Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T05:51:59.665Z Has data issue: false hasContentIssue false
  • English
  • Français

Shock–boundary layer interaction and energetics in transonic flutter

Published online by Cambridge University Press:  26 October 2017

Pradeepa T. Karnick  and
Kartik Venkatraman Open the ORCID record for Kartik Venkatraman [Opens in a new window]
Pradeepa T. Karnick
Affiliation:
Department of Aerospace Engineering, Indian Institute of Science, Bangalore, 560012, India
Kartik Venkatraman*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Science, Bangalore, 560012, India
*
†Email address for correspondence: kartik@aero.iisc.ernet.in
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the influence of shock and boundary layer interactions in transonic flutter of an aeroelastic system using a Reynolds-averaged Navier–Stokes (RANS) solver together with the Spalart–Allmaras turbulence model. We show that the transonic flutter boundary computed using a viscous flow solver can be divided into three distinct regimes: a low transonic Mach number range wherein viscosity mimics increasing airfoil thickness thereby mildly influencing the flutter boundary; an intermediate region of drastic change in the flutter boundary due to shock-induced separation; and a high transonic Mach number zone of no viscous effects when the shock moves close to the trailing edge. Inviscid transonic flutter simulations are a very good approximation of the aeroelastic system in predicting flutter in the first and third regions: that is when the shock is not strong enough to cause separation, and in regions where the shock-induced separated region is confined to a small region near the trailing edge of the airfoil. However, in the second interval of intermediate transonic Mach numbers, the power distribution on the airfoil surface is significantly influenced by shock-induced flow separation on the upper and lower surfaces leading to oscillations about a new equilibrium position. Though power contribution by viscous forces are three orders of magnitude less than the power due to pressure forces, these viscous effects manipulate the flow by influencing the strength and location of the shock such that the power contribution by pressure forces change significantly. Multiple flutter points that were part of the inviscid solution in this regime are now eliminated by viscous effects. Shock motion on the airfoil, shock reversal due to separation, and separation and reattachment of flow on the airfoil upper surface, also lead to multiple aerodynamic forcing frequencies. These flow features make the flutter boundary quantitatively sensitive to the turbulence model and numerical method adopted, but qualitatively they capture the essence of the physical phenomena.

JFM classification

Boundary Layers: Boundary layer separation Aerodynamics: High-speed flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 832 , 10 December 2017 , pp. 212 - 240
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alonso, J. J. & Jameson, A. 1994 Fully-implicit time-marching aeroelastic solutions. In 32nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV. AIAA Paper 94-0056.Google Scholar
Ashley, H. 1980 Role of shocks in the sub-transonic flutter phenomenon. J. Aircraft 17 (3), 187–197.CrossRefGoogle Scholar
Baldwin, B. S. & Lomax, H. 1978 Thin layer approximation and algebraic model for separated turbulent flows. In AIAA 16th Aerospace Sciences Meeting, Huntsville, Alabama.Google Scholar
Bendiksen, O. O.1992 Role of shock dynamics in transonic flutter. In Proceedings of the AIAA Dynamics Specialists Conference, Dallas, TX, USA, pp. 401–414. AIAA-92-2121-CP.CrossRefGoogle Scholar
Bendiksen, O. O. 1998 Transonic similarity rules for flutter and divergence. In 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Long Beach, California.Google Scholar
Bendiksen, O. O. 2009 Influence of shocks on transonic flutter of flexible wings. In 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Springs, California.Google Scholar
Bendiksen, O. O. 2011 Review of unsteady transonic aerodynamics: theory and applications. Prog. Aerosp. Sci. 47, 135–167.CrossRefGoogle Scholar
Bendiksen, O. O. & Kousen, K. A. 1987 Transonic flutter analysis using the Euler equations. In AIAA Dynamics Specialists Conference, Monterey, California.Google Scholar
Bohbot, J. & Darracq, D. 2001 Time domain analysis of two D.O.F. airfoil flutter using an Euler/turbulent Navier–Stokes implicit solver. In Proceedings of the International Forum on Aeroelasticity and Structural Dynamics, Madrid, Spain.Google Scholar
Castro, B. M., Ekaterinaris, J. A. & Platzer, M. F. 2002 Navier–Stokes analysis of wind–tunnel interference on transonic airfoil flutter. AIAA J. 40 (7), 1269–1276.CrossRefGoogle Scholar
Cook, P. H., McDonald, M. A. & Fermin, M. C. P. 1979 Airfoil RAE 2822 – pressure distributions, and boundary layers and wake measurements. In Experimental Data Base for Computer Program Assessment,, chap. Appendix A – 2-D Configurations. AGARD.Google Scholar
Davis, S. S. 1982 NACA 64A010 (NASA AMES model). Oscillatory pitching. In Compendium of Unsteady Aerodynamic Measurement, chap. Data Sets 2-D Configurations. AGARD.Google Scholar
Hirsch, C. 1994 Numerical Computation of Internal and External Flows, vol. 2. Wiley.Google Scholar
Isogai, K. 1979 On the transonic-dip mechanism of flutter of a sweptback wing. AIAA J. 17 (7), 793–795.CrossRefGoogle Scholar
Jameson, A. & Turkel, E. 1981 Implicit schemes and LU decompositions. Math. Comput. 37, 385–397.Google Scholar
Martinelli, L., Jameson, A. & Grasso, F. 1986 A multigrid method for the Navier–Stokes equations. In AIAA 24th Aerospace Sciences Meeting, Reno, Nevada.Google Scholar
Prananta, B. B., Hounjet, M. H. L. & Zwaan, R. J. 1998 Two-dimensional transonic aeroelastic analysis using thin-layer Navier-Stokes method. J. Fluids Struct. 12, 655–676.CrossRefGoogle Scholar
Raveh, D. E. 2008 A numerical study of an oscillating airfoil in transonic flows with large shock wave oscillations. In 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Schaumburg, Illinois.Google Scholar
Roe, P. L. 1981 Approximate Riemann solvers, parameter vectors and difference schemes. J. Comput. Phys. 43, 357–372.CrossRefGoogle Scholar
Spalart, P. R. & Allmaras, S. R. 1992 A one-equation turbulence model for aerodynamic flows. In AIAA 30th Aerospace Sciences Meeting and Exhibit, Reno, Nevada.Google Scholar
Thibert, J. J., Grandjacques, M. & Ohman, L. H. 1979 NACA 0012 airfoil. In Experimental Data Base for Computer Program Assessment, chap. Appendix A – 2-D Configurations. AGARD.Google Scholar
Tijdeman, H. 1977 Investigations of the transonic flow around oscillating airfoils. Tech. Rep. NLR Report TR 77090 U. National Aerospace Laboratories, Amsterdam, The Netherlands.Google Scholar
van Leer, B. 1979 Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32, 101–136.CrossRefGoogle Scholar
Wilcox, D. C. 1994 Turbulence Modeling for CFD. DCW Industries.Google Scholar
Zhang, Z., Yang, S., Liu, F. & Schuster, D. M. 2005 Prediction of flutter and LCO by an Euler method on non-moving cartesian grids with boundary layer corrections. In 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada.Google Scholar

Karnick and Venkatraman supplementary movie 1

Mach contours computed using the RANS (SA) model for a NACA 64A010 airfoil fluttering at a Mach number 0.875 and flutter speed index 1.93.

Download Karnick and Venkatraman supplementary movie 1(Video)
Video 69.7 MB

Karnick and Venkatraman supplementary movie 2

Mach contours computed using the Euler model for a NACA 64A010 airfoil fluttering at a Mach number 0.875 and flutter speed index 1.85.

Download Karnick and Venkatraman supplementary movie 2(Video)
Video 40.8 MB