Propulsive Performance of Flexible-Chord Foils

Transcription

1 1w j wm : Propulsive Performance of Flexible-Chord Foils by Mercedes E. Castelo Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science At the Massachusetts Institute of Technology June Massachusetts Institute of Technology. All rights reserved. Signature of Author..... Depqytment of Mechanical Engineering Certified by... U/^-,, Michael S. Triantafyllou Professor of Ocean Engineering Thesis Supervisor Accepted by... Ernestj( Cravalho Chairman of the Undergraduate Thesis Committee 1 AW MASSA CHISET-S INSTITUTE OF TECHNOLOGY JUN LIBRARIES

2 P-11- MOM..... Propulsive Performance of Flexible-Chord Foils by Mercedes E. Castelo Submitted to the Department of Mechanical Engineering on May 1, 22 in partial fulfillment of the requirements for the degree of Bachelor of Science in Mechanical Engineering. Abstract This thesis details the experiments conducted with two flexible-chord foils to compare their propulsive performance when moving in heave and pitch with that of a stiff foil. The two flexible foils were designed and fabricated with an aluminum base and urethane molded around this base to form the external foil shape. The most flexible of the two foils performed the best. In certain experiments it displayed up to 2% higher efficiency than the stiff foil and displayed about the same values of thrust. Flexible foils should be investigated for potentially even better efficiency results. Thesis Supervisor: Michael Triantafyllou Title: Professor of Ocean Engineering 2

3 , ft-1 Table of Contents 1. Introduction Previous Flexible Foil W ork Related Stiff Foil W ork M aterials, Apparatus, and Procedures Foil Design M olding Procedure Experim ental Apparatus Foil M otion Experim ental Procedure Results Discussion Conclusions and Recom m endations Bibliography

4 List of Figures 1 Efficiencies for a flexible foil, a stiff foil and a screw propeller Aluminum Plate-Parametric View Aluminum Plate-Close-up View Cross-sectional View of Flexible Foil Shore A 6 and 8 Elasticity Comparison Front V iew of the C arriage A ngle of A ttack Stiff Foil Thrust and Efficiency Shore 8 A Foil Thrust and Efficiency Shore 6A Foil Thrust and Efficiency Position and Force Data for the Shore A 6 and Stiff Foil Power Data for the Shore A 6 and Stiff Foil Efficiency Comparison for the three foils at a St of Efficiency Comparison for the three foils at a St of Efficiency Comparison for the three foils at a St of Efficiency Comparison for the three foils at a St of

5 I 1. Introduction In the development of ship propulsion, fish fins have been considered as alternate means for efficient locomotion. Through the evolutionary process, fish fins have been evolving and becoming better through time. Many characteristics of the fish fin facilitate better performance in water; the shape of the fin affects the fish's speed and the flexibility may be responsible for better efficiency while swimming. The following thesis details the test of three oscillating foils with different chord flexibility. Each foil was tested at different Strouhal numbers and angles of attack to coincide with the previous tests of a stiff foil conducted by Douglas Read [1]. 1.1 Previous Flexible Foil Work Previous work has been conducted on flexible foils and has revealed improvements in efficiency compared to the stiff foil. According to Yamaguchi [2], flapping foils with flexible chords are more efficient than stiff foils and even perform better than screw propellers. Yamaguchi designed a flexible foil for a small boat and ran the boat at the same operating conditions for a stiff foil. He found that the flexible foil gave better efficiencies as seen in Figure 1. 5

6 j.75. Elastic Foil(n =1.) U 7_ 44. Original Screw Propeller(nh i no sea margin - 15% sea margin.5 ' ' q Vs (kt) Figure 1. Above is a comparison of efficiencies for a flexible foil, a stiff foil and a MAU-55 screw propeller. [2] The middle line in the graph shows the efficiency of a screw propeller for the same boat and load. Both screw propeller and stiff foil fall repeatedly under the performance of the compliant foil, for this particular case considered 1.2 Related Stiff Foil Work An analysis of an oscillating stiff foil has been done at the MIT Tow Tank by Douglas Read [1]. Read's thesis investigated the efficiencies and thrust coefficients at various Strouhal numbers and angles of attack. The angle of attack is defined as the angle that the foil makes compared to the instantaneous flow direction(accounting for heave motion as well as forward motion), as described further in section 2.4 and in Read. Read found that at Strouhal numbers of there were peak efficiency areas for an angle of attack between 15' and 25 with a thrust coefficient around.7 and high efficiencies 6

7 around.5. The objective of this thesis is to compare the efficiency and the thrust of Doug Read's stiff foil to the flexible foils designed for the following experiments. 2. Materials, Apparatus, and Procedures Two foils, each with a different chord flexibility, were designed to experiment against the foil Douglas Read used for his thesis. The two foils used in the experiments were replicas of Read's NACA 12 stiff foil with 1 cm chord and 6 cm span. Since the foils needed to be flexible along the chord but not along the span, a new design for the foil was developed. 2.1 Foil Design An aluminum.25 inch thick piece of aluminum was machined into the shape shown in Figure 2 below. The aluminum piece is curved at all edges in order to keep the rubber from tearing off. The holes along the middle of the aluminum plate helped keep the rubber held tightly along the plate. 7

8 1.5 inches 23.5 inches Dowel Pins Figure 2. The aluminum plate is shown above with holes cut along the center. This plate was used to hold the rubber mold in place. The shafts are attached to the aluminum piece with dowel pins that keep them from rotating. The dowel pin holes, which are 1 inch from the ends of the aluminum piece, are shown in the above figure. The two stainless steel shafts shown in the figure fit inside the aluminum plate. The ends of the steel shafts fit into the gears and bearings on the experimental carriage, described later. 8

9 ~.4OO 3.65" Figure 3. Dimensions for the various parts are given in the above illustration; all dimensions are in inches. The holes along the center are.4 inches in diameter. The dowel pin holes are approximately.63 inches in diameter; the holes at the end of the Aluminum plate are.192 inches in diameter. The first two inches of shaft 1 are.189 inches in diameter and.25 inches in diameter for the rest of the shaft. The shafts were made from stainless steel in order to avoid corrosion as these shafts would be submerged in water, while the aluminum piece would be protected by the surrounding flexible urethane. 2.2 Molding Procedure Once the aluminum plate and shafts were designed, a plastic box was made to hold the aluminum tightly. In order to make the mold, Read's stiff foil was placed inside the box. Vacuumed RTV was then poured over the stiff foil that was held inside the box and allowed to cure. This RTV mold of the stiff foil provided a means of making flexible foils with the exact proportions of the original. 9

10 In order to make the molded foils, the plastic box with the RTV mold needed to be sealed with clear cement and allowed to dry over night in order to prevent leakage of the urethane compound. The procedure for molding the flexible foils consisted of preparing only a third of the molding compound, pouring it in, and repeating this until the entire molding box was full and the aluminum piece inside was covered. This procedure allowed enough time to pour the prepared urethane and for it to still adhere to the next poured amount of urethane that was prepared resulting in foils with smooth surfaces. Preparing the entire amount of urethane did not give sufficient time for the fluid to reach the bottom of the box before it turned to solid and resulted in foils that had deformations. Below in Figure 4 is a cross-sectional drawing of the foil with the aluminum piece inside. Shaft numflexible Are Figure 4. Sketch of the foil structure. The circle shown in the middle is the steel shaft and the area in between the shaft and the flexible area is the aluminum plate. Flexible Urethane surrounds the Aluminum plate. Two different stiffnesses were chosen to compare with the original stiff foil. Shore A 6 flexible urethane, a compound with a 'floppy' consistency and Shore A 8 flexible urethane, a compound with a compliance between that of Shore A 6 and the stiff foil, were chosen. These were all liquid urethane casting compounds from Forsh Polymer Corp. Figure 5 below shows the percent of elongation plotted against the force applied for the different materials. For forces within the range of interest in this study, the Shore 6 material is approximately four times as compliant as the Shore A 8 material. 1

11 Material Properties for Shore A 6 and Ultimate Tensile Strength Shore A 8 X U ---- ' F, 8-6- / owl ,, Shore A Force (Psi) Figure 5. Stiffness comparison for the two flexible urethane materials, Shore A 6 and 8 hardness. The Shore A 8 hardness needs about four times the force in order to elongate the material the same amount. 2.3 Experimental Apparatus The tests for the foils were conducted at the MIT Towing Tank. The tank is 3 m in length and 2.6 m in width. The foils were mounted on the carriage shown in Figure 6. 11

12 -L "MON"K16, MUMM Aw"WWAORWANOW-, -"- Mc~in Ccarric-geIVD Lower Carriace Pitch Servornotor - Torque Sensor - Potentiometer Fnside reo Snsor N Chain Drive Inside Strut Assembly NACA 12 FoR Figure 6. View of the Carriage. [1]. The entire carriage moved along the length of the tank at the speed of.4 m/s. A foil was placed at the bottom of the carriage and fastened inside the bearings on either side. Endplates were located at the ends of the foil to reduce 3-D effects. A KISTLER 9117 X-Y-Z piezo-electric force sensor was at one end of the carriage to sense forces in the x and y direction. At the other end was a gear that was rotated via a chain attached to the motor located above the water line. A potentiometer was attached to the motor shaft to sense the pitch angle and a torque sensor, a KISTLER model 965, measured the applied torque. A computer controlled the vertical motion at various frequencies and the horizontal motion along the tank while also simultaneously pitching the NACA 12 foil. 12

13 2.4 Foil Motion The motion of the foil heave is described in Equation 3.1 below. h(t) = ho sin(wt) (3.1) where h is the heave motion as a function of time, ho is the heave amplitude, o is the frequency in rad/sec. In addition to the motion due to the heave, the foil also experiences a pitch motion. This pitch motion is shown in Equation 3.2 below. (t) =. sin(ot + ig) (3.2) where is the pitch motion as a function of time, is the pitch amplitude in radians and W is the phase angle between pitch and heave in radians. The experiments in this thesis were all conducted with a phase angle, W, of 9' and an h/chord equal to.75. U I dhldt (t)b h(t) Figure 7. Angle of attack, a, for a heaving and pitching foil is shown above. [1] In Figure 7 above, the various angles formed by the pitch and heave are illustrated. The equation for the instantaneous angle of attack is given below: a(t) = {arctan (ho o cos(ot) / U)-, sin ((ot + x)} (3.3) 13

14 where a(t) is the angle of attack, U is the free-stream velocity. The angle of attack is derived more fully in Read [1]. The Strouhal number is defined as, St = o ho / n U (3.4) The Reynold's number for the experiments was approximately 4,. The Reynold's number is defined below: Re = U*chord/v (3.5) where v is the kinematic viscosity of water in m 2 /s. 2.5 Experimental Procedure The calibration procedure used for the experiments was the same as outlined in Read [1]. For the calibration of the forces in the x-direction, the foil was tilted at 9; a weight of.5 kg was hung from the shaft closest to the Kistler. For the calibration of the forces in the y-direction, the foil was placed in its normal position; the weight was hung around the center of the foil with the weight falling from the trailing edge to calibrate for both the torque and y-force. DASY Lab recorded the forces from the Kistler sensors. The pitch was then zeroed by running the foil in the tank and minimizing the lift forces. Next, the tests were run for a range of angles of attack and Strouhal numbers. The data was corrected for the natural drift within the Kistler sensors. With the given experimental set up, the lift, thrust, torque, pitch position, and heave position were recorded. Propulsive efficiency and the thrust coefficient were used to compare the performance of the three foils. The thrust coefficient is described below: CT = T/ (1/2 p U 2 *chord*span) (3.6) 14

15 Where CT is the thrust coefficient, T is the mean measured force, p is the density of water, U is the towing speed of.4m/s, chord is the length of the chord,. lm, and span is the length of the span,.6 m. Another important term in comparing the foils was the propulsive efficiency. It compares the power into the system with the power produced by the foil, T TU/ (yfy + OT) (3.7) where j is the propulsive efficiency, y is the heave velocity, Fy is the force in the y direction, is the pitch angular velocity and r is the torque. Experiments were taken for the following range of Strouhal numbers:.1,.2,.3, and.4 and for a range of the following maximum angles of attack: 1, 15, 2, 25', and 3. Each experiment was conducted twice to see if the results were repeatable 3. Results The following are the results from the experiments run at the Tow Tank. Figures 8, 9, and 1 show the results for the Stiff Foil, Shore A 8 Foil and Shore A 6 Foil respectively. In Figure 8, the efficiency and thrust coefficient for the Stiff foil are shown. The thrust coefficient increases as the Strouhal number increases at each angle of attack. The efficiency reaches a peak at around 1' - 15* and decreases after that. The data at a Strouhal of.1 seems to trail the others significantly. These same observations are true for Figures 9 and 1. The efficiencies for all foils display a peak between 1* and 15'. The efficiencies all tend to decrease as the angle of attack increases past that peak. 15

16 1.2 Thrust for Stiff Foil St. =.4 -c I ( St. = St. =.2 St. = : Angle of Attack ) EE W ) C- 2 CL Figure 8(a) Thrust for Stiff Foil Efficiency for Stiff Foil S t.4 "St. =.2 St. = Angle of Attack Figure 8(b) Efficiency for Stiff Foil Figure 8. Figure 8(a) above illustrates the thrust coefficients and Figure 8(b) shows the efficiencies for the Stiff foil. 16

17 1.21 Thrust for Shore A 8 Flexible Foil St. = St = St = Angle of Attack Figure 9(a) Thrust for Shore A 8 Foil St =.1 35 Efficiency for Shore A 8 Flexible Fail St.3 St =.2, L -.2 F St. = Angle of Attack Figure 9(b) Efficiency for Shore A 8 Foil Figure 9. Figure 9(a) above illustrates the thrust coefficients and Figure 9(b) shows the efficiencies for Flexible Shore A 8 Foil 17

18 1.2 IIII Thrust for Shore A 6 Foil I I St =.4.8- St. = x ~ -- - St.2 St. = L Angle of Attack Figure 1(a) Thrust for Shore A 6 Foil I L.8 Efficiency for Shore A 6 Foil <.... St St..3 St =.2.6-2, ie.4-.2 S.2- p St. = Angle of Attack Figure 1(b) Efficiency for Shore A 6 Foil Figure 1. Figure 1(a) above illustrates the thrust coefficients and Figure 1(b) shows the efficiencies for the Shore A 6 Foil. 18

19 L ift z 1 -$2 5 Thrust Pitch Position Heave Position Torque z S ic Toqe3 Poi Figure 11(b). Graphs for the Stiff Foil at St = 4 and Angle =2 Figure 11. Graphs for the Lift, Thrust, Pitch Position, Heave Position, and Torque as a function of time recorded from DASY Lab at St =.4 and Angle = 2 19

20 U Power vs. Time for Shore A 6 Flexible Foil ' -ii - I Time (s) Figure 12(a). Shore A 6 Flexible Foil Power Power vs. Time for the Stiff Foil Time (s) Figure 12(b). Stiff Foil Power Figure 12. The Solid Line shows the power from the heave velocity multiplied by the Lift. The dotted line is from the power from the pitch angular velocity multiplied by the Torque. Figure 13(a) illustrates the power for the Shore A 6 Foil and Figure 13(a) shows the power from the Stiff Foil. 2

21 MENG= - I In Figures 11(a) and 11(b), the position and force data are shown for experiments at a Strouhal number of.4 and an angle of attack of 2'. Figure 11(a) shows the experimental results for the Shore A 6 Flexible foil and Figure 11(b) shows the results for the stiff foil. The lift data for both have a different form. In figure 11(a) the lift seems to flatten at the top below 1 N while in figure 11(b), the lift spikes at the peak of 2N. The lift data for both figures is asymmetric. The dotted lines in Figures 12(a) and 12(b) show the power from the torque multiplied by the angular velocity. The solid lines show the contribution from the heave velocity multiplied by the lift force. The solid lines contribute significantly less power compared to the solid lines. The peak power ranges between 3.5 W and 5.75 W for the flexible foil and between 5 W and 7 W for the stiff foil. The following figures compare the efficiency for the three foils at different Strouhal numbers. In each of the graphs, the flexible foil performs better than the Shore A 8 foil and the stiff foil. The Shore A 8 foil closely resembles the performance of the stiff foil. In figures 14, 15, and 16 at the angles of 1 and 15', the efficiency for the Shore A 6 flexible foil is approximately 2% higher than the stiff foil. Comparing the results to the data Read collected, the stiff foil did not show the same performances for efficiency and thrust. The flexible Shore A 6 foil performed better than both the data collected by Read and by this thesis for the stiff foil. The vertical lines in the figures display the amount of error in the experiment. This error is the standard deviation from the data collected. There seems to be a large amount of error at the smallest angle of attack of 1. This may be due to the smaller forces present at this angle. The error would have a greater effect at smaller loads than at higher loads. 21

22 .8 E fficiencies for St rouhal = Shore A 6 Foil > LU boce A_84 tiff Foil Angle of Att ack 25 3 Figure 13. Efficiency at a Strouhal of.1 for all three foils. E ff lden cies for Strouhal = F.7 -hore A 6 Foil C w) hore A 8 FOJ Stiff Foil'\ Angl e of Attack 25 3 Figure 14. Efficiency at a Strouhal of.2 for all three foils. 22

23 } -S'hore A 6Foil Efficiencies for Strouhal =.3 ) N Shore A 8 Foil ' Angle of Attack 25 3 Figure 15. Efficiency at a Strouhal of.3 for all three foils E fi ciencies for Strouha =.4 J-lhore A 6 Foil.6 C Au.55.5 wu.45 Stiff Foil / ~ ~~ o~86 Foi -.. r Angle of Attack 25 3 Figure 16. Efficiency at a Strouhal of.4 for all three foils. 23

24 4. Discussion The three foils displayed similar results for their thrust coefficients. From the Figures 8-1, the graphs display the same basic trends in the efficiencies as well. The difference in the lift in Figures 11 and 12 may explain why the flexible foil performs so much better than the stiff foil. The Lift for the Shore A 6 flexible foil does not reach high peaks like the stiff foil. The Shore A 6 seems to flatten out at less than 1 N while the Stiff foil reaches up to 2 N. The data may have been affected by several sources of error. The Shore A 8 foil results may have been adversely affected by the deformations on its surface. From molding the foil improperly, the surface had a seam line that could have affected its performance. Instead of performing the same and at some points below the stiff foil, it may have performed better than the stiff foil had those deformations not been there. In the Shore A 6 foil, one of the shafts could be slightly rotated with a set of pliers. This would not adversely affect the results because the actual pitch position and torque, which give the power input to the foil, are measured at the chain drive at the end of the motor shaft, 'upstream' from the actual foil. In addition, the torques in this experiment would not be able to turn the shaft. The block at the Kistler end of the foil could be moved a bit due to a broken screw; moving this end caused the Kistler to record false data. Once this was observed, a 'C' clamp was used to keep that end fixed. This stopped the Kistler from recording the movements of the carriage. 24

25 5. Conclusions and Recommendations The results are promising in that the most flexible Shore A 6 foil performed better than the stiff and the Shore A 8 foil. Flexible foils should be further investigated because of their potential to increase efficiency. Another Shore A 6 foil should be made or the current one fixed to keep the shaft from rotating to compare with the results shown in this thesis. Foils with even more compliance than the Shore A 6 foil designed in this thesis should be developed and tested for their performance. An easier to use system for the carriage should also be developed. The current system did not allow for the easy switching of foils. Once the foil was switched, the system needed to be recalibrated and zeroed again. 25

26 Bibliography 1. Read, Douglas "Oscillating Foils for Propulsion and Maneuvering of Ships and Underwater Vehicles" MIT Masters Thesis. February 2 2. Yamaguchi, H. "Oscillating Foils for Marine Propulsion" Proceedings of the Fourth International Offshore and Polar Engineering Conference (1994): p