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.

Comparison of VAWT Blade Designs (Leading-Edge Tubercle, Leading and Trailing-Edge Tubercle, Unmodified) (Update 05)

Numerical simulations were run on SolidWorks Flow Simulation Premium (model files are available here) software to compare the torque characterizes of three distinct vertical-axis wind turbine blade designs shown in Fig. 1. The torque characteristics are shown in Fig. 2.

This publication was used to verify and validate the numerical methodology. The results were within 8% of the publication's results at the design point of TSR of 1.2 at 90 RPM and 7.85 m/s wind speed. The dimensions of the turbine, the  blades and the cross section used are mentioned in the publication.

Fig. 1. Top Row, L-R: VAWT with blades having tubercles at the leading edge (ten tubercles per blade span, configuration name 10T), VAWT with blades having tubercles at both the leading and the trailing edge (ten tubercles per blade span). Bottom Row, VAWT with blades having no modifications.

It is clear from the Fig. 2 that the baseline design provides the most stable torque. On average the turbine with no modifications on the blades produced 5.31 Nm torque in one complete rotation, while the turbine with tubercles at the leading edge only, produced 5.20 Nm torque. The turbine with tubercles added to both the leading and the trailing edge produced 5.09 Nm torque in one complete rotation.

The peak torque was maximum for the turbine with the leading edge tubercles, followed by the turbine with the tubercles added to both the leading and the trailing edge of the turbine blades and the turbine with no modifications on the blades at 21.59 Nm, 21.45 Nm and 20.58 Nm respectively.

Fig. 2. Top Row, L-R: Torque curves for VAWT with blades having tubercles at the leading edge, Torque curves for VAWT with blades having tubercles at both the leading and the trailing edge. Bottom Row, Torque curves for VAWT with blades having no modifications. Three colors denote each of the blades in the turbine.

CFD post processing will be added later (may be next week). The effect of leading edge tubercle geometry will be investigated next. The blade design with tubercles added to both the leading and the trailing edge will not be investigated further because it produced the lowest average torque and second highest peak torque.

Update 01:

Decreased the number of tubercles per unit length of the blade, i.e. made the wavelength of the tubercles longer, kept the sweep angle same. As a result, the average and peak torque decreased to 4.53 Nm, and 19.33 Nm, respectively. The figure is attached.

Fig. 3. T-B: Torque curves for VAWT with blades having large wavelength tubercles at the leading edge (five tubercles per blade span, configuration name 5T45). Three colors denote each of the blades in the turbine. Render of the blades.

Update 02:

Increased the number of tubercles per blade span, i.e. made the wavelength of the tubercles smaller, kept the sweep angle same. As a result, the average and peak torque increased to 5.80 Nm, and 23.36 Nm, respectively. The figure is attached.

Fig. 4. T-B: Torque curves for VAWT with blades having smaller wavelength tubercles at the leading edge (fifteen tubercles per blade span, configuration name 15T45). Three colors denote each of the blades in the turbine. Render of the blades.

Update 03:

Again, increased the number of tubercles per blade span, i.e. made the wavelength of the tubercles smaller, kept the sweep angle same. As a result, the average and peak torque increased to 6.1 Nm, and 24.12 Nm, respectively. The figure is attached.

Fig. 5. T-B: Torque curves for VAWT with blades having smaller wavelength tubercles at the leading edge (twenty tubercles per blade span, configuration name 20T45). Three colors denote each of the blades in the turbine. Render of the blades.

Update 04:

Once more, increased the number of tubercles per blade span, i.e. made the wavelength of the tubercles smaller, kept the sweep angle same. As a result, the average and peak torque increased to 6.42 Nm, and 24.63 Nm, respectively. The figure is attached.

Fig. 6. T-B: Torque curves for VAWT with blades having smaller wavelength tubercles at the leading edge (twenty-five tubercles per blade span, configuration name 25T45). Three colors denote each of the blades in the turbine. Render of the blades.

A table for the tubercle geometry is shown below.

Table 01, Tubercle Geometry

Configuration Name	Amplitude (m)	Wavelength (m)	Sweep Angle (°)
Baseline	0	0	0
5T45	0.12777778	0.25555556	45
10T45	0.06052632	0.12105263	45
15T45	0.03965517	0.07931034	45
20T45	0.02948718	0.05897436	45
25T45	0.02346939	0.04693878	45

It is evident from Table 2 that adding more tubercles to the wind turbine's blade causes an increase in both the peak and the average torque. But it is also clear from the Table 2 that the percentage difference in both the average and the peak torque from the previous configuration (less tubercles per blade span) decreases as the number of tubercles per blade span is increased. It appears to be converging to a value.

Table 02, Tubercle Efficiency

Configuration Name	Peak Torque (Nm)	Average Torque (Nm)	Percentage Difference in the Average Torque from the Previous Configuration	Percentage Difference in the Average Torque from then Baseline Configuration
Baseline	20.58	5.31	N/A	N/A
5T45	19.33	4.53	-17.22	-17.22
10T45	21.59	5.2	12.89	-2.12
15T45	23.36	5.8	10.35	8.45
20T45	24.12	6.1	4.92	12.95
25T45	24.63	6.42	4.98	17.29

I think the difference between both the peak and the average torque produced by 25T45 and 20T45 configuration is comparable, up next, a new sweep angle.

Update 05

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.

Thank you for reading.

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