Volumetric Three-Component Velocimetry and PIV Measurements of Laminar...

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 09-12 July, 2012

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Volumetric Three-Component Velocimetry and PIV Measurements of Laminar

Separation Bubbles on a NACA4412 Airfoil

Redha Wahidi1,*, Wing Lai2, James P. Hubner1 and Amy Lang1

1: Department of Aerospace Engineering and Mechanics, The University of Alabama, Tuscaloosa, AL, USA

2: TSI Incorporated, Fluid Mechanics Division, Shoreview, MN, USA * correspondent author: [email protected]

Abstract Measurements of laminar separation bubbles on a NACA4412 airfoil were performed using volumetric three-component velocimetry (V3V) and particle image velocimetry (PIV) at a Reynolds number of 50,000 and different angles of attack. The time-averaged V3V results are analyzed to estimate the locations of separation, onset of transition and reattachment by interpreting the relationships of the different Reynolds normal and shear stresses to these locations. The vortex cores and spanwise vorticity are discussed as well. Additionally, the reattachment region is investigated using time-resolved PIV results to validate some V3V results and uncover details of the instantaneous reattachment. The results show that the vortices resulting from the roll-up of the spanwise vorticity induce pairs of positive and negative wall-normal velocity. These pairs play a role in the unsteadiness of the reattachment of the separated shear layer. 1. Introduction

Laminar separation bubbles (LSB) occur on airfoils operating at low Reynolds numbers (50,000-1,000,000) (Carmichael 1981). The existence of a laminar separation bubble increases the pressure drag and, in some cases, depending on the Reynolds number, angle of attack and airfoil geometry, decreases the lift. The increase in drag and decrease in lift adversely affect the performance of airfoils operating in the low Reynolds number regime such as wings of sail planes, unmanned air vehicles (UAVs) and micro air vehicles (MAVs), wind turbine blades, and low pressure turbine blades. Moreover, the unsteady nature of the laminar separation bubble in general and its reattachment in particular creates an additional challenge to the design of UAVs and MAVs.

Low-Reynolds-number laminar flow over an airfoil can separate when it encounters the adverse pressure gradient. The laminar separated shear layer then transitions due to the growing disturbances initiated in the freestream. If the Reynolds number is high enough, or if the angle of attack is low enough, the separated shear layer reattaches to the surface of the airfoil as a turbulent boundary layer downstream of a reversed-flow vortex. The region enclosed between the locations of separation and reattachment is referred to as the laminar separation bubble.

Several investigations (Watmuff 1999, Alam and Sandham 2000; Lang et at. 2004; Marxen et al. 2004; Hain et al. 2009) have examined the details of the transition process on the separated shear layer of the laminar separation bubble. These investigations indicated that the Tollmien–Schlichting (TS) waves in the attached boundary layer increase in magnitude and the inviscid Kelvin-Helmholtz (KH) instabilities amplify in the separated shear layer resulting in the development of three-dimensional vortices and transition to turbulence. Burgmann et al. (2008) mentioned that the separated shear layer of the long bubble is governed by KH instabilities due to the stronger velocity gradient normal to the airfoil surface. These KH instabilities cause a quasi-periodic roll up of the shear layer and the formation of a large vortex in the reattachment region which separates from the recirculation region and travels downstream.


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Therefore, it is necessary to perform three-dimensional flow measurements to better understand the structure of the laminar separation bubble and the region of reattachment. Due to the recent advancement in flow measurement techniques such as stereoscopic PIV and volumetric three-component velocimetry (V3V), researchers are revisiting this flow phenomenon in an effort to uncover more details about separation-induced transition and the subsequent reattachment. The scanning PIV measurements of Burgmann et al. (2006), Burgmann et al. (2008) and Burgmann and Schröder (2008) delivered insight of the vortical structure in the reattachment region of a laminar separation bubble and showed three-dimensional vortical structure in the reattachment region of a “long” bubble; nevertheless, only more recently instantaneous three-dimensional three-component measurement technique became available. Measurements of laminar separation bubbles were carried out (Wolf et al. (2011), Wahidi et al. (2011)); however, details of the Reynolds normal and shear stresses, reversed-flow region and vorticity and vortical structures were not presented in details.

The purpose of this investigation is to measure the laminar separation bubble on an airfoil at Reynolds number of 50,000 using volumetric three-component velocimetry (V3V) which allows for instantaneous measurements of the three components of the velocity vectors in a three-dimensional volume. In addition to the V3V measurements, the reattachment region is investigated using time-resolved particle image velocimetry (TR-PIV) measurements at a Reynolds number of 75,600. The results from the TR-PIV measurements are used to validate the presence of certain flow features observed in the V3V results, and to investigate the instantaneous reattachment utilizing the higher spatial resolution of the PIV measurements.

2. Experimental Facility and Procedure

The experiments were carried out in a custom-built Eidetics 1520-EXT water tunnel facility at The University of Alabama. The length, width and height of the test section of the tunnel are 2.743 m (108 in), 0.381 m (15 in) and 0.762 m (30 in), respectively. The tunnel is capable of delivering freestream velocities of 0.5 m/s (1.64 ft/s) with a manufacturer-reported turbulence level of 0.4% at a freestream velocity of 0.051 m/s (2 in/s).

A two dimensional NACA4412 airfoil model was made of clear plexiglass and has a chord of 0.3048 m (12 in) and a span of 0.610 m (24 in). The model is vertically placed in the water tunnel by connecting it to amounting bracket at the top and a bushing at the bottom. This mounting system ensures that the airfoil is held securely in the water tunnel and allows the angle of attack to be changed. To minimize the effects of the tunnel walls, the airfoil’s chord line is positioned at the midpoint of the test section width. The airfoil extends 0.102 m (4 in) above the water free surface. However, due to the bushing connected to the bottom end of the airfoil, a gap of 0.0254 m (1 in) exists between the spanwise end of the airfoil and the bottom wall of the water tunnel.

The flow was measured using volumetric three-component Velocimetry (V3V) and time-resolved particle image Velocimetry (TR-PIV). For the V3V measurements, the flow is seeded with 50 µm polymer particles and the volume of interest is illuminated with a 425 mJ/pulse, dual-cavity Nd:YAG lasers. The volumetric 3-component velocimetry (V3V) camera has three apertures, where each aperture contains a 4 million pixel CCD sensor. The three CCD sensors are arranged in a triangular pattern which allows the search and identification of the location of the seed particles in the 3-D volume, using the triplet search algorithm. Similar to image capture in PIV, two laser straddled captures with the camera probe is taken synchronized with two laser pulses as one realization. Insight V3V 3GTM software then scans each image for particles which are identified and matched among the other two apertures according to a calibration map to determine the three-dimensional particle locations at the two time instances. The particles are tracked in 3-D space using a relaxation method and interpolated onto a regular grid to yield instantaneous volumes of approximate size 140 mm by 140 mm by 100 mm in the streamwise, spanwise and wall-normal


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directions, respectively. Five-hundred statistically-independent instantaneous velocity volumes were captured at 7.25 Hz.

The second system used for the flowfield measurement was a time-resolved digital particle image velocimetry (TR-DPIV). The system consists of a pulsed solid-state laser, a high speed digital camera, image acquisition software, and Insight 3GTM PIV processing software. For the PIV measurements, the flow is seeded with silver-coated hollow glass spheres with an average diameter of 14 µm, manufactured by Potters Industries, Inc. The laser used is a Quantronix Falcon 30 series Nd:YLF system. This laser generates a beam with a wavelength of 532 nm and a maximum power output of 20 watts. The camera used to record the raw PIV images is a Basler A504k 8-bit high-speed digital camera with a Nikon AF Micro Nikkor 105mm lens. This camera is capable of acquiring images with a resolution of 1280x1024 pixels at a frame rate of up to 500 frames per second. The measurement window is 70 mm and 500 realizations were captured at 500 Hz in this experiment. The images were processed using an image deformation scheme with the starting and final spot dimensions of 128 and 8 pixels, respectively.

The streamwise, spanwise and wall-normal coordinates used in this investigation are X, Y and Z, respectively. The corresponding velocity components are U, V and W for the streamwise, spanwise and wall-normal directions, respectively.

3. Results

A short laminar separation bubble appears as a perturbation to the surface pressure distribution (Cp) in the form of a constant pressure region (Carmichael 1981) (Fig. 1). The beginning of this pressure plateau indicates the location of separation (S) and its downstream end signifies the location of the onset of transition (T). The location of the time-averaged reattachment normally corresponds to the location where the slopes of the viscous (actual) and inviscid (or fully turbulent) Cp curves match (see Carmichael 1981; O’Meara and Mueller 1987; Liebeck 1992; Kim et al. 2009; Wahidi & Bridges 2012). Surface pressure data obtained from XFLR5 software, which is the free version of the XFOIL, was used to estimate the locations of separation (S), onset of transition (T) and time-averaged reattachment (R). In addition to locating the onset of transition at the end of the pressure plateau, the location of transition can be directly obtained from the XFLR5 software which utilizes the eN transition prediction method.

Figure 1 shows the Cp on a NACA4412 airfoil at a Reynolds number (Rec) of 50,000 at an angle of attack (α) of 4 degrees along with the inviscid Cp. The estimated locations of separation and reattachment are included in addition to the predicted locations of onset of transition. These estimated locations of separation, onset of transition and time-averaged reattachment will be included in the figures here as reference values. However, discussions will be provided on the differences between the estimated locations and the ones suggested by the experimental results of this study. 3.1. Time-averaged V3V results

Figure 2 shows iso-surfaces defined where U/U∞ < 0. The time-averaged reversed flow starts at

the same streamwise location as the predicted separation location. The reversed flow moves faster in the rear portion of the bubble reaching velocities slightly less than 14% of the freestream velocity. The recirculation region extends well downstream of the predicted location of reattachment. Additionally, scattered regions of recirculating flow extend to a location slightly upstream of the trailing edge of the airfoil. The existence of these scattered regions of reversed flow could be attributed to unsteadiness of the reattachment region as the results of Alam and Sandham (2000) showed that regions of backflow exist intermittently downstream of the mean reattachment location. A more appraised reason for the extension of the backflow region downstream of the


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predicted time-averaged reattachment location is that the LSB at Rec = 50,000 on the NACA4412 airfoil is of the “long” type with a reattachment location farther downstream.

The streamwise Reynolds normal stresses ( ∞Uu 2' ) on slices in the spanwise direction (X-Z plane) are shown in Fig. 3. In general, the locations of onset of transition (T) and reattachment (R) are not well defined by the streamwise Reynolds stress. Larger values of ( ∞Uu 2' ) are observed between the predicted locations of separation (S) and onset of transition (T). These values decrease near the location of the predicted onset of transition and then continue to increase at some distance downstream of (T). The larger values of ( ∞Uu 2' ) take place in the region of the separated shear layer. The peak in the streamwise Reynolds stress widens in the region of reattachment.

Figure 4 shows the spanwise Reynolds normal stresses ( ∞Uv 2' ) on a spanwise slice (X-Z plane) at Y/C = 0. The normalized Reynolds stresses increase to values greater than 0.075 near the predicted location of onset of transition (T). These stresses considerably magnify in the turbulent region downstream of the predicted location of reattachment (R). A threshold of 0.075 showed similar results for the cases at Rec = 50,000 at angles of attack of 4 and 6 degrees. The spanwise Reynolds normal stresses ( ∞Uv 2' ) are shown in Fig. 5 on iso-surfaces defined where U/U∞ = 0.5. The gradual increase in the Reynolds normal stresses is clearly present in the region of the bubble and downstream of reattachment with a 35% increase at the location of predicted reattachment (R) for the cases at α= 4 and 6 degrees. The Reynolds normal stresses spanwise variation in the turbulent region downstream of (R). However, slightly downstream of (R), the non-uniform behavior becomes more organized with a periodic behavior in the spanwise direction. This periodic behavior could be related to the rise of three-dimensional disturbances in the reattachment region.

The wall-normal Reynolds stress ( ∞Uw 2' ) slightly increases between (T) and (R) and shows a more significant increase at and downstream of (R) (see Fig. 6). Burgmann et al. (2008) noticed the same high values of Reynolds normal stress and explained that they are generated by the vortices in the reattachment region. The results of the spanwise and wall-normal Reynolds stresses show that these quantities can be used to estimate the location of reattachment, whereas the location of onset of transition is better estimated by the spanwise Reynolds stress. The growth and periodic behavior of the spanwise Reynolds stresses in the reattachment region and the growth of the wall-normal Reynolds stresses strongly suggest the evolution of three-dimensional disturbances manifesting themselves in three-dimensional vortices.

3.2 Time-resolved V3V results

The vortices are identified based on the λ2 criteria (Jeong and Hussain 1995). The vortex shedding from the separated shear layer is illustrated in Fig. 7 where values of λ2 are shown on slices in the spanwise direction (X-Z plane) at different instants of time. The distance between the vortices on this spanwise location is determined by locating the centers of the negative λ2 regions. The distance between the cores of λ2 ranges from 0.062C to 0.082C and is on average 0.075C (22.8 mm) with the most common distance between the vortices being 0.07C. Further investigation of the cores of λ2 shows that some of the vortices move slightly in the spanwise direction which makes them disappear from the plane at Y/C = 0. This is a possible reason for the discrepancies found in the distances between the vortices.

Figure 8 show the instantaneous wall-normal velocity (W/U∞) presented on the same slices as in Fig. 7. Additionally, lines of λ2 of greyscale are presented in the figures to demonstrate the relationship between the wall-normal velocity and the vortices. The pairs of positive and negative wall-normal velocities indicate a swirling motion about the Y-axis (spanwise direction) where the


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vortices induce this behavior of the wall-normal velocity. The relationship between the swirling motion and the wall-normal velocity is seen where the centers of the vortex cores are present between the positive and negative wall-normal velocities. The positive and negative pairs indicate the clockwise rotation of the vortex where W/U∞ > 0 is upstream of the vortex and W/U∞ < 0 is downstream. It is also observed that the negative values W/U∞ extend farther from the separated shear layer and the surface of the airfoil demonstrating that the fluid is moving towards the surface of the airfoil. The PIV results (discussed later) show that the vortex-induced wall-normal velocity in addition to these negative values of W/U∞ are related to the entrainment of fluid into the bubble which is necessary for the reattachment of the separated shear layer.

Contours of the spanwise vorticity ( ∞UCyω ) and lines of λ2 are shown in Fig. 9 on a spanwise slice. The regions colored in red represent strong vorticity which agree with the locations of negative λ2 representing a vortex core. In this case, the separated shear layer with concentrated vorticity rolls-up to form a spanwise vortex. The periodic nature of the spanwise vorticity and the presence of spanwise vortices suggest the existence of Kelvin-Helmholtz instabilities in the separated shear layer. This spanwise vorticity and vortices persist up to the trailing edge.

3.3 Time-resolved PIV results

The PIV measurements were acquired at a Reynolds number of 75,600 at α = 4 and 6 degrees to validate some flow features observed in the V3V results and view these features with the better spatial resolution of the PIV measurements. Figure 10 shows the streamwise velocity (U/U∞), wall-normal velocity (W/U∞) and spanwise vorticity (

∞UCzω ) at two different instants of time for the case at α = 4 degrees. The reversed-flow region is well resolved by the PIV measurements. The unsteady reattachment location is obvious in the figures as it changes at the two instants of time. The time-averaged reattachment location (R) was predicted at X/C = 0.68 from the Cp results generated by XFLR5; however, scattered regions of backflow exist all the way to X/C = 0.82. These results agree with the V3V results where scattered regions backflow appear downstream of (R). Although it was expected that the reattachment location fluctuates at the same frequency of the vortex shedding, no organized behavior of this unsteady reattachment was recognized due to the appearance of scattered regions of reversed flow along the chord of the airfoil. Nonetheless, the instantaneous reattachment location is affected by the roll up of the spanwise vorticity. The vortex cores are not calculated from the PIV data but the swirling motion of the fluid is observed and then related to the reattachment behavior. The first observation that indicates the presence of a vortex is based on the velocity vector field where the vectors show a swirling motion. Also, regions of rotating velocity vectors and pairs of positive and negative wall-normal velocities are considered regions of swirling motion. In addition to the velocity vectors and wall-normal velocity conditions, a region of swirling motion must have a large spanwise vorticity. Figure 10e indicates that the spanwise vorticity appears on the separated shear layer. This vorticity has a slight wavy behavior which then becomes stronger and interacts with the surface of the airfoil. This behavior indicates that the spanwise vorticity rolls up to create a vortex as was observed in the V3V data. Figure 10 shows that the location of the vorticity roll up is bounded by a pair of positive and negative wall-normal velocity which is induced by a vortex. Comparing the results of the streamwise and wall-normal velocities clearly demonstrates that the strong negative wall-normal velocity causes reattachment of the separated shear layer. The distance between regions of consecutive strong positive or negative wall-normal velocity is on average 0.07C. The same distance was found between the vortex cores calculated from the V3V results.

Figure 11 is similar to Fig. 10 but shows the results farther downstream. The relationship between the vorticity roll-up and pairs of positive and negative wall-normal velocity is clear in Fig. 11. Moreover, these wall-normal velocity pairs correspond to regions of high and low streamwise


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velocity. This observation suggests that the roll-up of vorticity induces strong fluctuations in the streamwise velocity in the reattachment region all the way to the trailing edge. These results explain the presence of regions of low streamwise velocity in regions where vortex cores exist as was shown in the V3V data in this study and by Burgmann et al. (2008) and Wolf et al. (2011). These footprints of the vortices exist closer to the surface of the airfoil than the vortices themselves. The figure also presents that the regions of large positive and negative wall-normal velocity exist farther from the surface of the airfoil with dissipating magnitude with time. Moreover, the relationship between the pairs of positive and negative wall-normal velocity with the spanwise vorticity is clearer in this region (closer to the trailing edge). The spanwise vorticity in this region is farther away from the wall with larger diameter. This observation confirms the V3V results where large vortical structures are found far from the wall and at locations where the local streamwise velocity reaches up to 1.3U∞. The same behavior is seen in the PIV results as illustrated by Figs. 11d and 11f.

Conclusion

Volumetric three-component measurements were carried out on a NACA4412 airfoil at low Reynolds number. The spanwise normal Reynolds stress predicts the location of onset of transition with good agreement with the predicted location based on the eN method. The spanwise and wall-normal Reynolds stresses suggest the reattachment location. The spanwise normal Reynolds stress indicates that three-dimensional disturbances exist in the reattachment region as illustrated by periodic appearance of positive and negative pairs. In addition to the V3V measurements, PIV measurements were carried out in the reattachment region. The PIV results are in general agreement with the V3V results. The V3V and PIV results clearly demonstrate that the vortices induce pairs of positive and negative wall-normal velocity. These pairs play a role in the fluctuations of the streamwise velocity in the reattachment region. Acknowledgement This material is based upon work supported by the National Science Foundation under Grant No. 0958668. The support of The University of Alabama is also acknowledged through the Research Stimulation Post-Doctoral Fellow Program.

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of a transitional separation bubble on a SD7003 airfoil. Exp Fluids 44:609-622.

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Meeting, Orlando, FL, January 5-8. AIAA Paper 2009-1472.

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Figure 1. Cp Curves for NACA4412 Airfoil at α = 4 degrees

Figure 2. Iso-surfaces defined where U/U∞ < 0 and flooded with U/U∞ - Rec = 50,000 at α = 4 degrees

Figure 3 Spanwise slices (X-Z plane) flooded with streamwise Reynolds normal stresses ( ∞Uu 2' ) - Rec =

50,000 at α = 4 degrees.


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Figure 4. Spanwise slices (X-Z plane) flooded with streamwise Reynolds normal stresses ( ∞Uv 2' ) - Rec =

50,000 at α = 4 degrees

Fig. 5. Iso-surfaces of U/U∞ = 0.5 flooded with ( ∞Uv 2' ) - Rec = 50,000 at α = 6 degrees.

Figure 6. Spanwise slices (X-Z plane) flooded with ∞Uw 2' - Rec = 50,000 at α = 6 degrees.


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Figure 7. Spanwise slices flooded with λ2 and vector field colored by U/U∞ - Rec = 50,000 at α = 4 degrees.(a) at t0, (b) t0+Δt.

Figure 8. Spanwise slices (X-Z plane) flooded with the wall-normal velocity (W/U∞) and lines colored by

λ2- Rec = 50,000 at α = 4 degrees .(a) at t0, (b) t0+7Δt.

Figure 9. Spanwise slices (X-Z plane) flooded with the spanwise vorticity ( ∞UCyω ) and lines colored by

λ2 - Rec = 50,000 at α = 4 degrees .(a) at t0, (b) t0+Δt, (c) t0+2Δt, (d) t0+3Δt

(a) (b)

(a) (b)

(a) (b)

(c) (d)


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Figure 10. Contours of (a) streamwise velocity (U/U∞) at t0, (b) U/U∞ at t0+0.04 sec, (c) wall-normal

velocity (W/U∞) at t0, (d) W/U∞ at t0+0.04 sec, (e) spanwise vorticity ∞UCyω at t0, (f) ∞UCyω at

t0+0.04 sec, - Rec = 75,600 at α = 4 degrees.

(a) (b)

(c) (d)

(e) (f)


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Figure 11. Contours of (a) streamwise velocity (U/U∞) at t0, (b) U/U∞ at t0+0.04 sec, (c) wall-normal

velocity (W/U∞) at t0, (d) W/U∞ at t0+0.04 sec, (e) spanwise vorticity ∞UCyω at t0, (f) ∞UCyω at

t0+0.04 sec, - Rec = 75,600 at α = 4 degrees.

(a) (b)

(c) (d)

(e) (f)

Volumetric Three-Component Velocimetry and PIV Measurements of Laminar...

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