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Biologically Inspired Wing Leading Edge for Enhanced Wind Turbine and Aircraft Performance

Taylor Swanson1

Arnold Engineering Development Center, Tullahoma TN 37388

and

K. M. Isaac2 Missouri University of Science & Technology, Rolla, MO 65409

Computational fluid dynamics simulations of tubercled leading edge wings are analyzed to determine the underlying mechanisms that may lead to potential performance improvements of wind turbines and aircraft. Reasons for performance improvements suggested in previous studies can probably be attributed to the formation of a complex vortex structure on the tubercled wings. A local trailing vortex cancelation mechanism is proposed to explain performance improvements of finite wings.

Nomenclature

- bump amplitude - angle of attack c - chord length Rec - Reynolds Number based on chord length SLE - Straight leading edge TLE - Tubercled leading edge

I. Introduction iklosovic et al [1,2] experimentally investigated whale flipper replicas in a wind tunnel at Rec = 5x105. The flipper replicas with tubercles were observed to experience a gentler stall than those without tubercles. They

found that the stall angle increased by 40%. A drag reduction was also noted. A theoretical aerodynamic model known as lifting line was applied to this problem by van Nierop et al.[3]. Two mechanisms were identified in their work. Sections of the wing behind a tubercle trough have a shorter distance and thus a higher adverse pressure gradient than sections behind a tubercle peak. Thus, trough sections separate and stall at angles of attack where peak sections remain unstalled. This reduces lift compared to an un-modified wing of the same chord, but flattens the lift curve which allows for a gentler stall and greater lift after stall. The second mechanism is downwash. The downwash behind a wing with tubercle modifications is non-uniform; it is greater at the bumps, further decreasing their effective angle of attack and delaying stall. Tubercle amplitude was determined to be important, as larger amplitude bumps flatten the lift curve more than smaller bumps, but altering the wavelength was not found to increase the stall angle of attack. See Fig. 1 for an image of tubercles [4]. Johari et al. [4] performed experiments on NACA 634-021 wings. They chose the NACA 634-021section because of its similarity to the cross section of humpback whale flippers. Two wavelengths, one quarter and one half chord, and three amplitudes, 0.025c, 0.05c, and 0.12c were investigated at Rec = 1.83x105. The model wings spanned the entire water tunnel width, thus eliminating tip effects and making it essentially a quasi two-dimensional (2D) study. Flow separation over the trough sections was confirmed with flow visualization using tufts. Tubercle amplitude had an effect, with larger amplitudes leading to higher lift after stall compared to conventional wings. However, post-stall drag is increased by tubercles. Wavelength was again found to have little effect. Miklosovic et

1 Aerospace Engineer 2 Professor, Mechanical & Aerospace Engineering Department, 194 Toomey Hall, Associate Fellow

M

6th AIAA Theoretical Fluid Mechanics Conference27 - 30 June 2011, Honolulu, Hawaii

AIAA 2011-3533

Copyright © 2011 by Kakkattukuzhy Mathai Isaac. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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al. [2] tested full-span and semi-span models of NACA 0020 cross section without and with tubercles at Reynolds numbers of 2.75x105 and 6.3x105. 2D effects were determined from the full-span model, showing lower lift and higher drag before stall, but higher lift and lower drag after stall compared to conventional wings. This pre-stall change was smaller for the three-dimensional (3D) wing. They explained the differences between the tubercled wings and the conventional wings as being caused by the scallops’ sweep angle creating a 3D flow. This in turn creates a vortex flow with decreased leading edge suction and lower pre-stall lift, but higher post-stall lift; however, this beneficial effect was confined to the 3D wings. Since the whale fins with tubercles allow a gentle stall and better post-stall behavior, the application of this idea in aerodynamics was investigated in this study. It is desired to determine tubercle amplitude and wavelength that maximize performance.

Figure 1. Whale with tubercled flippers [4].

II. Geometry and Mesh Airfoil coordinates for the base airfoils were modified in the nose region according to Eqs. 1 and 2, in which the

x coordinates near the nose, as specified by a fraction of the chord length, were stretched or contracted by a specified percentage. The y coordinates were unchanged.

1 for new old old tmx x A x x (1)

new oldy y (2)

Subscripts old and new refer to the original airfoil and the modified airfoil. Subscript tm refers to the location of maximum thickness. A is the amplitude of the bump expressed as a fraction of the original chord length. The airfoil is modified only from the location of maximum thickness to the nose as shown in Fig. 2. These points were read into NX5 [5] and curves constructed from them using the spline function. A peak curve was created at the z = 0 plane, and then a trough curve was created at half of a wavelength. The peak curve was then copied over to one wavelength. The resulting sections are shown in Fig. 2. Solid bodies were created from these curves using the freeform feature “surface through curves,” selecting the “normal to endpoints” option [6]. Figures 2 and 3 show the NACA 634-021 [7] and NACA 0020 in their original and modified forms. Figure 4 shows the body created from those curves. Note that one period was created, as periodic boundary conditions were employed in the simulations.

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Figure 2. Airfoil sections. Original, peak, and trough sections are shown.

Figure 3. Airfoil section curves: NACA 634-021 (left) and NACA 0020 (right.)

Figure 4. One period of a modified wing created from airfoil section curves: NACA 634-021 (left) and NACA 0020

(right.) The mesh was generated in two regions, the near wing region with higher density and an outer region with lower density. Fifty spanwise intervals were chosen across the domain and 200 intervals along the upper and lower edges of the wing. The domain was bordered on the left and right sides with periodic boundary conditions. Figure 5 shows the mesh.

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

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Figure 5. Two views for the mesh generated in Gambit, Fluent preprocessor for mesh generation. Fluent version 12 was the flow solver.

The parameter space for the subscale wing is given in Table 1. It spans a reasonable range of tubercle amplitude and frequency, and at transitioning and turbulent Reynolds numbers.

Table 1. Johari Wings [4]

Amplitude Wavelength Reynolds number, Rec 0, 2.5, 5, 10% 0, 4, and 8 tubercles per

1c wing span 1.8 x105 - 6.3x105

(a) (b) (c) (d) Figure 6. Geometries of the four Johari wings [4]. The wings are named the same way as in the experiments of Johari et al.[4]. Dimensions are in cm.

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III. Simulation Details

This investigation of leading edge tubercles is being conducted using a parallel processing version of Fluent 12 using six of the eight processors on a parallel processing machine. The airfoil mesh is generated in the standard C-mesh used for airfoil analysis. The mesh is then imported into Fluent and the velocity components are input for the various angles of attack. Initially, a few runs were made to validate the procedures. Four geometries shown in Fig. 6 were considered in this study. They are designated as (a) straight leading edge, (b) 4S, (c) 4M, and (d) 8S. The chord length and span for each wing is given in Fig. 6. The subscale cases at lower Reynolds numbers used the blade/wing dimensions shown in Fig. 6. For the full scale cases, the geometries in Fig. 6 were scaled up so that the Reynolds numbers were much higher and in the fully turbulent regime.

IV. Results

1. Subscale blade/wing. Rec = 183,000

Figure 7 shows initial validation results from the simulations. Pressure contours (Fig. 7a) and velocity contours (Fig. 7b) demonstrate that the grid generation for the tubercled wing has been successful as these contours have fine resolution and nearly follow those of the original NACA airfoil from which the new wing section was created.

Figure 8 is a sketch of the downstream vortex structure of a tubercled leading edge wing constructed from the

wake vorticiy pattern in Figs. 9-12. Note that the visible number of the vortex pairs in Figs. 9-12 differ from the 3 shown in Fig. 8. Their strength, size, and visibility vary depending on the geometric parameters and the angle of attack. The downstream vortices of the Tubercled leading edge (TLE) wings rotate clockwise and counterclockwise, alternatively, as shown in Fig. 8. Figures 9-12 show streamlines and x-vorticity contours for the four wings at = 0o, 4o, 8o, and 12.o The nature of the downstream vortices change significantly with change in the tubercle geometry and the angle of attack. At = 0,o all the three tubercled wings have four vortices. The pairings of the vortices resulting from the tubercles (an example of which is illustrated in Fig. 8) would result in a weaker vortex when they merge.

The surface streamlines in Figs. 13-15 are further indication of the complex flow resulting from the presence of the leading edge tubercles. An important aspect that is not fully established in the present study is the stall performance. Stall angle as well as stall

(a) (b)

Figure 7. Static pressure contours (a) and velocity contours (b) from simulations.

Figure 8. Clockwise and counterclockwise rotation of the downstream vortex pairs.

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characteristics need to be thoroughly studied to optimize tubercle geometry. The present results do show that stall is less abrupt for tubercled wings, which is obviously a desirable feature.

Figure 10. Streamlines for Case 1. Rec = 183,000, = 4o.

Figure 9. Streamlines for Case 1. Rec = 183,000, = 0o.

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Figure 12. Streamlines for Case 1. Rec = 183,000, = 12o.

Figure 11. Streamlines for Case 1. Rec = 183,000, = 8o.

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Figure 14. Surface Streamlines for the four geometries in Fig. 9. Rec = 183,000, = 4o.

Figure 13. Surface Streamlines for the four geometries in Fig. 8. Rec = 183,000, = 0o.

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Comparing the present results to the trailing edge vortex system of a straight leading edge (SLE) wing can shed

light on how the performance of a finite TLE wing might be better. The trailing vortices on an SLE wing rotate in the same direction. They merge downstream of the trailing edge to form the stronger wing tip vortex leading to induced drag. It can be reasoned that the local cancelation of the trailing vortices of the TLE wing might result in a weaker tip vortex.

The surface streamline pattern does not follow the trends discussed by Johari et al [4], whose experiments

showed a wide variety of vorticity and erratic flow patterns on the top surface. An explanation of this discrepancy could be that the flow patterns of Johari et al [4] were visualized by tufts attached to the surface. Visualization using tufts gives useful qualitative information; however, it is not a recommended technique for extracting detailed flow features. The tufts could possibly be outside the boundary layer and be subject to more diverse flow interactions different from those on the surface, as opposed to the present computational surface streamlines which are post-processed from data very close to the surface. 2. Higher Reynolds Number Results

This is a scaled Johari 4S geometry (Fig. 6) having a chord length c = 10 m and a planform area of 50 m.2 As in

the previous subscale simulations, this TLE wing covers only one period of the tubercles, i.e., one bump and one trough in the spanwise direction, which reduces computation time compared to a complete 3D geometry. A periodic boundary condition is imposed for the two ends of the wing. Because of using the periodic boundary condition, the results are for infinite span. End effects are thus excluded from the present simulations.

A comparison of the lift to drag ratios for three values of shown in Table 2 demonstrates that the SLE and the TLE wings show similar trends. One can notice that the TLE wing tends to have a lower lift coefficient, compared to the SLE wing, correlating with the conclusions drawn by Miklosovic and Murray[1]. Their study also indicated that the lift and drag coefficients tend to be fairly insensitive to higher Reynolds numbers. It should be noted that in this case, both the SLE and TLE wings were at Rec = 24,400,000, as opposed to the tests conducted by Miklosovic and Murray [2] in which the maximum Reynolds Number Rec was 631,000, and more generally around 277,000. This could lead to some discrepancies since the simulations were for fully turbulent flow at much higher Reynolds numbers as opposed to the comparison tests which were mostly in the laminar or transitional flow regimes. We have used the higher Reynolds numbers to simulate aircraft cruise conditions, and to stay away from the transition regime

Figure 15. Surface Streamlines for the four geometries in Fig. 10. Rec = 183,000, = 4o.

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for which reliable turbulence models are not available. Despite these differences, the lift and drag characteristics from the simulations tend to follow the data of Miklosovic and Murray for the lower Reynolds numbers.

Table 2. Summary Results from Straight and Tubercled Wing Leading Edges. Rec = 24,400,000

Straight Leading Edge (SLE) Tubercled Leading Edge (TLE) (deg) CL CD CL/CD CL CD CL/CD

0 0 0.0157 0 0 0.0164 0

4 0.455 0.018 25.46 0.411 0.0221 18.61

8 0.868 0.028 30.71 0.718 0.0450 15.96

V. Conclusions and Future Work The present study generally confirms the conclusions of previous work and sheds light on the underlying reasons

for the enhanced performance of tubercled leading edges. Tubercles modify flow features beneficially in terms of aerodynamic performance. Tubercle geometry should be carefully optimized for best performance. The vortex pattern seen in the present results have not been reported in previous studies of tubercled wings. This may be due to the very low resolution of the tuft-based flow visualization used in the previous work. The vortex pattern in the present results help identify the mechanisms that lead to the unique performance characteristics of the tubercled blades/wings. The clockwise and counter clockwise vortices formed at each tubercle tend to cancel each other. The trailing vortices on a conventional blade/wing with straight leading edge rotate in the same direction and they grow stronger when they merge to form the tip vortex. This is only a plausible explanation at this stage as the flow simulations are for a quasi 2D geometry. Full 3D simulations of the tubercled finite-span blade/wing would help confirm the above effect.

It would also be useful to confirm the presence of the computationally observed vortex structure by doing additional experiments using techniques having much better resolution than those of previous studies. Dye flow visualization in water and particle image velocimetry measurements would be suitable for future experimental studies.

Acknowledgments We acknowledge industry support, as well as graduate student support from NASA Space Grant and

Missouri S&T.

References 1. Miklosovic, D. S., Murray, M. M., Howle, L. E., and Fish, F. E., “Leading-edge Tubercles Delay Stall on Humpback Whale

(Megaptera novaeangliae) Flippers,” Phys. Fluids, v. 16, n. 5, May 2004, pp. 39-42. 2. Miklosovic, D. S., Murray, M. M., and Howle, L. E., “Experimental Evaluation of Sinusoidal Leading Edges,” J. Aircraft, v.

44, n. 4, 2006, pp. 1404-1408. 3. van Nierop, E. A., Alben, S., and Brenner, M. P., “How Bumps on Whale Flippers Delay Stall: An Aerodynamic Model,”

Phys. Rev. Letters, v. 100, Feb. 2008, pp. 054502-1-054502-4 4. Johari, H., Henoch, C., Custodio, D., and Levshin, A., "Effects of Leading-Edge Protuberances on Airfoil Performance,”

AIAA Journal, v. 45, n. 11, Nov. 2007, pp. 2634-2642. 5. NX5, v. 5.0.2, Siemens PLM Software, Plano, TX, 2007. 6. Leu, M. C., and Joshi, A., “NX5 for Engineering Design,” http://web.mst.edu/~mleu/UG-NX5_tutorial_1_Leu__1.pdf. 7. Abbott, I. H., and von Doenhoff, A. E., “Theory of Wing Sections,” Dover, 1959. 8. FLUENT Computational Fluid Dynamics Software Package, v. 12, FLUENT Inc., Lebanon, NH, 2009.