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.

Coffee Lake Configurations for Computational Fluid Dynamics and Gaming with no Mechanical Storage, Pakistani Market Prices.

     These setups feature no mechanical hard drive(s).

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Estimated price PKR 157,000.

     For the processor, choose the Intel Core i7-8700 for PKR 43,000. Motherboard of choice should be the Gigabyte Z370 AORUS Gaming 3 for PKR 20,500. For memory, go with the Corsair Vengeance LPX 1x16GB DDR4-3000 for PKR 23,000. Samsung 850 EVO 1TB SSD for PKR 39,500 should be the only storage option. The Asus PH-GTX1050TI-4G GTX 1050Ti for PKR 21,300 graphics card. The Corsair Carbide SPEC-04 Casing for PKR 5,500. Powering the whole thing should be at least a Thermaltake Lite-Power 550W PSU for PKR 4,400.

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Estimated price PKR 137,000.

     For the processor, choose the Intel Core i5-8700 for PKR 23,000. Motherboard of choice should be the Gigabyte Z370 AORUS Gaming 3 for PKR 20,500. For memory, go with the Corsair Vengeance LPX 1x16GB DDR4-3000 for PKR 23,000. Western Digital Blue 500GB SSD for PKR 17,500 should be the storage option. The Asus STRIX-GTX1060-DC2O6G GTX 1060 for PKR 43,000 graphics card. The Corsair Carbide SPEC-04 Casing for PKR 5,500. Powering the whole thing should be at least a Thermaltake Lite-Power 550W PSU for PKR 4,400.

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     Only the first configuration is suitable for both gaming and computational fluid dynamics (CFD). If you need a system for CFD alone, then the second configuration will be sufficient, all other configurations can be referred to as general purpose gaming PCs.

Wind Turbine SolidWorks Flow Simulation Premium Computational Fluid Dynamics: Verification and Validation

Numerical Methodology

Computational Fluid Dynamics analysis was performed using commercially available code SolidWorks Flow Simulation Premium© in the present study. SolidWorks Flow Simulation Premium© is a CAD embedded CFD tool; employs κ-ε turbulence model with damping functions, SIMPLE-R (modified) as the numerical algorithm and second order upwind and central approximations as the spatial discretization schemes for the convective fluxes and diffusive terms. The time derivatives are approximated with an implicit first-order Euler scheme. The Flow Simulation© solves the Navier-Stokes equations; mentioned below; which are formulations of mass and momentum conservation laws for fluid flows. To predict turbulent flows, the Favre-averaged Navier-Stokes equations are used.

∂ρ/∂t+∂(ρui)/∂xi=0

∂(ρui)/∂t+∂(ρuiuj)/∂xj+∂p/∂xi= ∂(τij+τijR)/∂xj+Si     i=1,2,3

where, Si is a mass-distributed external force per unit mass due to a porous media resistance (Siporous), a buoyancy (Sigravity=-ρgi is the gravitational acceleration component along the i-th coordinate direction) and the coordinate system’s rotation (Sirotation), i.e., Si=Siporous+Sigravity+Sirotation. The subscripts are used to denote summation over the three coordinate directions.

All the simulations were performed to predict three-dimensional transient flow over the wind turbine. The Local rotating region(s) (Sliding) feature within SolidWorks Flow Simulation Premium© software was employed to simulate the wind turbine’s rotation in standard atmosphere.

Validation and Verification

To ensure validation of the numerical methodology, the numerical results of the present study were compared with the experimental results. A total of six tip-speed ratios were selected for the present study, as mentioned in table 1. The NREL Phase VI wind turbine without contra-rotating technology was selected for validation and verification because there is no reliable experimental data available for the NREL Phase VI wind turbine incorporating the contra rotating technology. The operating rotational velocity for the NREL Phase VI wind turbine is 7.5 rad.s-1. The diameter of the wind turbine is 10.058 m.

Table 1; TSR and the corresponding wind speeds

TSR	Wind Speed [ms-1]
7.5	5
5.03	7.5
3.77	10
3.02	12.5
2.52	15
1.89	20

The comparison between the experimentally determined shaft torques and numerical results of the present study, along with the number of mesh cells and the time step employed at various wind speeds is shown in table 2. A comparison of the present study with other studies conducted on the NREL Phase VI wind turbine is presented in Figure 1.

The computational domain selected had a size of 4Dx4Dx2.8D. The computational domain had a large enough volume to accurately trace the fluid flow around the wind turbine and for the solver to operate without any reversed flow or unwanted vortex formation or any other numerical difficulties.

Flow Simulation© considers the real model created within SolidWorks© and automatically generates a Cartesian computational mesh in the computational domain distinguishing the fluid and solid domains. The resulting mesh, employs the immersed boundary method, has three types of cells, namely Fluid cells; the cells located entirely in the fluid, Solid cells; the cells located entirely in the solid and Partial cells are the cells which are partly in the solid and partly in the fluid [22]. The Cartesian mesh with immersed boundary method has certain advantages, like the mesh is very quick to generate and results in high quality elements. The solution converges faster and the mesh distortion and numerical errors are relatively lower. During the process of mesh generation, it was made sure that the region of interest; the region immediately surrounding the wind turbine; had a very fine mesh as compared to the boundaries of the computational domain, to make the simulations converge. The Local Mesh option within the SolidWorks Flow Simulation Premium© software was employed to increase the mesh density in the critical areas.

Table 2; Comparison of the Experimental and Numerical Results

Wind Speed [ms-1]	Experimental Power [W]	Numerical Power [W]	Percentage Difference	Mesh Cells [x105]	Time Step [x10-3 s]
5	2,000	2,043	2.1	3.77	5.41
7.5	6,000	6,105	1.72	3.77	5.41
10	10,000	10,230	2.25	3.77	5.41
12.5	9,500	9,343	1.65	7.79	1.9
15	9,000	7,606	15.49	7.79	1.9
20	8,500	8,696	2.25	9.21	1.96

Figure 1; Comparison of results from present study with previous works

Project Files and Illustrations
     The project files are available here. An illustration of the rotor is provided below.

CFD Post Processing

SolidWorks Animation: Transient NREL Phase-VI Wind Turbine CFD Simulation [Validated]

     10 KW wind turbine CFD simulation using Flow Simulation Premium. Design points: 10 m/s wind speed, rotational velocity 7.5 rad/s.

     The rendered volume shows vorticity (curl of the velocity field). It is colored by dynamic pressure. Low pressure in the center of the helix shows very small wind speed.

     Power from the CFD analysis was 9,854.96 W while the experimental power is 10,000 W, a difference of only 1.45 %, that too by using only 693,141 cells in the mesh.

     Do you want me to make a tutorial about the simulation setup with SolidWorks Flow Simulation Premium?