Investigating Ideal Flow Parameters for an Autonomous Air Swimmer

Transcription

1 Investigating Ideal Flow Parameters for an Autonomous Air Swimmer Brigid M. Flood Dr. S. Girimaji 1, Aditya Konduri 1, Yi Yang 1, Daniel Isokpunwu 2, Allen Mehrafshan 3 Texas A&M University Aerospace Engineering 1, Prairie View A&M University 2, University of Texas at Austin 3 Abstract: Air Swimmers are helium-filled fish balloons that swim through the air via a remote that controls tail flapping and pitch. The aerospace industry is currently exploring different ways to design newer, better satellites and high altitude balloons. One option is to use balloons that run on turbofan technology, but balloons that utilize the tail flap configuration have the potential to be lighter, more cost effective, and more efficient. In order to translate the Air Swimmer toy into a useful engineering tool, it is necessary to investigate the functionality of the balloon, especially the tail, and how we can manipulate it (along with flow parameters) to maximize thrust produced. An experiment was designed to test several different fish tail shapes in a wind tunnel at varying flap frequencies and amplitudes. Two different methods to obtain thrust can be employed in conjunction with this experimental setup: first, a wake rake mounted with Pitot probes downstream of the model; second, a force balance attached to the tail calibrated to record thrust measurements. The tools necessary for each of these techniques have been constructed and mounted in the test section. In addition, tests have been performed on several tail models using the force balance, and some preliminary analysis has been completed. Finally, a smoke-wire tool for flow visualization was designed and manufactured. Ultimately, as this project continues, our team aims to work more closely with the theory team so that computational and experimental hypotheses can be correlated and analyzed. I. Introduction It s a long-standing fact that engineers can learn from and often implement behaviors observed in nature. Particularly, in the aerospace industry, special attention has been paid recently to fish and their method of locomotion. Balloons have become a popular choice for weather and other observations, because they re lightweight and generally inexpensive to manufacture. The performance of these balloons relies heavily on buoyancy, which leads to more careful study of fish propulsion. Currently, there is a desire to improve the weather satellites and balloons that NASA uses. One option is to use motor fans, but these are heavy and often inefficient; we hypothesize that employing a flapping tail as the method of propulsion on these balloons would be more effective. A toy fish balloon currently on the market, known as the Air Swimmer, uses this type of flapping tail and was the inspiration for this study. With this in mind, there is one main question to be addressed: what flow parameters (flap frequency, tail shape, and wind speed) will yield the highest thrust from the tail? This study is experimental in nature, but many previous works have computationally investigated fish and swimming. One study by Akhtar and Mittal 1 used simulations to observe the thrust produced by a flapping tail in the wake of another flapping tail. Another study done at Harvard by Drucker and Lauder 3 examined the behavior of the median fins, particularly the dorsal fin, during both steady and unsteady swimming of the rainbow trout. Research like this has inspired further examination of fish propulsion and its possible applications. Furthermore, a group of students at Texas A&M is also studying Air Swimmers but on the theoretical and computational side. It is expected that the experimental effort presented here will help to solidify computational data and help us to create our own autonomous flapping balloon in the future. In this study, we aimed to experimentally determine the ideal flow parameters for an autonomous balloon. To further simplify this, we focused only on the tail. Access was granted to a low-speed, closed-circuit wind tunnel, thus it was first necessary to design and manufacture mounting systems both for the driving mechanism and for the force balance. Next, it was decided what shapes should be tested, and of what material they should be made. Once the wind tunnel setup was complete, flow visualization was performed to ensure that the correct flow patterns, namely, vortices off the trailing edge of the

2 tail, were being generated. Further explanation of the setup for this experiment is discussed in the Methods section of the paper. Finally, our force balance was mounted and calibrated, and we performed wind tunnel tests on each of the tail shapes at varying Strouhal numbers and flap amplitudes. The data collected from these tests is presented in the Results, and comparisons are made among shapes, frequencies, and amplitudes in the Discussion. Additionally, a back-up method of calculating thrust was prepared and tested. This consisted of a wake rake, fitted with several Pitot probes, inserted in the wind tunnel s test section downstream of the tail model. Using the pressure difference across the tail, along with Bernoulli s equation and momentum conservation, it was possible to calculate thrust. Unfortunately, reliable results were not obtained from these tests. This is also discoursed in the Discussion of this paper. This study is just one part of a larger project involving Air Swimmers; the data presented here is merely preliminary. Future plans and expectations are explained in the Discussion section as well. test section can come into play. The shapes were scaled accordingly. A mounting system for the force balance was also designed in SolidWorks and made out of ABS plastic. These systems area all connected by a stainless steel rod that runs horizontally through the test section. The tail is connected to this rod with metal clamp looms and screws; the servo motor s output shaft is connected to a metal screw connector, which tightens around the stainless steel rod; finally, the stainless steel rod is inserted directly into the force balance. Special care was paid to the force balancerod assembly. In order for the force balance to experience the same forces that the tail does, there needs to be a rigid connection between the force balance and the tail. The stainless steel rod ensures this condition is met. Furthermore, the rod cannot make contact with any surface between the tail and the force balance. Thus, we had to make sure that the stainless steel rod would not touch the walls of the test section, despite any deflection that would occur while the tail was flapping. The final set-up, including servo motor, tail, and force balance, can be seen in Figure 1. Figure 2 shows the force balance and its mounting system more closely. II. Methods We were given access to a low-speed, closedcircuit wind tunnel with a 1 foot by 1 foot test section in the Aerospace Engineering lab at Texas A&M. With the goal of determining the conditions that maximize thrust in mind, our first major task was to set up the flapping tail in the test section of the wind tunnel. It was decided that on one side of the test section, the driving system would be mounted, and on the other side, the force balance would be mounted, so as to maximize the space available. A servo motor was chosen as the driving mechanism for the tail, since it s so lightweight and simple to set up. The servo motor was controlled by an Arduino board, which is a microcontroller with its own computer language. So, a program was written that allowed user-input frequency and amplitude; that is, how fast the tail would flap (in Hz) and how far up and down the tail would rotate (in degrees). Next, a mounting system for the servo motor was designed in SolidWorks and manufactured out of ABS plastic in a 3D printer at Texas A&M. This mounting system is essentially a box that extrudes from the window of the test section, and the servo motor is secured onto this box with screws. Next, the tail designs were configured; for this, the Theoretical/Computations team of the Air Swimmers project was consulted. Five different tail shapes (rectangle, trapezoid with 1 sweep angle, trapezoid with 2 sweep angle, chevron, and crescent) were cut out of 1/16 thick balsa wood. The width of the tails was constrained by the fact that only 1% of the cross-sectional area of the test section can be blocked at any time; otherwise, turbulent flow and/or wall effects from the floor and ceiling of the Figure 1: Test section set-up Figure 2: Force balance and mount

3 After the testing equipment was mounted in the test section, it was necessary to perform some simple flow visualization tests, to make sure that our system worked properly and produced the type of flow in which we were interested. To do this, we inserted the output tube of a fog machine into the test section, level with and just upstream of the flapping tail. As the fog was expelled from this tube, it followed the flow pattern of the air in the wind tunnel, giving us a visual representation of the flow through the test section. We were able to see some vortices form and shed at the trailing edge of the tail, which was excellent: we could be reasonably sure that the data we collected was relevant to the project, since the flapping tail created the flow conditions for which we were looking. However, using a fog machine (which is manufactured for haunted houses) is a crude way to create visible flow. In an attempt to improve the quality of the flow visualization, a smoke wire was built. Essentially, the smoke wire is just a strip of metal (we used nickel chromium, or Nichrome) placed vertically through the test section and coated with liquid smoke or oil (we used liquid smoke). When a voltage is applied across the wire, the liquid heats up and vaporizes, creating streaks of fog that travel over the flapping tail and give a better picture of flow behavior. There is improvement to be made on the smoke wire, but each method gave us a better understanding of the flow regime. Using a force balance is probably the easiest method to calculate the thrust produced by the flapping tail, but in order to validate our results, we wanted to also perform tests using another technique. So, a wake-deficit analysis was performed. A wake rake, which holds Pitot probes downstream of the tail, was modeled in SolidWorks and manufactured in the 3D printer. Differential pressure transducers were connected both to the Pitot probes on the wake rake and to a single Pitot probe in front of the tail; therefore, the pressures reported in each case represented dynamic pressures. Thus, the velocity of the flow before and after the tail could be easily calculated. Then, using conservation of momentum, the relationship ( ) (where s represents the length of the span, represents the wind speed behind the tail, and represents the wind speed in front of the tail) 2 was developed and evaluated to determine the total drag or thrust force on the tail. The results obtained using this procedure were inconclusive, and are evaluated in the Discussion. The final task in this study was to perform wind tunnel tests on our tail models using the force balance, which we believed to be the most reliable tool for obtaining thrust. The variables of interest in this case were shape, flap frequency (effectively, Strouhal number), and amplitude. Thus, for each of the five tail shapes, we performed tests at three different Strouhal numbers and three different amplitudes, while keeping the wind speed constant at 2 m/s. Results can be compared both between shapes (at constant Strouhal numbers), and within each individual shape (at constant amplitudes). Although we could have simplified results by varying fewer parameters, this configuration was chosen because we believed it would yield the most useful information. Data acquisition software was included with the force balance. The output files consisted of six columns: forces and moments in the x, y, and z directions. For each test, data was collected for five seconds and at a sampling rate of 1, Hz, yielding 5, data points. After testing was complete, the data files were imported into Excel and grouped by shape and then by Strouhal number. Therefore, for each shape, three plots (one for each Strouhal number) were generated, with three curves (one for each amplitude) on each plot. As the final step of data analysis, an average x-direction force needed to be calculated, so that conclusions could be drawn. Since there was no function describing the force experienced by the tail through time, a form of the trapezoidal rule was used. The expression for the integral of force ( ), shows the average force quite easily. The integral on the left side of the equation is the mathematical expression for the physical area under the curve. Using the expression (where represents the force at that time instance, and represents the force at the previous time instance), the area under the curve for each data point with respect to the previous data point was calculated. The summation of this area over all 5, points, divided by the test time, yielded the average force experienced by the tail during the test. It s important to note that positive forces represent drag, while negative forces represent thrust. All comparisons made between shapes and Strouhal numbers used this average force as the basis. III. Results For each of the 45 tests, the raw data file comprised six columns: one column for the force in each direction (x, y, and z), in Newtons, and one column for the moment about each axis (x, y, and z), in Newton-meters. The x-direction force was of primary interest in this study. The trapezoidal rule was used to calculate an average x- direction force for each test. Then, the average forces for each shape were plotted by frequency and amplitude, as shown in Figures 3-7.

4 Rectangle: Average Force vs. Amplitude Chevron: Average Force vs. Amplitude Figure 3: Average Force vs. Amplitude, Rectangle. Figure 6: Average Force vs. Amplitude, Chevron. 1 Trapezoid: Average Force vs. Amplitude Figure 4: Average Force vs. Amplitude, 1 sweep angle Trapezoid. 2 Trapezoid: Average Force vs. Amplitude Crescent: Average Force vs. Amplitude Figure 7: Average Force vs. Amplitude, Crescent. The premise of this study is to determine the ideal flow parameters (including shape, frequency, and amplitude) for the autonomous air swimmer s tail. Therefore, it was important to screen the results both by frequency and by amplitude, to get a better picture of which configurations yielded the highest thrust. Figure 8 is a plot of the highest thrust produced by shape, with respect to frequency, while Figure 9 is a plot of the highest thrust produced by shape, with respect to amplitude. Figure 5: Average Force vs. Amplitude, 2 sweep angle Trapezoid.

5 Force in x-direction (N) Figure 8: Maximum x-direction Force, with respect to frequency. Force in x-direction (N) Maximum x-direction Force by Frequency Frequency (Hz) Rectangle 1 Deg Trap 2 Deg Trap Chevron Maximum x-direction Force by Amplitude Rectangle 1 Deg Trap 2 Deg Trap Chevron Crescent Figure 9: Maximum x-direction Force, with respect to amplitude. From these plots, we can see that the highest thrust is produced by the trapezoid with a 2 sweep angle, at and 2 amplitude. The time-history plot for the test performed under these conditions is shown in Figure 1. Fx (N) vs. Time (ms) -, 2 Amplitude Time (ms) Figure 1: Force in x-direction vs. Time for 2 Trapezoid at and 2 amplitude. IV. Discussion Many inferences can be made by analyzing the data above. First and foremost, a graph like the one shown in Figure 1 was plotted for each test that was performed. The sinusoidal shape of these plots corresponds to the frequency at which the tail flapped. For example, the force in Figure 1 fluctuates through a full five cycles in the fivesecond time frame. This test was performed at a flapping frequency of, so these two frequencies match. This was also the case for each of the other tests, which attests to the validity of the method used. Another justification can be seen in Figures 3-7. In each plot, it s clear that the and frequencies follow the same general pattern of force as the amplitude changes. The curve doesn t always follow this same trend. There are a few possible explanations for this: first of all, the servo motor was not as accurate in its rotation at this frequency; additionally, this frequency may exceed the normal swimming frequency of most fish. For most shapes, it is easily seen that produces less thrust than other frequencies. It s worth noting that the crescent shape was the only tail model that did not produce an average thrust force in any of its tests. Perhaps this is due to the fact that a pure crescent is an unnatural tail shape. Finally, the ideal combination of flow parameters is found to be the trapezoid with the 2 sweep angle, flapping at a frequency of and amplitude of 2. In fact, this trapezoid produced the highest average thrust forces across the board. This tail shape seems to resemble an actual fish s tail most closely.

6 Although we believe our methods were sound, there are of course several factors to consider when evaluating these results. First of all, the tail models in this study were made of balsa wood. This is probably not the best material to use when emulating either a fish or a balloon, but we knew it would hold up in the wind tunnel and would be easy to mount on the stainless steel rod. Secondly, the tests were performed at extremely low Strouhal numbers (.2,.4, and.6, for 1, 2, and, respectively). The Strouhal number is a dimensionless characteristic used in unsteady oscillating flow, and the typical Strouhal number for fish in nature is about Strouhal numbers of this magnitude weren t easily attained in this study, mainly because of the constraints placed on the tail due to the wind tunnel we used. In order to avoid wall effects, or turbulence in the test section due to the model blocking more than 1% of the cross-sectional area, our tail s chord length had to be less than 2 inches (.51 meters). Strouhal number, expressed as (where f represents frequency, c represents chord length, and u represents wind speed), is proportional to the chord, so this restriction in chord length pinned our Strouhal number far below the normal range. In addition, the wind tunnel we used could only go as low as 2 m/s. If a larger wind tunnel with lower minimum speed could be used, our Strouhal number could match the natural range, which would produce more widely applicable results. Unfortunately, there were also parts of our study that did not work out as expected. As mentioned, a wake rake was made, fitted with 11 Pitot probe ports, and mounted behind the tail model, in hopes to corroborate the results we would find by using the force balance. The Pitot probes in the tail s wake, as well as one Pitot probe in front of the model, were connected to differential pressure transducers and also to a Scanivalve, so that dynamic pressures were recorded at each port. When tests were run under this configuration, the dynamic pressure recorded in front of the model varied widely. Since the wind speed in the tunnel was held constant, this dynamic pressure should have also remained relatively constant. Thus, the data taken couldn t be used. One possible reason for this is that the transducers used could detect a pressure range of -5 millimeters of water, or -12, Pascals. The dynamic pressure we were attempting to fix in the front of the test section was about 5 Pascals, so it s possible that the transducers couldn t distinguish this miniscule pressure difference well enough. Using transducers with a higher resolution could improve the accuracy of this technique. Also, the smoke wire that was produced to improve our flow visualization didn t function as we had hoped; smoke didn t flow off the Nichrome wire in streaks, so we couldn t get a picture of the flow regime over the tail. Increasing the surface tension by using more than one Nichrome wire, as well as using a more viscous oil, could improve the quality of smoke produced. These changes are worth examining and will be incorporated in the future of the project. This study is just the first investigation into Air Swimmers and how we can use and improve upon them. In the future, we hope that the theoretical and experimental results will coincide with each other; that is, when simulations are run under certain parameters, the results will be comparable with the results obtained from experiments performed under those same parameters. Additionally, there are other facets of the Air Swimmer to explore. We would like to manufacture our own completely autonomous Air Swimmer prototype and launch it to see if its maneuverability is actually superior to that of a fan-type balloon. The results we achieved in this study are encouraging and prompt further study of Air Swimmers. V. Conclusions In summary, this study was conducted to gain some preliminary insight into Air Swimmers and their possible applications. In particular, we were interested to determine the flow parameters (including tail shape, flap frequency, and amplitude) that would yield the most thrust. To do this, an experiment was designed in a low speed wind tunnel with a 1 foot-by-1 foot test section. A servo motor mounted on the test section door controlled the rotation of a stainless steel rod, on which was clamped one of several balsa wood tail models. In turn, the steel rod was connected to an extremely small force balance on the opposite side of the test section. Five different tail models were made and tested at three different frequencies and three different amplitudes, yielding 45 tests in total. After data was collected, the average force in the x-direction was calculated for each test using the trapezoidal rule. Ultimately, it was determined that the trapezoid with the 2 sweep angle produced the most thrust under any combination of thrust and frequency. In particular, the 2 trapezoid flapped at with 2 amplitude resulted in.49 N of force in the negative x-direction (thrust). The shape that produced the least thrust was the crescent, which actually produced only drag. We are confident that our method produced reliable results. On the other hand, another method we tried, involving a Pitot probe wake rake, produced erratic results and was unsuccessful. This study was just the beginning of an investigation into autonomous balloons and the tail-flap configuration. As the project continues, we aim to improve results by testing more fish-like tail materials and by collaborating with the theoretical/computational team.

7 Acknowledgements I would like to acknowledge, first and foremost, the National Science Foundation s Research Experience for Undergraduates (REU) for their grant. I would also like to thank Dr. Girimaji for his expertise and for allowing me to be a part of this project. The graduate students that advised us on this project, Aditya Konduri and Yi Yang, were so helpful and our results would not have been possible without them. Finally, thank you to my coworkers on this project, Allen Mehrafshan and Daniel Isokpunwu. References [1] Akhtar, I., and Mittal, R., A Biologically Inspired Computational Study of Flow Past Tandem Flapping Foils, 35 th AIAA Fluid Dynamics Conference and Exhibit, Toronto, Ontario. [2] Anderson, John D., Jr., Fundamentals of Aerodynamics, 5 th Ed., McGraw-Hill, New York, 21. [3] Drucker, Eliot G., and Lauder, George V., Locomotor Function of the Dorsal Fin in Rainbow Trout: Kinematic Patterns and Hydrodynamic Forces, The Journal of Experimental Biology, Volume 28, pp