A Numerical Simulation Comparing the Efficiencies of Tubercle Versus Straight

Leading­Edge Airfoils for a Darrieus Vertical­Axis Wind

Turbine

By: Ross Neal

Abstract:

The efficiencies of sinusoidal and straight leading­edge airfoils (NACA 0015) in a three­straight­wing Darrieus vertical axis wind turbine (VAWT) were compared using a fluid numerical solver (CFX). The airfoils and surrounding air modeled were meshed with body sizing and inflation layer methods and a cylinder mesh containing the surfaces of the airfoils was meshed separately as the mesh would be rotated during numerical solve. To save computing time, only a portion of the height of the VAWT was modeled as the streamlines should be repeating along the vertical leading­edge of the airfoils. The numerical solver computed the torque applied to the rotated cylinder containing the airfoil surfaces at speeds from 15 to 35 rad/s for both designs at 10 m/s inlet wind speed of air with 1.185 kg/m3 density for 4 complete rotations. The resulting torques from the time­series data were averaged and converted to units of power (W) and coefficient of power and were graphed over rotation speed and tip speed ratio respectively to compare both airfoil designs. Introduction:

Now that gasoline prices have greatly decreased, it is becoming harder for green energy,

such as wind energy, to compete for investments over cheap,

traditional, and polluting power sources such as coal.

Therefore, it is more important now more than ever to make

green energy more attractive by making them more efficient

at producing power. One such solution came from a

company called Whale Power based in Toronto. The

company used biomimetics to design more efficient

airplane wings, vacuum pumps, hydroelectric turbines

and horizontal wind turbines.

The company believed that the unique shape of

the tubercles on the leading­edge of the pectoral fins of

humpback whales allowed the whales to swim more efficiently than having smooth on fins

allowing the animal to swim with much less effort. In fact, there have been several papers,

experiments, prototypes (shown in Figure 1), and even products (shown in Figure 2)

demonstrating that the tubercle leading­edge airfoils consistently outperform their leading­edge

smooth counterparts . The tubercles on 1 2 3

the leading­edge of the airfoils combine

the best of swept forward and backward

wing designs to redirect streamlines into

bands (shown on Figure 3) which reduces

the turbulent vortices/cavitations and

laminar flow separation that would

normally cause stalls on traditional wings

by increasing the angle of attack (the relative angle between the airspeed vector and the chord of

the airfoil blade) shown in Figure 4. The stalling robustness of the tubercle airfoil allows for

1 Saadat, Haj­Hariri, and Fish, “Explanation of the Effects of Leading­Edge Tubercles on the Aerodynamics of Airfoils and Finite Wings,” The American Physical Society Division of Fluid Dynamics 21 Nov. 2010, <http://meetings.aps.org/Meeting/DFD10/Event/132841>. 2 Murray, Gruber, and Fredriksson, “Effect of Leading Edge Tubercles on Marine Tidal Turbine Blades,” The American Physical Society Division of Fluid Dynamics 22 Nov. 2010, <http://meetings.aps.org/Meeting/DFD10/Event/133206>. 3 Custodio, Henoch, and Johari, “Separation Control on a Hydrofoil Using Leading Edge Protuberances,” The American Physical Society Division of Fluid Dynamics 19 Nov. 2006, <http://meetings.aps.org/Meeting/DFD06/Event/53973>.

higher angles of attack of the airfoil without stalls or as much drag and therefore more lift is

created due to increased fluid pressure under the airfoil (more cross­sectional area of the airfoil is

directly exposed to the fluid). This technology could be applied to airplane wings that could save

on fuel due to less drag caused by the wings and to blades of wind/hydroelectric turbines that

would generate more torque at lower fluid speeds leading to more power and electricity

generated.

However, most research involving this technology has been put into fan blades and

airplane wings, but not in vertical axis wind turbines (VAWT) like the Darrieus design shown in

Figure 5. Theoretically, if the modified tubercle airfoil increases the efficiency of lift for wings

on airplanes and on fan blades, the same idea could be applied to vertical axis wind turbines. The

tubercle technology would be especially advantageous for Darrieus VAWTs over more popular

horizontal axis wind turbines (HAWT) because it can accentuate the advantages VAWTs have

over HAWTs; VAWTs can operate at especially low wind speeds and therefore at lower

elevations and this technology would theoretically increase the power generated at those speeds

significantly. Also, since not as much power is needed to rotate the tubercle VAWT, less starting

electricity would be needed/wasted to start rotation of the VAWT (VAWTs are not self starting

from standstill unlike HAWTs). Plus, since the wind speed is the same along the entire length of

the airfoil on VAWTs unlike HAWTs, the tubercles size/shapes can be more easily optimized for

the average wind speed experienced at a particular location leading to a relatively simpler shape

to manufacture compared to HAWTs where the cross­sectional airfoil shape has to be constantly

optimized at different radial speeds experienced along the blade in addition to the tubercles.

To validate the claims of increased efficiencies of the tubercle leading­edge airfoils over

traditional straight­edge designs and to test if the technology would equally apply Darrieus

VAWTs, I decided to numerically model and compute the power generated by tubercle and

straight leading­edge Darrieus VAWTs.

Modeling:

I decided to use a well­understood simple popular airfoil for the VAWT as a National

Advisory Committee for Aeronautics (NACA) 0015 airfoil show in Figure 6. The four digit

number represent constants in the symmetrical four­digit airfoil NACA equation:

where c is the chord length, x and yt are the normalized horizontal and vertical coordinates of the

edge of the airfoil respectively, and t is the maximum thickness normalized to the fraction size of

the chord length (last two digits of the NACA is 100*t). The overall design was three NACA

0015 equidistant airfoils around a circle of 1

m diameter with 20 cm chords (shown in

Figure 7 with force vectors). The pitch

angle Θ was chosen to be 10o (close to the

NACA 0015 stall angle shown in Figure 8

for a given Reynolds number calculated

later) for both the tubercle and non­tubercle

airfoils so that I could directly compare both

airfoils and accentuate the theoretical

advantages of the low drag at higher angle

of attack for the tubercle airfoil. The Reynolds number can be calculated for an airfoil (fluid

dynamics) as: Re=V*c/v where Re is the Reynolds number, V is the flight/wind speed, c is the

chord length, and v is the kinematic viscosity of the fluid (air in this case). For a chosen 10 m/s

wind speed, the Reynolds number ranges

from around 120,000 to 140,000 for

elevations between 1700 m and sea level

respectively which means the magenta line

in Figure 8 most closely matches the

simulation.

To model the tubercles on the

leading­edge of the airfoil, the following

sinusoidal equation was used in Figure

9. To get a 3D model of a tubercle

airfoil, the base NACA 0015 shape was

vertically extruded with the sine wave as

a leading edge guideline. Then, a second

NACA 0015 shape was extruded

normally (straight up vertically) and

both 3D objects were intersected and

joined to get a straight tailing­edge and a

sinusoidal leading­edge shown in Figure

10. Then, three copies of the airfoil were arranged as previously shown in Figure 7 with the

center of rotation inside a 8x3x0.3 m rectangular prism located 2 m from one end and centered

along the 3 m side. To reduce element count and facilitate meshing and to allow rotation of

airfoils, two more cylinders were centered on axis of rotation of diameter 0.75 m and 1.5 m with

height of 0.3 m as shown in Figure 11.

The outer box and the innermost cylinder were meshed (using ANSYS software) with a

body sizing method of 5 mm and a multi­zone method with hexa/prism shapes with free mesh

tetrahedrons while the outer cylinder minus the inner cylinder and the airfoils (airfoils aren’t

meshed) were meshed with a body sizing method of 2 mm shown in Figure 12. All the

interfaces between shapes/regions touching have 20 inflation layers at a 1.2 growth rate

including the surface of the airfoils shown zoomed in on Figure 13.

After meshing the model, a fluid dynamics numerical solver was used (CFX) to calculate

the drag and lift forces on the airfoils. The boundary conditions were set up as shown in Figure

14. The inlet wind (air at 25oC with 1.185 kg/m3 density which is about 350 m of elevation above

sea level) conditions is set to 10 m/s at 5% intensity to simulate a median wind speed. The red

symmetry boundaries allow for the VAWT to be taller if need be since the airflow should be

roughly the same at any height along the airfoil. In order to get a power curve data to properly

calculate torque generated by airfoils, the wind speed in the inlet remained the same 10 m/s,

while the rotational speed of the airfoils varied between 15 and 35 rad/s in 5 rad/s increments

(the entire cylinder mesh region was rotated about the big blue arrow in Figure 14 to rotate the

airfoil surfaces). To balance accurate results and be computationally shorter, 400 timesteps and

100 maximum loops per timestep at .0001 variance (100 per revolution or approximately 3o

rotation increments) for each simulation was chosen. Therefore, the entire simulation length was

calculated by 4*2π*(rad/s) for 4 revolutions and the time step (dt) is 1/400 the entire simulation

length which values are shown on Figure 15.

Since the Darrieus VAWT blades were strictly vertical and not a twisted helical blades

(twisted helical blades would have required more height of the airfoil to be calculated whereas

the simulations took a full month of computer time already), the torque applied to the airfoil

varies over time as each of the three airfoil go from the optimum angle (leading­edge of the

airfoil is close to facing directly the wind speed vector) to generate the most useful lift at

different time throughout the rotation cycle. Therefore, in order to compare the efficiencies of

both smooth and tubercle airfoils in

Darrieus VAWTs, the torque

applied to the blades (the rotating

cylinder) had to be averaged over

the entire simulation time (shown as

an example in Figure 16). The first

revolution of torque data on the

airfoils had to be discarded due to

the time it takes for the streamlines of the wind of the inlet to fully penetrate the entire VAWT

simulation.

Results:

The results were very encouraging as the tubercle leading­edge airfoil VAWT

consistently and significantly outperformed the smooth leading­edge airfoil VAWT in average

torque and power generated; the minimum improvement of power generated by the tubercle was

just under twice (up to a maximum of 6 times more) than that over the traditional design. The

average power generated was calculated by multiplying the rotational speed to the average

torque generated. The coefficient of power was also calculated by the following equation:

where Cp is the coefficient of power, P is the power generated (W) calculated from

the torque, p is the density of the fluid (air at 1.185 kg/m3), A is the area swept by the airfoils (0.3

m height with 1 m diameter makes 0.3 m2 area swept), and V is the velocity of the fluid (air at 10

m/s). The tip speed ratio (TSR) was calculated from multiplying the rotation speed (rad/s) and

the radius of the rotation (0.5 m) divided by wind speed (10 m/s). All the calculated averages of

generated torques, powers, coefficients of power as well as the percent improvement of the

tubercle over normal airfoil designs are shown in Figure 17 and was entered in two separate

graphs with different units yet show the same percentage improvements shown in Figure 18.

The Tubercle airfoil generates some incredible efficiencies approaching a coefficient of power

greater than 0.6 or maybe 0.7 for higher TSRs whereas the normal airfoil has a localized stall at

25 rad/s (TSR of 1.25) and the coefficient of power may be plateauing between 0.3 and 0.4 for

TSRs higher than 1.75.

Conclusion:

Given more computational power and resources, a more complete coefficient of power

versus TSR graph could be made to show optimum TSR for coefficient of power. In addition, a

more complex helical airfoils could be introduced to mitigate varying torques generate over each

cycle of rotation which could also reduce mechanical stresses and failures due to reduced

vibrations. Plus, a scaled­down experiment could be made in a wind tunnel to see how well the

numerical simulation matches experimentation. Also, a separate study could be completed on

just the on the equation for the leading­edge tubercle airfoil (NACA shape airfoil and pitch could

be also be optimized for tubercle technology) to see if varying the amplitude and frequency

could be optimized for certain wind speeds since there hasn’t been much research on that

particular subject matter.

The added efficiencies of adding a simple sinusoidal leading­edge airfoil were found to

be between 2­6 times for efficient compared to the traditional straight­edged airfoils in a

Darrieus VAWT. The relative stalling robustness of the tubercle airfoil over the traditional

straight­edged airfoil allowed for greater percentage of the rotation cycle to have useable lift and

increase overall efficiency. The sheer efficiency improvement should be more than enough to

justify any additional manufacturing costs of the propellers especially with the relatively smaller

blades Darrieus VAWTs typically have compare to modern giant HAWTs.