Aerodynamic Resonance in Transonic Airfoil Flow J. Nitzsche, R. H. M. Giepman Institute of Aeroelasticity, German Aerospace Center (DLR), Göttingen
Source: A. Šoda, PhD thesis, 2006 Slide 2/39
Introduction Overview Introduction Shock buffet phenomenon Simulation method 2-d URANS Numerical experiments Angle of attack sweeps Subcritical excitation Forced harmonic motion Impulse response Active shock buffet control Recent wind tunnel test results Conclusions Slide 3/39
Introduction The shock buffet phenomenon Slide 4/39
Introduction The shock buffet phenomenon Pure aerodynamic, self-excited shock oscillations due to shock- /boundary layer interaction in transonic flow Large-scale, low-frequency (Sr 0.1), beyond critical (Ma, Fixed airfoil, i.e. no elastic response Can be simulated with CFD (qualitatively) Slide 5/39
Introduction The shock buffet phenomenon Pure aerodynamic, self-excited shock oscillations due to shock- /boundary layer interaction in transonic flow Large-scale, low-frequency (Sr 0.1), beyond critical (Ma, Fixed airfoil, i.e. no elastic response Can be simulated with CFD (qualitatively) Flow physics behind feedback mechanism still not clear! Slide 6/39
Introduction The shock buffet phenomenon Questions: Why is it oscillating at all? When do the oscillations begin? What unsteady loads do we have to fear? Slide 7/39
Introduction The shock buffet phenomenon Angle of attack α stable flow unstable flow This Thistalk talk SB Onset Mach number Ma Slide 8/39
Simulation method Solver & mesh DLR-TAU: finite-volume, unstructured, central scheme Time-accurate 2-d URANS with Spalart-Allmaras (SAO) and LEA k- Supercritical airfoil BAC 3-11/RES/30/21 Ma = 0.75, Re = 4.5 106 x 1.5% x 1.5% x 0.5% x 0.5% Slide 9/39
Numerical experiments Angle of attack sweep lift coefficient Sweep down Sweep up SB SB onset onset (LEA (LEA only, only, SAO SAO always alwaysstable) stable) angle of attack Slide 10/39
Numerical experiments Angle of attack sweep Slide 11/39
Numerical experiments Angle of attack sweep Self-sustained flow field oscillation Shock amplitude: 10% chord Cyclic separation and reattachment Slide 12/39
Numerical experiments Subcritical flow oscillations Lift response after a sudden step in from 3 to 4 (below SB onset): lift coefficient frequency frequency and and damping damping rate rate converge converge for for infinitely infinitely small small amplitudes amplitudes traveled chords Slide 13/39
Numerical experiments Forced harmonic motion Excitation of the flow with small, harmonic perturbations 25%-chord trailing edge flap Flap amplitude: β = β 0 ± 0.01 Shock amplitude: 0.1% chord (1 order smaller than x) All field variables respond almost exclusively with the excitation frequency Slide 14/39
Numerical experiments Forced harmonic motion Amplitude ratio Phase lag Imag Motion Lift Real Motion Lift Slide 15/39
Numerical experiments Forced harmonic motion Excitation of the flow with small, harmonic perturbations Four different mean flows: 0 = 0, 2, 3, 4 Step sine excitation for reduced frequencies 0.01 * 1 complex complex derivative derivative c c l / β l / β Slide 16/39
Numerical experiments Forced harmonic motion Excitation of the flow with small, harmonic perturbations Four different mean flows: 0 = 0, 2, 3, 4 Step sine excitation for reduced frequencies 0.01 * 1 complex complex derivative derivative c c l / β l / β Slide 17/39
Numerical experiments Forced harmonic motion Excitation of the flow with small, harmonic perturbations Four different mean flows: 0 = 0, 2, 3, 4 Step sine excitation for reduced frequencies 0.01 * 1 complex complex derivative derivative c c l / β l / β Slide 18/39
Numerical experiments Forced harmonic motion Excitation of the flow with small, harmonic perturbations Four different mean flows: 0 = 0, 2, 3, 4 Step sine excitation for reduced frequencies 0.01 * 1 complex complex derivative derivative c c l / β l / β Slide 19/39
Numerical experiments Forced harmonic motion What is the difference between these four mean flow fields at 0 = 0, 2, 3, 4? SB SB onset onset inverse shock motion regular shock motion shock foot Slide 20/39
Numerical experiments Forced harmonic motion Eigendynamics should be independent of the way of excitation Additionally to flap rotation excitation via rigid body pitching around x/c = 25% with =0.01 translation parallel to onflow vector with =0.01% c complex complex derivatives derivatives Slide 21/39
Numerical experiments Forced harmonic motion Eigendynamics should be independent of the way of excitation Additionally to flap rotation excitation via rigid body pitching around x/c = 25% with =0.01 translation parallel to onflow vector with =0.01% c phase phase of of surface surface pressure pressure c c p p aerodynamic aerodynamic mode mode shape! shape! Slide 22/39
Numerical experiments Forced harmonic motion How do the shock and separation point respond? (at =4 )?!?! Slide 23/39
Numerical experiments Forced harmonic motion Phase response of shock motion w.r.t. pitch excitation (at =4 ): inverse inverse shock shock motion motion phase [deg] regular regular shock shock motion motion The shock buffet resonance is located, where the shock exhibits a phase reversal from inverse (+180 ) to regular (0 ) shock motion! Slide 24/39
Numerical experiments Forced harmonic motion Generalized Generalized aerodynamic aerodynamic forces forces aileron aileronbuzz! 1-DOF 1-DOF flutter! flutter! Slide 25/39
Numerical experiments Impulse response How does the assumed complex eigenvalue λ=δ+jω* depend on the angle of attack α 0? Curve fitting procedure on aerodynamic impulse response: Highly Highly accurate accurate fitting! fitting! Slide 26/39
Numerical experiments Impulse response How does the assumed complex eigenvalue λ=δ+jω* depend on the angle of attack α 0? Curve fitting procedure on aerodynamic impulse response: LEA coarse LEA coarse LEA coarse LEA coarse Slide 27/39
Numerical experiments Impulse response How does the assumed complex eigenvalue λ=δ+jω* depend on the angle of attack α 0? Curve fitting procedure on aerodynamic impulse response: LEA coarse LEA coarse SAO fine SAO fine SAO fine SAO fine SAO coarse SAO coarse SAO coarse SAO coarse LEA coarse LEA coarse Slide 28/39
Numerical experiments Impulse response Reason for eigenvalue variation? LEA coarse LEA coarse SAO coarse SAO coarse SAO fine SAO fine Slide 29/39
Numerical experiments Shock buffet control Can we control sub-/supercritical shock buffet oscillations with active torsion? Motivation: Accelerate convergence of weakly damped solutions to steady-state fixed point. Controller design (PID-like): K i and K a calibrated on the basis of the linearized aerodynamic model Slide 30/39
Numerical experiments Shock buffet control subcritical subcritical α=4 α=4 supercritical supercritical α=4.6 α=4.6 Works even in local time stepping mode Rapid non-conservative convergence acceleration Slide 31/39
Wind tunnel tests Recent results Transonic Wind Tunnel Göttingen, 2011 2-d pitching NACA0010 Ma 0.80, Re 2 10 6 Slide 32/39
Wind tunnel tests Recent results Transonic Wind Tunnel Göttingen, 2011 2-d pitching NACA0010 Ma 0.80, Re 2 10 6 Slide 33/39
Wind tunnel tests Recent results Transonic Wind Tunnel Göttingen, 2011 2-d pitching NACA0010 Ma 0.80, Re 2 10 6 Slide 34/39
Wind tunnel tests Recent results Transonic Wind Tunnel Göttingen, 2011 2-d pitching NACA0010 Ma 0.80, Re 2 10 6 Slide 35/39
Wind tunnel tests Simulation vs. exp Ma Ma 0.80 0.80 α=2.8 α=2.8 Slide 36/39
Wind tunnel tests Simulation vs. exp 2-d URANS simulation Incorporation of upper/ lower w/t wall following streamline-based pseudo-wall approach Slide 37/39
Wind tunnel tests Recent results Is there even more? Another mode/resonance? If there are two modes do they interact? Slide 38/39
Conclusions and future work Shock buffet is the self-amplified special case of an aerodynamic eigenvalue/eigenmode inherent to the steady-state flow. The shock buffet resonance frequency is located, where the shock exhibits a phase reversal from inverse to regular shock motion. The aerodynamic feedback mechanism is fully active already on the smallest scale. Task: Correlate steady flow field features with aerodynamic eigenvalue. Most likely, the shock buffet onset problem can be approached as a classic stabiltity problem. Task: Eigenvalue analysis of TAUs flux Jacobian [δr i /δw j ] Slide 39/39
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Farfield Farfield solution solution Slide 41/39
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Euler Euler wall wall farfield farfield farfield farfield Euler Euler wall wall Slide 46/39