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

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

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.

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.

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. 2009) 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.

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

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

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

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

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. 1984. The trend depending on Reynolds number is well reproduced by XFOIL

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.

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

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.

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 )