Nonlinear and Time-Dependent Aerodynamics: Implications for Testing and Flight Mechanics Analysis Jerry E. Jenkins Voluntary Emeritus Corps AFRL Wright-Patterson AFB, OH

The Delta Wing Model

Free-to-Roll Tests Instantaneous motion state insufficient Bypasses stable trim points

Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing AIAA Free-to-Roll tests perplexing results –Aerodynamic responses at moderate angles of attack Not determined by instantaneous motion state Highly dependent on motion history

Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing AIAA Free-to-Roll tests perplexing results –Aerodynamic responses at moderate angles of attack Often not determined by instantaneous motion state Highly dependent on motion history Viscous effects superimposed on potential flow –L. E. Vortex system structure –Vortex breakdown dynamics

Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing AIAA Flow Structure The steady-state flow-field can become unstable –At some flight conditions (Critical States) –Bifurcations in static force and moment characteristics

Critical States

Flow Structure & Bifurcations Left Wing

Flow Structure & Bifurcations Right Wing

Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing AIAA Flow Structure The steady-state flow-field can become unstable –At some flight conditions (Critical States) –Bifurcations in static force and moment characteristics Must transition to a new stable state when perturbed –Can require a considerable amount of time –Static tests give us no clue as to how long

Nonlinear & Unsteady Aero Characteristics: 65° Delta Wing AIAA Flow Dynamics Flow processes acting on at least three time scales –Transitions between equilibrium states –Potential flow phenomena –Vortex breakdown movement in response to the motion

Ramp Across a Critical State 65 o Delta Wing

Attached and Vortical Flow Contributions

Can isolate CS transients including motion history

Harmonic Motion With and Without Critical State Encounters Rolling Moment Pitching Moment k = 0.02 & 0.14

Harmonic Motion With and Without Critical State Encounters Rolling Moment Pitching Moment k = 0.02 & 0.14

Static Nonlinearities - AIAA Region Region 5

Multiple Time Scales in Linear Region AIAA Slow responses cannot keep up with rapid motions

Broadband Input Allwine, et. al., “Nonlinear Modeling of Unsteady Aerodynamics at High Angle of Attack,” AIAA

Multiple Time Scales (F-16XL) AIAA Variation of in-phase & out-of-phase components Lift-Curve slope Lift due to pitch rate Reduced freq.

Schroeder sweep Murphy, P.C., and Klein, V., “Estimation of Aircraft Unsteady Aerodynamic Parameters from Dynamic Wind Tunnel Testing,” AIAA

Langley Fighter Model

Roll-Damping “Derivative” AIAA

Nonlinear & Unsteady Aero Characteristics: Summary Free-to-Roll tests difficult to explain results –Aerodynamic responses at moderate angles of attack Often not determined by instantaneous motion state Highly dependent on motion history Traced to leading edge vortex system dynamics –Vortex system structure –Vortex breakdown phenomenon Response characteristics not unique to delta wings –Static discontinuities, i.e. flow-field instabilities –Multiple time scales

Unsteady and Nonlinear Aerodynamics: A Flight Mechanics Viewpoint Unsteady Aero prescribed motion Flight Mechanics motion is unknown a priori –Stability and Control –Flight Control System Design

Unsteady and Nonlinear Aerodynamics: A Flight Mechanics Viewpoint Unsteady Aero prescribed motion Flight Mechanics motion is unknown a priori –Stability and Control –Flight Control System Design Small-amplitude dynamic data inadequate –Stability “derivatives” –Exhibit frequency and amplitude dependence –Powerless to describe the aerodynamics

Unsteady and Nonlinear Aerodynamics: A Flight Mechanics Viewpoint Unsteady Aero prescribed motion Flight Mechanics motion is unknown a priori –Stability and Control –Flight Control System Design Small-amplitude dynamic data inadequate –Stability “derivatives” –Exhibit frequency and amplitude dependence –Powerless to describe the aerodynamics Need math models for aerodynamics –Applicable to arbitrary motions –Functions of the translational and rotational DOF

Nonlinear & Unsteady Aero Characteristics: AIAA AIAA AIAA Results were for single DOF motions in wind tunnel Understanding requires that we –acknowledge the existence of multiple time scales –Consider the individual effects of translation and rotation –Include lags present in both responses

Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached? Assumptions: –Square-Cube Law holds

Vehicle Inertia Variation with Mass

Vehicle Weight Variation with Wing Area

Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached? Assumptions: –Square-Cube Law holds –Want to fly in similar C L range Conclusions:

Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached? Assumptions: –Square-Cube Law holds –Want to fly in similar C L range –Hold non-dimensional derivatives constant i.e. ignore R e effects Conclusions:

Stability Derivatives – Reduced Frequency Range What happens as MAV scales are approached? Consequences: –Magnitude of atmospheric disturbances do not scale Relative angular disturbances, –Responses to disturbances up to not attenuated Control system rates must increase –Sensor sampling rates –Servo response times –Aerodynamic effects Convective time lags unaltered Separated, vortex dominated flows ( low )

Static Test Recommendations Closely spaced static data –Critical state detection Examine all components of the force and moment –Critical States are flow field events Make sweeps should in both directions –Hysteresis detection –Another indication of critical states

Dynamic Test Recommendations Structure dynamic tests based on static test results

Dynamic Test Recommendations Structure dynamic tests based on static test results Filtering (except anti-aliasing) should not be used –Ensemble averaging recommended

Dynamic Test Recommendations Structure dynamic tests based on static test results Filtering (except anti-aliasing) should not be used –Ensemble averaging recommended Record the complete response –potential nonlinear effects -- Linearize off line

Dynamic Test Recommendations Structure dynamic tests based on static test results Filtering (except anti-aliasing) should not be used –Ensemble averaging recommended Record the complete response –potential nonlinear effects -- Linearize off line Cover wide range reduced frequencies –Try to saturate the viscous effects –Extract both "static" and dynamic stability derivatives –Frequency dependence multiple time scales

Linear Aero Model from Broadband Data AIAA Linear system ID works quite well

Dynamic Test Recommendations Structure dynamic tests based on static test results Filtering (except anti-aliasing) should not be used –Ensemble averaging recommended Record the complete response –potential nonlinear effects -- Linearize off line Cover wide range reduced frequencies –Try to saturate the viscous effects –Extract both "static" and dynamic stability derivatives –Frequency dependence multiple time scales Ramp and hold motions invaluable –Isolate critical state transients –Provide quantitative measures for response times –Examine history effects. –Consider other types of "motion and hold" experiments

Ramp-Between-Harmonics

Nonlinear Model Constructed from SSM’s AIAA