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An experimental investigation of laminar separation bubble formation on flexible membrane wing
European Journal of Mechanics / B Fluids 65 (2017) 326–338
Contents lists available at ScienceDirect
European Journal of Mechanics / B Fluids journal homepage: www.elsevier.com/locate/ejmflu
An experimental investigation of laminar separation bubble formation on flexible membrane wing Hacımurat Demir a,b,1 , Mustafa Serdar Genç a, * a b
Wind Engineering and Aerodynamic Research Laboratory, Department of Energy Systems Engineering, Erciyes University, 38039, Kayseri, Turkey Department of Mechanical Engineering, Aksaray University, 68100, Aksaray, Turkey
highlights • Unsteadiness included in laminar separation bubble lead to complicated unstable deformations. • Different vibrational modes observe due to laminar separation bubble. • Separation bubbles cause to time-dependent variations on membrane vibration.
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Article history: Received 4 November 2016 Received in revised form 8 May 2017 Accepted 30 May 2017 Available online 12 June 2017 Keywords: Flexible membrane wing Fluid–structure interaction Laminar separation bubble Unsteady aerodynamics
a b s t r a c t In this study, fluid–structure interaction over a flexible membrane wing with aspect ratio (AR) of 3 at low Reynolds numbers was investigated experimentally. Smoke wire flow visualization technique was performed for analyzing time-dependent behavior of flow over this flexible membrane wing. Furthermore, time dependent deformation of flexible membrane wing was measured. It was clearly seen that the value of membrane deformation increased with increasing angle of attack. Moreover, it was stated that the size of laminar separation bubble (LSB) changed with time due to the unsteady flow characteristics of membrane wing. The unsteady behavior over the flexible membrane wing caused different deformation modes to form at different angles of attack. For the flexible wings with higher aspect ratios, the LSB was more dominant in the membrane wings at low Re numbers, and caused the membrane vibration to increase based on the angle of attack which the LSB started to be overpowering. © 2017 Elsevier Masson SAS. All rights reserved.
1. Introduction In recent years, scientific surveys related to aerodynamics have been concentrated upon low Reynolds number aerodynamics, transition and laminar separation bubble and effects this bubble on aerodynamic performance owing to the improvement in wind turbines, micro air vehicles (MAVs) and unmanned aerial vehicles (UAVs) [1–6]. That is why it is seen that there is an increasing concern in the study of membrane wings. Because of the strong viscous effects, flows in low Reynolds number regard to MAVs result in laminar-transitional, separated flow hindering lift generation [7]. Both experimental and numerical results of studies in regard to low Reynolds number aerodynamics demonstrate that flow has a susceptibility to separate because of the lower inertia forces compared to the comparatively higher viscous forces. In other respects, owing to this phenomenon
* Corresponding author. Tel.: +90 352 207 66 66-32320 E-mail address: [email protected] (M.S. Genç). 1 Fax: +90 352 437 57 84.
http://dx.doi.org/10.1016/j.euromechflu.2017.05.010 0997-7546/© 2017 Elsevier Masson SAS. All rights reserved.
and adverse pressure gradients encountered on airfoils, LSB is presumably to be formed [2,3,8]. Genç [9] investigated on unsteady aerodynamics over the cambered membrane wing. Acquired experimental results exhibited that membrane wing’s camber having excessive length induced the separated shear layer. Due to this circumstance, coefficient of lift increased. Besides, wings with excess length indicated small separated regions because shear layer was closer to the wing surface, although camber of the wing raised. As a deduction, it was stated that unsteadiness included vortex shedding and tip vortices, and the coalescence of vortex shedding and tip vortices occasioned complicated unsteady deformations of membrane wings. Bleischwitz et al. [10] presented ground effect on aeromechanics of membrane wings and observed that ground-effect caused to higher lift production and a constant low drag at low to moderate angles of attack for both flat plates or membrane wings. Ke et al. [11] studied on aeroelasticity for flexible oscillating wing and noticed that adopting new kind driving way would not have flutter problems for the oscillating wing and it could generate propulsive force. Osterberg [12] deduced that membrane wings ensured
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Nomenclature AR c DIC E f LSB Re St t U y/s Z Zstd
Aspect ratio Chord length Digital image correlation Young’s modulus, MPa Frequency Laminar separation bubble Reynolds number Strouhal number Time, s Freestream velocity Location of smoke wire Flexible membrane displacement Standard deviation of flexible membrane displacement
Greek letters
α ρm
angle of attack, ◦ density of rubber latex sheet, g/cm3
remarkable improvements in maximum CL when comparing to a rigid wing under pitching conditions. Zhang et al. [13] stated that membrane wing ensured higher lift curve declination, stallregion lift and lift-to-drag ratio when comparing to the rigid flat plate. Song et al. [14] stated that membrane wings had maximum lift coefficients, higher lift declination and led to delay stall. Hu et al. [15] examined flexible membrane wings aerodynamics experimentally utilizing particular flexibility of skin in flapping flight. According to obtained results, flapping motion ensured remarkable aerodynamic advantages at unsteady flapping flight regime. Greenhalgh et al. [16] noticed that increasing excess length led to decrease angle of attack at which separation occurred. Wrist et al. [17] made comparison between aerodynamic features for silicone rubber MAV wings with cambered and flat frames. It was deduced that cambering the frames of wings raised aerodynamic efficiency comparing the flat frames. Lian et al. [18] described the membrane aerodynamic and suitable rigid wings under flight condition of micro aerial vehicles. They realized that membrane wing both delayed stall and what is more adapted to the unsteady flight environments. Rojratsirikul et al. [19] investigated experimentally flowinduced vibrations of rectangular membrane wings with aspect ratio (AR) of 2. They conducted flow field and time-accurate measurements of membrane deformations. Deformations showed different vibration mode shapes as a function of the Re number and angle of attack. The membrane oscillations were observed in a chordwise two mode at higher angles of attack. Since the combination of tip and leading edge vortices caused a mixture of chordwise and spanwise vibrational modes. Moreover, they deduced that vortex shedding frequency of rigid wings emerged remarkably slight influence of aspect ratio even when it was as nominal as unity. Furthermore, Rojratsirikul et al. [20] studied about the effects of pre-strain and excess length of membrane in terms of unsteady fluid–structure interactions. They observed that airfoil with excess length ensured the largest strain and camber. Additionally, for the excess length airfoils, prelude of the wing vibration was detained to a higher angle of attack. In addition to this, with increasing angle of attack, both St number and mode number were disposed to diminish. The purpose of this study is to survey flow over flexible membrane wings and the formation of separation bubbles occurring in the flow and effects of bubbles on the wing deformation. In
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this regard, aspect ratio of 3 (AR = 3) flexible membrane wing was utilized and formation of separation bubble in the region of wing center at which tip vortices had no effect were investigated at different low Reynolds numbers and miscellaneous angles of attack. 2. Measurement procedure The study was conducted in the wind tunnel in Erciyes University. The test section of wind tunnel is geometrically square. The size of tunnel is 500 mm by 500 mm consisting of optically transparent walls. Free-stream turbulence intensities of tunnel are 0.3% for maximum speed of 40 m/s and 0.7% for lowest speed of 5 m/s, respectively, [3,21,22] which are appropriate to perform experiments at low Reynolds numbers in order to determine separation and reattachment point, LSB and stall in accordance with Mayle, [23]. All the flexible membrane wings used in this study were designed in conjunction with 0.2 mm black latex rubber sheet which had Young’s modulus (E) of 2.2 MPa, and density (ρm ) of 1 g/cm3 [20]. There was no pre-stress or excess length on latex rubber sheet. To this end, flexible material was glued to the airfoilformed frame which was made of rigid stainless steel. As illustrated in Fig. 1, this rigid frame was manufactured for having a crosssection of airfoil shape. 2.1. Flow visualization experiments In order to visualize flow, smoke wire technique was opted, since it was simple and reliable to conduct. A smoke-wire which was strained between the upper and lower tunnel walls was used for heating the machine oil and fluid for marking the streamlines to visualize flow in the tunnel. Adequate quantity of voltage was applied to smoke-wire that was coated with oil. The oil evaporated forming smoke lines in the tunnel. The smoke lines were fulfilled by this technique indicated the flow over the related airfoil and the flow phenomena such as laminar separation bubble or stall were made easily visible. Canon EOS-D1100 camera was used for capturing related images during experiments. The picture frequency of Canon EOS-D1100 camera was chosen as 30 frames per second. Reflection of images in tunnel’s wall test section that was manufactured by plexiglass was the main problem. That is why camera and lighting arrangements were conducted thoughtfully to gain dark medium. As shown in Fig. 1, the location of smoke wire was designated as y/s, and the flow visualization experiments were conducted for two locations (y/s = 0.4 and y/s = 0.1) to indicate the effects of LSB and tip vortices. However, with increasing the Reynolds number, it gets difficult to capture a convenient image of streamlines and the image becomes blurred, because the filaments are quickly dissipated in the flow. 2.2. Evaluation of deformation Deformations and displacements of flexible membrane wing were measured by means of Digital Image Correlation (DIC) system as illustrated in Fig. 2. In accordance with this purpose, deformation measurements of the AR = 3 membrane wing were conducted by way of utilizing DANTEC Dynamics three-dimensional highspeed image correlation system (Q-450: the number of pixels was 1280 × 800) and DANTEC Al-11-BMB_9 × 9 was chosen as calibration target. Furthermore, frame rate was 1 kHz. Throughout the deformation measurements, 1000 frames were captured for each experimental case. This system captures successive images afterwards calculates the displacement over AR = 3 flexible membrane wing by following the deformation of spots (Fig. 3) fulfilled to the surface of the AR = 3 flexible membrane wing using a cross-correlation method. The minimum and maximum uncertainties of deformation measurement were ±0.030 mm at
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Fig. 1. Dimensions of the flexible membrane wing and position of smoke wire on membrane wing.
α = 0◦ and 0.013 mm at α = 36◦ , respectively; and the average uncertainty of the deformation measurement was ±0.02 mm. 2.3. Measurement of aerodynamics performance An automatic angle changer mechanism was utilized for measuring aerodynamic forces of the membrane wing at the angles of attack in the range of 0◦ –45◦ . Strain gauges were used for measuring lift and drag forces separately. Measured time-averaged forces in the normal direction and tangential direction to the angle of attack of wing were converted to the lift (CL ) and drag (CD ) force coefficients in x and y axes via transformation of coordinates. The maximum uncertainties of the lift force coefficient and the drag force coefficient were approximately 6% and 7% for Re = 2.5 × 104 , respectively. And it reduces as Reynolds number rises [3] (see Fig. 4).
3. Results and discussion 3.1. Flow visualization results It was seen that separation bubbles on the flexible membrane wing did not occur significantly at low angles of attack (except small disturbances on the flow due to the frame of wing) and leading edge separations increased gradually with increasing angle of attack and these vortices stroke on the wing and moved towards to the trailing edge at y/s = 0.4 as seen in Figs. 5 and 6. Leading edge vortices which were grew up with increasing angle of attack could not attach on the wing after at 20◦ for Re = 2.5 × 104 and at 22◦ for Re = 5 × 104 . However, it was observed that these leading-edge separations were to be smaller comparing to the rigid wing [3].
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Fig. 2. Experimental set-up for DIC measurement.
Fig. 4. Photography of force measurement system.
Fig. 3. AR = 3 flexible membrane wing with white speckle patterns for deformation measurements.
Moreover when the flow visualization figures of the membrane wing at y/s = 0.1 (Figs. 7 and 8) were investigated, it was seen that as the angle of attack increased, tip vortices and wake region of the membrane wing grew up. The LSB shrank at the tip of the wing owing to these tip vortices, but these vortices could not affect entirely the flow over the membrane wing because the aspect ratio was high. In the membrane wings with low aspect ratio, the tip vortices caused the stall to delay [4,9,19] but the flow over the membrane wing with higher aspect ratio was seriously affected the LSB [6]. Separation bubbles were more effective because there was no significant effect of tip vortices in the middle of wing for AR = 3 and increasing Reynolds number led to increase in inertial forces on the wing. Due to this situation, flow over the wing became more stable. At Re = 2.5 × 104 (Fig. 5), inertia of fluid flow was not dominant and flow separations and vortices were larger by the
effect of viscous forces. Vortices were large but had low energy. At Re = 5 × 104 (Fig. 6), vortices were contracted by means of more stable flow condition comparing with respect to Re = 2.5 × 104 . After the smoke-wire experiments of instantaneous images of vortices which were occurred on the wing, all images obtaining at specific angles of attack were examined individually and then vortex formation was revealed depending on time. Figs. 9–11 demonstrated the results of time (t) dependent flow visualizations at y/s = 0.4 for angles of attack of α = 6◦ , α = 10◦ and α = 12◦ for various time intervals. When comparing obtained results at different times between t = 0.08 s and t = 0.20 s, timedependent behaviors of LSB was clearly seen. In Fig. 9, at constant angle of attack of α = 12◦ , the size of bubble became bigger at t = 0.16 s and then smaller at t = 0.20 s for Re = 2.5 × 104 . On the other hand, at Re = 5 × 104 and at α = 6◦ , it was observed that the size of laminar separation bubble grew up from t = 0.08 s to t = 0.12 s and then this bubble became smaller at t = 0.16 s. At the end of t = 0.20 s, it grew once again as seen in Fig. 10. Furthermore, the size of laminar separation bubble grew up until t = 0.12 s and then became smaller t = 0.16 s at
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Fig. 5. Smoke-wire visualization of AR = 3 membrane wing for Re = 2.5 × 104 at y/s = 0.4.
α = 12◦ and Re = 5 × 104 for AR = 3 flexible membrane wing as illustrated in Fig. 11. To this end, it can be stated that the size of bubble changed with time due to the unsteady flow characteristics of membrane wing. Moreover, as it was seen in time-dependent images, inertial forces were low at Re = 2.5 × 104 so energy of
vortex was less and formation of vortex completed tardily whereas formation of vortex was occurred expeditiously and more stable at Re = 5 × 104 due to the having high inertial forces and vortex energy. This situation affected the deformation occurring on the flexible membrane wing.
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Fig. 6. Smoke-wire visualization of AR = 3 membrane wing for Re = 5 × 104 at y/s = 0.4.
3.2. Aerodynamic force coefficients measurement results
α = 6◦ , the linearity of the CL curve changed because the LSB grew
The time-averaged force coefficients versus angle of attack were given in Fig. 12. The stall angles changed based on Reynolds number, and the stall for Re = 2.5 × 104 occurred early. At Re = 2.5 × 104 , at
at the leading edge as shown from the photographs of the smokewire flow visualization. After α = 12◦ , the LSB became dominant and the leading-edge separation set in motion. At Re = 5 × 104 , the effect of inertia force increased and the LSB shrank, and stall occurred late, and also the CL raised since the membrane chamber
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Fig. 7. Smoke-wire visualization of AR = 3 membrane wing for Re = 2.5 × 104 at y/s = 0.1.
increased. Moreover, when comparing the lift force coefficient of AR = 3 membrane wing and the normal force coefficient obtained by Rojratsirikul et al. [19] for AR = 2 membrane wing, it was seen that the stall delayed owing to the tip vortices around the AR = 2 membrane wing while the flow over the membrane wing
with AR = 3 was affected the LSB. In addition, when the drag force coefficients (CD ) which were no in the study of Rojratsirikul et al. [19] were investigated, while CD were same for both Re number at lower angles of attack, it increased owing to separated flow at higher angles of attack.
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Fig. 8. Smoke-wire visualization of AR = 3 membrane wing for Re = 5 × 104 at y/s = 0.1.
3.3. Deformation measurement results Membrane deformation and time-averaged standard deviation reflecting the transient deformation part (vibrations which were formed due to the membrane deformation induced from flow) results for flexible membrane wing with respect to different angles
of attack at Reynolds numbers of Re = 2.5 × 104 and Re = 5 × 104 were illustrated in Figs. 13–16. It was seen that maximum deformation on the wing increased with increasing angle of attack from α = 0◦ to α = 36◦ . Besides, maximum deformation region in spanwise of the wing was geometrically similar. At Re = 2.5 × 104 , although vibrational modes were not explicit at low angles of
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Fig. 9. Smoke-wire visualization of AR = 3 membrane wing for Re = 2.5 × 104 and α = 12◦ at y/s = 0.4 [6].
Fig. 10. Smoke-wire visualization of AR = 3 membrane wing for Re = 5 × 104 and α = 6◦ at y/s = 0.4 [6].
Fig. 11. Smoke-wire visualization of AR = 3 membrane wing for Re = 5 × 104 and α = 10◦ at y/s = 0.4 [6].
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Fig. 15. Distributions of time-averaged deformation of AR = 3 flexible membrane wing at Re = 5 × 104 for various angles of attack. Fig. 12. CL and CD coefficients of the wing at different angles of attack (α ) at low Re numbers.
attack (α = 0◦ –4◦ ), chordwise vibrational mode 1 which means one half wave of membrane deformation was observed at α = 6◦ and α = 8◦ . The dominant mode number was determined by counting the peaks which are maximum deformation points
(antinodes) in graph of standard deviation of deformation. Vibration mode 2 occurred because of increasing angle of attack to α = 16◦ and this effect proceeded through α = 22◦ . Vibration mode 1 took place at α = 24◦ and continued until α = 36◦ . The value of maximum deformation and number of vibrational mode increased with increasing Reynolds number from 2.5 × 104 to 5 × 104 because of LSB.
Fig. 13. Distributions of time-averaged deformation of AR = 3 flexible membrane wing at Re = 2.5 × 104 for various angles of attack.
Fig. 14. Distributions of time-averaged standard deviation of the deformation for AR = 3 flexible membrane wing at Re = 2.5 × 104 for various angles of attack.
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Fig. 16. Distributions of time-averaged standard deviation of the deformation of AR = 3 flexible membrane wing at Re = 5 × 104 for various angles of attack.
At Re = 5 × 104 , for low angles of attack (α = 0◦ , α = 2◦ ) maximum standard deviation was more intense at the tip of the wing. At α = 6◦ and α = 8◦ , spanwise vibration modes 2 and 3 and chordwise vibration mode 4 were observed. Due to the effect of separation bubble, vibrational modes decreased in the middle section and combined at the tip region at α = 10◦ and these vibrational modes became chordwise mode of two at α = 12◦ and continued until α = 24◦ . It was seen that at α = 12◦ and α = 24◦ vibration mode 2 which was near to the trailing edge decreased through span owing to the effect of tip vortices. Between α = 30◦ and α = 36◦ , vibration mode 1 was observed and the value of maximum standard deviation region decreased with increasing angle of attack. When looking through the results of standard deviation, vibrational modes which were occurred with changing angle of attack were partly mode one, two, there and four. These various vibrational modes occurred owing to the both leading edge separation and vortices forming on the wing. At Re = 2.5 × 104 , standard deviations were low because of having bulky but low energy vortex, whereas at Re = 5 × 104 small and beany vortex had high energy especially at low angles of attack, and thus vibration modes 4 were observed. LSB occurred over the membrane wing varied with time, and this situation caused in vibrations of the membrane to change. Since LSB was more effective on the membrane wing with AR = 3, vibrational modes occurred distinctly comparing with the membrane wings with lower aspect ratio. When comparing the graphs of standard deviation of the deformations given in the study of Rojratsirikul et al. [19] for Re = 5 × 104 with those of our study (Fig. 17 in this study), it was seen that the membrane wing with AR = 2 at moderate angles of attack in chordwise
vibration mode 2 occurred whereas chordwise vibration mode 4 formed in the AR = 3 membrane wing. As the angle of attack increased; tip vortices growing caused the size of LSB to decrease and the flow complexity to increase, and so vibrational modes increased over the AR = 2 flexible membrane wing. The variation of maximum deformation was decreased by means of LSB in the range of the angle of attack of 8◦ and 18◦ , then increased due to the tip vortices which became effective with increasing the angle of attack for the AR = 2 membrane wing (Fig. 18 in this study). When examining the power spectra graphs given in Fig. 11(c) by Rojratsirikul et al. [19], secondary vibrational band was observed at the angle of attack from 8◦ to 12◦ corresponded to the frequency of St = 1.2, and from 13◦ to 18◦ corresponded to the frequency around St = 1.0. For the AR = 3 flexible membrane wing, due to the effect of LSB at lower angles of attack, high vibrational modes and less maximum deformations were observed as seen in Fig. 18 in this study, and vibrational modes occurred less than the modes of the AR = 2 membrane wing at the angle of attack of 14◦ because of the LSB growing. As the angle of attack reached to the stall angle, vibration mode 2 were observed for both AR = 2 and AR = 3 membrane wings, and bigger leading edge- and tip vortices which were spread towards the wake region had no effect on the deformation of the membrane wing under separated flow condition. The variations of vibrational modes on the membrane wing were also seen in the distribution of power spectra given in Fig. 19(b) in this study. In these distributions, there was a darker band at St = 1.2 for angles of attack in the range of 6 and 14◦ , while second dark band was noticed at St = 0.6 for angles of attack in the range of 8–24◦ . Especially, vibrational bands occurred around St = 1.2
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Fig. 17. Comparison of time-averaged standard deviation of the deformation of AR = 2 [19] and AR = 3 flexible membrane wings at Re = 5 × 104 for different angles of attack.
and St = 0.6 at lower angles of attack pointed out the leading edge separation and the trailing edge separation, respectively. In addition to this, as the aspect ratio was decreased, the vibration band around St = 0.6 started to become at lower angles of attack. In the results of power spectra for Re = 2.5 × 104 in Fig. 19(a), vibration mode 2 occurred and darker band was observed at angles of attack between 16◦ and 22◦ as shown in the standard deviation graphs. As can be seen from the studies of Rojratsirikul et al. [19] and Genç [9], vibrations of the membrane wing increased with ascending the Re number (Fig. 19). Furthermore, the obtained results of Rojratsirikul et al. [19,20] and this study, LSB became more effective in membrane wings under low Re number flow regimes with rising the aspect ratio, and LSB caused membrane vibrations to increase, secondary darker bands (modes) formed at vibrations of the membrane wing according to the angle of attack which the LSB started to be effective. Consequently, in membrane wings, unsteadiness included LSB lead to complicated unstable deformations of these wings. 4. Conclusions Unsteady flow behavior around AR = 3 flexible membrane wings was surveyed experimentally at Reynolds number of 2.5 × 104 and 5 × 104 in this study. Flow visualization by smoke wire technique was conducted to analyze time-dependent behavior of flow over flexible membrane wing. In addition to this, DIC system was utilized for time dependent deformation measurement of flexible membrane wing. Moreover, as seen in instantaneous images at Re = 2.5 × 104 inertial force was low so energy of vortex was low and formation of vortex completed lately while at Re = 5 × 104 inertial force and energy of vortex were higher so vortex formation was faster and more stable. This situation affected the deformation
Fig. 18. Comparison of normalized maximum time-averaged displacement of AR = 2 [19] and AR = 3 flexible membrane wings versus the angle of attack at Re = 5 × 104 .
occurring on the flexible membrane wing and different vibrational modes were observed due to the separation at leading-edge and vortices with changing angle of attack. Especially at low angles of attack, vibration modes 3 and 4 were observed and vibrational mode reduced to two with increasing angle of attack and vibration mode 1 on the wing was obtained after the flow separation on the wing completed entirely. As a consequence, formation of leading edge separations on the flexible membrane wing were affected by both Reynolds number and leading-edge vortices occurring due to the separation bubbles caused time-dependent variations on membrane wing vibration. With increasing the aspect ratio, LSB became more dominant in the membrane wings at low Re numbers, and caused membrane vibrations to increase based on
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Fig. 19. Power spectra distributions of the membrane vibrations versus the angle of attack for AR = 3 flexible membrane wing at (a) Re = 2.5 × 104 ; (b) Re = 5 × 104 .
the angle of attack which the LSB started to be effective. Consequently, in membrane wings, unsteadiness included in LSB lead to complicated unstable deformations of these wings. Acknowledgments The authors would like to thank the Scientific and Technological Research Council of Turkey (TÜBİTAK) under the project number: 213M329, and the Scientific Research Projects Unit of Erciyes University under the contract numbers: FDK-2015-6171, FDA-20145273 and FBG-2014-5337 for funding. References [1] M.S. Genç, U. Kaynak, G.D. Lock, Flow over an Aerofoil without and with leading edge slat at a transitional Reynolds number, Proc. IMechE G: J. Aerosp. Eng. 223 (3) (2009) 217–231. [2] M.S. Genç, I. Karasu, H.H. Açıkel, M.T. Akpolat, Low Reynolds number flows and transition, in: M. Serdar Genç (Ed.), Low Reynolds Number Aerodynamics and Transition, Intech-Sciyo Publishing, ISBN: 979-953-307-627-9, 2012.
[3] M.S. Genç, I. Karasu, H.H. Açıkel, An experimental study on aerodynamics of NACA2415 aerofoil at low Re numbers, Exp. Therm Fluid Sci. 39 (2012) 252–264. [4] M.S. Genç, H.H. Açıkel, H. Demir, M. Özden, M. Çağdaş, I. Isabekov, Effect of tip vortices on membrane vibration of flexible membrane wings with different aspect ratios, in: 10th International Conference on Experimental Fluid Mechanics, 17–20 November 2015, Liberec, Czech Republic, 2015. [5] M.S. Genç, M. Özden, H.H. Açıkel, H. Demir, I. Isabekov, Unsteady flow over flexible membrane wings at different low Reynolds numbers, in: 10th International Conference on Experimental Fluid Mechanics, 17–20 November 2015, Liberec, Czech Republic, 2015. [6] M.S. Genç, H. Demir, H.H. Açıkel, Time dependent laminar separation bubble formation and deformation over flexible membrane wing, in: The International Symposium on Sustainable Aviation (ISSA-2016), 29 May - 1 June 2016, Istanbul, Turkey. [7] I. Gursul, Vortex flows on UAVs: Issues and challenges, Aeronaut. J. 108 (1090) (2004) 597–610. [8] I. Tani, Low-speed flows involving bubble separations, Prog. Aerosp. Sci. 5 (1964) 70–103. [9] M.S. Genç, Unsteady aerodynamics and flow-induced vibrations of a low aspect ratio rectangular membrane wing with excess length, Exp. Therm Fluid Sci. 44 (2013) 749–759. [10] R. Bleischwitz, R. De Kat, B. Ganapathisubramani, Aeromechanics of membrane wings in ground-effect, in: 45th AIAA Fluid Dynamics Conf, Vol. 2764, 2015. [11] S. Ke, W. Zhigang, Y. Chao, Analysis and flexible structural modeling for oscillating wing utilizing aeroelasticity, Chin. J. Aeronaut. 21 (5) (2008) 402–410. [12] N. Osterberg, Experimental investigation of dynamic stall on pliant wings for micro air vehicles, in: 54th AIAA Aerospace Sciences Meeting, 2016, p. 0146. [13] Z. Zhang, J.P. Hubner, A. Timpe, L. Ukeiley, Y. Abudaramv, P. Ifju, Effect of aspect ratio on flat-plate membrane airfoils, in: 50th Aerospace Sciences Meeting and Exhibit, AIAA Paper, Vol. 1084, 2012. [14] A. Song, X.D. Tian, E. Israeli, R. Galvao, K. Bishop, S.M. Swartz, K.S. Breuer, Aeromechanics of membrane wings with implications for animal flight, AIAA J. 46 (2008) 2096–2106. [15] H. Hu, A.G. Kumar, G. Abate, R. Albertani, An experimental investigation on the aerodynamic performances of flexible membrane wings in flapping flight, Aerosp. Sci. Technol. 14 (8) (2010) 575–586. [16] S. Greenhalgh, H.C. Curtiss, Smith, Aerodynamic properties of a twodimensional inextensible flexible airfoil, AIAA J. 22 (7) (1984) 865–870. [17] A. Wrist, D. Pepley, Z. Zhang, J.P. Hubner, Aerodynamic comparison of flat and cambered frames for flexible MAV wings, in: 53rd Aerospace Sciences Meeting, AIAA, Vol. 1299, 2015. [18] Y. Lian, W. Shyy, D. Viieru, B. Zhang, Membrane wing aerodynamics for micro air vehicles, Prog. Aerosp. Sci. 39 (6–7) (2003) 425–465. [19] P. Rojratsirikul, M.S. Genç, Z. Wang, I. Gursul, Flow-induced vibrations of low aspect ratio rectangular membrane wings, J. Fluids Struct. 27 (2011) 1296–1309. [20] P. Rojratsirikul, Z. Wang, I. Gursul, Effects of pre-strain and excess length on unsteady fluid–structure interactions of membrane airfoils, J. Fluids Struct. 26 (2010) 359–376. [21] I. Karasu, Experimental and numerical investigations of transition to turbulence and laminar separation bubble over aerofoil at low Reynolds number flows. M.Sc. Thesis, Erciyes University, Turkey, 2011. [22] I. Karasu, M.S. Genc, H.H. Acıkel, Numerical study on low Reynolds number flows over an Aerofoil, J. Appl. Mech. Eng. 2 (2013) 131. [23] R.E. Mayle, The role of laminar-turbulent transition in gas turbine engines, J. Turbomach. 13 (1991) 509–537.
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European Journal of Mechanics / B Fluids journal homepage: www.elsevier.com/locate/ejmflu
An experimental investigation of laminar separation bubble formation on flexible membrane wing Hacımurat Demir a,b,1 , Mustafa Serdar Genç a, * a b
Wind Engineering and Aerodynamic Research Laboratory, Department of Energy Systems Engineering, Erciyes University, 38039, Kayseri, Turkey Department of Mechanical Engineering, Aksaray University, 68100, Aksaray, Turkey
highlights • Unsteadiness included in laminar separation bubble lead to complicated unstable deformations. • Different vibrational modes observe due to laminar separation bubble. • Separation bubbles cause to time-dependent variations on membrane vibration.
article
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Article history: Received 4 November 2016 Received in revised form 8 May 2017 Accepted 30 May 2017 Available online 12 June 2017 Keywords: Flexible membrane wing Fluid–structure interaction Laminar separation bubble Unsteady aerodynamics
a b s t r a c t In this study, fluid–structure interaction over a flexible membrane wing with aspect ratio (AR) of 3 at low Reynolds numbers was investigated experimentally. Smoke wire flow visualization technique was performed for analyzing time-dependent behavior of flow over this flexible membrane wing. Furthermore, time dependent deformation of flexible membrane wing was measured. It was clearly seen that the value of membrane deformation increased with increasing angle of attack. Moreover, it was stated that the size of laminar separation bubble (LSB) changed with time due to the unsteady flow characteristics of membrane wing. The unsteady behavior over the flexible membrane wing caused different deformation modes to form at different angles of attack. For the flexible wings with higher aspect ratios, the LSB was more dominant in the membrane wings at low Re numbers, and caused the membrane vibration to increase based on the angle of attack which the LSB started to be overpowering. © 2017 Elsevier Masson SAS. All rights reserved.
1. Introduction In recent years, scientific surveys related to aerodynamics have been concentrated upon low Reynolds number aerodynamics, transition and laminar separation bubble and effects this bubble on aerodynamic performance owing to the improvement in wind turbines, micro air vehicles (MAVs) and unmanned aerial vehicles (UAVs) [1–6]. That is why it is seen that there is an increasing concern in the study of membrane wings. Because of the strong viscous effects, flows in low Reynolds number regard to MAVs result in laminar-transitional, separated flow hindering lift generation [7]. Both experimental and numerical results of studies in regard to low Reynolds number aerodynamics demonstrate that flow has a susceptibility to separate because of the lower inertia forces compared to the comparatively higher viscous forces. In other respects, owing to this phenomenon
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http://dx.doi.org/10.1016/j.euromechflu.2017.05.010 0997-7546/© 2017 Elsevier Masson SAS. All rights reserved.
and adverse pressure gradients encountered on airfoils, LSB is presumably to be formed [2,3,8]. Genç [9] investigated on unsteady aerodynamics over the cambered membrane wing. Acquired experimental results exhibited that membrane wing’s camber having excessive length induced the separated shear layer. Due to this circumstance, coefficient of lift increased. Besides, wings with excess length indicated small separated regions because shear layer was closer to the wing surface, although camber of the wing raised. As a deduction, it was stated that unsteadiness included vortex shedding and tip vortices, and the coalescence of vortex shedding and tip vortices occasioned complicated unsteady deformations of membrane wings. Bleischwitz et al. [10] presented ground effect on aeromechanics of membrane wings and observed that ground-effect caused to higher lift production and a constant low drag at low to moderate angles of attack for both flat plates or membrane wings. Ke et al. [11] studied on aeroelasticity for flexible oscillating wing and noticed that adopting new kind driving way would not have flutter problems for the oscillating wing and it could generate propulsive force. Osterberg [12] deduced that membrane wings ensured
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Nomenclature AR c DIC E f LSB Re St t U y/s Z Zstd
Aspect ratio Chord length Digital image correlation Young’s modulus, MPa Frequency Laminar separation bubble Reynolds number Strouhal number Time, s Freestream velocity Location of smoke wire Flexible membrane displacement Standard deviation of flexible membrane displacement
Greek letters
α ρm
angle of attack, ◦ density of rubber latex sheet, g/cm3
remarkable improvements in maximum CL when comparing to a rigid wing under pitching conditions. Zhang et al. [13] stated that membrane wing ensured higher lift curve declination, stallregion lift and lift-to-drag ratio when comparing to the rigid flat plate. Song et al. [14] stated that membrane wings had maximum lift coefficients, higher lift declination and led to delay stall. Hu et al. [15] examined flexible membrane wings aerodynamics experimentally utilizing particular flexibility of skin in flapping flight. According to obtained results, flapping motion ensured remarkable aerodynamic advantages at unsteady flapping flight regime. Greenhalgh et al. [16] noticed that increasing excess length led to decrease angle of attack at which separation occurred. Wrist et al. [17] made comparison between aerodynamic features for silicone rubber MAV wings with cambered and flat frames. It was deduced that cambering the frames of wings raised aerodynamic efficiency comparing the flat frames. Lian et al. [18] described the membrane aerodynamic and suitable rigid wings under flight condition of micro aerial vehicles. They realized that membrane wing both delayed stall and what is more adapted to the unsteady flight environments. Rojratsirikul et al. [19] investigated experimentally flowinduced vibrations of rectangular membrane wings with aspect ratio (AR) of 2. They conducted flow field and time-accurate measurements of membrane deformations. Deformations showed different vibration mode shapes as a function of the Re number and angle of attack. The membrane oscillations were observed in a chordwise two mode at higher angles of attack. Since the combination of tip and leading edge vortices caused a mixture of chordwise and spanwise vibrational modes. Moreover, they deduced that vortex shedding frequency of rigid wings emerged remarkably slight influence of aspect ratio even when it was as nominal as unity. Furthermore, Rojratsirikul et al. [20] studied about the effects of pre-strain and excess length of membrane in terms of unsteady fluid–structure interactions. They observed that airfoil with excess length ensured the largest strain and camber. Additionally, for the excess length airfoils, prelude of the wing vibration was detained to a higher angle of attack. In addition to this, with increasing angle of attack, both St number and mode number were disposed to diminish. The purpose of this study is to survey flow over flexible membrane wings and the formation of separation bubbles occurring in the flow and effects of bubbles on the wing deformation. In
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this regard, aspect ratio of 3 (AR = 3) flexible membrane wing was utilized and formation of separation bubble in the region of wing center at which tip vortices had no effect were investigated at different low Reynolds numbers and miscellaneous angles of attack. 2. Measurement procedure The study was conducted in the wind tunnel in Erciyes University. The test section of wind tunnel is geometrically square. The size of tunnel is 500 mm by 500 mm consisting of optically transparent walls. Free-stream turbulence intensities of tunnel are 0.3% for maximum speed of 40 m/s and 0.7% for lowest speed of 5 m/s, respectively, [3,21,22] which are appropriate to perform experiments at low Reynolds numbers in order to determine separation and reattachment point, LSB and stall in accordance with Mayle, [23]. All the flexible membrane wings used in this study were designed in conjunction with 0.2 mm black latex rubber sheet which had Young’s modulus (E) of 2.2 MPa, and density (ρm ) of 1 g/cm3 [20]. There was no pre-stress or excess length on latex rubber sheet. To this end, flexible material was glued to the airfoilformed frame which was made of rigid stainless steel. As illustrated in Fig. 1, this rigid frame was manufactured for having a crosssection of airfoil shape. 2.1. Flow visualization experiments In order to visualize flow, smoke wire technique was opted, since it was simple and reliable to conduct. A smoke-wire which was strained between the upper and lower tunnel walls was used for heating the machine oil and fluid for marking the streamlines to visualize flow in the tunnel. Adequate quantity of voltage was applied to smoke-wire that was coated with oil. The oil evaporated forming smoke lines in the tunnel. The smoke lines were fulfilled by this technique indicated the flow over the related airfoil and the flow phenomena such as laminar separation bubble or stall were made easily visible. Canon EOS-D1100 camera was used for capturing related images during experiments. The picture frequency of Canon EOS-D1100 camera was chosen as 30 frames per second. Reflection of images in tunnel’s wall test section that was manufactured by plexiglass was the main problem. That is why camera and lighting arrangements were conducted thoughtfully to gain dark medium. As shown in Fig. 1, the location of smoke wire was designated as y/s, and the flow visualization experiments were conducted for two locations (y/s = 0.4 and y/s = 0.1) to indicate the effects of LSB and tip vortices. However, with increasing the Reynolds number, it gets difficult to capture a convenient image of streamlines and the image becomes blurred, because the filaments are quickly dissipated in the flow. 2.2. Evaluation of deformation Deformations and displacements of flexible membrane wing were measured by means of Digital Image Correlation (DIC) system as illustrated in Fig. 2. In accordance with this purpose, deformation measurements of the AR = 3 membrane wing were conducted by way of utilizing DANTEC Dynamics three-dimensional highspeed image correlation system (Q-450: the number of pixels was 1280 × 800) and DANTEC Al-11-BMB_9 × 9 was chosen as calibration target. Furthermore, frame rate was 1 kHz. Throughout the deformation measurements, 1000 frames were captured for each experimental case. This system captures successive images afterwards calculates the displacement over AR = 3 flexible membrane wing by following the deformation of spots (Fig. 3) fulfilled to the surface of the AR = 3 flexible membrane wing using a cross-correlation method. The minimum and maximum uncertainties of deformation measurement were ±0.030 mm at
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Fig. 1. Dimensions of the flexible membrane wing and position of smoke wire on membrane wing.
α = 0◦ and 0.013 mm at α = 36◦ , respectively; and the average uncertainty of the deformation measurement was ±0.02 mm. 2.3. Measurement of aerodynamics performance An automatic angle changer mechanism was utilized for measuring aerodynamic forces of the membrane wing at the angles of attack in the range of 0◦ –45◦ . Strain gauges were used for measuring lift and drag forces separately. Measured time-averaged forces in the normal direction and tangential direction to the angle of attack of wing were converted to the lift (CL ) and drag (CD ) force coefficients in x and y axes via transformation of coordinates. The maximum uncertainties of the lift force coefficient and the drag force coefficient were approximately 6% and 7% for Re = 2.5 × 104 , respectively. And it reduces as Reynolds number rises [3] (see Fig. 4).
3. Results and discussion 3.1. Flow visualization results It was seen that separation bubbles on the flexible membrane wing did not occur significantly at low angles of attack (except small disturbances on the flow due to the frame of wing) and leading edge separations increased gradually with increasing angle of attack and these vortices stroke on the wing and moved towards to the trailing edge at y/s = 0.4 as seen in Figs. 5 and 6. Leading edge vortices which were grew up with increasing angle of attack could not attach on the wing after at 20◦ for Re = 2.5 × 104 and at 22◦ for Re = 5 × 104 . However, it was observed that these leading-edge separations were to be smaller comparing to the rigid wing [3].
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Fig. 2. Experimental set-up for DIC measurement.
Fig. 4. Photography of force measurement system.
Fig. 3. AR = 3 flexible membrane wing with white speckle patterns for deformation measurements.
Moreover when the flow visualization figures of the membrane wing at y/s = 0.1 (Figs. 7 and 8) were investigated, it was seen that as the angle of attack increased, tip vortices and wake region of the membrane wing grew up. The LSB shrank at the tip of the wing owing to these tip vortices, but these vortices could not affect entirely the flow over the membrane wing because the aspect ratio was high. In the membrane wings with low aspect ratio, the tip vortices caused the stall to delay [4,9,19] but the flow over the membrane wing with higher aspect ratio was seriously affected the LSB [6]. Separation bubbles were more effective because there was no significant effect of tip vortices in the middle of wing for AR = 3 and increasing Reynolds number led to increase in inertial forces on the wing. Due to this situation, flow over the wing became more stable. At Re = 2.5 × 104 (Fig. 5), inertia of fluid flow was not dominant and flow separations and vortices were larger by the
effect of viscous forces. Vortices were large but had low energy. At Re = 5 × 104 (Fig. 6), vortices were contracted by means of more stable flow condition comparing with respect to Re = 2.5 × 104 . After the smoke-wire experiments of instantaneous images of vortices which were occurred on the wing, all images obtaining at specific angles of attack were examined individually and then vortex formation was revealed depending on time. Figs. 9–11 demonstrated the results of time (t) dependent flow visualizations at y/s = 0.4 for angles of attack of α = 6◦ , α = 10◦ and α = 12◦ for various time intervals. When comparing obtained results at different times between t = 0.08 s and t = 0.20 s, timedependent behaviors of LSB was clearly seen. In Fig. 9, at constant angle of attack of α = 12◦ , the size of bubble became bigger at t = 0.16 s and then smaller at t = 0.20 s for Re = 2.5 × 104 . On the other hand, at Re = 5 × 104 and at α = 6◦ , it was observed that the size of laminar separation bubble grew up from t = 0.08 s to t = 0.12 s and then this bubble became smaller at t = 0.16 s. At the end of t = 0.20 s, it grew once again as seen in Fig. 10. Furthermore, the size of laminar separation bubble grew up until t = 0.12 s and then became smaller t = 0.16 s at
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Fig. 5. Smoke-wire visualization of AR = 3 membrane wing for Re = 2.5 × 104 at y/s = 0.4.
α = 12◦ and Re = 5 × 104 for AR = 3 flexible membrane wing as illustrated in Fig. 11. To this end, it can be stated that the size of bubble changed with time due to the unsteady flow characteristics of membrane wing. Moreover, as it was seen in time-dependent images, inertial forces were low at Re = 2.5 × 104 so energy of
vortex was less and formation of vortex completed tardily whereas formation of vortex was occurred expeditiously and more stable at Re = 5 × 104 due to the having high inertial forces and vortex energy. This situation affected the deformation occurring on the flexible membrane wing.
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Fig. 6. Smoke-wire visualization of AR = 3 membrane wing for Re = 5 × 104 at y/s = 0.4.
3.2. Aerodynamic force coefficients measurement results
α = 6◦ , the linearity of the CL curve changed because the LSB grew
The time-averaged force coefficients versus angle of attack were given in Fig. 12. The stall angles changed based on Reynolds number, and the stall for Re = 2.5 × 104 occurred early. At Re = 2.5 × 104 , at
at the leading edge as shown from the photographs of the smokewire flow visualization. After α = 12◦ , the LSB became dominant and the leading-edge separation set in motion. At Re = 5 × 104 , the effect of inertia force increased and the LSB shrank, and stall occurred late, and also the CL raised since the membrane chamber
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Fig. 7. Smoke-wire visualization of AR = 3 membrane wing for Re = 2.5 × 104 at y/s = 0.1.
increased. Moreover, when comparing the lift force coefficient of AR = 3 membrane wing and the normal force coefficient obtained by Rojratsirikul et al. [19] for AR = 2 membrane wing, it was seen that the stall delayed owing to the tip vortices around the AR = 2 membrane wing while the flow over the membrane wing
with AR = 3 was affected the LSB. In addition, when the drag force coefficients (CD ) which were no in the study of Rojratsirikul et al. [19] were investigated, while CD were same for both Re number at lower angles of attack, it increased owing to separated flow at higher angles of attack.
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Fig. 8. Smoke-wire visualization of AR = 3 membrane wing for Re = 5 × 104 at y/s = 0.1.
3.3. Deformation measurement results Membrane deformation and time-averaged standard deviation reflecting the transient deformation part (vibrations which were formed due to the membrane deformation induced from flow) results for flexible membrane wing with respect to different angles
of attack at Reynolds numbers of Re = 2.5 × 104 and Re = 5 × 104 were illustrated in Figs. 13–16. It was seen that maximum deformation on the wing increased with increasing angle of attack from α = 0◦ to α = 36◦ . Besides, maximum deformation region in spanwise of the wing was geometrically similar. At Re = 2.5 × 104 , although vibrational modes were not explicit at low angles of
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Fig. 9. Smoke-wire visualization of AR = 3 membrane wing for Re = 2.5 × 104 and α = 12◦ at y/s = 0.4 [6].
Fig. 10. Smoke-wire visualization of AR = 3 membrane wing for Re = 5 × 104 and α = 6◦ at y/s = 0.4 [6].
Fig. 11. Smoke-wire visualization of AR = 3 membrane wing for Re = 5 × 104 and α = 10◦ at y/s = 0.4 [6].
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Fig. 15. Distributions of time-averaged deformation of AR = 3 flexible membrane wing at Re = 5 × 104 for various angles of attack. Fig. 12. CL and CD coefficients of the wing at different angles of attack (α ) at low Re numbers.
attack (α = 0◦ –4◦ ), chordwise vibrational mode 1 which means one half wave of membrane deformation was observed at α = 6◦ and α = 8◦ . The dominant mode number was determined by counting the peaks which are maximum deformation points
(antinodes) in graph of standard deviation of deformation. Vibration mode 2 occurred because of increasing angle of attack to α = 16◦ and this effect proceeded through α = 22◦ . Vibration mode 1 took place at α = 24◦ and continued until α = 36◦ . The value of maximum deformation and number of vibrational mode increased with increasing Reynolds number from 2.5 × 104 to 5 × 104 because of LSB.
Fig. 13. Distributions of time-averaged deformation of AR = 3 flexible membrane wing at Re = 2.5 × 104 for various angles of attack.
Fig. 14. Distributions of time-averaged standard deviation of the deformation for AR = 3 flexible membrane wing at Re = 2.5 × 104 for various angles of attack.
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Fig. 16. Distributions of time-averaged standard deviation of the deformation of AR = 3 flexible membrane wing at Re = 5 × 104 for various angles of attack.
At Re = 5 × 104 , for low angles of attack (α = 0◦ , α = 2◦ ) maximum standard deviation was more intense at the tip of the wing. At α = 6◦ and α = 8◦ , spanwise vibration modes 2 and 3 and chordwise vibration mode 4 were observed. Due to the effect of separation bubble, vibrational modes decreased in the middle section and combined at the tip region at α = 10◦ and these vibrational modes became chordwise mode of two at α = 12◦ and continued until α = 24◦ . It was seen that at α = 12◦ and α = 24◦ vibration mode 2 which was near to the trailing edge decreased through span owing to the effect of tip vortices. Between α = 30◦ and α = 36◦ , vibration mode 1 was observed and the value of maximum standard deviation region decreased with increasing angle of attack. When looking through the results of standard deviation, vibrational modes which were occurred with changing angle of attack were partly mode one, two, there and four. These various vibrational modes occurred owing to the both leading edge separation and vortices forming on the wing. At Re = 2.5 × 104 , standard deviations were low because of having bulky but low energy vortex, whereas at Re = 5 × 104 small and beany vortex had high energy especially at low angles of attack, and thus vibration modes 4 were observed. LSB occurred over the membrane wing varied with time, and this situation caused in vibrations of the membrane to change. Since LSB was more effective on the membrane wing with AR = 3, vibrational modes occurred distinctly comparing with the membrane wings with lower aspect ratio. When comparing the graphs of standard deviation of the deformations given in the study of Rojratsirikul et al. [19] for Re = 5 × 104 with those of our study (Fig. 17 in this study), it was seen that the membrane wing with AR = 2 at moderate angles of attack in chordwise
vibration mode 2 occurred whereas chordwise vibration mode 4 formed in the AR = 3 membrane wing. As the angle of attack increased; tip vortices growing caused the size of LSB to decrease and the flow complexity to increase, and so vibrational modes increased over the AR = 2 flexible membrane wing. The variation of maximum deformation was decreased by means of LSB in the range of the angle of attack of 8◦ and 18◦ , then increased due to the tip vortices which became effective with increasing the angle of attack for the AR = 2 membrane wing (Fig. 18 in this study). When examining the power spectra graphs given in Fig. 11(c) by Rojratsirikul et al. [19], secondary vibrational band was observed at the angle of attack from 8◦ to 12◦ corresponded to the frequency of St = 1.2, and from 13◦ to 18◦ corresponded to the frequency around St = 1.0. For the AR = 3 flexible membrane wing, due to the effect of LSB at lower angles of attack, high vibrational modes and less maximum deformations were observed as seen in Fig. 18 in this study, and vibrational modes occurred less than the modes of the AR = 2 membrane wing at the angle of attack of 14◦ because of the LSB growing. As the angle of attack reached to the stall angle, vibration mode 2 were observed for both AR = 2 and AR = 3 membrane wings, and bigger leading edge- and tip vortices which were spread towards the wake region had no effect on the deformation of the membrane wing under separated flow condition. The variations of vibrational modes on the membrane wing were also seen in the distribution of power spectra given in Fig. 19(b) in this study. In these distributions, there was a darker band at St = 1.2 for angles of attack in the range of 6 and 14◦ , while second dark band was noticed at St = 0.6 for angles of attack in the range of 8–24◦ . Especially, vibrational bands occurred around St = 1.2
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Fig. 17. Comparison of time-averaged standard deviation of the deformation of AR = 2 [19] and AR = 3 flexible membrane wings at Re = 5 × 104 for different angles of attack.
and St = 0.6 at lower angles of attack pointed out the leading edge separation and the trailing edge separation, respectively. In addition to this, as the aspect ratio was decreased, the vibration band around St = 0.6 started to become at lower angles of attack. In the results of power spectra for Re = 2.5 × 104 in Fig. 19(a), vibration mode 2 occurred and darker band was observed at angles of attack between 16◦ and 22◦ as shown in the standard deviation graphs. As can be seen from the studies of Rojratsirikul et al. [19] and Genç [9], vibrations of the membrane wing increased with ascending the Re number (Fig. 19). Furthermore, the obtained results of Rojratsirikul et al. [19,20] and this study, LSB became more effective in membrane wings under low Re number flow regimes with rising the aspect ratio, and LSB caused membrane vibrations to increase, secondary darker bands (modes) formed at vibrations of the membrane wing according to the angle of attack which the LSB started to be effective. Consequently, in membrane wings, unsteadiness included LSB lead to complicated unstable deformations of these wings. 4. Conclusions Unsteady flow behavior around AR = 3 flexible membrane wings was surveyed experimentally at Reynolds number of 2.5 × 104 and 5 × 104 in this study. Flow visualization by smoke wire technique was conducted to analyze time-dependent behavior of flow over flexible membrane wing. In addition to this, DIC system was utilized for time dependent deformation measurement of flexible membrane wing. Moreover, as seen in instantaneous images at Re = 2.5 × 104 inertial force was low so energy of vortex was low and formation of vortex completed lately while at Re = 5 × 104 inertial force and energy of vortex were higher so vortex formation was faster and more stable. This situation affected the deformation
Fig. 18. Comparison of normalized maximum time-averaged displacement of AR = 2 [19] and AR = 3 flexible membrane wings versus the angle of attack at Re = 5 × 104 .
occurring on the flexible membrane wing and different vibrational modes were observed due to the separation at leading-edge and vortices with changing angle of attack. Especially at low angles of attack, vibration modes 3 and 4 were observed and vibrational mode reduced to two with increasing angle of attack and vibration mode 1 on the wing was obtained after the flow separation on the wing completed entirely. As a consequence, formation of leading edge separations on the flexible membrane wing were affected by both Reynolds number and leading-edge vortices occurring due to the separation bubbles caused time-dependent variations on membrane wing vibration. With increasing the aspect ratio, LSB became more dominant in the membrane wings at low Re numbers, and caused membrane vibrations to increase based on
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Fig. 19. Power spectra distributions of the membrane vibrations versus the angle of attack for AR = 3 flexible membrane wing at (a) Re = 2.5 × 104 ; (b) Re = 5 × 104 .
the angle of attack which the LSB started to be effective. Consequently, in membrane wings, unsteadiness included in LSB lead to complicated unstable deformations of these wings. Acknowledgments The authors would like to thank the Scientific and Technological Research Council of Turkey (TÜBİTAK) under the project number: 213M329, and the Scientific Research Projects Unit of Erciyes University under the contract numbers: FDK-2015-6171, FDA-20145273 and FBG-2014-5337 for funding. References [1] M.S. Genç, U. Kaynak, G.D. Lock, Flow over an Aerofoil without and with leading edge slat at a transitional Reynolds number, Proc. IMechE G: J. Aerosp. Eng. 223 (3) (2009) 217–231. [2] M.S. Genç, I. Karasu, H.H. Açıkel, M.T. Akpolat, Low Reynolds number flows and transition, in: M. Serdar Genç (Ed.), Low Reynolds Number Aerodynamics and Transition, Intech-Sciyo Publishing, ISBN: 979-953-307-627-9, 2012.
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