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1 TOPICAL PROBLEMS OF FLUID MECHANICS 159 DOI: UNSTEADY CFD ANALYSIS OF AN OSCILLATING AEROFOIL INSPIRED BY DRAGONFLY WINGS W.H. Ho 1, T.H. New 2, E. Matare 1 1 Department of Mechanical and Industrial Engineering, University of South Africa 2 School of Mechanical and Aerospace Engineering, Nanyang Technological Engineering, Singapore Abstract An unsteady two-dimensional CFD analysis of an oscillating (dynamically pitching) aerofoil inspired by dragonfly wings was conducted to investigate its aerodynamic and flow characteristics. The aerofoil morphology was an idealised geometry based on the crosssection near the mid-span of a dragonfly wing. The aerofoil was made to oscillate at 2Hz with amplitude of 10 with an upstream flow such that the chord Reynolds number was 14,000. The methodology mirrored a previous study but with slight differences due to the difference in geometry. Complex flow structures near to the aerofoil surface revealed significant effect on lift and drag characteristics. Lift and drag hysteresis indicate that there is net lift generated but no net thrust. Instantaneous lift and drag shows there is a difference in both the negative and positive peak lift and drag values between when the aerofoil is pitching up and when it is pitching down. This is consistent with previous studies. Comparisons with previous studies on oscillating smooth aerofoils do not indicate that such corrugated aerofoils exhibit any advantages. It is possible that any performance enhancements will only manifest itself when operating in tandem with other aerofoils in close proximity such as between the fore and hind-wing of a dragonfly. Keywords: computational fluid dynamics; particle image velocimetry; oscillating airfoil; bioinspired airfoil 1 Introduction Increasingly engineers are looking for inspiration in the natural world to improve the performances of mechanical devices and to develop new technologies [1, 2, 3, 4, 5, 6]. Novel morphologies and physiological operations investigated by biologists are now inspirations for engineers in technological development [1] with the aim of emulating the performance of living systems where a performance exceeds current technologies [2, 3]. One such example is the agility of dragonflies that are able to dip and dart in all directions very quickly. Previous investigations have shown that the lift coefficients of flapping flight far exceed the steady-state values of non-flapping dragonfly wings [4, 5, 6, 7] suggesting that unsteady aerodynamic effects are significant to the generation of lift. Dragonfly wings are corrugated and not smooth like conventional aerofoils and this unique cross-section has been shown to be the cause of the superior performance [8, 9, 10, 11] by delaying stall and reducing separation regions at high angle-ofattack. Oscillating smooth conventional aerofoils have been studied in the past by a number of researchers [12, 13, 14, 15]. Recently Flint et al. [16] reported an investigation on the oscillation of such a corrugated bio-inspired aerofoil showing the intricate flow details around the corrugations. The geometry used in that study is one of the common shapes used in previous studies [11, 10] but is more closely related to wing cross-section close to the wing root where there is a large tail near the trailing edge and not in the main section of the wing [17]. The cross-section of the wing around the mid-span of a dragonfly s wing has multiple smaller corrugates and resembles more the geometries used by Gao et al. [18] and Murphy and Hu [9]. The aim of the study seeks to provide insight into the characteristics of viscous flows forming around oscillating airfoil and how corrugations similar to those seen on dragonfly wings affect their unsteady aerodynamic properties. The present study intends to expand the work by Flint et al. [16] and other researchers by comparing the flow dynamics of an oscillating aerofoil with a cross-sectional area resembling a dragonfly s wing at mid-span [17]. The authors are not aware of any previous such studies being reported.

160 Prague, February 15-17, 2017 2 Geometry, computational domain and methodology Rigid two-dimensional aerofoils were modelled in ANSYS Fluent version 16.1. Past experimental studies found no intrinsic three-dimensional effects at low Reynolds numbers further suggesting the suitability of two-dimensional studies [19, 20, 21].

It is not clear if spanwise flow is significant if there is no variation in the spanwise crosssections of the aerofoil.

The simulations were conducted to calculate the lift and drag as well as details of the flow field near the aerofoil body.

of the chord length from the leading edge.

2 160 Prague, February 15-17, Geometry, computational domain and methodology Rigid two-dimensional aerofoils were modelled in ANSYS Fluent version Past experimental studies found no intrinsic three-dimensional effects at low Reynolds numbers further suggesting the suitability of two-dimensional studies [19, 20, 21]. However a very recent study by Chen and Skote [22] suggested the presence of spanwise flow in bio-inspired aerofoils, their studies have spanwise variations in the crosssectional area. It is not clear if spanwise flow is significant if there is no variation in the spanwise crosssections of the aerofoil. In fact previous experimental work was conducted as two-dimensional measurements [8, 11]. The simulations were conducted to calculate the lift and drag as well as details of the flow field near the aerofoil body. Oscillations were introduced to the simulation through the use of a user-defined function and sliding body mesh with the centre of rotation located in the middle of the plate thickness at a-quarter of the chord length from the leading edge. The aerofoil is undergoing twodimensional oscillation (dynamically changing its pitch angle) with the axis of oscillation being perpendicular to the simulation plane (i.e. into the plane) with the amplitude and frequency for the oscillations being 10 and 2Hz respectively. The black dot on Figure 1b shows the approximate location of the centre of rotation. The geometry corresponds to the CorrugatedA section used in the experiments of [11] and computational study of [23] and details of the coordinates can be found in the latter. This corresponds to a Strouhal number of 0.21 which is on the lower end of the range for efficient cruising locomotion [24]. The computational domain is identical to that of Flint et al. [16] comprising of a stationary outer rectangular domain and an inner smaller circular domain containing the aerofoil. The relative position of the aerofoil within the domain is also the same as the previous study and is presented in Figure 1. The left-hand edge of the outer rectangular domain is a velocity inlet and the right-hand edge pressure outlet whilst the aerofoil surface is a standard wall. The boundaries between the inner and outer domains are matching interfaces and the top and bottom of the boundary having symmetry conditions. Turbulence intensity at the inlet was set to 1.1% similar to that of Flint et al. [16]. A sliding mesh model was used to simulate the oscillation of the inner domain which included aerofoil. Pitch-up will be used to describe the aerofoil rotating clockwise and increasing its angle-ofattack, and vice-versa. The sliding mesh model is used because it is computationally less expensive as it eliminates the need for any re-meshing or mesh deformation. 3c 7c 6c c/4 c 14/3c (a) Figure 1: Computational domain and mesh (b) The mesh was quad-based with equal meshing on both sides of the matching interface. An inflation layer was also incorporated adjacent to the aerofoil body and a region of finer cells at the trailing edge of the aerofoil to capture the shedding of the vortices accurately. The overall mesh had elements and the y + value everywhere in the domain was between 0.17 and A pictorial illustration of the mesh in the domain and in the vicinity of the aerofoil surface is shown in Figure 1.

3 TOPICAL PROBLEMS OF FLUID MECHANICS 161 A mesh independence study was conducted and the results are shown in Figure 2. Since this study is a follow on from Flint et al. [16], the initial baseline mesh (Mesh1) was done according to parameters from that study. One further refinement of the mesh (Mesh2) was performed to check if refinement was necessary. The rms of the difference in lift coefficient values between the mesh were 4% and the mean and maximum difference in the values were 0.017% and 11.3% respectively. Although these indicated that Mesh1 was sufficient, it was decided to use Mesh2 to improve the accuracy of the results. Figure 2: Comparison of Lift Coefficient between meshes The model was solved using a coupled pressure based solver. Steady-state simulations with pseudo transient turned one was first solved before proceeding with the transient simulations without reinitialisation. This was done to save on the number of iterations and accelerate convergence during the transient solution phase. The turbulence model used was SST-kω and Scaled-Adaptive Simulation (SAS) respectively. SAS uses a RANS based model in regions of steady flow transitioning to an LES model in regions of unsteady or separated flow and is the highest fidelity turbulence model available in twodimensional Fluent [25, 26]. It was chosen due to its ability to handle unsteady flow structures. A user defined function was used to set the oscillatory rotational motion of the internal fluid domain and hence the airfoil. The transient solution was solved with Courant number of 2 and the time-step used in the simulations was s. Pressure discretisation was done using the PRESTO! scheme due to its good performance for swirling flows and second-order upwind discretisation scheme for all other variables. Gradients were evaluated using the least squares cell based method. Higher order term relaxation, double precision solver and a bounded second order//implicit transient formulation was used for accuracy and stability. The convergence criterion for each time step was set to Results and Discussions One of the important applications of oscillating aerofoils is in the production of lift and drag (thrust). Figure 3 plots the time variations of lift and drag coefficients of the current study together with the wing position in terms of pitch angle. The wing position is plotted to be consistent with Figure 6 of Flint et al. [16] in terms of definition of positive and negative angles for ease of comparison of trends. It can be seen that the overall trends match those of previous studies. There is delay between the lift and drag peaks and the oscillation angle peak also the frequency of lift oscillation coincides with that of the pitch angle oscillations but drag oscillation has a frequency that is double. There are very obvious differences between the values in Cd (Figure 3a) between the one peak and the adjacent one but this is not prominent in the Cl values (Figure 3b). This is due to the fact that in one oscillation cycle, there are two Cd peaks corresponding to the maximum pitch up and pitch down angles and also that the aerofoil is not symmetrical. The positive portion of the graph is/are slightly larger than the parts below indicating that there is no overall net thrust production. Flint et al. [16] also reported similar variations in the peak values (although the differences in the peak drag values are not so prominent). Since the sense of pitch-up and pitch down motion presented here is consistent between both studies, it can be observed that the thrust produced (negative drag) is higher during pitching up than when pitching down, being consistent with that study although more prominent as discussed above. In terms of instantaneous lift coefficients shown in Figure 3b, there is a larger area above the x-axis indicating overall net lift is generated. However the flattening of the peak reported by Flint et al. [16]

4 162 Prague, February 15-17, 2017 does not appear here. The reason for that is because there is not the large curve near the trailing edge of the aerofoil. The drag and lift hysteresis are plotted in Figure 4, it shows more clearly that there is net lift being generated but not net thrust. It can also be observed that the cross-over point of the drag hysteresis is very close to the y-axis but slightly to the left (i.e. very slightly pitching up). The non-symmetry of the drag hysteresis is an indication of the differences in peak drag coefficients (both positive and negative) shown in Figure 3. (a) Drag Coefficient (Cd) (b) Lift Coefficient (Cl) (c) Wing Position in ( ) Figure 3: Time variations of Drag, Lift and Wing Position

TOPICAL PROBLEMS OF FLUID MECHANICS 163 (a) Drag coefficient (b) Lift coefficient Figure 4: Lift and Drag hysteresis plotted against wing

It can be observed clearly that vortices are formed in the corrugations and convect downstream as expected.

One observation is the presence of a large positive vortex region sitting right at the second corrugation on the underside of the aerofoil

[16] instead there was a large positive vortex is between the first and the second corrugation siting closer to the first corrugation.

This could be due to the large hump in the previous study of which there is a large concave region on the underside.

This concave region is not present in the current geometry.

5 TOPICAL PROBLEMS OF FLUID MECHANICS 163 (a) Drag coefficient (b) Lift coefficient Figure 4: Lift and Drag hysteresis plotted against wing position (a) (b) (c) (d) (e) Figure 5: Vorticity contours during oscillations Plots of vorticity contours are presented in Figure 5. It can be observed clearly that vortices are formed in the corrugations and convect downstream as expected. The shape of the lift curve depends of the timing of the shed vortices which varies with both oscillating amplitude and frequency. One observation is the presence of a large positive vortex region sitting right at the second corrugation on the underside of the aerofoil during pitching-down motion. This is not present in the results presented by Flint et al. [16] instead there was a large positive vortex is between the first and the second corrugation siting closer to the first corrugation. That is the large positive vortex convects further downstream in this geometry than the previous study. This could be due to the large hump in the previous study of which there is a large concave region on the underside. This concave region would trap vortices better thus slowing down the convection of other vortices. This concave region is not present in the current geometry. This indicate that the current small corrugations have less ability to trap vortices and may result in overall less lift but better drag characteristics. Without exact numerical data from Flint et al. [16], it is not possible to do qualitative comparison at this moment. However we note that at the same oscillation frequency and amplitude, a forthcoming publication by Flint et al. [27] also showed no net thrust being

6 164 Prague, February 15-17, 2017 generated. It is also interesting to note that the large positive vortex region sitting on the underside of the aerofoil occurs only during the pitch-down motion and is not present on the topside of the aerofoil even though the corrugations are similar in sizes. The reason for this is not known but it presents a possible reason for the differences between the peak drag coefficients between the pitch-up and down cycles. Figure 6: Comparison of thrust generation of vs Strouhal number Thrust generation of an oscillating aerofoil is related to the Strouhal number calculated from the oscillation parameters and flow conditions [28]. Compared with earlier studies on smooth oscillating aerofoils shows that at the current condition (shown in Figure 6), this aerofoil does not have an advantage as compared with smooth aerofoil. It is possible that the evolutionary advantages of such corrugated aerofoils does not manifests itself when working in solitude and any performance improvements over smooth aerofoil shapes will only be present and significant when working in tandem as in a real dragonfly. It has been shown that relative phase angles and wing spacing affects lift and thrust generation [29] but it is unclear if corrugations will alter these effects. 4 Conclusion A two-dimensional CFD simulation of an aerofoil with cross-section resembling a dragonfly wing at midspan oscillating (dynamically pitching) at a frequency of 2Hz with amplitude of 10 has been performed successfully. The calculations show previously unreported intricacies of the near field flow structure with good spatial and time resolutions as well as lift and drag calculations of such corrugated airfoil extending the work of Flint et al. [16] to another common corrugated aerofoil in previous static studies. Lift and drag hysteresis indicate that although there is net lift generated but not thrust as evident by the relative size of the hysteresis graphs above and below the x-axis. Instantaneous lift and drag shows there is a difference in both the negative and positive peak lift and drag between when the aerofoil is pitching up and pitching down. This is consistent with previous report from Flint et al. [16]. The studied corrugated aerofoil does not seem to exhibit superior performance over smooth aerofoil whilst working in solitude. These results indicate that other benefits of having corrugated wings, such as structural benefits, may be more evolutionarily favourable for the dragonfly than oscillatory pitching performance or perhaps any aerodynamic superiority will only manifest itself when working in tandem [29]. Following on this study, a larger range of oscillating frequencies and amplitudes will be solved to increase the understanding of their effects on this aerofoil. It would also be interesting to compare the relative lift and drag of this

7 TOPICAL PROBLEMS OF FLUID MECHANICS 165 geometry and that of Flint et al. [16] as well as the effect of corrugates on aerofoils oscillating in tandem. Together with Flint et al. [16], this is the first report of detailed studies on oscillating bio-inspired corrugated aerofoil extracting information on both the flow features and the aerofoil performance parameters. The authors are not aware of any previous such studies being reported. References [1] F. E. Fish, P. W. Weber, M. M. Murray and L. E. Howle: The Tubercles on Humpback Whales' Flippers: Application of Bio-Inspired Technology. Integrative and Comparative Biology, vol. 51, no. 1, pp , [2] G. Taubes: Biologist and engineerings create a new generation of robots that imitate life. Science, no. 5463, pp , [3] F. E. Fish: Limits of nature and advances of technology in marine systems: what does biomimetics have to offer to aquatic robots?. Applied Bionics and Biomechanics, vol. 3, no. 1, pp , [4] R. A. Norberg: Hovering Flight of the Dragonfly Aeschna juncea L. Kinematics and Aerodynamics. in Swimming and Flying in Nature, , [5] J. M. Wakeling and C. P. Ellington: Dragonfly Flight I Gliding Flight and Steady-State Aerodynamics. Journal of Experimental Biology, vol. 200, pp , [6] J. M. Wakeling and C. P. Ellington: Dragonfly Flight II Velocities, Accelerations and Kinematics of Flapping Flight. Journal of Experimental Biology, vol. 200, pp , [7] J. M. Wakeling and C. P. Ellington: Dragonfly Flight III Lift and Power Requirements. Journal of Experimental Biology, vol. 200, pp , [8] H. Hu and M. Tamai: Bioinspired Corrugated Airfoil at Low Reynolds Numbers. Journal of Aircraft, vol. 45, no. 6, pp , [9] J. Murphy and H. Hu: An Experimental Study of a Bio-Inspired Corrugated Airfoil for Micro Air Vehicle Applications. Experiments in Fluids, vol. 49, no. 2, pp , [10] D.-E. Levy and A. Seifert: Simplified Dragonfly Airfoil Aerodynamics at Reynolds Numbers Below Physics of Fluids, vol. 21, [11] T. H. New, Y. X. Chan, G. C. Koh, H. M. Chung and S. Shi: Effects of Corrugate Aerofoil Surface Features on Flow-Separation Control. AIAA Journal, vol. 52, no. 1, pp , [12] K. Lu, Y. H. Xie, D. Zhang and J. B. Lan: Numerical investigations into the asymmetric effects on the aerodynamic response of a pitching airfoil. Journal of Fluids and Sturctures, no , p. 39, [13] Z. Zhou, C. Li, J. B. Nie and Y. Chen: Effect of oscillation frequency on wind turbine airfoil dynamic stall. Materials Science and Engineering, vol. 52, pp. 1-5, [14] J. Panda and K. B. M. Q. Zaman: Experimental Investigation of the flowfield of an oscillating airfoil. 10th AIAA Applied Aerodynamics Conference, [15] T. Lee: Flow Past Two In-Tandem Airfoils Undergoing Sinusoidal Oscillations. Experiments in Fluids, vol. 51, no. 6, pp , [16] T. Flint, W. H. Ho, T. H. New and M. C. Jermy: Validated Unsteady Computational Fluid Dynamic Analysis of an Oscillating Bio-Inspired Airfoil. Applied Mechanics and Materials, Vols , pp , [17] M. Mingallon and S. Ramaswamy: The Architecture of the Dragonfly Wing: A Study of the Structural and Fluid Dynamic Capabilities of the Anisoptera s Forewing. in Proceedings of the ASME 2011 International Mechanical Engineering Congress & Exposition (IMECE2011), [18] H. Gao, H. Hu and Z. J. Wang: Computational Study of Unsteady Flows around Dragonfly and Smooth Airfoils at Low Reynolds Numbers. in 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, 2008.

8 166 Prague, February 15-17, 2017 [19] A. B. Kesel: Aerodynamic Characteristics of Dragonfly Wing Sections compared with Technical Aerofoils. Journal of Experimental Biology, no. 203, pp , [20] M. Okamoto, K. Yasuda and A. Azuma: Aerodynamic Characteristics of the Wings and Body of a Dragonfly. Journal of Experimental Biology, vol. 199, pp , [21] C. Barnes and M. Visbal: Numerical exploration of the origin of aerodynamic enhancements in low- Reynolds number corrugated airfoils. Physics of Fluids, vol. 25, no. 11, [22] Y. H. Chen and M. Skote: Gliding performance of 3-D corrugated dragonfly wing with spanwise variation. Journal of Fluids and Structures, vol. 62, pp. 1-13, [23] W. H. Ho and T. H. New: Unsteady numerical investigation of two different corrugated airfoils. Proceedings of IMechE Part G - Journal of Aerospace Engineering, p. In Press, [24] G. K. Taylor, R. L. Nudds and A. L. R. Thomas: Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature, vol. 425, pp , [25] F. R. Menter: Best Practice: Scale-Resolving Simulations in ANSYS CFD Version vol. 32, no. 8, pp , [26] F. R. Menter and Y. Egorov: Scale-Adaptive Simulation Method for Unsteady Flow Predictions Part 1: Theory and Model Description. Flow, Turbulence and Combustion, vol. 85, no. 1, pp , [27] T. Flint, M. Jermy, T. H. New and W. H. Ho: Computational study of a pitching bio-inspired airfoil. International Journal of Heat and Fluid Flow, (accepted 28th of December) [28] M. S. Triantafyllou, G. S. Triantafyllou and R. Gopalkrishnan: Wake Mechanics for Thrust Generation in Oscillating Foils. Physics of Fluids A, vol. 3, no. 12, pp , [29] T. M. Broering and Y.-S. Lian: The effect of phase angle and wing spacing on tandem flapping wings. Acta Mechanica Sinica, no. 6, pp , [30] J. M. Benyus: Biomimicry. New York: HarperCollins, [31] S. Vogel: Cat's paws and catapults. New York: WW Norton, [32] P. Forbes: The Gecko's foot. New York: Norton, [33] Y. Bar-Cohen: Biomimetics: Biologically Inspired Technologies. Boca Raton: CRC, [34] T. Muller: Biomemetics: Design by nature. National Geographic, no. 213, pp , [35] R. Allen: Bulletproof feathers. Chicago: University of Chicago Press, [36] J. Murphy and H. Hu: An Experimental Investigation on a Bio-inspired Corrugated Airfoil. in 47th AIAA Aerospace Sciences Meeting and Exhibit, Orlando, [37] I. H. Ibrahim, J. Joy and T. H. New: Numerical investigation on flow separation control of low Reynolds number sinusoidal aerofoils. in 46th AIAA Fluid Dynamics Conference, 2016.

TOPICAL PROBLEMS OF FLUID MECHANICS 23 EFFECT OF LEADING EDGE PROTUBERANCE ON THRUST PRODUCTION OF A DYNAMICALLY PITCHING AEROFOIL

TOPICAL PROBLEMS OF FLUID MECHANICS 23 DOI: https://doi.org/10.14311/tpfm.2017.004 EFFECT OF LEADING EDGE PROTUBERANCE ON THRUST PRODUCTION OF A DYNAMICALLY PITCHING AEROFOIL M Benaissa 1,2, IH Ibrahim