1. Analysis on aerodynamic performance of Inverse tapered small wind turbine based on BEM
Ashikaga Institute of technology　JAPAN
〇Mitsumasa Iino
　 John Ochieng Anyango
　 Izumi Ushiyama
Thank you chairman for the introduction.
Today I would like to talk about the inverse tapered small wind turbine and its analysis using blade element and momentum theory

2. Contents 1. Background –what is inverse tapered rotor- 2. Purpose
3. Method
4. Results
5. Discussion
6. Conclusion
The contents is below
So, First I will explain the background

3. Wind turbine shape before 20th
Background
Multi blades, Straight or inversely tapered, High solidity
Back in days, the design of most wind turbines were
And this kind of multiblade inverse tapered rotor have high torque and good starting performance
which is suitable for the purpose in old days usage like pumping or milling.
And also thought to be optimum in view of aerodynamics and worked not badly
High torque, good starting performance
⇐meets the purpose of the turbine.
Thought to be optimum in view of aerodynamics
⇐empirical knowledge. But worked not badly.

4. Optimum wind turbine rotor
Background
After Blade Element and Momentum theory (BEM)
Optimum turbine design is　
Low solidity (reduce swirl loss)
Tapered chord distribution
State of art wind turbine Cp≒0.5
[1] R. K. Singh and M. R. Ahmed, “Blade design and performance testing of a small wind turbine rotor for low wind speed applications,” Renew. Energy, vol. 50, pp. 812–819, 2013.
However for small (micro) wind turbines
・low Re induces performance reduction(Cp<0.3)
・small torque induces bad startup characteristics
However, the recent development of the aerodynamic theory especially blade element and momentum theory revealed
That the optimum design for large wind turbine is low solidity, and tapered chord length distribution.
Likewise this wind turbine state of art technology achieved power coefficient around 0.5 based on this idea.
However If we apply this idea simply to small wind turbine especially micro wind turbines with diameter below 2 or 3m,
Low Reynolds number induces performance reduction.
So, some manufacturer or researchers uses high solidity design special augmentation like diffuser or winglet
Therefore, event though the optimum design idea is established in large wind turbine sector
The best practice for small wind turbine design is still unclear
Tokuyama(2008)*
Ohya (2009)**
Photo taken by Toru Nagao
The best practice of small (micro) wind turbine design?
*H. TOKUYAMA, T. TAKAHASHI, M. IINO, and M. IIDA, “Proposal of an evaluation method of equivalent fatigue load for small wind turbine blade,” Trans. JSME (in Japanese), vol. 80, no. 816, p. TEP0232-TEP0232, 2014.

5. Inverse tapered wind turbine
Background
*Y. Nishizawa and M. Suzuki, “An experimental study of the shapes of rotor for a horizontal-axis small wind turbines,” ,2009.
Design of Inverse tapered rotor*
(Nishizawa et. al )
足利工業大学で試験された逆 テーパ型風車
Design Tip speed ratio
𝜆 𝑑𝑒𝑠𝑖𝑔𝑛 =2.0
Airfoil : Clark-Y
Tapered wind turbine rotor
Calculate
optimum chord and twist distribution based on BEM**
Tapered
Inverse tapered
Wind tunnel
Open type 1.0m x 1.0m
Higher Cp with Inverse tapered
Wind speed
10 m/s
Rotor diameter
0.6m
Design tip speed ratio
2.0
Tapered rotor
So, within such difficult design region of the micro wind turbines,
Nishizawa et. Al. proposed inversely tapered rotor shape like wind turbines in old days.
The one on the right figure is the inverse tapered, the left is the tapered rotor.
In order to design this inverse tapered rotor, one simple step is added in the blade design.
Basically the blade is designed based on design tip speed ratio and airfoil characteristics.
By using these information, Blade element and momentum theory produces optimum chord distribution.
Then the tapered rotor is designed.
In order to design inverse tapered rotor, one single step is added here.
The chord length of the root and tip is inverted
By simply inverting the chord length, the performance around design tip speed ratio and below is improved.
With very small diameter. In other word low Reynolds number region.
Invert the chord length at blade tip and blade root
Inverse tapered rotor is better in low 𝑅𝑒 region
1. The detailed mechanism is not fully revealed.
2. Theoretical analysis method is needed for future design.
Inverse tapered rotor
Cp-λ from wind tunnel testing
with diameter of 0.6m, V=10m/s (Nishizawa 2009)
**E. H. Lysen, “Introduction to wind energy,” 1982.

6. Purpose and today’s contents
Establish theoretical analysis method of inverse tapered wind turbine performance
Expected outcomes or future usages
1. Better understanding of physics
2. More practical wind turbine design (incl. aerodynamic optimization, load calculation of aeroelastic model etc.)
Contents
Examine the applicability of BEM to the inverse tapered wind turbine
Methods
Introduction of tested turbine and simulation flow
Results
2D verification of CL CD analysis using XFOIL
3D rotor performance analysis using BEM
Discussion
Were characteristics of the inverse tapered rotor reproduced by BEM?
So, the purpose of this research is to establish a theoretical analysis method of inverse tapered wind turbine performance.
Expected outcome is first, the better understanding of the physics.
Second, more practical wind turbine design will become possible.
The content today is the examination of the applicability of blade element and momentum theory to the inverse tapered wind turbine
The latter of this presentation I explain the method, results and discussion of this examination

7. Target wind turbines Method Wind tunnel 1.Tapered 2.Inverse tapered
(Open type 1.0m x 1.0m outlet)
1.Tapered
2.Inverse tapered
Higher Cp with Inverse tapered
Wind speed
10 m/s
Rotor diameter
0.6m
Design tip speed ratio
2.0
Airfoil
Clark-Y
The target for Blade element and momentum theory is the inverse tapered rotor which is presented in previous slide.
As a data for comparison the Cp-ラムダ　curve obtained in the wind tunnel test is used
In order to verify the relative trend, Tapered rotor is also simulated byBEM
So, these two rotors are today’s target.
Next I explain the basics of the rotor performance simulation
How accurate BEM can reproduce the rotor performance
Can relative trend reproduced by BEM
Cp-λ　obtained in the wind tunnel

8. Rotor performance calculation
Method
・Blade element and momentum theory
Iterative calculation for each blade element
Blade is divided to blade elements along the span
1.Momentum conservation
Along the annular stream tube
a. Work done by blade element 9
(1−2𝑎)𝑉 𝑖𝑛 8 7 6
𝑉 𝑖𝑛 5 4 3 2 1
2.Airfoil lift and drag
From CL-α and CD-α
Lift
b. Reduced Inflow wind speed to the rotor (induced velocity)
Drag
As I mensioned in the title,
Blade element and momentum theory is used in this presentation.
In this theory, first, blade is divided into many blade elements
Then at each blade element, annular area is set.
Then along this annular area momentum conservation along the stream tube includes inlet and outlet is considered.
Then the relative inflow speed is obtained considering the work done by the blade element.
From the inflow wind speed, the work done by blade element is calculated.
Then the work done by the blade element is updated and the relative inflow speed is re-calculated.
By doing this iterative process the work done by blade element and the velocity deficit can be obtained.
The advantage of this method is
The disadvantage is the assumption there is no interaction between blade elements
Therefore 3 dimentional effect like radial flow from centrifugal force cannot be considered
Even this poor assumption of 3D effect this method shows very good agreement to recent wind turbines.
Relative inflow velocity
Pros.
・low computational cost
・Easily understood and minimum know-how is needed.
Con.
・3D effect or time dependent effect is not physically modeled
(can be corrected by empirical, theoretical factor)
Iterate until a and b converges
・Rotor area is divided to annular ring shaped stream tube
・The work of the blade is calculated based on 2D Lift and drag force of airfoil
Suitable for Design tool
Examine the applicability of this method to the inverse tapered rotor

9. Simulation flow Method
Calculated Reynolds number distribution
Calculate Reynolds number of each blade element at Design tip speed ratio
Reynolds number
of each blade element
Calculate Reynolds number at each radial position
CL CD calculation by XFOIL analysis
Blade element momentum theory analysis
Calculate 𝑅𝑒 dependent
CL and CD of each blade element (XFOIL)
XFOIL
Qblade
Potential flow based 2D flow simulation software
Wind tubine design software incl. BEM analysis
Lift drag
Characteristics
of each blade element
XFOIL calculated CL-α, CD - α
The flow we did is presented here.
First, the Reynolds number at each blade element is calculated.
This is the calculated results of Reynolds number. As you can see, the Reynolds number increases with the radial position.
And also very low Reynolds number in all the region
Then the Lift and drag coefficient is calculated using XFOIL.
By using the lift and drag coefficient, BEM analysis is done by a software Qblade.
So, this is the work we did.
Then I explain the result of Lift and drag coefficient and rotor performance which is the final goal of today.
BEM analysis (Qblade)
Lift and drag coefficient from XFOIL in low Re region
Rotor performance of both Inverse tapered and tapered rotor

10. The trend depending on Reynolds number is well reproduced by XFOIL
CL and CD from XFOIL
Results
Comparison of XFOIL simulation and experimental result* at low Reynolds number
Airfoil Clark-Y
The result of XFOIL is presented here.
The data for comparison is he wind tunnel test results in a literature
The broken line are from experiment and the solid lines are from XFOIL.
As you can see, With the increase of the Re, Lift coefficient and stall angle increases. And the drag coefficient is on the contrary, decreases.
Then lets go to the main issue of this work.
Increase of 𝑅𝑒 →　Increase of CL and stall angle, decrease of CD
*J. F. Marchman and T. D. Werme, “Clark-Y Airfoil Performance at Low Reynolds Numbers,” AIAA 22nd Aerospace Sciences Meeting
The trend depending on Reynolds number is well reproduced by XFOIL

11. Rotor performance from BEM
Results
Cp-λ curve with 0.6m diameter and V=10m/s
Tapered
Inverse tapered
Cp of both types of rotor well reproduced within 10 % error around design tip speed ratio λ=2
Analysis of both rotor showed error within 10% from experimental result around design tip speed ratio λdesign=2.0
The rotor performance curve from BEM for inverse tapered rotor
Next I discuss the relative characterisitics of these two types
※Due to high induced velocity, BEM is not converged in high tip speed ratio region
In view of accuracy, BEM reproduced the Cp well.

12. Was the advantage of inverse tapered rotor reproduced?
Discussion
In view of relative trend of inverse tapered rotor…
1.Better performance below λdesign=2.0
Well reproduced
Increased solidity by inversely tapered must be dominant reason
2.Better performance around λdesign=2.0(around peak)
Not reproduced
Wind tunnel
BEM analysis
In view of relative trend the advantage is inverse tapered rotor is partially reproduced.
First, the better perforomance below design tip speed ratio is well reproduced.
However the better performance around the design tip speed ratio is not reproduced well.
So, as for the relative trend, BEM did not reproduced the wind tunnel result perfectly.
The next slide discusses this discrepancy around the peak of the power coefficient

13. Why BEM could not reproduce peak Cp enhancement
Discussion
1. Uncertainty in the wind tunnel test
Blockage effect, measurement uncertainty
2. Three dimensional effect(not considered in BEM)
Previous PIV measurement* and 3D CFD** indicates reduced radial flow and consequent reduction of suction side flow separation
This kind of effect can only be considered using correction factor in BEM (Prandtl’s tip loss or hub loss etc.)
Results from related literature **
3D CFD results of stream lines
(Yamashita et. al.(2013))*
Inverse
Tapered
Suction side radial direction vortex from hub side is reduced by inverse tapered design
→3D effect improve performance of the airfoils
this is the final slide before conclusion which shows possible reasons of discrepancy in the peak power coefficient
1 is uncertainty in the wind tunnel test. Because the inverse tapered rotor might have higher thrust, the effect of blockage should be carefully checked.
2 is three dimentional effect
on this point, some interesting related literature revealed that with the inverse tapered blade, suction side vortex from the hub to tip could be reduced compared with tapred blade.
So, this might one possible reason.
And of course, blade element and momentum theory cannot deal with this kind of 3D effect, we should make a correction model or consider the modification of the existing correction factor.
3D effect is possibly be one of the dominant factor to determine the relative trend
*C. Otieno Saoke, “Power Performance of an Inversely Tapered Wind Rotor and its Air Flow Visualization Analysis Using Particle Image Velocimetry (PIV),” Am. J. Phys. Appl., vol. 3, no. 1, p. 6, 2015.
**Y. Yamashita, Y. Nishi, and T. Inagaki, “Study of Horizontal-axis Wind Turbine with the Inverse Tapered Blades (in Japanese),” Japan Soc. Mech. Eng. Ibaraki -Kouenkai Proc., 2013.

14. Conclusion
What we did
・Examined Applicability of BEM for Inverse tapered rotor
Findings
Accuracy
・BEM can reproduce the performance around design tip speed ratio within 10% both for tapered and inverse tapered rotor
Comparative trend
・BEM could reproduce the power enhancement in low tip speed ratio
・BEM could not reproduce the power enhancement around design tip speed ratio.
Future tasks
・Check 3D effect in the wind tunnel (check the effect of the root chord on the performance)
・Understanding structural characteristics (reduced chord of the blade root may reduce the strength )