Flow Structures around an Oscillating Airfoil in Steady Current

Flow Structures around an Oscillating Airfoil in Steady Current Idil Fenercioglu 1, Oksan Cetiner 2 1: Department of Astronautical Engineering, Istanbul Technical University, Istanbul, Turkey, fenercio@itu.edu.tr 2: Department of Astronautical Engineering, Istanbul Technical University, Istanbul, Turkey, cetiner@itu.edu.tr Abstract Time dependent velocity fields around a SD7003 airfoil have been investigated using Digital Particle Image Velocimetry (DPIV) at Reynolds numbers of 20 000 and 27 500. The airfoil known to be optimized for flows with large separation bubble undergoes combined pitching and plunging motion. Depending on the freestream velocity, the reduced frequency of the motion is either 0.31 or 0.23 and the amplitude ratio is 0.48 or 0.66 respectively. The plunging motion leads the pitching by π/2. Two stitched images for each experimental run and two runs of experiment for each case have been accomplished to cover the field of view including the airfoil and its near wake nearly at all positions of its flapping motion. 256 PIV images are collected both at 2Hz and 10Hz for the same case to allow phase averaging and detailed analysis of the motion cycle. In parallel to the objectives of the study, flow structures and separation on the surface of the airfoil are visualized and quantified; and the near-wake vorticity patterns and velocity profiles are determined in order to be able to comment on the thrust or drag production. Considering the actual reference frame for the flapping motion, the freestream velocity vector is subtracted from all the vectors and streamline topology is obtained for the cases in consideration. As opposed to the streamlines obtained in the laboratory reference frame and related vorticity plots, the streamlines in a moving reference frame announce a large separation zone starting from the leading edge of the airfoil for most of the phases of the oscillation cycle. The data acquired at low frequency is used for phase averaging and exhibits a nearly perfect repeatability for Karman like shedding from the trailing edge at the upper limit of the plunge motion and qualitatively a quite well repeatability for large separation zone made of small scale vorticity concentrations over the upper side of the airfoil during the downstroke at small angle of attacks. 1. Introduction Low Reynolds number aerodynamics has been recognized nowadays as an important research area considering the practical applications related to micro-air-vehicles (MAV). On the other hand, the propulsive energy of flapping motion guided investigations towards the study of oscillating airfoils and related unsteady flow structure interaction problems. Biological flows around aquatic animals, birds and insects are receiving considerable interest in this perspective. As unsteady flow over airfoils also constitute a popular investigation topic for the performance of the helicopter rotors, investigations have been especially focused on sinusoidal pitching motions, which closely represent the incidence variations experienced by real rotor blades. Since Kramer (1932) who was the first to study the rapid incidence variations of an airfoil and put forward associated dynamic features, many experimental and numerical studies are devoted to pitching oscillations of airfoils, i.e., McCroskey and Fisher (1972), Carr et al. (1977), De Ruyck and Hirsch (1983), Kim and Park (1988), Leishman (1990), Panda and Zaman (1994). The interest in MAV results in devotion of recent investigations still on pure pitching motion, however they focus on low Reynolds numbers and/or low reduced frequencies such as the work of Birch and Lee (2005) and Jung and Park (2005). Flapping airfoil investigations are more concentrated in the present decade, i.e., Windte et al. (2006), Ames et al. (2001), Jones et al. (2001), Young and Lai (2007). On the other hand, in recent years, flexible flapping airfoil propulsion has been also studied by Miao and Ho (2006), and Heathcote and Gursul (2007). Reviews on the topic are given by McCroskey (1982) who thoroughly studied unsteady flow over airfoils, by Mueller and DeLaurier (2003) who - 1 -

addressed aerodynamic design issues of small aerial vehicles and by Triantafyllou et al. (2004) who summarized the experimental work in biomimetic foils focusing in flapping motion for the improvement in propulsive efficiency. When both the airfoil surface and its near wake are visualized together, there are two aspects of the flow to be investigated, namely the performance related to the separation over the surface and the thrust indication of the airfoil wake. As indicated by different researchers, e.g. Windte et al. (2006), Mueller and DeLaurier (2003), low Reynolds number aerodynamic design of airfoils face a flow phenomenon called laminar separation bubble (LSB) which causes deterioration in airfoil performance. On the other hand, for pitching airfoils under dynamic stall conditions, at large angles of attack, the leading edge vortex (LEV) passes off the trailing edge; the flow fully separates over the upper surface, and is accompanied by a sudden loss of lift and increase in the negative pitching moment. Thrust generation of oscillating airfoils has been known for quite a long time. When the airfoil is oscillated at sufficiently high amplitude and frequency, the time-averaged flow downstream is jetlike and thus is indicative of a net thrust on the airfoil. Thrust indicative wakes are composed of alternately shed vortices similar to the well-known Karman vortex street except that the vorticity is reversed. Koochesfahani (1989) showed that at certain high reduced frequencies, the wake of an airfoil pitching at small amplitudes transforms into a jet-like flow with thrust generation. Since then, different aspects of thrust generation are investigated, i.e., Schouveiler et al. (2005) studied performance of flapping foil propulsion, Heathcote and Gursul (2007) focused on jet switching. The scope of this study is to investigate time dependent velocity fields around a SD7003 airfoil using Digital Particle Image Velocimetry at Reynolds numbers of 20 000 and 27 500. The airfoil known to be optimized for flows with large separation bubble [Windte et al. (2006)] undergoes combined pitching and plunging motion. Depending on the freestream velocity, the reduced frequency of the motion is either 0.31 or 0.23 and the amplitude ratio is 0.48 or 0.66 respectively. The main objectives of the study are to quantify and visualize the vortical structures, separation on the surface of the airfoil, and to determine the near-wake vorticity patterns and velocity profiles in order to be able to comment on the thrust or drag indication at different phases of the airfoil motion. 2. Experimental Setup Experiments were performed in a large scale water channel in Trisonic Laboratories at the Faculty of Aeronautics and Astronautics of Istanbul Technical University. The cross-sectional dimensions of the main test section are 1010mm 790mm. The experiments were conducted at flow speeds ranging from 0.10 m/s to 0.15 m/s corresponding to Reynolds numbers of 20 000 < Re <30 000. The airfoil made of plexiglas and manufactured in CNC milling machine is transparent and allows laser light to illuminate both the suction and pressure sides. It has a chord length of 20cm and span of 60cm. The airfoil is mounted vertically in the water channel about its quarter chord, the top end is attached to a servo motor which itself is connected to a linear table. Two end plates made of plexiglas were positioned about 3mm above and below the airfoil. The top end plate has a slit to ensure the maximum plunging motion amplitude. The pitch and plunge motions of the airfoil are accomplished with two Kollmorgen/Danaher Motion servo motors. The servo motors are connected to the computer via ServoSTAR300 digital servo amplifiers. Motor motion profiles are generated by a signal generator Labview VI (Virtual - 2 -

Instrument) for the given amplitude and frequency. The same VI triggers the PIV system at the beginning of the third motion cycle. The airfoil motion has been described with the following equations: h ( t ) = h cos(2π f1 t + ψ ) α t ) = α + α cos ( 2π f ) ( 0 2 t where h(t) is the linear plunge motion, transverse to the freestream velocity, α(t) is the angular pitch motion, and ψ is the phase angle between plunge and pitch. h is the plunge amplitude, α is the pitch amplitude and α 0 is the initial angle of attack. f 1 and f 2 are the oscillation frequencies for plunge and pitch motion respectively. The amplitudes are made dimensionless as λ=αc/2kh and the reduced frequency can be defined as κ=πfc/u. The maximum pitch angle considered in this study is α+α 0 =16.6 0 (α=8 0 and α 0 =8.6 0 ) and the maximum plunging motion amplitude h max =±0.5c. Oscillation frequencies are equal to each other and set to be 0.05Hz. Depending on the freestream velocity, the dimensionless parameters of amplitude ratio and reduced frequency are as follows: Re Λ κ 20 000 0.48 0.31 27 500 0.66 0.23 The airfoil starting from the channel center at an angle of attack of 16.6 0 rises to its upper limit of its plunge motion yielding a phase difference of π/2 where the plunge leaded the pitch. The resulting flapping motion is described in Fig. 1. Fig. 1 The flapping motion of the airfoil and PIV image areas Quantitative flow images are captured and processed by a Digital Particle Image Velocimetry (DPIV) system. Two 8-bit cameras with 1600 1200 pixels resolution are used for image acquisition. The flow is illuminated by a dual cavity Nd:Yag laser (max. 120 mj/pulse). The water is seeded with silver coated spheres of 10µm diameter. Although wide angle lenses are used to cover a larger plane of visualization, successful results in terms of PIV quality are obtained with 60mm lenses. The two images are stitched before interrogation using two marker points in the - 3 -

illumination plane. However, each experiment had to be conducted in two runs for two camera locations since this arrangement couldn t cover all the plunge oscillation amplitude of the airfoil. The results are overlapped at presentation stage. To allow phase averaging and detailed analysis of the motion cycle, 256 images are acquired both at 2Hz and 10Hz for the same studied case. Stitched PIV images are interrogated using a double frame, cross-correlation technique with a window size of 64 64 pixels and 50% overlapping in each direction. The magnification factor of the cameras, very close to each other, is about 12.9. The final grid resolution of velocity vectors is 3.08 mm 3.08 mm in the plane of the flow. The resulting measurement plane covers an area of 289 mm 114 mm and is represented with approximately 3350 velocity vectors. The schematic of the experimental setup is shown in Fig. 2. Fig. 2 Experimental setup 3. Results To characterize the motion of the airfoil and corresponding vorticity patterns, a period of motion cycle is visualized with 8 images taken from 10Hz data where 256 images correspond to a few more than a motion cycle. Additionally the ninth image is selected to show the repeatability of the flow structures around the airfoil and in its near wake. Fig. 3 presents the results obtained at Re=20 000. All the presented vorticity plots in the paper are obtained with ±10 1 /s limits and increments of 0.5 1 /s. However, in certain cases the minimum may reach up to 20 1 /s and the maximum up to +60 1 /s. During the upstroke, separating shear layers from the trailing edge are evident when the airfoil passes through its centerline position. Starting from the upper limit of the plunge motion, the airfoil near wake exhibits Karman like shedding from the trailing edge. The formation length of vortices is shorter with decreasing angle of attack. On the other hand, when the airfoil is in downstroke motion, a large separation zone covers the upper side of the airfoil with decreasing angle of attack. Small scale vorticity patterns are swept over the surface at the beginning of the upstroke, just after the airfoil passes through its minimum of the plunge motion. The velocity field and zoomed in vorticity patterns for the center image of Fig. 3 (t=3t+4t/8) are shown in Fig. 4. The angles of attack where these vorticity patterns cover the entire upper surface of the airfoil are very low, or even slightly negative. Small laminar separation bubbles are observed, flow separates and reattaches consecutively. Even for large angle of attack values where the airfoil is at stall limits, the results do not reveal the existence of any dynamic stall vortex evolved from the leading edge. - 4 -

t=3t+0 t=3t+t/8 t=3t+2t/8 t=3t+3t/8 t=3t+4t/8 t=3t+5t/8 t=3t+6t/8 t=3t+7t/8 t=4t Fig. 3 Vorticity patterns at different phases of the airfoil flapping (Re=20 000) [ω = ±10 1 /s, ω = 0.5 1 /s] Fig. 4 Velocity and vorticity field on the upper surface of the airfoil at Re= 20 000 (t=3t+4t/8) [ω = ±10 1 /s, ω = 0.5 1 /s] Vorticity pattern results obtained at Re=27 500 are presented in Fig. 5. Similar variations are observed in vorticity patterns depending on the phase of the motion. The increase in flow speed diminishes the vertical extent of small scale vorticity patterns and they are swept from the airfoil surface earlier. Another comparison remark can be made on the persistence of the Karman like shedding. It is only evident in the image presenting the airfoil at its upper limit of plunge motion. - 5 -

t=3t+0 t=3t+t/8 t=3t+2t/8 t=3t+3t/8 t=3t+4t/8 t=3t+5t/8 t=3t+6t/8 t=3t+7t/8 t=4t Fig. 5 Vorticity patterns at different phases of the airfoil flapping (Re=27 500) [ω = ±10 1 /s, ω = 0.5 1 /s] Considering the actual reference frame for the flapping motion, the freestream velocity vector is subtracted from all the vectors and streamline topology is obtained for the two cases in consideration. Fig. 6 shows the patterns for Re=20 000 and Fig. 7 those for Re=27 500. For most of the images, the streamlines announce a large separation zone starting from the leading edge of the airfoil. For Re=20 000, except the mid plunge position, the separation bubble does not cover more than half of the chord length on the upper surface of the airfoil. Its extent seems to be decreased for higher flow speed, namely at Re=27 500. Small scale vortices are still evident at the mid plunge position and just after, during the downstroke and especially at Re=27 500. Karman like shedding is also observable at this reference frame as indicated by the images acquired at beginning of the downstroke, especially for Re=20 000. In order to investigate in detail the repeatability of the vortex structures, 7 images are extracted from the data acquired at 2Hz corresponding to t=3t/8 of each cycle of oscillations. Fig. 8 presents those seven instantaneous images along with the phase averaged result. The image corresponding to the same phase of the oscillation acquired at 10Hz during a different run and presented previously in the sequence has been also shown in the figure. The repeat is remarkable and visual decision is confirmed by the averaged data where the vorticity levels are preserved. - 6 -

14th Int Symp on Applications of Laser Techniques to Fluid Mechanics t=3t+0 t=3t+t/8 t=3t+2t/8 t=3t+3t/8 t=3t+4t/8 t=3t+5t/8 t=3t+6t/8 t=3t+7t/8 t=4t Fig. 6 Streamline patterns at different phases of the airfoil flapping (Re=20 000) t=3t+0 t=3t+t/8 t=3t+2t/8 t=3t+3t/8 t=3t+4t/8 t=3t+5t/8 t=3t+6t/8 t=3t+7t/8 t=4t Fig. 7 Streamline patterns at different phases of the airfoil flapping (Re=27 500) -7-

t=3t+3t/8 t=4t+3t/8 t=5t+3t/8 t=6t+3t/8 t=7t+3t/8 t=8t+3t/8 t=9t+3t/8 Average of previous 7 images acquired at 2Hz Instantaneous image acquired at 10 Hz Fig. 8 Instantaneous images and phase averaged image for t=3t/8 of each cycle of oscillations (Re=20 000) As expected, small scale vorticity concentrations do not repeat perfectly at each cycle of oscillations. The phase average of the data obtained at t=4t/8 of each cycle of oscillations along with its constituent instantaneous vorticity concentrations are presented in Fig. 9. They cover all over the upper surface of the airfoil and their vertical extent is at the same order. Although the instantaneous vorticity plots look alike, the maximum and minimum vorticity values of the phase averaged plot are reduced down by half compared to the limits of the instantaneous images. This reduction was only 20% at maximum for the previous data obtained at t=3t/8. t=3t+4t/8 t=4t+4t/8 t=5t+4t/8 t=6t+4t/8 t=7t+4t/8 t=8t+4t/8 Average of previous 6 images acquired at 2Hz Instantaneous image acquired at 10 Hz Fig. 9 Instantaneous images and phase averaged image for t=4t/8 of each cycle of oscillations (Re=20 000) - 8 -

Finally, the zoomed in view of the airfoil trailing edge and vortex shedding along with overlapped velocity profiles are shown in Fig. 10 for t=3t/8. The velocity profiles do not exhibit any jet like behavior and vorticity patterns, independent of the reference frame, show a classic Karman like shedding. ( a ) ( b ) Fig. 10 (a) phase averaged (2Hz) (b) instantaneous (10Hz) plots of vorticity patterns and velocity field at the trailing edge of the airfoil 4. Conclusion Time dependent velocity fields around a SD7003 airfoil, known to be optimized for flows with large separation bubble and undergoing combined pitching and plunging motion have been investigated using Digital Particle Image Velocimetry at Reynolds numbers of 20 000 and 27 500. Two stitched images for each experimental run and two runs of experiment for each case have been accomplished to cover the field of view including the airfoil and its near wake nearly at all positions of its flapping motion. The images are acquired at two different frequencies to allow either detailed analysis of a single cycle of oscillation or phase averaging over approximately 6 cycles of oscillations. The major findings are summarized are as follows: - Starting from the upper limit of the plunge motion, the airfoil near wake exhibits a classical Karman like shedding from the trailing edge. Any thrust indicative wake couldn t be observed. - During the downstroke, at small angle of attacks, a large separation zone made of small scale vorticity concentrations covers the upper side of the airfoil. On the other hand, even at very large effective angle of attack values, the results do not reveal the existence of any dynamic stall vortex evolved from the leading edge. - Phased averaged images show a nearly perfect repeatability for Karman like shedding from the trailing edge. This synchronization at low angle of attacks is not as perfect for the separation zone covering all the upper surface of the airfoil. Although the small scale patterns are not exactly at the same location and at the same strength at each cycle of oscillations they qualitatively repeat quite well. References - 9 -

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