The experimental setup consists of a rigid semi-wing with a distributed propulsion system affixed to a flexible mount that provides pitch and plunge degrees of freedom. The rigid semi-wing has an aspect ratio of 5, and is a NACA 0018 airfoil section with four electric motors on the leading edge, each pitched at an angle relative to the chordline. Pitching the motors relative to the chord line provides a component of thrust normal to the chord line which can be used in a flutter suppression controller to actively influence motion in pitch and plunge directions. The flexible mount a scaled down version of the Pitch And Plunge Apparatus (PAPA) mount created by NASA and resized to accommodate the Oregon State University wind tunnel.The experimental setup consists of a rigid semi-wing with a distributed propulsion system affixed to a flexible mount that provides pitch and plunge degrees of freedom. The rigid semi-wing has an aspect ratio of 5, and is a NACA 0018 airfoil section with four electric motors on the leading edge, each pitched at an angle relative to the chordline. Pitching the motors relative to the chord line provides a component of thrust normal to the chord line which can be used in a flutter suppression controller to actively influence motion in pitch and plunge directions. The flexible mount a scaled down version of the Pitch And Plunge Apparatus (PAPA) mount created by NASA and resized to accommodate the Oregon State University wind tunnel.

 

The flexible mount is composed of 5 rods with fixed-fixed end conditions to provide linear stiffness in pitch (rotation about z-axis) and plunge (translation along y-axis). Stiffness predictions for the mount are derived with beam theory and superposition. The steel mount provides very little structural damping, a desirable feature for studying flutter suppression. The result of the mount can be thought of as a single beam with fixed-fixed end conditions in which the deflection slope of the beam is zero at both ends.

 

Equation of motion for the system is derived by combining rigid body dynamics of a wing with pitch and plunge degrees of freedom with forces from unsteady aerodynamics and contributions from the distributed propulsion system. Rigid body dynamics of the wing are derived through LaGrangian mechanics. Theodorsens theory of unsteady aerodynamics is used and the entire equation of motion is linearized about the equilibrium with a first order Taylor series expansion of sinΘ ≅ Θ and cosΘ ≅ 1. Theodorsens function, C(k), is set equal to one for simplicity in the numerical predictions.

 

Numerical predictions of the system showed flutter to occur at a flow speed of 5 m/s. A closed-loop state-space controller was designed with LQR gains and predictions showed the controller to be able to successfully suppress flutter at flow speed of 5 m/s.

 

Ground vibration testing was performed to compare numerical predictions to experimental results for wind-off structural dynamic properties of the system. Measurements were gathered using a visual image correlation system (VIC) to track 3D displacements of a target with a stereoscopic camera system. Measured stiffness of the mount in both pitch and plunge were lower than predicted, and measured natural frequency in pitch and plunge were lower than predicted.

 

Natural frequency predictions are made using measured mount stiffness, not predicted stiffness. Differences between measured and predicted natural frequency for the system are attributed to errors in mass and moment of inertia predictions from the CAD model. The CAD model does not account for difficult to model components such as balas ribs, wires, and body filler (bondo) used to repair 3D printed nacelles. Dynamic thrust testing of the motors showed good agreement between predicted and measured thrust for a throttle oscillating frequency of 4 Hz between 25% throttle and 95% throttle. Predictions of thrust are made based on a zero rise time actuator dynamic model where thrust is approximated as a linear function of throttle.

 

Forced vibration experiments were run to evaluate authority of the distributed propulsion system. Throttle of the distributed propulsion system was oscillated at a frequency near each measured natural frequency to identify maximum possible displacements in pitch and plunge. Throttle of the distributed propulsion system was oscillated at 3.1 Hz for maximum plunge displacement and 7.2 Hz for maximum pitch displacement.

 

A maximum displacement of about 10 mm was observed for forced vibration experiments of 3.1 Hz and a maximum displacement of 2.2° for forced vibration at of 7.2 Hz. Results show the distributed propulsion system is capable of generating large deflections in the flexible mount and is capable of providing adequate authority. Wind tunnel testing of the rigid wing was done in two phases: static and dynamic wind tunnel testing. Static wind tunnel testing was done to measure static aerodynamic coefficients of the rigid semi-wing with a JR3 load cell. For all wind tunnel testing, a splitter plate and fairing was used to shield the flexible mount and load cell from generating significant aerodynamic forces. Test setup is similar to that used by NASA with the PAPA mount.

 

Aerodynamic coefficients were corrected for wind tunnel effects and match published results of a NACA 0018 wing at similar Reynolds numbers. Results from dynamic wind tunnel testing in which the flexible mount was set to 0° angle of attack and an initial condition in pitch and plunge did not match numerical predictions shown in Figure 4. Testing up to the maximum flow velocity of 18 m/s, flutter was never observed. This discrepancy between numerical predictions and experimental results is attributed to setting Theodorsens function, C(k) equal to one. The next dynamic wind tunnel tests involved changing the angle of attack of the flexible mount and observing the systems response with no initial condition. At a flow speed of 14.5 m/s and angle of attack of 15° a steady motion in pitch and plunge was observed, but no divergent motion associated with flutter was present. At a flow speed of 13.5 m/s and angle of attack of 13°, a steady motion in just pitch was observed.

 

Future work of the project will focus on reducing discrepancy between numerical predictions and experimental results for dynamic wind tunnel testing by increasing the chord length and reducing the aspect ratio to support setting C(k) equal to unity.