Comparison of Laminar Separation Bubble ...

Comparison of Laminar Separation Bubble Measurements on a Low Reynolds Number Airfoil in Three Facilities Michael V. Ol

∗

Air Force Research Laboratory, Wright-Patterson Air Force Base

Brian R. McAuliffe

†

Department of Mechanical and Aerospace Engineering, Carleton University

Ernest S. Hanff‡ Institute for Aerospace Research, National Research Council of Canada

Ulrich Scholz§ and Christian K¨ahler¶ Institute of Fluid Mechanics, Technical University at Braunschweig

This paper describes a series of experiments on the SD7003 airfoil, conducted in three different facilities: a low-turbulence wind tunnel, a water tunnel, and a tow tank. An attempt was made to achieve commonality of model geometry, Reynolds number and test conditions, in order to directly compare the experimental results. The SD7003 airfoil was chosen because of its robust, thin laminar separation bubble, which challenges the capability of current Particle Image Velocimetry (PIV) methods to accurately resolve the near-wall flowfield. Chordwise locations of separation, reattachment, and transition were compared. Since the time-averaged bubble geometry is a strong function of the flowfield ambient turbulence level, comparison of bubble geometry gives some assessment of facility flow quality, and hence of facility suitability for low Reynolds number testing in general.

I.

Introduction

mprovement in the performance of Small Unmanned Air Vehicles, including Micro Air Vehicles (MAVs), Ibatteries, is frequently regarded as being contingent more upon the evolution of component technologies such as than on improvement of airframe aerodynamics. Nevertheless, the formation, presence and burst of laminar separation bubbles (LSBs) has long been known as a detriment to the performance of airfoils at low Reynolds number, directly affecting not only MAV endurance - an issue conceivably ameliorated by improved batteries and so forth - but, more importantly, degrading vehicle handling and stability, due to the timedependency of separated structures sensitive to disturbances encountered in flight. Better understanding and ultimately management of LSBs is therefore useful for improving the flight mechanics of MAVs. Recent reviews on the subject of MAV flight are given by McMichael & Francis1 , Shyy et al.2 , Mueller3 , Lian et al.4 , and Rozhdestvensky & Ryzhov5 . The LSB is a classical topic in laminar to turbulent transition, having been extensively examined both from the viewpoint of fundamental fluid mechanics6–9 and in the context of aerodynamics of airfoils and wings10–14 . The present study seeks to apply modern flow diagnostic methods, principally particle image velocimetry (PIV) methods, to track the development of the LSB over a range of angles of attack, from low angles where ∗ Aerospace

Engineer, [email protected], AIAA Senior Member Student, [email protected], AIAA Student Member ‡ Principal Research Officer, [email protected] § Research Engineer, [email protected] ¶ Research Scientist, [email protected] † Ph.D.

1 of 11 American Institute of Aeronautics and Astronautics

the bubble is stable and well-defined, to higher angles, where burst eventually occurs. Of primary interest is to produce a data set suitable for validation of computations. Therefore, emphasis is on resolving the velocity field and its statistics, rather than obtaining integrated forces and moments. In particular, the near-wall velocity distribution can be compared with the results of commonly-used airfoil analysis codes, for example XFOIL15 , by looking at the predicted vs. the measured shape of the LSB for a given critical amplification factor. The code is expected to be reliable for those conditions where the bubble is stable and closes well upstream of the airfoil trailing edge. The secondary objective of this study is to benchmark and compare three recently constructed experimental facilities of very different type; a water tow tank, a wind tunnel and a water tunnel, by testing a common geometry at nominally identical experimental conditions: matching the model, the Reynolds number and the angle of attack. The SD7003 airfoil16 was chosen as the common geometry because of the long, stable LSB that it exhibits over a broad range of angle of attack, at Reynolds numbers below 100,000.

II.

Experimental Setup

The three facilities used in the present study are described below. In each case, data were obtained with conventional 2-component digital particle image velocimetry, with a light sheet formed by a doublepulsed Nd:YAG laser. In the first two cases, a LaVision17 system was used; a system based on Pixelflow18 components was used in the latter case. The SD7003 models had nominally 8” chord (201mm-203 mm), with an aspect ratio of 3.62 in the first case, and spanning the test section in the other two cases. The common Reynolds number was 60,000, based on chord. Camera resolution was 1280x1024 pixels in the first two cases, and 1024x1024 pixels in the last case. A.

Institute for Aerospace Research (IAR) Tow Tank

The first data set was obtained in the Institute for Aerospace Research’s Low Reynolds Number Tow Tank (Figure 1), with test section of 1m x 1m and 3m in length. The major advantage of a tow tank over wind or water tunnels is the excellent ”inflow quality” due to nominally quiescent free-stream conditions. Upstream of the glass-walled test section is a 1.2 m-long access section for model insertion and removal. The facility differs from conventional tow tanks by the absence of a free surface, which has been eliminated by with a roof with a longitudinal slot at the centerline. The roof is slightly sloped up towards the center, to allow the escape of air bubbles through the slot. The vertical sides of the slot support a pair of inflatable rubber seals facing each other, which make contact when inflated, sealing the slot, yet allowing the passage of the model support strut. The tank is filled with the test medium up to and slightly above the line of contact between the opposing seals, which ensures the absence of a free surface and provides lubrication between the seal and the model support strut. The top end of this strut is mounted on a motorized carriage that travels along longitudinal precision tracks located above the tank. Tightly controlled arbitrary motions can be imparted to the model, though in the present study the motions were limited to steady translation. To perform flow visualization and PIV tests, additional tracks are installed under and to one side of the tank (Figure 1), parallel to the track supporting the model carriage. PIV tests were conducted by mounting the laser unit on the bottom carriage, producing a streamwise-oriented vertical light sheet. The camera was mounted on the side carriage with its optical axis nominally normal to the light sheet, as seen in Figure 2. Implementing PIV in this type of facility poses special problems, because the model and optical equipment, rather than being stationary as is the case in the wind and water tunnel experiments, must all move synchronously. In spite of the fact that the carriages are mounted on precision tracks and linear bearings, and are reasonably accurately controlled by servomotors, there are residual model and camera motion errors that must be corrected. Two sources of PIV measurement error have been identified due to these residual motions, and correction algorithms have been implemented to reduce their effects. The first of the measurement errors, called the “tracking error,” is due to relative motion between the camera and airfoil model, and is corrected by use of light emitting diode (LED) markers inserted into the model which act as reference points in the image frames. Continuous images comprising one PIV pair are translated and rotated to zero-out the marker displacement, thus eliminating the tracking error. The second source of measurement error is due to residual model motion and causes a variation in the free-stream velocity levels relative to the airfoil. This “jitter error” gives rise to high RMS velocities in the free-stream which, by virtue of the stagnant fluid in the tow-tank, should be negligible. This error


Figure 1. IAR tow tank

Figure 2. IAR PIV system setup

is corrected by adding a constant velocity-vector offset to each of the previously obtained velocity fields, such that the instantaneous mean velocity field outside the boundary layer is made to correspond to the ensemble average mean velocity field for the series of runs under a given set of test conditions. In general, the error in the motion of the model can have both translational and rotational components, however the translational components dominate since the ”jitter” is primarily due to variations in the model forward speed. The constant velocity-vector offset for a given vector field is calculated by averaging the deviation vectors (difference from ensemble average) over a region well-outside the airfoil boundary layer. Implementation of the two error correction algorithms reduces the velocity field uncertainty to values below 5%, whereas errors for uncorrected data could be on the order of 50%. Details of the tracking-error correction, as well as an older form of the jitter-correction, are given by Hanff 19 . The current jitter-error correction method is found in Ref. 20. B.

Technical University of Braunschweig (TU-BS) Low-Noise Wind Tunnel

The second data set was obtained in the Technical University of Braunschweig’s Low-Noise Wind Tunnel (Figure 3), an Eiffel-type tunnel with closed test section, built specifically for studying low Reynolds number flows of particular interest to MAV applications. The tunnel is driven by a 3 kW motor, resulting in a test section free stream velocity range between 5-20 m/s. Care was taken to promote quiet flow in the facility, using open-celled acoustic foam attached to the ceiling and an acoustically encapsulated motor. The nozzle has a rectangular cross section with a Borger-type cross sectional area distribution to minimize the length of the contraction section. Air enters the intake through a 30 mm-thick fleece mat, to promote flow uniformity; it then passes through a 14-mm thick aluminum honeycomb straightener, and a fine-mesh woven screen.

Figure 3. TU-BS low noise wind tunnel


Figure 4. AFRL horizontal free-surface water tunnel

The contraction ratio is about 16:1. A 0.1% turbulence level was observed at 10 m/s. The test section has a height of 600 mm, a width of 400 mm and length of 1500 mm, and is fully transparent for flow analysis with optical methods. C.

Air Force Research Laboratory (AFRL) Free-Surface Water Tunnel

The third data set was obtained in the Air Force Research Lab’s “Horizontal Free-Surface Water Tunnel” (HFWT). A view of the tunnel, as well as hot-film data on test section mean flow velocity and rms u2 component velocity (u02 /U∞ ), are given in Figure C. This facility was recently relocated from the California Institute of Technology, and reassembled in a slightly different configuration. The test section is 18” wide by 24” high. Based on the hot-film data, filtered at 500Hz, a turbulence intensity of less than 0.1% is quoted over the speed range of interest in the present study. More details on the facility are given in Ol21 .

III. A.

Results

IAR Tow Tank

20 micron polyamid particle seeding material was selected for its specific gravity of 1.03, which results in a negligible settling speed, an important requirement in a tow tank. Given the significant distance between the camera and subject (∼3m) the camera field of view is approximately 75 mm wide (37% chord) with a 300mm lens, resulting in somewhat limited spatial resolution, especially in regions of thin boundary layers, such as near the airfoil leading edge. The results for Reynolds number of 60,000 and angle-of-attack of 4◦ , corrected for the previously described motion errors, are shown in Figure 5. These measurements were made at quarter-span to minimize interference effects from the mounting strut on the pressure side. The airfoil was imaged piecewise in three overlapping fields of view. In the forward and middle fields of view, averaged data were obtained using 528 vector fields, which appears sufficient for flow statistics to converge when the boundary layer and separated shear layer are laminar. No significant Reynolds stresses develop in these regions. In the aft field of view, averaged data were calculated using 1070 vector fields. The data were processed using an interrogation window size of 16x16 pixels with 75% overlap, which gives a window width of 0.94mm (0.46% of chord) and vector spacing of 0.23mm (0.12% of chord). A comparison of the PIV resolution for the three data sets is given in Table 1. The PIV algorithm used was an iterative multi-grid approach with a second-order cross-correlation algorithm, deformable interrogation windows, and intermediate smoothing to reduce the number of outliers (within LaVision Davis 6.2 software package). To prevent PIV evaluation errors associated with reflections at the model surface, which are significant for the current data set, masking of the airfoil along with a thin surface layer (2-4 pixel thickness) has been performed during the evaluation. The uncertainty in ensemble-averaged mean velocity is based on the observed levels


Figure 5. Contours of mean velocity and Reynolds stresses; IAR data set, α=4◦

of RMS velocity in the free-stream flow far from the model surface (3-5% of the airfoil forward speed), since the free-stream turbulence level for the tow tank is nominally zero. This free-stream RMS is dominated by residual post-correction errors for which u0 and v 0 are uncorrelated. The result is a negligible u0 v 0 correlation due to measurement errors, and gives an uncertainty in u0 v 0 much lower than the observed RMS level. Near-wall velocities near the forward part of the airfoil are in error due the low spatial resolution of the PIV setup. In these regions the shear layers are extremely thin and the steep velocity gradients are “smeared-out” within the relatively large interrogation windows. A large occurrence of outliers also occurs in these regions. Due to the thin boundary layer at separation and the low spatial resolution of the PIV measurements in this region, the separation point cannot be evaluated from the averaged velocity vector fields. However, the raw PIV images provide information on separation and its possible time-dependency. For reasons associated with the short length of the tow-tank (3m) and the long settling times between measurement runs (>10min.), the images show a lack of seeding material in the forward part of the separation bubble. This results in a visible and very distinct dividing streamline which, when extrapolated upstream to where it intersects the model surface, provides an estimate of the separation point, to within 1% of the airfoil chord length. The separation point established through this procedure is found to be steady and is located at 33% of chord. The deficiency of seeding material below the dividing streamline also causes difficulties in resolving the reverse flow within the separation bubble; there is no time-averaged recirculation region resolved in the IAR dataset. In spite of this, visual inspection of the raw PIV image pairs has confirmed that a separation bubble with reverse flow is present. This lack of reverse-flow vectors causes a problem with evaluating the reattachment point. However, reattachment can be estimated as the stream-wise location where the velocity magnitude of the vectors adjacent the wall begins to increase from the near-zero values within the bubble20 . Based on this approach, the reattachment point is estimated at 63% of chord, with an uncertainty of 2% of chord.

Table 1. Comparison of PIV resolution for the three data sets

Facility IAR TU-BS AFRL

Window Width [pix (%chord)] 16(0.46%) 16(0.16%) 32(0.44%)

Vector Spacing [pix (%chord)] 4(0.12%) 8(0.08%) 16(0.22%)


Figure 6. Contours of mean velocity and Reynolds stresses with streamlines in the LSB; TU-BS data set, α=4◦

There are various techniques that one can use to estimate the location of transition onset in a separated shear layer, for example: intermittency methods22 and fluctuation growth methods23 . A Reynolds-stress threshold method has been selected for the current study. Transition onset is estimated as the stream-wise 2 location where the normalized Reynolds stress (−u0 v 0 /U∞ ) first reaches a value of 0.001. This threshold is consistent with experimental studies in the literature for which Reynolds stress and intermittency measurements were performed using two-component hot-wire anemometry24 . Also, this location corresponds to the appearance of instability waves in the separated shear layer, which can be seen in the instantaneous vector fields. For the IAR dataset, transition occurs at 57 ± 2% of chord. B.

TU-BS Wind Tunnel

Approximately 1µm-diameter vegetable oil droplets were used for seeding25 . The airfoil was imaged piecewise in nine fields of view of 27.27mm × 21.81mm each. For each field of view 1000 images were taken in order to get sufficient reliable mean values and Reynolds stresses. The Braunschweig data set differs from the other two, in that for each PIV field the camera was angled to align its CCD array nominally parallel to the local airfoil contour, in an effort to circumvent problems with applying a commercial PIV package to inclined surfaces. A multi-pass PIV algorithm was applied with an interrogation window size of 16×16 pixels and 50% overlap, which is a compromise between accuracy and resolution25 . This led to a spatial resolution of 0.17mm, with absolute particle image displacement between 0.004 pixels and 14.36 pixels. According to Stanislas et. al.26 the accuracy of determining the particle image displacement is around 0.05pixel, which leads to a dynamic range of 287 and a full range measurement error of 0.35%. Averaged flow velocity data for Reynolds number of 60,000 and angle-of-attack of 4◦ , including a detail of the LSB streamlines are shown in Figure 6.


Figure 7. Contours of mean velocity and Reynolds stresses with streamlines in the LSB; AFRL data set, α=4◦

C.

AFRL Water Tunnel

Titanium dioxide seeding particles were used, with nominally 2-3 micron diameter and specific gravity of 4.217 . The high specific gravity is acceptable for a water tunnel, while the small particle size should improve the capacity of the particles to track with the ambient flow. The small optical scatter cross-section of these particles and their relatively high resistance to ”clumping” helps to keep particle image size to less than ∼ 4 × 4 pixels on the CCD, even at the high magnifications of this study. Clumping of particles, which is common for example with silver-coated glass particles, can result in ”blooming” on the camera CCD array, where long vertical streaks of saturated pixels contaminate the image and ruin cross-correlations. Titanium dioxide does have the disadvantage of adhering to the composite model in water, especially when the model surface has been exposed to high laser power for a significant time. In practice, this is solved by manually cleaning the model after every PIV run (approximately once per minute). Again, the airfoil was imaged piecewise, this time in six fields of view, skipping the aft ∼30% of the chord. The averaged velocity data were based on 840 images (420 velocity fields) in the two upstream fields, and 1176 images (588 velocity fields) in the four downstream fields, with 28.9mm × 28.9mm field size. The PIV algorithm was two-pass, (locally adapted window translation in the second pass, but no window resizing) with 32×32 pixel windows and 50% overlap. The large window size was chosen to minimize the number of PIV outliers, at the potential expense of reduced spatial resolution. Average velocity contours, a detail of the LSB streamlines, and contours of Reynolds stress are shown in Figure 7 for Reynolds number of 60,000 and angle-of-attack of 4◦ . The Reynolds stress contour plot reveals a thin, long “sliver” of apparent turbulence upstream of a broader wedge-like eruption of turbulence associated with the aft end of the LSB. This sliver is conjectured to be spurious - the result of possibly inadequate spatial resolution. Data were also taken at α = 8◦ (Figures 9) and α = 11◦ (Figures 9). Force balance measurements in the AFRL water tunnel indicated that maximum lift occurs at α = 11◦ (Ref. 27). For α = 8◦ an LSB is still visible; it is much shorter, thinner and further upstream than for α = 4◦ . Recirculating streamlines are no longer resolved, however. Evidently, this is due to comparative lack of resolution, either due to the thinness 7 of 11 American Institute of Aeronautics and Astronautics

Figure 8. Contours of mean velocity and Reynolds stresses with streamlines in the LSB; AFRL data set, α=8◦

Figure 9. Contours of mean velocity and Reynolds stresses; AFRL data set, α=11◦


Table 2. Measured and computed SD7003 LSB properties, Re = 60, 000, α = 4◦

Data Set IAR TU-BS AFRL XFOIL * Distance

Free-stream Turbulence, T u[%] 0 0.1 ∼0.1 0.070 (N=9)

Separation xs /c 0.33 0.30 0.18 0.21

Transition xt /c 0.57 0.53 0.47 0.57

Reattachment xr /c 0.63 0.62 0.58 0.59

Max Bubble Height*, hb /c 0.027 0.028 0.029 -

from surface to velocity profile maximum at edge of shear layer.

of the bubble and hence the decrease of PIV velocity vector density in the wall-normal direction, relative to the bubble thickness; or greater flow unsteadiness, requiring more PIV image pairs for the flow statistics to be adequately converged; or both. The problem of insufficient convergence of flow statistics becomes progressively worse at α = 11◦ , where mismatch in both mean velocity and Reynolds stress contours, in going from PIV interrogation field to field, is quite clear.

IV.

Discussion

The locations of separation, transition onset, time-averaged reattachment, and maximum bubble height for the three cases are listed in Table 2, along with the estimated facility turbulence intensity. Respective locations predicted by XFOIL for N=9 are also given, with separation and reattachment inferred from streamwise coordinates where the skin friction coefficient first reaches zero declining from positive (separation) and returning back to positive (reattachment); see Figure 10. IAR and TU-BS data on the LSB separation, reattachment and transition points agree quite well. In the AFRL data set, the bubble forms considerably further upstream and reattaches further upstream, though its length is somewhat longer than in the IAR and TU-BS results (∼40%c compared to ∼30%c). The IAR results show a reduced velocity magnitude at the suction peak, conceivably due to the finite aspect ratio of the wing which induces a smaller effective angle of attack than in the other two cases. This effect has also been observed by Bastedo & Mueller12 for a low-Reynolds number airfoil of similar aspect ratio. In the AFRL case, the true angle of attack may be slightly larger than the nominal. Provisions are being made to test a full-span model in the IAR facility to assess the effects of a finite aspect ratio model. Good agreement between all three facilities is observed for the maximum bubble height (hb ). However, the reverse flow within this region of the bubble is only captured by the TU-BS and AFRL measurements. The presence, or lack, of reverse flow in the measurements is dependent on the PIV resolution; primarily the interrogation window width. To correctly resolve the velocity field in regions of high gradients, interrogation windows should be small in relation to the width of the shear layer28 . The TU-BS data set has a good combination of small interrogation window width (6% of hb ) and vector resolution (35 vectors across bubble at hb ) and has likely captured much of the turbulence spectrum associated with transition. The IAR and AFRL measurements, on the other-hand, have larger interrogation windows (16% of hb ) which may not capture the complete spectrum of turbulence, particularly near and downstream of reattachment. However, the length scale of the transitional turbulent structures is expected to be large in relation to the shear layer thickness because, for this operating condition, transition is dominated by the Kelvin-Helmholtz instability mechanism which leads to the roll-up, pairing, and subsequent shedding of large-scale vortices23 , as opposed to turbulent spot-based transition in which bursting of small-scale turbulence occurs directly within the separated shear layer29 . Therefore the locations of transition onset listed in Table 2 are reliable measurements and are probably not affected by spatial resolution errors. The deficiency of reverse flow in the IAR measurements is likely a result of measurement error combined with the intermediate smoothing of the multi-grid evaluation approach which will generate a slight bias towards the higher positive velocities found in the outer shear layer. The close agreement of separation and reattachment locations between the AFRL data set and the XFOIL simulations at α = 4◦ presently lacks a good explanation. Agreement is still reasonable at α = 8◦ ; XFOIL simulations show that with increasing angle of attack, the LSB shortens and moves upstream, as is observed


Figure 10. XFOIL results, α = 4◦

in the AFRL data set. At α = 4◦ , the AFRL data place separation at x/c = 0.05 and reattachment at x/c = 0.16, and XFOIL gives x/c = 0.03 and 0.18, respectively. Additional measurements performed in the IAR facility at a lower Reynolds number (40,000), some of which are presented by McAuliffe & Yaras23 , show the same trend of declining LSB length and upstream progression with increasing angle of attack. Reasons for lack of discernable recirculation streamlines at α = 8◦ in the LSB of the AFRL data set are expected to be the same as for α = 4◦ in the IAR data set.

V.

Conclusions

Modern, yet off-the-shelf, 2D particle image velocimetry is capable of resolving averaged velocity fields in an airfoil laminar separation bubble at a Reynolds number of 60,000. Comparison of nominally identical experiments in three very different facilities - a water tow tank, a wind tunnel and a water tunnel - shows encouraging qualitative similarity in the bubble shape and velocity fields, as well as Reynolds stress distributions. However, discrepancies in the measured location and flow structure of the bubble remain. The former is perhaps due to minor variations in angle of attack or ambient turbulence intensity; the latter being a result of inadequate spatial (magnification too low) or temporal (insufficient number of PIV samples) resolution. Results from the present study form a promising database for validation of low Reynolds number airfoil numerical solutions.


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