Unsteady Aerodynamic Forces: Experiments, Simulations, and Models. Steve Brunton & Clancy Rowley FAA/JUP Quarterly Meeting April 6, 2011

Transcription

1 Unsteady Aerodynamic Forces: Experiments, Simulations, and Models Steve Brunton & Clancy Rowley FAA/JUP Quarterly Meeting April 6, Wednesday, March 8,

2 Motivation Applications of Unsteady Models Conventional UAVs (performance/robustness) Micro air vehicles (MAVs) Flow control, flight dynamic control Autopilots / Flight simulators Gust disturbance mitigation Predator (General Atomics) Need for State-Space Models Need models suitable for control Combining with flight models FLYIT Simulators, Inc. Daedalus Dakota Wednesday, March 8,

3 Flight Dynamic Control coupled model reference trajectory, wind disturbances flight dynamics deviation from desired path, or state thrust, elevator, aileron, blowing/suction aerodynamics position, aerodynamic state controller estimator Wednesday, March 8,

4 Stall velocity and size Smaller, lower stall velocity RQ- Predator (7 m/s stall) Daedalus Dakota (8m/s stall) Puma AE ( m/s stall) S Wing surface area V stall = ρ (C L max S) W W L C L V Aircraft weight Lift force Lift coefficient Velocity of aircraft Wednesday, March 8,

5 Lift vs. Angle of Attack.6.4. Average Lift pre Shedding Average Lift post Shedding Min/Max of Limit Cycle Lift Coefficient, C L Angle of Attack, (deg) Need model that captures lift due to moving airfoil! Wednesday, March 8,

6 Lift vs. Angle of Attack.6.4. Average Lift pre Shedding Average Lift post Shedding Min/Max of Limit Cycle Sinusoidal (f=.,a=3) Lift Coefficient, C L Angle of Attack, (deg) Need model that captures lift due to moving airfoil! Wednesday, March 8,

7 Lift vs. Angle of Attack.6.4. Average Lift pre Shedding Average Lift post Shedding Min/Max of Limit Cycle Sinusoidal (f=.,a=3) Canonical (a=,a=) Lift Coefficient, C L Angle of Attack, (deg) Need model that captures lift due to moving airfoil! Wednesday, March 8,

8 Added-Mass D Model Problem Transient Periodic Vortex Shedding Lift Drag Re = 3 α = 3 Wednesday, March 8,

9 Added-Mass D Model Problem Transient Periodic Vortex Shedding Lift Drag Re = 3 α = 3 Wednesday, March 8,

10 Reduced Order Indicial Response C L (t) =C S L(t)α() + t!"#$%&$'(#)*+,+#))()+-#$$ C L α C S L(t τ) α(τ)dτ fast dynamics d dt x A r x α = α + α α Reduced-order model B r α input C L = x C r C Lα C L α α + C L α α α α C L α s + C L quasi-steady and added-mass C Lα s G(s) Model Summary Linearized about α = Based on experiment, simulation or theory.#$'+)*/#-%$ Recovers stability derivatives C Lα,C L α,c L α associated with quasi-steady and added-mass Brunton and Rowley, in preparation. ODE model ideal for control design Wednesday, March 8,

11 Lift vs. Angle of Attack.6.4. Average Lift pre Shedding Average Lift post Shedding Min/Max of Limit Cycle Lift Coefficient, C L !"#$%&$'(#)*+,+#))()+-#$$ C L α. C L α s α + C L Models linearized at α = Angle of Attack, (deg) C Lα s G(s).#$'+)*/#-%$ Wednesday, March 8,

12 Bode Plot - Pitch (QC) Frequency response input is α ( α is angle of attack) 6 4 Quarter-Chord Pitching output is lift coefficient C L Pitching at quarter chord Magnitude (db) Reduced order model with ERA r=3 accurately reproduces Indicial Response 4 Indicial Response and ROM agree better with DNS than Theodorsen s model. Asymptotes are correct for Indicial Response because it is based on experiment Model for pitch/plunge dynamics [ERA, r=3 (MIMO)] works as well, for the same order model Phase (deg) 5 5 Frequency (rad U/c) Indicial Response ROM, r=3 Wagner/Theodorsen DNS ROM, r=3 (MIMO) Brunton and Rowley, in preparation. Wednesday, March 8,

13 Lift vs. Angle of Attack.6.4. Average Lift pre Shedding Average Lift post Shedding Min/Max of Limit Cycle Lift Coefficient, C L !"#$%&$'(#)*+,+#))()+-#$$ C L α. C L α s α + C L Models linearized at α = Angle of Attack, (deg) C Lα s G(s).#$'+)*/#-%$ Wednesday, March 8,

14 Magnitude (db) 6 4 Bode Plot of Model (-) vs Data (x) Frequency Response Linearized at various! ERA,!= DNS,!= ERA,!= DNS,!= ERA,!= DNS,!= 4 5 Phase 5 Brunton and Rowley, AIAA ASM Wednesday, March 8, Frequency Direct numerical simulation confirms that local linearized models are accurate for small amplitude sinusoidal maneuvers

15 (Indicial) Step Response u A u u T Time u k u(t) y(t) y k PLANT Previously, models are based on aerodynamic step response Idea: Have pilot fly aircraft around for 5- minutes, back out the Markov parameters, and construct ERA model. Wednesday, March 8,

16 Random Input Maneuver α α α C L (t) Idea: Have pilot fly aircraft around for 5- minutes, back out the Markov parameters, and construct ERA model. Wednesday, March 8,

17 Wind Tunnel Setup Test section NACA 6 Airfoil (4.6 cm chord) Push rods and sting Servo tubes Wednesday, March 8,

18 Experimental Information Andrew Fejer Unsteady Flow Wind Tunnel (.6m x.6m x 3.5m test section) NACA 6 Airfoil Chord Length:.46 m Free Stream Velocity: 4. m/s. Convection time =.6 seconds Reynolds Number: 65, Pitch point x/c =. (% chord) Velocity measurement: Pitot tube, Validyne DP-3 pressure transducer Force measurement: ATI Nano5 force transducer Pushrod position measurement: linear potentiometer Pushrod actuation: Copley servo tubes Acknowledgments: Professor David Williams Seth Buntain and Vien Quatch Wednesday, March 8,

19 Phase Averaged Data Convective Time Step Up, Step Down, 5 degrees Phase averaged over cycles Wednesday, March 8, Convective Time

20 Wing Maneuver Commanded Angle Measured Angle Angle (degrees) Convective Times (s=tu/c) Wednesday, March 8,

21 What are we modeling? Angle (degrees) Angle (degrees) Measured Force ROM, r=3 3 Measured Force ROM, r= Model using command acceleration Model using measured acceleration Wednesday, March 8,

22 What are we modeling? Angle (degrees) Angle (degrees) Measured Force ROM, r=3 3 Measured Force ROM, r= Model using command acceleration Model using measured acceleration our model α pos α cmnd α pot C Simulink Actuator Aerodynamics L Wednesday, March 8,

23 Four Test Maneuvers Angle (degrees) Angle (degrees) Maneuver Maneuver Measured Force ROM, r=3 3 Measured Force ROM, r= Angle (degrees) Maneuver 3 Maneuver 4 Angle (degrees) Measured Force ROM, r=3 3 Measured Force ROM, r= Wednesday, March 8,

24 Bode Plots for AoA= 6 Model using measured acceleration 4 Magnitude (db) Phase (degrees) 5 5 maneuver maneuver maneuver 3 maneuver 4 3 Frequency (rad/s c/u) Idea: lets combine all maneuvers into one large system ID maneuver! Wednesday, March 8,

25 Bode Plot for AoA= Angle (degrees) Measured Force ROM, r=3 Magnitude (db) Phase (deg) Bode Diagram Wednesday, March 8, Resonant peak Added-mass bump

26 C Lα C L α{ { Model using ALL data Angle (degrees) Measured Force ROM, r= Theory Experimental H i from OKID H i αc Lα H i αc Lα C L α. C L α Impulse response in α Markov parameter.5..5 Wednesday, March 8, 5 5

27 3Hz Mechanical Oscillation. Step Up, Step Down, 5 degrees Convective Time Wednesday, March 8,

28 Models agree with data Angle (degrees) Angle (degrees) Experiment Model Model Model 3 Model 4 3 Experiment Model Model Model 3 Model Angle (degrees) Angle (degrees) Experiment 3 Model Model Model 3 Model 4 3 Experiment 4 Model Model Model 3 Model Wednesday, March 8,

29 Model for Plunging Magnitude (db) Phase (deg) Bode Diagram Frequency (rad/sec) Vertical Position (inches) Measured Force ROM, r= Wednesday, March 8,

30 Conclusions Reduced order model based on indicial response at non-zero angle of attack - Based on eigensystem realization algorithm (ERA) - Models appear to capture dynamics up to Hopf bifurcation Observer/Kalman Filter Identification with more realistic input/output data - Efficient computation of reduced-order models - Ideal for simulation or experimental data Confirmation with experimental data - Tested modeling procedure in Dave Williams wind tunnel experiment - Flexible procedure works with various geometry, Reynolds number Wagner, 95. Theodorsen, 935. Leishman, 6. OL, Altman, Eldredge, Garmann, and Lian, Wednesday, March 8, Brunton and Rowley, AIAA ASM 9- Juang and Pappa, 985. Ma, Ahuja, Rowley,. Juang, Phan, Horta, Longman, 99.