Fluid Structure Interactions in Low Aspect Ratio Membrane

17th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2014

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Fluid Structure Interactions in Low Aspect Ratio Membrane Wings

Manuel A. Arce and Lawrence Ukeiley*

Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA

* Correspondent author [email protected] Abstract Time dependent particle image velocimetry and digital image correlation are used to study fluid structure interactions for low Reynolds number flow over a membrane wing. The use of flexible wings has been observed in many natural flyers and their use has translated to beneficial properties in many engineered small air vehicles. Typically these benefits have been reported as increased flight stability which can be linked to how the flow and the membranes interact both statically and dynamically. Here we study multi-cell aspect ratio two membrane wings which have a scalloped free trailing edge with different levels of pretension in the membrane. The pretension is shown to affect the extension magnitude and membrane motion frequency which are both also affected by aerodynamic loading. The membrane motions are highly correlated with the flow showing how its characteristics affect the flow over wing leading to changes in the aerodynamic properties such as the stall angle and the wake deficit. 1. Introduction Biological systems have inspired many engineers to investigate the use of flexible membranes in wings for applications involving small flying vehicles. The flexibility in the wing surfaces allow for passive shape adaption (adaptive cambering), which has been shown to increase aerodynamic efficiency in empirical and experimental studies9,17,20,22. Additionally, the adaptive surfaces help the vehicle or natural flyer fly in a difficult regime with low Reynolds number (Re) flow (104 through 105), which then easily transitions to turbulence; and where wind gusts are typically of the same order of flight speed (10-20 m/s). Research by Lian and Shyy have shown turbulent transition over low Re wings and found improved behavior for wings incorporating membrane surfaces, possibly leading to more stable flight12,13. Tian et al.24 and Song et al.21 have linked the flexibility in bat wings to their exceptional flight maneuverability through direct study of bat aeromechanics and engineered membrane wing designs. The promising performance of micro air vehicles (MAVs) utilizing batten-reinforced or perimeter reinforced membrane wings (22,20,13,26,16) has led to further research into the fluid-structure interaction (FSI) between low Re flow and vibrating membrane surfaces. Vehicles and natural flyers in this flight regime are typically small and light as possible, while the use of membranes surfaces keeps weight minimal, the aspect ratio (AR) of wings are also typically low (AR ~1-4) and tip/edge effects become important to the aerodynamics. In a series of studies with perimeter reinforced membrane wings, Gursul, Rojratsirikul, Tregido and co-workers (18,27) linked vibration characteristics with wake shedding frequencies and oscillating shear layer behavior. Jaworski and Gordnier11 were able to validate much of the findings in simulations with similar geometry wings, through combined 1D structural and high-order fluid solvers. Gordnier and Attar8 further examined a perimeter reinforced aspect ratio 2 wing validating their advanced numerical techniques. One key results they showed was how the mean cambering and the dynamic motion of the wing was able to reduce the size of the separated flow region along with reduction of pitching moment at high angles of attack. Attar et al.4,5 have examined free trailing edge membrane wings experimentally and computationally to see the effect of different pre-strain levels ranging from 2 to 10 percent. Their work showed “almost no sensitivity” in the frequency of the limit cycle oscillation to the static angle of attack, at least for small angles of attack. Additionally, for the Reynolds numbers they examined there was little effect of pre-strain levels on the pre-stall lift behavior while the induced drag was significantly altered for the membrane wings than the rigid theoretical results. Research by Hubner, Ukeiley, Ifju and co-workers (1,10,15,19,25,28) have studied the effects of membrane cell AR, cell scalloping, and membrane pretension in a series of collaborative works;


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investigating aerodynamic forces as well as details of flow and membrane behaviors focusing on batten reinforced membrane wings. The ongoing research has shown that moderate scalloping of membranes with incorporating pretension is aerodynamically advantageous in force measurements. Meanwhile, the use of synchronized particle image velocimetry (PIV) and digital image correlation (DIC) revealed some natures of the membrane vibrations and high correlations between vibration and surrounding flow fluctuations, as well as a reduction in flow separation about the wing at the center span. The current work utilizes PIV and DIC in synchronous fashion to extend the study of the fluid structure interactions to low aspect ratio wings (AR=2) batten reinforced membrane wings. 2. Experiment

The experimental results discussed in this study have been performed in two different wind tunnels. These were an open jet facility, designed for low speed aerodynamics, and a conventional closed return wind tunnel. This discussion in this section will include a description of the experimental facilities, instrumentation utilized and the models tested.

A. Wind Tunnel Facilities The initial experiments within this investigation were conducted in the Aerodynamic Characterization

Facility (ACF) located at the University of Florida’s Research and Engineering Education Facility. The ACF is an open jet, open circuit suction style wind tunnel specifically designed to create low turbulence flow in the 1-20 m/s range for MAV research. It is powered by a 1.52 m, 37.3 kW axial blower combined with variable frequency drive (VFD). The flow passes through settling screens and honeycomb in the bell mouth and is contracted through an 8:1 area ratio resulting in a 1.07 m by 1.07 m square jet test section with a 3.05 m length. The flow has been characterized yielding a potential core of at least 60 percent of the inlet contracted exit area and a turbulence intensity of 0.16 percent at a freestream velocity of 10 m/s 20.

Additional experiments were performed in a closed loop recirculating facility which was designed and built by Engineering Laboratory Designs (ELD). The air is moved through the tunnel by an inline 200 Hp axial blower with variable frequency drive. Turning veins are used at each intersection to help direct the flow around the bends. Air enters the conditioning region where it passes through an aluminum honeycomb and several anti-turbulence screens. Next, the air then goes through a 25 to 4 area ratio contraction where it finally enters the test section at a cross-sectional area of 0.61 m by 0.61 m (24 in by 24 in). Using hot-wire anemometer the ELD-WT yielded a turbulence intensity (|u’|/u) of 0.1% at a freestream velocity of 10 m/s. More details describing the ELD-WT and flow quality can be found in Sytsma23.

B. PIV Equipment The flow field measurements (U and V components) were acquired using a time resolved PIV system

from Dantec Dynamics. This system consisted of a Series 800 double-cavity Nd:YAG laser (Lee Laser) set to a wavelength of 532 nm and two IDT XS-5 high-speed CMOS cameras equipped with Nikon 105 mm lenses set to an f-number equal to 2.8. Dantec’s Dynamic Studio software (v3.31) was used to acquire double frame images at 800 Hz and to compute two-component vector fields through a three-step iteration, adaptive-window, cross-correlation algorithm. Since images are stored on board the cameras limited memory, the cameras resolution was changed to 1280 pixels by 600 pixels. This reduction in pixels was done to obtain more images at the desired sampling rate. The combination of optics, resolution, and seeding allowed for 16 pixel by 16 pixel interrogation areas with 25 percent overlap.

C. DIC Equipment The structural deformation measurements were acquired with a system provided by Correlated Solutions.

This system consisted of two VisionResearch high-speed phantom v7.1 SR-CMOS cameras. The phantom cameras had a maximum frame rate of 4800 Hz at full resolution (800 pixels by 600 pixels) and were equipped with aspherical 28-300 mm f-length lenses set at f5.6. The software included Correlated Solutions’ Vic-3D 2010 and Vic-Snap, as well as Phantom Camera Control v675.2. The various programs were utilized to operate and calibrate the cameras and to run digital image correlation, obtaining three-dimensional membrane displacements. A minimal amount of paint was used to create random speckle patterns (shown in Figure 1) on the membrane portion of the models. From the speckle patterns and the dual camera stereo calibration, the software performs grey-scale cross-correlation and triangulation analyses to decipher deformation. To synchronize the DIC system and the PIV system a Tektronix type-114 Pulse Generator was


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used. A pulse from the PIV cameras’ sync-out was sent the pulse generator where it was reshaped to a signal that could be used to trigger the DIC cameras. HOYA multi-coated (HMC) high-pass (>600 nm) optical filters, which offer zero percent transmittance of the 532 nm laser light, are employed on the DIC cameras to ensure intense laser light did not interfere with the digital image correlation.

D. Models Models used in the experiments are made from 7071-T Aluminum frames with a silicone rubber adhered

to them and are depicted in Figure 1 along with the pertinent dimensions. The wings were manufactured by heating the silicone rubber then gluing it to the metal frame using a technique described in Abudaram et al1. Depending on the temperature the silicone rubber is heated to, when cooled a measurable pre-strain will exists within the membranes. Two different membrane models are used throughout this investigation, a 1 percent pre-tension membrane and a 4 percent pre-tension membrane both models have the same 3-cell batten pattern. A rigid plate was also tested and used as a baseline case. All membrane cells were scalloped to a depth of 25 percent of the wing chord length. The model displayed in Figure 1 show the batten spacing as well as the white paint speckle pattern used for the DIC technique, while the topside silicone membrane is matte black, helping reduce laser glare for the PIV measurements.

Figure 1: Aspect ratio 2 membrane model with dimensions in mm

E. Experimental Details Synchronized PIV and DIC experiments were conducted in the ACF at 10 m/s. The Reynolds number, based on freestream velocity and model’s chord length, was calculated as 50,500 (≈50,000), this value was kept fixed throughout all tests. Each model was placed in the ACF (wind tunnel) with the leading edge approximately 0.3 m from the inlet’s exit. Mounting was arranged to allow an unobstructed view of the model from one side for the PIV cameras and an unobstructed view of the models speckle pattern for the DIC cameras. Due to some physical constraints in the placement of the PIV laser, it was necessary to invert the models for testing, such that the PIV laser issued from below the inlet to strike the mid-plane of the inverted model’s top surface. Figure 2 portrays the synchronized experimental setup. During testing, a 250 W halogen light was shined from directly above the model to ensure sufficient light reflection of membrane speckle pattern for DIC. One PIV camera was focused over the membrane surface at the center span plane and the other on the immediate wake, with slightly larger and slightly overlapping field of view. The flow velocity was maintained at 10 m/s, while synchronized PIV-DIC data sets were acquired for the models at 4˚, 8˚, 12˚, 16˚, and 20° angle of attack. A digital inclinometer was used to set the angle of attack to ± 0.2 degrees. A thousand samples were acquired for all test configurations, which proved enough to converge PIV measured fluctuating velocity statistics to ± 2% in regions of unsteady flow. Further investigation into the membrane’s motion was conducted in the ELD-WT. These experiments were to supplement the synchronized data previously taken. Models and air speed during these experiments remained the same as previous, i.e., a 1 percent pre-tension membrane model and a 4 percent pre-tension membrane model were tested at 10 m/s. The independent DIC experiments were conducted for a range of AoAs of 4°, 8°, 12°, 16°, 20°, 24°, 28°, and 32°. Since this was the first time these experiments were conducted in the ELD-WT, a new mounting arm needed to be created. To insure the mounting arm and wind


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tunnel did not influence the membrane’s motions, vibration tests were taken on both the mounting arm and the wind tunnel showing a rigid mount where significant vibrations were not transmitted to the model. Even though PIV data was not taken, the models were still inverted to match previous experiments. The DIC cameras and lamp were positioned above the test section such that all three membrane cells fit into the cameras field of view. Again, the membrane wings were supported as they were in the previous experiment, two thin symmetric airfoil hangers attached to the outer portion of the wings. The hangers were then attached to a circular rod. To further analyze the influence of the wing tip vortices, the model’s mounting hardware was changed to a single airfoil hanger supporting the center of the membrane’s frame. Experiments were repeated at AoAs of 8°, 16°, and 24° while being supported only by the center mount.

Figure 2. Synchronized experimental setup in ACF

3. Results In the following section the results of both the velocity field and membrane will be discussed which will be followed by some correlation analysis between the two measurements to gain insight into the fluid structure interactions. A. Flow Field Measurement The 2-component (U-component and V-component) flow-field measurements were acquired using the time resolved PIV system discussed previously. The flow above a flat plate model, and in its near wake region, provided a baseline case to compare the effects of the membranes. This baseline case was used to compare both the 1 percent pre-tension and 4 percent pre-tension membrane models. In all the plots presented here the length scales and velocity scales have been normalized by the full chord length (76.2 mm) and freestream velocity (10 m/s). PIV data was obtained in the streamwise direction along the center of the middle cell for the membrane models, and also in the center of the flat plate model. Data was recorded on each model at five different AoAs, 4°, 8°, 12°, 16°, and 20°. The analysis includes both mean and turbulent time averaged velocity fields to highlight different aspects within the flow-field. For all of the velocity field igures the flat plate cases (column A) have a solid wing geometry frame superimposed on the PIV plots to help visualize the flow. The membrane models (columns B and C) have a 20 percent solid leading edge frame geometry while the remaining 80 percent of the frame is represented by dashed lines to denote the battens. Also within the figures, one cycle of membrane oscillations obtained from DIC have been superimposed to further help visualize the flow dynamics.

DIC Cameras

PIV Cameras

Inverted model in seeded air

PIV laser

DIC light

Flow


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Figure 3: Normalized mean U-component of the flow-field with streamlines for the different models. Column A) flat plate model. Column B) 4 percent pre-tension model. Column C) 1 percent pre-tension model.

Figure 4: Normalized Urms contours for the different models. Column A) flat plate model. Column B) 4 percent pre-tension model. Column C) 1 percent pre-tension model.

Examining the flat plate model, the evolution of the streamwise velocity component for the flow-field is shown in Figure 3. At 4° AoA the flow slightly increases in amplitude over the leading edge and appears to remain attached as it traverses down the wing. As the AoA is increased, the flow still remains attached however there is a noticeable decrease in velocity near the surface. Comparing the flat plate model to its larger aspect ratio counterpart investigated by Timpe et al.25 the lower aspect ratio wing experiences a delay in AoA before the flow becomes stalled. For this wing, stall sets between 8 and 12 degrees while for the larger aspect ratio wing this happens at angles of slightly less than 8°. The same delay in stall was also seen in Zhang et al.28 were they measured force data on both low and high aspect ratio flat plate models. This delay is consider to be the effects attributed to the stronger influence the wing tip vortices have on the flow


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surrounding the model. Torres and Mueller26 proposed as the aspect ratio decreases the effects of wing tip vortices become stronger. The stronger vortices energized the flow above the wing’s surface thus delaying the onset of separated flow (26,14). It is not until 12° AoA that the flow above the flat plate model experiences reverse flow along its entire surface. The flow at 12° no longer has enough momentum to remain attached, thus separating and creating a separation bubble. Due to the size of the separation bubble, reverse flow is now present within the near wake of the model resulting in a significant increase in wake deficit. Using a steady control volume approach, the near wake momentum deficit can be proportionally related to drag, hence an increase in wake deficit is an indication of an increase in drag. As the flat plate is increased to a higher AoAs an increase in the shear layer height, amount of reverse flow, and wake deficit were all observed. Finally at the last angle recorded, 20° AoA, the flat plate experienced a massive separated region above the surface as well as a large amount of reverse flow in the near wake, creating a massive wake deficit. Turbulence properties for the 4 percent pre-tension membrane model and 1 percent pre-tension membrane model, Figure 4 and Figure 5 columns B and C respectively, will be compared to the baseline flat plate case. When examining the plots there are a few trends that initially stand out. One of the first trends to note is the reduction in shear layer height. Examining the U-RMS fluctuations in Figure 4 this reduction can be seen throughout all AoAs tested. The membrane’s compliant feature is seen to help pull the shear layer closer to the membrane’s surface. As the shear layer remains closer to the membrane’s surface an increase in the amplitude of the streamwise flow at the leading edge is noted. The membrane models demonstrated accelerated flow at the leading edge of approximately 15 percent greater than the flat plate case. Another trend to note is the significant decrease in reverse flow above the model’s surface and in the near wake. Comparing with the flat plate model at 12° AoA where a large separation bubble was present, the flow over the membrane models have a relatively small separation bubble closer to the leading edge. Increasing the AoA further highlights the reduction in both the amount of reverse flow as well as the levels of the turbulent fluctuations in the near wake that the membrane models produce compared to the flat plate model. Part of the reduction in reverse flow can be attributed to the membrane models being able to change their camber in the presence of a pressure difference. The increase in camber effectively allows the flow to reattach whereas in the flat plate case the flow remains separated. Examining the near wake leads to another trend, the membrane models have a major decrease in peak wake deficit velocities. At lower AoAs, the membrane models have a smaller but wider wake deficit. However at higher AoAs, a narrowing of the wake and a substantial decrease in deficit is experienced.

Figure 5: Normalized RSS for the different models. Column A) flat plate model. Column B) 4 percent pre-tension model. Column C) 1 percent pre-tension model.


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Looking at both the RSS and instantaneous vorticity generated by the membrane models leads to some insight on how the membrane motions help aid in the reduction of reverse flow present in the near wake, Figure 5 and Figure 6 respectively. Examining the RSS obtained for the flat plate cases, momentum transfer of positive sign (opposite sign deviations) is seen within the shear layer. While momentum transfer of negative sign (same sign deviations) is seen beginning at the leading edge and trailing edge. As the AoA is increased the RSS continues to grow. The membrane models share similar features at low AoA with positive RSS values seen in the shear layer as well as negative RSS values seen at the leading and trailing edge. At higher AoAs (α>8) the membrane’s influences becomes apparent. The membrane models have a slight reduction in positive RSS values (lower momentum fluid) within the shear layer while the negative RSS values produced at the rear of the model are seen to move closer to the trailing edge helping to introduce high momentum fluid into the near wake. Observing the instantaneous vorticity generated by the 1 percent pre-tension membrane at 20° AoA, plot A of Figure 6 one sees high momentum fluid building up on the lower surface of the membrane. This build up creates a pressure bubble that traverses down the membrane, then at the trailing edge the high pressure is released, plots B and C. The release of high pressure into the lower pressure region at the trailing edge causes a vortex structure of opposite sense (compared to the leading edge) to form, plot D. The vortex structure introduced at the trailing edge interacts with the shear layer reducing its overall size. These structures also introduce mixing into the near wake allowing higher momentum fluid to mix with lower momentum. While both membrane models had similar features the 1 percent pre-tension membrane seemed to slightly out preform the 4 percent pre-tension membrane based on the size of the separation bubble, shear layer height, and wake deficit. This is further supported by the results obtain by Zhang et al.29 where force measurements were taken on identical membrane models. The 1 percent pre-tension membrane had a slight improvement in aerodynamic efficiency compared to the 4 percent pre-tension membrane model.

Figure 6: Normalized instantaneous vorticity for the 1 percent pre-tension membrane at 20° AoA.


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B. Membrane Surface Deflections The 3D surface membrane deflections were captured using the high speed DIC system discussed earlier. The intent of investigating the membrane surface deflections is to provide a better understanding of the membrane’s motions and how it is affected by the fluid flow. All length scales plotted within this section have been normalized by the full chord length. The time averaged deflections of the membrane models are presented in Figure 7 for both the 1 percent pre-tension model and the 4 percent pre-tension model through a range of AoAs: 4°, 8°, 12°, 16°, and 20°. The outer frame and battens for the membrane models have been superimposed in the contour plots to better help establish the orientation in which the membranes lie. The membrane models shared similar trends with both models experienced an increase in deflections as AoA is increased (increase in aerodynamic loading) and as expected the lower pre-strain membrane stretching further. One feature to note about the deflections is the asymmetric shape that the outer membranes exhibit (discussed later) whereas the middle membrane exhibits a symmetric distribution. The symmetric displacements at the middle membrane are similar to the results of the higher aspect ratio membrane models obtained by Timpe et al.15 since that study analyzed the center membrane where 3D tip effects were thought to be of minimal influence. One discrepancy to note is the deflections at the leading edge of the left membrane. After construction, the left membrane had a slight sag at static conditions. The sag at the leading edge allowed the membrane to have an increase in deflection at that specific location.

Figure 7: Normalized mean membrane deflections and normalized RMS deflections through a range of AoAs for the Independent DIC data with outer supported models.


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The average fluctuations of the membranes motions are shown in the RMS plots also displayed in Figure 7. Since the membrane models had metalic battens and have scalloped trailing edges the models experienced max fluctuations at the center trailing edge of each cell for all tested cases. While looking at the contour plots no clear trend stands out, however one item is noted, membrane fluctuations dramatically decrease after a certain AoAs. Another similar feature was the greater fluctuations experienced at the outer edges of the left and right membranes. The wing tip vortices were thought to be the cause of these asymmetric fluctuations however the mounting hardware was also believed to be a contributing factor since the models were supported by the outer edges. The effects of wing supports were investigated in Arce3 where it was found to have minimal effect supporting the hypothesis that the asymmetry on the outer membranes is flow related. The membrane motions have further been examined by looking at the trailing edge fluctuations. Figure 8 shows power spectral density plots of the membranes motion obtained at the center of the trailing edge of each membrane cell (left, middle and right) for the 1 percent pre-tension membrane column A and the 4 percent pre-tension membrane column B. While only AoAs of 8°, 12°, and 16° are shown, angles of 4°, 20°, 24°, 28°, and 32° exhibits similar feature and their graphs have been omitted. The different cells within the 1 percent pre-tension model all tend to experience the same dominate frequency with the exception of the 8° AoA case. At 8° AoA the middle membrane seems to experience a peak shifting phenomena, shifting it’s dominate frequency slightly higher. Each cell within the 4 percent pre-tension model also experiences the same dominate frequency as each other. Furthermore, an additional peak at a higher frequency is also present

Figure 8: Trailing edge PSD for each membrane. Column A) 1 percent pre-tension membrane model. Column B) 4 percent pre-tension membrane model.


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Figure 9: First peak frequency vs. AoA for each membrane during independent DIC testing.

throughout all AoAs. The additional peak experienced within the PSD is thought to be contributed to the RMS fluctuations, where the membranes are seen to have two distinct peaks in the RMS plots. Again, at 8° AoA the higher frequency experiences a slight peak shifting phenomena. The membrane’s first peak frequency as a function of AoA was extracted from the spectral plots and is displayed in Figure 9. From these plots one can observe the effects of both the pre-tension and the added aerodynamic tensioning as the wing is brought to higher AoAs. The 1 percent pre-tension membrane tends to have a lower frequency compared to the 4 percent pre-tension membrane as one would expect based on a higher tension in the membrane. Furthermore, there is a general trend in the frequency of the membranes, where frequency increases with increasing AoA. This is expected as the aerodynamic load increases the membrane’s tension with increasing AoA. While the flow provides the excitation for the membranes, the membrane’s properties drive its motion, not shedding from the wing as will be shown based on a Strouhal number analysis, which has been reported for some cases of fully supported membrane wings (6,18). Although not shown here it should be noted that as the models AoA is further increased the amplitude of the membrane’s oscillations levels off where again the membranes seems to have reached their material limits. The membrane’s motions were again examined by looking at the trailing edge fluctuations, however, this time they were observed qualitatively. Figure 10 a) plots the center trailing edge fluctuations for the 1 percent pre-tension model at AoAs of 4°, 12°, and 20°. Comparing the different cells within the model (left, middle, and right) at low AoAs the membranes appear to be randomly phased. They are thought to have started their cycles of oscillations and randomly come in and out of phase with each other. However, at higher AoAs, where there is a stronger aerodynamic loading present, the membranes are seen beating with each other and appear to be in phase. Continuing examining the membrane models qualitatively, Figure 10 b) plots a segment of instantaneous membrane surface position at the center chord of the middle cell. The vertical axis within these plots represents the chordwise direction of the model, while the horizontal axis represents time in milliseconds. The plots are for the 1 percent pre-tension membrane model at AoAs of 4°, 12°, and 20°. Similar behavior can be seen at other AoAs as well as in the 4 percent pre-tension membrane model. The normalized deflections visually show the wave type behavior of the membrane’s motion. The motions display features of both a standing wave and traveling wave. A pure standing wave would plot straight vertical lines of alternating colors, portions of a standing wave can be seen in the upper regions of the plots (near the trailing edge of the model). A pure traveling wave would plot diagonal lines of alternating colors, this can be seen in the middle portion of the plots (mid-chord of the model). While these plots visually show the membrane’s motion is a combination of a standing wave and a traveling wave, a more detail description was desired


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A B

Figure 10: 1 percent pre-tension membrane model a) Instantaneous trailing edge membrane surface deflections for all three membranes b) Instantaneous membrane surface deflections for a slice along the center membrane.

Figure 11: Middle cell average wave speed vs. AoA for both membrane models


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An attempt was made to determine the speed of the traveling wave within the membrane through a temporal based correlation analysis. Wave speeds were determined by correlating 15 different spatial locations along the membrane and averaged to determine the values displayed Figure 11 where they are plotted as a function of AoA for both membrane models. The 4 percent pre-tension membrane produced higher wave speeds throughout all AoAs as one would expect based on the higher tension in the membrane. At the lower AoAs, the higher wave propagation is thought to be due to the location of the shear layer. Since the shear layer is relatively close to the membrane’s surface, some of the higher free stream velocity is entrained and transitioned into the membrane aiding in the wave speed. As the AoA is increased, the shear layer grows in both size and height, thus not allowing the higher momentum fluid to reach the membrane’s surface. The wave propagation relies on the tensioning within the membrane as well as the tensioning associated with the increase in aerodynamic loading. As AoA is increased the membrane’s frontal projection area is also increased, this allows a larger portion of the membrane to experience an increase in loading. This increase in loading is proportional to the tensioning within the membrane where an increase in tension leads to an increase in wave speed.

Figure 12: PSD of both the middle membrane’s trailing edge and select locations of the flow-field for the 1 percent pre-tension membrane at 8° AoA. Plot A) U-mean plot specifying the exact locations where PSD was obtained at. Plot B) Plots the PSD of the specified locations in plot A, along with the PSD of the middle membrane’s trailing edge.

C. Fluid Structure Interactions The examination of the flow-field fluctuations and membrane oscillations highlighted some of the couplings associated with the membrane and flow. Since PIV and DIC were acquired simultaneously, both of their respective PSD’s are compared. The PSD of the flow-field was obtained in the same fashion as in the


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membrane’s PSD. Figure 12 A shows the normalized U-component of the velocity field for the 1 percent pre-tension membrane model at 8° AoA. The diamond shapes signify the locations where PSD was calculated. Figure 12 B plots the PSD at each of the diamond locations along with the previously found PSD of the middle membrane’s trailing edge. One of the main features in Figure 12 B is the presence of the membrane’s dominate frequency appearing throughout the flow-field. This suggests the membrane motions are driving the surrounding flow-field. The powers associated with the flow-field’s dominant frequency are dependent upon location relative to the membrane. Amplitudes at the leading edge are significantly less than the powers associated with the flow around the trailing edge and near wake. The near wake provides the highest powers due to the large fluctuations experienced within the U-component of velocity. Although not included this type of behavior existed for all angles of attack and both pretensioned membranes examined. Additional examination of coherence between these two signals showed a peak at the dominant frequency and low broad band levels. The Strouhal number for the membranes vibrating frequencies was also investigated. It should be noted that we are using a length scale associated with the projected area of the model, c*sin(AoA). Using the membrane’s dominant frequency previously found as the frequency, the modified Strouhal number is evaluated. Figure 13 plots the modified Strouhal number vs. AoA for both membrane models. Additionally within the plot is a line displaying the approximate expected Strouhal number (St≈0.17) if the flow was dominated by vortex shedding. Fage and Johansen7 showed for a rectangular flat plate at lower AoAs (α <30°) the modified Strouhal number varied between 0.15-0.22. Examining Figure 13, the Strouhal number increases with increases AoA until 28° where it then starts to decrease. This decrease is thought to be a byproduct of the models reaching their material limits. Comparing the membrane models trend to the trend obtained by Fage and Johansen, the membrane models appear to driving the surrounding flow significantly altering it from a traditional rectangular flat plate model.

Figure 13: Modified Strouhal number vs. AoA.

4. Summary This study investigated both the fluid and structure characteristic of a low aspect ratio, batten reinforced, multi-cell, scalloped membrane wing in a low Reynolds number flow. Two different membrane models were investigated, the first model had a 1 percent pre-tension membrane while the second model had a 4 percent pre-tension membrane. Time averaged flow-fields of both membrane models and a flat plate model were obtained by PIV. Comparing both membrane models, the 1 percent pre-tension membrane showed a slight improvement, in both a smaller separation bubble and wake deficit compared to the 4 percent pre-tension model. This slight improvement can help explain the force data presented in Zhang et al.29. The Reynolds shear stress term and U-RMS fluctuations provided insight on both momentum transport and shear layer growth. At low AoAs (α<12°) the membrane models had a slight decrease in shear layer size compared to the flat plate case. At


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larger AoAs, membrane models continued to have a smaller shear layer size as well as in increase momentum transport and turbulent mixing. Analysis of the membrane’s deflections led to the following trends, as the AoA was increased the mean deflection (averaged camber) also increased. While the 1 percent pre-tension membrane had greater deflections throughout all AoA, at higher AoA both membrane model deflections leveled off where the models seem to have reached their material limits. A similar trend was also found in the frequency which the membranes oscillate at. Frequencies increased with AoA where the 4 percent pre-tension membrane generally vibrated at a higher frequency throughout the AoAs. Eventually, the frequencies leveled off and started to decrease at the higher AoA. RMS fluctuations shared similar experiences, as AoA was increased the fluctuations also increased. However, the fluctuations quickly subsided as the AoA was increased to higher angles. In preliminary results the outer asymmetric deflections were thought to be a byproduct of both wing tip vortices and mounting hardware effects. Final results show mounting hardware had no major effect on the asymmetric deflections however fluctuations did increase at the outer membranes when the center mounting hardware was used. The synchronized experiments were able to provide highlights in the coupled membrane and flow interactions. Comparisons of the membrane’s dominant frequency to that the flow-field’s showed the membrane’s ability to influence the surrounding flow. There is a dependency on location within the flow-field, however flows approximately close to the trailing edge and near wake exhibited the same frequency characteristics to that of the membrane. Examination of the instantaneous vortices shows the membrane’s ability to produce a positive vortex structure at the trailing edge. These structures introduced higher momentum fluid in the near wake aiding in a more favorable wake. 5. Acknowledgments The authors would like to the collaborations of Zheng Zhang, Yakoov Abudaram, Peter Ifju and Paul Hubner as well as the financial support of AFOSR. 6. References

1. Abudaram, Y., Ifju, P., Ukeiley, L., Hubner, J. (2014) "Controlling Pre-Tension of Silicone Membranes on Micro Air Vehicle Wings," Journal of Strain Analysis for Engineering Design, Vol. 49(3):161-170.

2. Albertani R., Khambatta, P., Hart, A., Ukeiley, L. S., Oyarzun, M., Cattafesta, L., Abate, G., “Validation of a Low Reynolds Number Aerodynamic Characterization Facility,” (2009) AIAA conf. paper: 2009-880.

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Fluid Structure Interactions in Low Aspect Ratio Membrane