Flow around a Suddenly Accelerated Rotating Plate at Low Reynolds Number

Transcription

1 Flow around a Suddenly Accelerated Rotating Plate at Low Reynolds Number M. Percin 1,*, L. Ziegler 2, B. W. van Oudheusden 1 1: Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands 2:Faculty of Mechanical Engineering, Technical University of Munich, Garching, Germany * correspondent author: m.percin@tudelft.nl Abstract The study explores the evolution of flow field and forces of a low-aspect-ratio flat plate undergoing an accelerated rotating surge motion from rest. The measurements were performed in a water tank at Reynolds numbers of 20,000, based on the chord length and terminal velocity at 75% span. A tomographic Particle Image Velocimetry (Tomographic-PIV) technique was used in order to capture three-dimensional velocity fields at different phases of the rotational motion, in combination with direct force measurements with a six-component water submergible force sensor. Experiments were performed for angles of attack of 30, 45 and 60. The results show the temporal development of the generation of lift and drag in conjunction with the development of vortical structures around the wing. The force measurements reveal the temporal variation of the forces during the motion: initial added mass peak at the end of the acceleration phase; subsequent decrease and increase to the maximum with circulatory effects; and decrease to steady state values. Although the general trend is similar for the different angles of attack, the magnitudes and phasing of the circulatory peak differs. Three dimensional flow fields show the evolution of vortical structures, starting from the formation of coherent and well-defined vortices (i.e. leading edge vortex, trailing edge vortex and tip vortex) to a stalled wing flow field with several small-scale structures. The leading edge vortex moves downstream on the top of the wing surface while it bursts into small scale structures. Surprisingly, this bursting and loss of vortex coherence is not reflected in a loss of lift. The spanwise flow structure also changes in accordance with the behavior of vortex formations such that initially it is mostly confined in the cores of leading and trailing edge vortices, however, as the motion progresses, it occurs around the trailing edge. 1. Introduction Expanding design efforts in the area of Micro Air Vehicles (MAVs) have triggered the research interest in bio-inspired flapping wing aerodynamics, especially over the last decade. First attempts to understand the underlying physics were made by use of two-dimensional flapping wing models, in order to isolate the impacts of different motion kinematics (Anderson et al. 1998, Lai and Platzer 1999, Platzer et al. 2008, Tuncer and Kaya 2005, Young and Lai 2002, Young and Lai 2007a, Young and Lai 2007b). However, actual natural flapping flight is three-dimensional in essence and combines pitch, plunge and sweeping motions of the wing, with three-dimensional effects being further enhanced by low wing aspect ratio. Further studies hence revealed that, in consequence of this, it is not possible to explain unsteady force generation mechanisms of flapping flight completely, without taking these three-dimensional effects into account (Birch and Dickinson 2001, Ellington et al. 1996, Wang et al. 2004). This requirement of extending investigations into the third dimension, together with the flow-diagnostic capabilities offered by the availability of threedimensional Particle Image Velocimetry (PIV) techniques (Elsinga et al. 2006, Scarano 2013) have motivated the current experimental investigation for characterizing the flow around three-dimensional wings undergoing flapping motions. Earlier studies performed on mechanical wing flappers and insects (Dickinson and Götz 1993, Ellington 1984) showed that Leading Edge Vortex (LEV) is one of the most prominent mechanisms responsible for the generation of aerodynamic forces in flapping flight. The stability of the LEV was also shown to be of importance in terms of persistence of the lift generation throughout the flapping motion. Therefore several studies were performed to investigate the behavior of the LEV in relation to lift generation especially on rotating wings (Usherwood and Ellington 2002), which provide a more realistic representation of natural flapping flight, in view of the presence of spanwise flow that is suggested to be influential on the stability of the LEV (Jones and Babinsky 2010). Ozen and Rockwell (2012) performed PIV measurements around a - 1 -

2 rotating plate at a Reynolds number range, based on the velocity at the radius of gyration, from 3,600 to 14,500. They found that a stable LEV is preserved over angles of attack from 30 to 75. However it should be noted that measurements were carried out well after the start-up of the motion, so that the transient effects are not significant. On the other hand, Jones and Babinsky (2011) focused on the onset of waving wing motion at Reynolds numbers ranging from 10,000 to 60,000. They reported shedding of the LEV in early phases of wing stroke correlated with a sharp decrease in lift. Recently, Venkata and Jones (2013) studied LEV formation over multiple revolutions of a rotating flat plate wing. They performed force measurements and flow visualization in a water tank at Reynolds numbers of 5,000 and 10,000. They observed peaks in both lift and drag at the onset of the motion, due to non-circulatory effects. As the wing starts the second revolution, steady state values of lift and drag coefficient decreases due to the interaction of the wing with its wake from the previous revolution. Flow visualization results revealed the formation of the LEV and spanwise flow already at the very early phases of the wing stroke. The specific aim of the present study is to investigate the formation of vortical structures and generation of forces on a flat rectangular wing undergoing a revolving surge motion in which the wing starts from rest at a constant angle of attack and accelerates to terminal velocity. The angle of attack (α) was varied in order to investigate its effect on the three-dimensional flow structures and unsteady loading. 2. Experimental Setup and Methods The experiments were conducted in a water tank (Fig. 1a) at the Aerodynamic Laboratory of Delft University of Technology (TUDelft). The octagonal water tank (600 mm of diameter and 600mm of height) is made of Plexiglass allowing full optical access for illumination and optical imaging (Fig. 1a). A Plexiglass flat plate with sharp edges and constant thickness of 3 mm was used as the rectangular wing model. It has a chord length (c) of 50 mm and a span length (b) of 100 mm, resulting in a wing aspect ratio of 2 (Fig. 1b). The main axis of the setup is mounted vertically in the water tank to control the revolving motion. The pitching axis coinciding with the wing leading edge is positioned perpendicular to the main axis, at approximately 5c distance from the water surface, 7c distance from the bottom wall and 5c (wing tip to wall) distance from the side wall in order to prevent any wall or free-surface interference effects (Dickinson et al. 1999). The model was driven by a brushed DC motor and a gearbox (gear ratio of 132:1) in revolution and a waterproof servo motor in pitching motion. Fig. 1 (a) Experimental arrangement in the water tank (b) Dimensions of the wing model The wing motion was initiated by a constant acceleration of the wing from the rest position to a pre-defined terminal velocity (V t ), over a prescribed convective time interval (t * =V t t c where t is time in seconds)

3 This is then followed by a period in which the wing remains in a constant rotational motion, at the terminal velocity. The entire motion cycle (acceleration and constant velocity phases) is performed at a constant angle of attack (Fig. 2). The three-quarter span length was used as a reference position for defining the terminal velocity and nondimensional parameters. Experiments were carried out at terminal velocities of 0.2 and 0.4 m/s, corresponding to the Reynolds numbers of 10,000 and 20,000, respectively. In all experiments the entire travel distance in terms of chord length (chords travelled - cht) is 14 with respect to the reference position corresponding to one full rotation. Although the forces were captured for the full motion, flow field measurements were limited to the first 7c of travel. The acceleration period is executed over t * of 1 or 2 (which, in view of the constant acceleration rate corresponds to cht=0.5 and 1, respectively). The angle of attack (α) was varied in the experiments between 30, 45 and 60. In this paper, the results of the experiments performed at the Reynolds number of 20,000 with an acceleration period of t * of 2 (cht=1) for the considered angles of attack are discussed. Fig. 2 Motion kinematics at α=45 Six components of forces and moments were measured by use of a water submergible ATI Nano17/IP68 force sensor. The sensor is calibrated to have a maximum sensing value of 25 N in x, y and 35 N in z direction with a resolution of 1/160 N, and a torque capacity of 250 N.mm with a resolution 1/32 N.mm. Force and moments were acquired at 2 khz data acquisition frequency via an in-house developed LabVIEW code that also controls the motors and synchronizes the wing motion with the force data acquisition and the PIV measurements. Ensemble averaging of forces and moments was performed over 20 repetitions of the experiments. Then, a 0.05 s moving average filter was applied to provide a clear representation of the data, in view of the contamination of the force signal by model vibrations. Finally, the forces are expressed in nondimensionalized format by use of the terminal velocity and chord length to assess lift and drag coefficients. Phase-locked Tomographic-PIV measurements were carried out in order to acquire three-dimensional quantitative information of the flow around the wing model. At each run, a double-frame image was captured by the cameras at a specific phase of the flapping motion. Individual runs were performed with sufficient time intervals to restore quiescent initial conditions in the water tank. The measurement volume of mm3 in size was positioned at two different spanwise locations side by side as shown in Fig. 3b. The starting position of the wing was changed based on the desired measurement phase so to have the wing oriented normal to the measurement volume during image acquisition. The volume was illuminated by a double-pulsed Nd:Yag laser at a wavelength of 532 nm. Polyamide spherical particles of 56 µm diameter were employed as tracer particles at a concentration of 0.23 particles/mm3. The motion of tracer particles was captured by four 12 bit CCD cameras with a resolution of pixels and a pixel pitch of 6.45 µm. Three cameras were arranged along different azimuthal directions in a horizontal plane while the fourth camera was positioned above the mid-camera in a vertical plane as shown in Fig. 3a. Each camera was equipped with a Nikon 60 mm focal objective with numerical aperture f#=11. Scheimpflug adapters were - 3 -

4 used on three cameras to align the mid-plane of the measurement volume with the focal plane. The digital resolution is 15 pixels/mm and the average particle image density is approximately particles per pixel (ppp). Image pre-processing, volume calibration, self-calibration (Wieneke 2008), reconstruction, and three- dimensional cross-correlation based interrogation were performed in commercial software DaVis (LaVision). The measurement volume was calibrated by a scanning plate with 9 10 dots throughh the volume in depth of 25 mm with steps of 5 mm. In each of the calibration planes, the relation between the physical coordinates and image coordinates is describedd by a 3rd order polynomial fit. Linear interpolation is then used to find corresponding image coordinates at intermediatee z-locations. Fig.3 (a) Schematic representation of top view (b) Measurement volume arrangement Image pre-processing with background intensity removal, particle intensity normalization and a Gaussian smooth with 3 3 kernel size was performed in order to improve the volume reconstruction process. Particle images weree interrogated using windows of final size voxels with an overlap factor of 50% for the preliminary results presented in this paper. The resultant vector spacing is 1.0 mm in each direction forming a dataset of velocity vectors in the measurement volume. 3. Results This section presents the force and flow field measurement results for the case of revolving surge motion accelerating over t * of 2 (cht of 1) at Re = 20,0000 for the considered angles of attack. In Figure 4a and b, temporal evolution of lift and drag coefficients, respectively, are plotted as a function of cht for different angles of attack. During the acceleration phase of the motion, there are multiple peaks in the force coefficients, whichh is a natural result of the test rig vibrations due to the impulsive start of the motion. This initial vibratory behavior of the force coefficients is then followed by a rise to the maximum of the acceleration period. Regardless of the influence of the model vibrations, this initial fast increase of the forces is due to non-circulatory effects (i.e. added mass due to acceleration of the surrounding fluid). However, in the current experiments this added mass effect does not generate lift or drag greater that the steady state values, in contrast to the study of Venkata and Jones (2013), which is due to the relatively small wing used in this study (small relative contribution of the added mass effect). Thereafter, both lift and drag slightly decrease and then start to increase with circulatory effects for all cases. The highest lift is generated in the case of α=45 in which the maximum value (c L =1.15) is reached at cht= Subsequently the lift decreasess to steady-state value of For the same case, the maximum drag (c D D=1.04) is also generated at cht=4.21 which is then followed by a steady state value of approximately 1.0. The similarities of the lift and drag histories for the case of α=45 points to the generation of normal forces which is a natural result of vortex

5 dominated flow structure and related pressure fields. The highest drag, is generated in the case of α=60,, which has a similar trend with the case of 45 : an initial decrease of both lift and drag after the added masss peak; subsequent increase to the maximum value (c L =0.97 at cht=3.65 and c D =1.54 at cht=3.8); and a declinee to the steady state values (c L =0.81 and c D =1.44). The lowest angle of attack case also displays similar behavior, however in this case the initial circulatory peak (c L =0.86 and c D =0.515) is reached sooner than for the other cases (cht=3. 1). Moreover, the forces remain relatively unaltered for the subsequent time, with ensuing steady-state values nearly identical to the initial maximum values (c L =0.85 and c D =0.51).. Fig.4 Temporal variation of (a) lift and (b) drag coefficients Three-dimensional vortex formations for the α of 45 are visualized in Fig. 5 by means of isosurfaces of Q criterion at different phases of the motion. Note that only the outer half of the wing is depictedd in the flow fields, as corresponding to the measurement domain depictedd in Figure 3(b). As the motion startss (cht=0.5), a vortical structure comprised of a Leading Edge Vortex (LEV), a Tip Vortex (TV) and a Trailing Edge Vortex (TEV) is formed around the wing. In this phase, all these structures display rather two-dimensional characteristics. At the end of the acceleration phase (cht=1.0), the TEV is away from the wing and there are swirling features of small scale structures appearing around the TV. These small structures are linked to secondary TEVs shed into the wake, which becomes more evident at cht=1.5 (see also Fig. 6). The occurrence of these secondary TEVs is correlated with the small humps present in the force histories after the end of acceleration. The TV has a conical shape with a coherent structure in its core linked to the TEV. The LEV starts moving away from the leading edge as the plate motion progresses. At cht=2.0, the TV is elongated into the wake and the TEV is mostly out of the measurement volume. The travel of the LEV continues in the following phase (cht=3.0) towards to the trailing edge but it does not completely shed from the wing, which explains the continuous increase of the forces. However, the TV loses its coherency and appears as segments of longitudinall vortical structures extending along the wing tip. In the following phase (cht=4.0), both the LEV and the TV bursts into small scale structures and create a chaotic flow field around the wing model. The LEV is hardly visible in the wake of the wing aligned with the trailing edge more inwards the wing. In the subsequent phases, there is a continuous feeding of small scale structures from the leading edge and the tip of the plate. To better observe the behavior of the LEV, contours of out-of-plane vorticity are plotted in the referencee plane in Fig. 6. The LEV is positioned very close to the wing surface at the first phase. It lifts off from the wing surface and grows in strength during the phases of cht=1.0 and 1.5. At cht= =2.0, the LEV is nearly aligned with the half-chord position and it is detached from the wing surface. However, it maintains its connection with the wing my means of a shear layer emanating from the leading edge. The LEV is positioned more downstream at cht=3.0 when it also breaks into smaller segments. At cht=4.0, the initial LEV appears as small fragments with the shear layer of the leading edgee elongated towards these structures. From this phase on, there is not a well-definedd LEV as the initial one but leading edge and trailing edgee vorticity occupy the areaa behind the wing

6 th 17 International Symposium on Applications of Laser Techniques to Fluid Mechanics Fig.5 Isosurfaces of Q criterion (isovalue of Q=6 10-4) at different phases of the revolving surge motion at α=45 at Re=20,000 The evolution of the spanwise flow in the reference plane throughout the motion is plotted in Fig.7. It is clear that until cht=2.0, the spanwise flow is confined within the LEV and TEV and it is directed towards the tip. Its magnitude increases in correlation with the growth of the LEV and TEV, which might be explained by an increasing pressure gradient along the wing span. However, as the LEV moves downstream, the spanwise flow pattern that is around the leading edge starts to move towards the trailing edge such that at cht=5.0, there is no prominent spanwise flow observed around the leading edge but mostly it occurs around the trailing edge. Fig.6 Contours of out-of-plane vorticity plotted in the reference plane at different phases of the revolving surge motion at α=45 at Re=20,000-6-

7 th 17 International Symposium on Applications of Laser Techniques to Fluid Mechanics Fig.7 Contours of out-of-plane velocity (spanwise flow velocity) plotted in the reference plane at different phases of the revolving surge motion at α=45 at Re=20,000 In Fig. 8, the evolution of flow field is shown for the α of 60. Generally, the vortices display a similar behavior as for the case of 45, however, due to increased angle of attack, the morphology of the features is different. Swirling patterns of vortex structures around the TV are oriented more vertically and persist longer than in the previous case. Moreover, the segmentation of the TV into these structures and the burst of the LEV occurs relatively early in this case. Therefore, starting from cht=3.0, these small scale vortical structures start to appear around the wing. Fig.8 Isosurfaces of Q criterion (isovalue of Q=6 10-4) at different phases of the revolving surge motion at α=60 at Re=20,000 For the smallest angle of attack case (Fig.9), the LEV displays a similar behavior as for the other cases: it moves towards the trailing edge of the wing starting from cht=1.5 till cht=3.0. After this phase, the complete -7-

8 wing surface is covered with layers of small scale structures emanating from the leading edge and the wing tip. Furthermore, the segmentation of the TV is not as prominent as the other cases. Fig.9 Isosurfaces of Q criterion (isovalue of Q= ) at different phases of the revolving surge motion at α=30 at Re=20, Conclusion The flow field around a suddenly accelerated revolving low-aspect-ratio flat-plate wing is investigated experimentally via Tomographic PIV. Measurements were performed in two adjacent volumes positioned at two different spanwise locations, providing a total measurement volume of size mm 3 (chordwise normal spanwise). A water-submergible force sensor was used to measure the fluid forces exerted on the wing model. Experiments were carried out for a revolving surge motion for Reynolds number of 20,000, in which the wing accelerates from rest to a terminal velocity and continues its revolution with a constant velocity at a fixed angle of attack. The angle of attack value was varied in different experiments, in order to investigate its effect on force generation and flow structures. Comparison of forces for three different angles of attack (30, 45 and 60 ) reveals that mostly normal force is generated during the motion. Highest lift is acquired in the case of 45 whereas highest drag is experienced in the case of 60. The evolution of forces have some common features for all cases: initial non-circulatory peak at the end of the acceleration phase; following decrease and increase of both lift and drag to the maximum; and decline to steady-state values. However, the phase of the hump, when the maximum occurs, differs based on the angle of attack. This hump appears earliest in the case of 30 and latest in the case of 45. The three-dimensional flow fields also represent evolution characteristics in accordance with the temporal variation of the forces. In the first two chords of length of travel, coherent vortical structures (i.e. leading edge vortex, tip vortex and trailing edge vortex) appear and develop in size as the motion progresses. The spanwise flow also grows in magnitude within the cores of the leading and trailing edge vortices. The tip vortex displays a conical shape with swirling patterns of small scale structures which are most prominent for the case of 45 and 60. Following an initial coherent growth, the leading edge vortex then detaches from the wing surface and travels downstream while it bursts into small scale structures, however, it does not fully shed from the wing at least until 4 chords of travel. After this phase, no coherent structure is present around the wing and the flow field displays stalled wing characteristics. The spanwise flow structure also changes with the travel of the leading edge vortex from a pattern in the vortex core to a pattern concentrated around the trailing edge

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