Signature redacted Signature of Author:... Department of Mechanical Engineering

Review of Flapping Foil Actuation and Testing of Impulsive Motions for Large, Transient Lift and Thrust Profiles by Miranda Kotidis Submitted to the Department of Mechanical Engineering on May 13, 217 in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science in Mechanical Engineering ABSTRACT Flapping foils were tested to produce large, transient forces in still water. These swift, onetime strokes take advantage of added mass/inertial effects and large, stably attached vortices to avoid delay due to the realization of a jet wake for propulsion [1]. Previous work has produced trajectories, characterized by heave and pitch, for which the lift and thrust profiles were confirmed. Two trajectories were reproductions from previous studies, and the lift and thrust force profiles match those produced before. An additional trajectory was tested, which produced a much different profile. All three trajectories included a smooth sweeping motion, but the third trajectory included a subsequent sharp change in pitch. This sharp change in pitch, or pure rotation, produced sharp force peaks and oscillations in thrust, in addition to force peaks from the sweeping motion which resembled the other two trajectories' profiles. Further work includes confirming the lift and thrust coefficients and exploring additional trajectories or optimizing current trajectories for producing large, transient forces for underwater vehicle propulsion and control. Thesis Supervisor: Michael Triantafyllou Tile: Professor of Mechanical and Ocean Engineering 2

Acknowledgments I would like to thank Professor Michael Triantafyllou for his guidance on this project. I would also like to acknowledge Jacob Izraelevitz and Fiona Grant for their help and support with the experiments and analysis. Finally, I would like to thank my family and friends for supporting me through every step of my undergraduate experience, and throughout this project. 3

Table of Contents Abstract 2 Acknowledgements 3 Table of Contents 4 List of Figures 5 1. Introduction 6 2. Background 6 2.1 Method 1 6 2.2 Method 2 7 3. Experimental Setup 8 3.1 Apparatus 8 3.2 Kinematics 9 3.2.1 Trajectory 1 9 3.2.2 Trajectory 2 11 3.2.3 Trajectory 3 12 4. Results and Discussion 14 4.1 Trajectory 1 14 4.2 Trajectory 2 14 4.3 Trajectory 3 15 5. Conclusion and Future Work 16 6. References 17 4

List of Figures Figure 1: Trajectory of Method 1 from Triantafyllou et at. [1] 7 Figure 2: Lift and thrust results for Method 1. 7 Figure 3: Trajectory of Method 2 from Triantafyllou et al. [1] 8 Figure 4: Lift and Thrust Results for Method 2. 8 Figure 5: Experimental Setup. 9 Figure 6: Heave and Pitch Motions for Trajectory 1. 1 Figure 7: Top-view Visualization of Trajectory 1. 1 Figure 8: Heave and Pitch Motions for Trajectory 2. 11 Figure 9: Top-view Visualization of Trajectory 2. 12 Figure 1: Heave and Pitch Motions for Trajectory 3. 13 Figure 11: Top-view Visualization of Trajectory 3. 13 Figure 12: Lift and Thrust Profiles for Trajectory 1. 14 Figure 13: Lift and Thrust Profiles for Trajectory 2. 15 Figure 14: Lift and Thrust Profiles for Trajectory 3. 16 5

1. Introduction Underwater vehicles are emerging as incredibly effective platforms for ocean monitoring and exploration, underwater structure installation and maintenance, and accident/hazard mitigation [2]. Many of these tasks require the vehicle to produce large forces to move through unsteady currents or react to disturbances. Currently, many of these vehicles rely primarily on propellers or similar thrusters to produce forces to move through the water, but this form of propulsion comes at a price. In order for the vehicle to produce a useful force, a jet wake must materialize before the vehicle actually moves [2]. Therefore, there is a time delay between the vehicle turning on its thrusters and translating through the water [2]. In order to minimize or even eliminate this delay, new types of bio-mimetic actuation are being developed. Nature has provided a large amount of inspiration, as underwater animals use their fins to move around and maneuver very accurately and quickly. In particular, many fish hover in place, and with one flap of their fins, can escape a predator or hunt prey. The project focused mainly on this type of movement, where a single flap can create a large amount of lift and/or thrust [1]. This movement is intended to be implemented as a starting or hovering maneuver for a biomimetic underwater vehicle [2]. These flapping foil actuators take advantage of inertial/addedmass forces and forces that arise from large, stably attached vortices to create large, transient forces in still water [2]. 2. Background In 23, Triantafyllou et al produced results for this type of propulsion [1]. They tested three trajectories, referred to as methods in the paper. Two methods were known as "nonreturning" and one known as "returning". All the methods were described by the heave and pitch of the stroke, h(t) and e(t) respectively, and the speed of the stroke was determined by the maximum heave velocity, hmax. The non-returning methods were reproduced experimentally in this project, and confirmed the findings of lift and thrust force. 2.1 Method 1 This method began with the foil in the = position, and swept to =+/2 at the end of the stroke, as shown in Figure 1. The lift and thrust forces produced by this method at hmax =.5 m/s are shown in Figure 2. These results were compared to the experimental results, which are discussed in Section 4. 6

Initial Position 1 ------------ - -------- -------- ---------------- - -------------------------------------- ---------- ------------------ Final Position (No return stroke) Figure 1: Trajectory of Method I from Triantafyllou et al. [I]. The foil began at the O= position and swept to O= +7/2, as it headed downward. o= 1 - -.- Thrust Z 5 - max=.5 m/--- Lift -5.5.6.7.8.9 1 1.1 1.2 1.3 1.4 1.5 Time [s] Figure 2: Lift and thrust force results for Method I from Triantafyllou et al. [I]. The force profile was characterized by the two initial peaks in lift, as the thrust remained mostly around N. 2.2 Method 2 This method began with the foil at = -a/2, and swept to = +n/2, as shown in Figure 3 [1]. Similar to Method 1, the results at /mx=.5 m/s were of interest. Figure 4 shows the lift and thrust forces produced by Method 2. Again, these results were confirmed in Section 4. 7

Initial Position 1 ----------------------------------- ----------- ------------------ SS --------------------------- ---------- ------------------------------------ ------------------------------ Final Position (No return stroke) Figure 3: Trajectory of Method 2 from Triantafyllou et al. [1]. The foil began at the = - 7t/2 position and swept to = +n/2, as it headed downward. 15 ---- Lift 1 ------------------------------------------------------------ hmax=.5 m/s 5 -- ------------------ - -- - - - - - - - - - - -- - - - - - - - - - - - - U. -------- '-- -5.5 1 II 1.5 2 2.5 Time [sec] Figure 4: Lift and thrust force results for Method 2 from Triantafyllou et al. [1]. This profile was characterized by a peak in thrust followed almost immediately by a peak in lift and a smaller peak in thrust 3. Experimental Setup 3.1 Apparatus All experiments were conducted in the MIT Testing Tank. The carriage mounted to the tank is equipped with an ATI Gamma forcemeter, which recorded lift and drag forces. The carriage is equipped with a NACA 12 foil, with span =.36 m and chord =.55 m, and actuators to produce planar motions and rotation. The experimental setup is shown in Figure 5. 8

Figure 5: Experimental setup in the MIT Testing Tank. Shown is the carriage, tank, and NACA 12 foil used for testing. The carriage had actuators mounted to produce linear motions and rotation. 3.2 Kinematics Three distinct trajectories were tested. Trajectories 1 and 2 were reproductions of methods from Triantafyllou et al. [1], discussed briefly in Section 2, and Trajectory 3 was a new trajectory tested in this project. Each trajectory was characterized by heave and pitch motions, h(t) and (t) respectively. As in Triantafyllou et al, the speed of the trajectory was characterized by hmax =.5 m/s [1]. All the trajectories involved a half-cycle motion, starting at one extreme heave position, and ending at the opposite extreme heave position. After the stroke, the foil stayed at its final position to allow the lift and thrust forces to remain undisturbed. For all trajectories, the following variables remained constant: 3.2.1 Trajectory 1 ho= chord length =.55m = max ho Trajectory 1 was a replication of Method 1 in Triantafyllou et al. [1], described in Section 2.1, and as such, it was expected to produce very similar lift and thrust profiles. It began with the foil at the = position, and swept to = +n/2, as it headed downward. Equations 1 and 2 show the heave, h(t), and pitch, (t), for Trajectory 1. Figure 6 shows h(t) and (t) vs. time of the stroke, while Figure 7 shows a visualization of the stroke, as a view from above the Testing Tank (see Section 3.1 for experimental setup). h(t) = ho cos(ot) (1) 9

6(t) = Cos (O.5Wt + ((2) 2.1 Trajectory I Heave Motion - Heave Position E a) -.1.5.5 1 1.5 2 Trajectory 1 Pitch Motion - Pitch angle (normalized by pi) I 2.5 -.5.5 1 1.5 2 Figure 6: Trajectory 1 heave and pitch motions. The pitch angle started at = and swept to = n/2 as the foil headed downward. After the stroke, the foil remained in its final position to ensure that the lift and thrust forces were undisturbed. 2.5.5 Trajectory 1: Motion from Observer E - CA o -.5-4 -.1 -.1 -.5.5 X Displacement (m) Figure 7: Trajectory I visualization, from above the Testing Tank. This trajectory mimicked Method 1 in Triantafyllou et al. [1], and was expected to produce similar lift and thrust profile. 1

3.2.2 Trajectory 2 Like Trajectory 1, Trajectory 2 was a replication of Method 2 in Triantafyllou et al [1]; it began at = -n/2 and sweeps to = +a/2. The lift and thrust results from this trajectory were expected to have a similar profile to those from Triantafyllou et al. [1], described in Section 2.2. Equations 3 and 4 describe the heave, h(t), and pitch, (t), that characterized Trajectory 2. Figure 8 shows h(t) and (t) vs. time of the stroke, and Figure 9 shows a visualization of the trajectory as viewed from the top of the Testing Tank. h(t) = ho cos(wt) (3) 6(t) = cos(o.5wt + wt) (4) 2.1 E-Heave > a) r Trajectory 2 Heave Motion Position -.1.5 1 1.5 2 2.5 a).5 Trajectory 2 Pitch Motion 1 - - Pitch angle (normalized b i -.5.5 1 1.5 2 2.5 Figure 8: Trajectory 2 heave and pitch motions. The pitch angle started at = -n/2 and swept to = +7r/2 as the foil headed downward. After the stroke, the foil remained in its final position to ensure that the lift and thrust forces were undisturbed. 11

.1 Trajectory 2: Motion from Observer.5 F a) E (U 5 -.5 F C, -.1 I I I E -.15 -.1 -.5.5.1 X Displacement (m) Figure 9: Trajectory 2 visualization, from above the Testing Tank. mimicked Method 1 in Triantafyllou et al. and was expected to produce thrust profile. This trajectory similar lift and 3.2.3 Trajectory 3 Trajectory 3 was a novel trajectory, where the foil began at = -n/4, and swept to = +7/4 while heaving appropriately, then quickly rotated to = +n/2. It differed from the other two in that it involved a sharp movement, while the other two were smooth, which may have had an effect on the lift and thrust forces produced. Equations 5 and 6 show the sweeping motion of the stroke, but does not describe the sharp rotation. This sharp rotation was a linear change in from +n/4 to +n/2 in.2s. Figure 1 shows the h(t) and (t) for the entire stroke, including the sharp change in pitch, and Figure 11 shows a visualization of the stroke. h(t) = ho cos(wt) (5) (t) =- cos(2wt) 4 (6) 12

E.6.4.2 Trajectory 3 Heave Motion - Heave Position (D.5 1 1.5 2 2. 5 Trajectory 3 Pitch Motion.5 -Pitch angle (normalized by p1) -.5.5 1 1.5 2 2. 5 Figure 1: Trajectory 3 heave and pitch motions. The pitch angle started at = -n/4 and swept to = +n/4 as the foil headed downward. After the sweep, the pitch angle moved very quickly to a/2, as shown in the bottom plot, around t=.5 s. Similar to Trajectories 1 and 2, after the stroke, the foil remained in its final position to ensure that the lift and thrust forces were undisturbed. Trajectory 3: Motion from Observer E CD, CD) 5.8-.6-.4-.2 O F -.2 4 C) -.4 -.1 -.5.5 X Displacement (m) Figure 11: Trajectory 3 visualization, from above the Testing Tank. This trajectory was much different than Trajectories 1 and 2, as it was not a replication of previous work and that it had a sharp, pure rotation as part of the stroke. 13

4. Results and Discussion All three trajectories were tested in the MIT Testing Tank, and the resulting lift and drag forces were recorded. Trajectories 1 and 2 were compared to the results from Triantafyllou et al. [1] and produced a basis for analyzing Trajectory 3. 4.1 Trajectory 1 As stated above, Trajectory 1 was a replication of Method 1 in Triantafyllou et al. [1], and was expected to produce similar lift and thrust force profiles. Figure 12 shows the results for Trajectory 1. Comparing Figure 12 to Figure 2 in Section 2.1, the force profiles were incredibly similar, with two peaks in lift immediately after the stroke begins, and then decaying away quickly. The thrust values remained mostly around zero, with a negative peak appearing concurrently with the lift peak. Trajectory 1: Lift and Thrust Forces - Thrust 3 - - -Lift U- 2 a) 2-1 -1-2.5 1 1.5 2 2.5 Figure 12: Lift and thrust results for Trajectory 1. The force profile was very similar to the profile found in Triantafyllou et al. [1], as shown in Figure 2 in Section 3.1. The lift profile was characterized by two peaks immediately after the stroke began, followed by a sharp decay to zero force. The thrust profile remained mostly around zero, with a negative peak occurring at approximately the same time as the lift peaks. 4.2 Trajectory 2 Similar to Trajectory 1, Trajectory 2 was a replication of Method 2 in Triantafyllou et al. [1], so the force profiles were expected to be very similar. Figure 13 shows the lift and thrust profiles for Trajectory 2. Comparing Figure 13 to Figure 3, the force profiles were very similar, with one large peak in lift and two smaller peaks in thrust, and the lift peak occurred just after the first peak in thrust. After the stroke, the lift force decayed to zero, while the thrust force decayed to approximately zero force. 14

5 4I Trajectory 2: Lift and Thrust Forces - Thrust --- Lift 3 I.5 1 1.5 2 2.5 Figure 13: Lift and thrust profiles for Trajectory 2. This profile was very similar to the results of Method 2 in Triantafyllou et al. [1], as shown in Figure 3 in Section 3.1. Both profiles featured a large peak in lift directly after a smaller peak in thrust. The lift force then experienced a slight negative peak, then decayed to zero, while the thrust included a second peak in thrust, followed by a decay to approximately zero force. 4.3 Trajectory 3 Replicating Trajectories 1 and 2 from Triantafyllou et al. [1] allowed for a more thorough analysis of Trajectory 3. The force profile for Trajectory 3 also differed from the other two trajectories in that it involved a sharp motion, which produced some sharp peaks in lift and thrust, as shown in Figure 14. Overall, the lift profile included an initial peak, similar to Trajectories 1 and 2, but then produced two very sharp, opposing peaks as the foil rotated in place from = 7r/4 to =n/2. As for the thrust profile, two small peaks occurred in the beginning of the stroke, similar to Trajectory 2, but as the foil sharply rotates, a large peak in thrust was produced, then the thrust oscillated and decayed to approximately zero. 15

Trajectory 3: Lift and Thrust Forces - Thrust - - -Lift 3-2 I il K 2 i U- -2-3 - II -4.5 1 1.5 2 2.5 Figure 14: Lift and thrust profiles for Trajectory 3. As this was a new trajectory, there was no reference point for the profiles. The lift profile began with a peak similar to Trajectory 2, but the sharp rotation in this trajectory produced steep, opposing peaks in lift before decaying to zero force. The thrust profile began with slightly delayed peaks, followed by a large, steep peak as the foil rotates in place. The thrust then decayed to approximately zero as time reaches 2.5s. 5. Conclusion and Future Work Flapping foils were tested to produce large, transient forces using swift motions of the foil in still water. Three trajectories were tested in the MIT Testing Tank, and their lift and thrust profiles were produced. All three trajectories were characterized by their heave, h(t), and their pitch, (t). Two trajectories, Trajectories 1 and 2, were reproduced from Triantafyllou et al. [1], and the third, Trajectory 3, was a new trajectory. Trajectories 1 and 2 were very smooth, while Trajectory 3 included a sharp pure rotation from = +n/4 to = +7t/2. The lift and thrust profiles for Trajectories 1 and 2 matched the corresponding methods in Triantafyllou et al. [1], and Trajectory 3 produced its own lift and thrust profiles. Due to the sharp pure rotation in Trajectory 3, the lift and thrust forces had very sharp peaks in the profiles. These peaks may make it difficult to successfully implement as a starting motion for an underwater vehicle, as these peaks could be hard to control. However, the other two trajectories yielded very reproducible lift and thrust profiles, and could be used as starting motions for an underwater vehicle. Moving forward, optimizing these trajectories for producing cleaner, larger forces, testing additional new trajectories, and confirming the lift and thrust coefficients from Triantafyllou et al. [1] would further justify this type of actuation that takes advantage of added mass forces and large, stably attached vortices to produce large and transient lift and thrust forces [2]. Eventually, implementing flapping foil actuators onto autonomous underwater vehicles could vastly increase their efficiency and maneuverability, and therefore their versatility. 16

6. References [1] Triantafyllou, M.S., Hover, F.S., and Licht, S., 23, "The Mechanics of Force Production in Flapping Foils Under Steady-State and Transient Motion Conditions," Massachusetts Institute of Technology Department of Ocean Engineering Testing Tank Facility Report. pp 27-36. [2] Triantafyllou, M.S., 216, "SMART-USE Technical Proposal". pp. 5-8. 17