Vertical Axis Wind Turbine Computational Fluid Dynamics Analysis

     This post is be about the validation and verification of the computational fluid dynamics analysis of a three blade vertical axis wind turbine. The turbine had a diameter of 2 m with each blade being 1 m tall. The blades had an NACA-0018 airfoil cross section.

     The computational fluid dynamics analysis employed the κ-ε turbulence model with damping functions as the turbulence model, SIMPLE-R as the numerical algorithm. The spatial discretization schemes for the convective fluxes and diffusive terms used are the second order upwind and central approximations, respectively. An implicit first-order Euler scheme is employed to approximate the time derivatives.

     The Cartesian computational mesh with immersed boundary method had a total of 769,357 cells. Among those 769,357 cells, 166,188 cells were around the turbine blades. Mesh controls were employed to refine the mesh near the turbine blades. A time step of 3e^-3 was employed. The computational domain inlet was 1.5 D away from the turbine and the outlet was 3D away. The computational domain walls on the sides were 1D x 1.5D, where D represents the turbine diameter. The mesh and the computational domain are shown in Fig. 1. The vertical teal arrow represents the force of gravity, the curved teal arrow represents the direction of turbine rotation. The dark blue arrow represents the direction of free stream velocity.

Fig. 1, Mesh and computational domain.

     The simulations ran at a tip-speed ratio of 1.87 at a wind speed of 4.03 m.s^-1. The velocity distribution around the turbine after 4 revolutions is shown in Fig. 2. Validation of the numerical analysis was carried out using [1]. The results of power produced by the turbine were with in 4% of the experimental results [1]. An animation of the numerical analysis is also shown.

Fig. 1, Flow field around the turbine.

     Thank you for reading. If you would like to contribute to the research, both financially and scientifically, please feel free to reach out.





[1] Yi-Xin Peng, You-Lin Xu, Sheng Zhan and Kei-Man Shum, High-solidity straight-bladed vertical axis wind turbine: Aerodynamic force measurements, Journal of Wind Engineering and Industrial Aerodynamics, January 2019.

Wing with Leading Edge Tubercles: Update 01

Tubercles (bumps) added to the leading edge of the aeronautic wings are a class of vortex generators. As shown in the Figure 1.

Figure 1, Modified wing geometry

Figure 2, Baseline wing geometry

The wing's cross section is NACA 0012. The dimensions used for this analysis were as used by [Chen, J. H., S. S. Li, and V. T. Nguyen. "The effect of leading edge protuberances on the performance of small aspect ratio foils." 15th International Symposium on Flow Visualization. 2012]. The flow conditions were reproduced from the research paper mentioned. In the wing with the leading edge tubercles, the tubercle wavelength was kept at two-thirds of the wing span. The tubercle amplitude was kept at half of the wing chord.

Computational fluid dynamics analysis was conducted to analyze the effect of the leading edge tubercles on wing performance. For validation of the numerical methodology, the lift and drag produced by the wing was compared to the experiments conducted for the mentioned research paper at 25 degree angle of attack. The forces calculated using computational fluid dynamics were within 7.3 % and 1.4 % of the experimental values, respectively.

The addition of tubercles at the leading edge of a wing creates a non-uniform pressure distribution on the wing’s surface, as shown in Figure 3. This non uniform pressure distribution and the changed wing geometry is responsible for the creation of a counter rotating chord-wise vortex pair behind each tubercle trough, as shown in Figure 4. To read more about non uniform pressure distribution, refer to Non Uniform Pressure Distribution.

Figure 3, Non-uniform pressure distribution. L-R; Modified Wing, Baseline Wing

Figure 4, Counter-rotating chord-wise vortex formation. L-R; modified wing, baseline wing. Notice the absence of vortex structures, represented by circles in the modified wing, in the baseline wing.

These vortices re-energize the boundary layer between them by carrying high momentum flow close to the wing surface, as shown by the dynamic pressure distribution in Figure 5, which leads to a delay in stall for the wing with leading edge tubercles, as shown in Figure 6. It can be seen clearly from both Figure 5-6 that the flow is attached behind the tubercle crest in the wing with leading edge tubercles while the baseline wing had stalled completely. To read more, refer to Counter Rotating Chord-wise Vortex Formation and Reduction in the Blade Tip Vortices, Delayed Stall and Reduction in the Span-wise Flow.

Figure 5, Dynamic pressure distribution around the wings. Top; modified wing. L-R; tubercle crest, tubercle trough. Bottom; baseline wing, same span-wise locations where the tubercle crest and trough is for the modified wing.

Figure 6, Streamlines around the wings. L-R baseline wing, modified wing.

Another effect of adding the leading edge tubercles to the wing is reduced span-wise flow and wing-tip vortices. The reason for this is that the counter rotating chord-wise vortices generated as a result of adding tubercles to the wing geometry act as a barrier to any span-wise flow, as shown in Figure 7-8.

Figure 7, Velocity flow trajectories. L-R modified wing, baseline wing. Notice the reduced size and strength of the tip vortex for the modified wing in comparison with the baseline wing.

Figure 8, Streamlines on the surface of the wings. L-R; modified wing, baseline wing. Reduced span-wise flow, (T-B of the screen), is clearly visible in the modified wing.

Thank you for reading. I hope this post added to your knowledge about tubercles. Next up will be the results of the counter-rotating configuration for the NREL Phase VI wind turbine. For verification and validation of the said wind turbine numerical simulations, refer to Verification and Validation.

Some of the reviewed literature:

[1] Watts, P., and Fish, F. E., “The Influence of Passive, Leading Edge Tubercles on Wing Performance,” Proceedings of the Unmanned Untethered Submersible Technology (UUST01), 2001.

[2] Fernandes, Irelyn, Yogesh Sapkota, Tania Mammen, Atif Rasheed, Calvin Rebello, and Young H. Kim, "Theoretical and Experimental Investigation of Leading Edge Tubercles on the Wing Performance," Proceedings of the Aviation Technology, Integration, and Operations Conference, Los Angeles, CA, 2013.
doi.org/10.2514/6.2013-4300
[3] Frank E. Fish, Paul W. Weber, Mark M. Murray, Laurens E. Howle, “The Tubercles on Humpback Whales' Flippers: Application of Bio-Inspired Technology,” Integrative and Comparative Biology, Vol. 51, No. 1, 2011, pp. 203–213.
doi.org/10.1093/icb/icr016
[4] Pedro, H. T. C., and Kobayashi, M. H., “Numerical Study of Stall Delay on Humpback Whale Flippers,” 46th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2008-0584, Reno, NV, 2008.
doi.org/10.2514/6.2008-584
[5] Fish, F. E., and Lauder, G. V., “Passive and Active Flow Control by Swimming Fishes and Mammals,” Annual Review of Fluid Mechanics, Vol. 38, 2006, pp. 193–224.
doi.org/10.1146/annurev.fluid.38.050304.092201
[6] Weber, P. W., Howle, L. E., Murray, M. M., & Miklosovic, D. S., “Computational Evaluation of the Performance of Lifting Surfaces with Leading-Edge Protuberances,” Journal of Aircraft, Vol. 48, No. 2, 2011, pp. 591-600.
doi.org/10.2514/1.C031163
[7] Miklosovic, D. S., Howle, L. E., Murray, M. M., & Frank E. Fish, “Leading-edge tubercles delay stall on humpback whale (Megaptera novaeangliae) flippers,” Physics of Fluids, Vol. 16, No. 5, 2004.
dx.doi.org/10.1063/1.1688341
[8] N. Rostamzadeh, K. L. Hansen, R. M. Kelso & B. B. Dally, “The formation mechanism and impact of streamwise vortices on NACA 0021 airfoil's performance with undulating leading edge modification,” Physics of Fluids, Vol. 26, No. 10, 2014.
dx.doi.org/10.1063/1.4896748
[9] K. L. Hansen, R. M. Kelso & B. B. Dally, “Performance Variations of Leading-Edge Tubercles for Distinct Airfoil Profiles,” AIAA Journal, Vol. 49, No. 1, 2011.
doi.org/10.2514/1.J050631
[10] Ernst A. van Nierop, Silas Alben, and Michael P. Brenner, “How Bumps on Whale Flippers Delay Stall: An Aerodynamic Model,” Physical Review Letters, Vol. 100, No. 5, 2008.
doi.org/10.1103/PhysRevLett.100.054502
[11] K.L. Hansen, R.M. Kelso, B.B. Dally, E.R. Hassan, “Analysis of the Streamwise Vortices Generated Between Leading Edge Tubercles,” Proceedings of 6th Australian Conference on Laser Diagnostics in Fluid Mechanics and Combustion, Canberra, 2011
[12] Shi, Weichao, Mehmet Atlar, Rosemary Norman, Batuhan Aktas, and Serkan Turkmen, "Numerical optimization and experimental validation for a tidal turbine blade with leading-edge tubercles," Renewable Energy, Vol. 96, Part A, 2016, pp. 42-55.
doi.org/10.1016/j.renene.2016.04.064
[13] Ri-Kui Zhang and Jie-Zhi Wu, “Aerodynamic characteristics of wind turbine blades with a sinusoidal leading edge,” Wind Energy, Vol. 15, No. 3, 2012, pp 407-424.
doi.org/10.1002/we.479
[14] Ibrahim, I. H., and T. H. New, "A numerical study on the effects of leading-edge modifications upon propeller flow characteristics," Proceedings of Ninth International Symposium on Turbulence and Shear Flow Phenomena. Melbourne, 2015.
[15] Moore, K., and A. Ning, "Aerodynamic Performance Characterization of Leading Edge Protrusions," 54th AIAA Aerospace Sciences Meeting, AIAA Paper 2016-1786, San Diego, CA, 2016.
doi.org/10.2514/6.2016-1786
[16] Ning, Zhe, and Hui Hu, "An Experimental Study on the Aerodynamics and Aeroacoustic Characteristics of Small Propellers of UAV," 54th AIAA Aerospace Sciences Meeting, AIAA Paper 2016-1785, San Diego, CA, 2016.
doi.org/10.2514/6.2016-1785

Update 01

Following are my publications relating to the subject of this post.

Butt, F.R., and Talha, T., "A Numerical Investigation of the Effect of Leading-Edge Tubercles on Propeller Performance," Journal of Aircraft. Vol. 56, No. 2 or No. 3, 2019, pp. XX. (Issue/page number(s) to assigned soon. Active DOI: https://arc.aiaa.org/doi/10.2514/1.C034845)

Butt, F.R., and Talha, T., "A Parametric Study of the Effect of the Leading-Edge Tubercles Geometry on the Performance of Aeronautic Propeller using Computational Fluid Dynamics (CFD)," Proceedings of the World Congress on Engineering, Vol. 2, Newswood Limited, Hong Kong, 2018, pp. 586-595, (active link: http://www.iaeng.org/publication/WCE2018/WCE2018_pp586-595.pdf).

Butt, F.R., and Talha, T., "Optimization of the Geometry and the Span-wise Positioning of the Leading-Edge Tubercles on a Helical Vertical-Axis Marine Turbine Blade ," AIAA Science and Technology Forum and Exposition 2019, Turbomachinery and Energy Systems, accepted for publication.