinear Aeroelasticity and Unsteady Aerodynamics , 2002 .

[49]  Jeffrey P. Thomas,et al.  Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows , 2000 .

[50]  Ken Badcock,et al.  Implicit Harmonic Balance Solver for Transonic Flow with Forced Motions , 2009 .

[51]  W. Silva,et al.  Identification of Nonlinear Aeroelastic Systems Based on the Volterra Theory: Progress and Opportunities , 2005 .

[52]  Ante Soda,et al.  Analysis of transonic aerodynamic interference in the wing-nacelle region for a generic transport aircraft , 2005 .

[53]  Earl H. Dowell,et al.  Modeling of Fluid-Structure Interaction , 2001 .

[54]  Weiwei Zhang,et al.  Effect of control surface on airfoil flutter in transonic flow , 2010 .

[55]  S. Deck Numerical Simulation of Transonic Buffet over a Supercritical Airfoil , 2005 .

[56]  B.H.K. Lee,et al.  Self-sustained shock oscillations on airfoils at transonic speeds , 2001 .

[57]  Daniella E. Raveh,et al.  Aeroelastic Responses of Elastically Suspended Airfoil Systems in Transonic Buffeting Flows , 2014 .

[58]  Antony Jameson,et al.  The computational efficiency of non-linear frequency domain methods , 2006, J. Comput. Phys..

[59]  Jeffrey P. Thomas,et al.  Transonic Limit Cycle Oscillation Analysis Using Reduced Order Aerodynamic Models , 2001 .

[60]  E. Goncalvès,et al.  Turbulence model and numerical scheme assessment for buffet computations , 2004 .

[61]  H. E. Bailey,et al.  Calculation of Transonic Aileron Buzz , 1979 .

[62]  W. Geissler Numerical study of buffet and transonic flutter on the NLR 7301 airfoil , 2003 .

[63]  John W. Edwards,et al.  AIAA 98-2421 An Overview of Recent Developments in Computational Aeroelasticity , 1998 .

[64]  Sun Jian,et al.  Active flutter suppression control law design method based on balanced proper orthogonal decomposition reduced order model , 2012 .