Rotor Blade Performance Analysis with Blade Element Momentum Theory

Transcription

1 Available online at ScienceDiect Enegy Pocedia 5 (7 ) 3 9 The 8 th Intenational Confeence on Applied Enegy ICAE6 Roto Blade Pefomance Analysis with Blade Element Momentum Theoy Faisal Mahmuddin a * a Maine Engineeing Depatment, Engineeing Faculty, Hasanuddin Univesity Jalan Peintis Kemedekaan km. Tamalanea, Makassa, Indonesia 945 Abstact In ode to optimally exploe and utilize wind enegy, an optimal design of wind tubine popelle blades needs to be obtained. Theefoe, a computational method to analyze and optimize the pefomance of the blades needs to be developed. Fo that pupose, a computational method based on the Blade Element Momentum (BEM) theoy is developed in the pesent study. In this method, the popelle blade is divided into seveal elements and it is assumed that thee is no aeodynamic inteaction amongst the elements. Futhemoe, the equations fom momentum and blade element theoies ae combined to obtain equations which ae useful in blades design pocess. In the analysis, tip and oot losses poposed by Pandtl ae also implemented. The computation esults ae validated using Qblade softwae. A good ageement can be found fom compaison of the esults computed fom the developed BEM and QBlade. 7 6 The The Authos. Authos. Published Published by Elsevie by Elsevie Ltd. This Ltd. is an open access aticle unde the CC BY-NC-ND license ( Selection and/o pee-eview unde esponsibility of ICAE Pee-eview unde esponsibility of the scientific committee of the 8th Intenational Confeence on Applied Enegy. Keywods: Blade element momentum; momentum theoy; NACA45 aifoil; QBlade; oto design; wind tubine. Nomenclatue a axial induction facto P tubine powe a angula induction facto T thust foce C L lift coefficient V wind speed C D dag coefficients otational speed F axial foce angula speed * Coesponding autho. Tel.: addess: f.mahmuddin@gmail.com The Authos. Published by Elsevie Ltd. This is an open access aticle unde the CC BY-NC-ND license ( Pee-eview unde esponsibility of the scientific committee of the 8th Intenational Confeence on Applied Enegy. doi:.6/j.egypo

2 4 Faisal Mahmuddin / Enegy Pocedia 5 ( 7 ) 3 9. Intoduction Consideing the impotance of exploation and exploitation of enewable enegy esouces including wind enegy in ecent decade, a wind tubine with optimal blades pefomance needs to be developed. Theefoe, fo designing the wind tubine blades with optimal pefomance, vaious methods have been established and implemented by eseaches and scientists to analyze and optimize the pefomance of the wind tubine blades. Choosing the appopiate method to be adopted in blades designing pocess depends on the level of equied esults accuacy. In the pesent study, a computational method based on the Blade Element Momentum (BEM) theoy is developed. The BEM method is known to able to povide a closed fom solution with elatively simple pocedues. The method was oiginally developed fom momentum theoy and blade element theoy []. By combining both methods, useful elations to be used in popelle blades design can be obtained. Fom this oiginal method, vaious modifications have been pefomed and coections ae included by seveal eseaches such as Pandtl tip and oot losses [], 3D coection [], Reynold numbe dag coection [3], etc. When using the BEM method, the popelle blade is divided into seveal elements. It is assumed that each element is independent and the fluid flow ove elements has no inteaction. Moeove, the foces and moments ae computed in each element so that total foces and moments ae obtained by integating the individual foces and moments on each element. In ode to demonstate the computation pocedues and validate the esults of the BEM method developed in the pesent study, a popelle blade with NACA45 aifoil shape, is chosen. Only tip and oot losses poposed by Pandtl [] which ae implemented in the pesent study. The computation esults fom the developed BEM is validated using a softwae package called QBlade [4]. It is a fee softwae based on GNU license which povides fiendly inteface fo popelle design analysis and optimization pocesses based on the BEM method. It is found fom the study that the esults computed fom the developed BEM method has a good ageement with the ones fom QBlade softwae.. Solution Method In the pesent study, the Blade Element Momentum (BEM) theoy is adopted as the main computation method. The method is combination of momentum theoy and blade element theoy. The blade element theoy sometimes is also called stip theoy... Momentum Theoy Fom momentum theoy, when assuming that the blades could poduce powe without otation, the axial foce (F) can be obtained using the following equation [5] V df 4a a a d () Whee ρ a is ai density, V the wind velocity fa downsteam, the distance of the element fom hub and a the axial induction facto which could be witten as V V a T () V Whee V T is the wind velocity fa upsteam. When otation is intoduced in the model, the thust (T) can be obtained using the following elation [5]

3 Faisal Mahmuddin / Enegy Pocedia 5 (7 ) V dt 4 a' a a d (3) Whee a is the angula induction facto which can be witten as a ' (4) Whee is blade otation speed, and the angula speed... Blade Element Theoy In the blade element theoy, the elements ae consideed to have infinitesimal thickness. These stips ae aeodynamically independent and do not have intefeence between them. With those assumptions, the axial and thust foces can be witten as [5] df BCW d C cos C sin (5) a L D dt BCW d C sin C cos (6) a L D Whee B is numbe of blades, the inflow angle, W the esultant velocity, C the aifoil chod, and C L and C D the lift and dag coefficients, espectively..3. Blade Element Momentum (BEM) Theoy The main pinciple of the BEM method is to combine the equations fom momentum theoy and blade element theoy to obtain useful elations. Equating Eq. () with Eq. (5) and Eq. (3) with Eq. (6), the following elations can be obtained. 8 a( a) V BCW CLcosCDsin (7) 8 a'(a) V BCW CLsinCDcos Substituting W into Eq. (7) and eaanging them, the following elations can be witten [6] a C cos sin L C D (8) a 4 sin a' CLsin CDcos a' 4 sn i cos Whee σ is known as local solidity atio which can be witten as BC () Tip and Root Losses Losses will be expeienced by the blade at the tip and oot. The losses need to be also consideed. An appoximate method of estimating the tip losses effect has been given by L. Pandtl as follows [] (9)

4 6 Faisal Mahmuddin / Enegy Pocedia 5 ( 7 ) 3 9 F B R in cos exp s whee R is the maximum oto adius. By including the tip and oot losses effect, the elations shown in Eqs. (8) and (9) ae modified to be a CLcos CDsin () ( a) 4F sin a CLsin CDcos ( a) 4F sincos As can be seen in Eqs. () and (3), thee ae seveal unknown vaiables which need to be detemined which ae a, a, and. In ode to detemine these vaiables, equations above need to be solved simultaneously using a standad iteation method. Afte the axial and angula induction factos can be detemined, they ae used to compute the tubine thust foces and powe. 3. Roto Design Pocedue In ode to design a popelle oto using the blade element momentum (BEM) method descibed in the pevious subsection, seveal vaiable needs to be detemined in the beginning. These vaiables ae numbe of blades, blade adius, pitch and twist angles, oto otation, and wind speed. Using the input data, the following pocedue is pefomed Guess the axial and angula induction factos (a and a ) Detemine the wind inflow angle () Detemine the angle of attack () Detemine the value of C L and C D fom extapolated aifoil expeimental data Re-compute a and a Compae the new a and a with the ones obtained fom pevious iteation Continue iteation until conveged The value of a and a obtained afte the computations ae conveged, ae used to compute the total axial foce (thust) and powe of the tubine. 4. Computation Model The pesent study uses aifoil shape of 45 fo demonstating the computation pocedues and esults of the developed BEM. The same aifoil has been used by Mahmuddin [7] to study the effect of flat plate theoy assumption in extapolating lift and coefficients using Vitena method. The shape of the aifoil is shown in the following figue. NACA Paametes m=.c t=.5c p =.4c () (3) Figue. NACA45 aifoil shape [7]

5 Faisal Mahmuddin / Enegy Pocedia 5 (7 ) Using the aifoil shape shown in. Fig., the lift and dag coefficients of the aifoil is computed fom QBlade softwae. The computation esults ae shown in the following figue..5.5 Lift Coefficients (C L ) Dag Coefficients (C D ) (a) (deg) NACA45 Lift Coefficient (b) (deg) NACA45 Dag Coefficient Figue. NACA45 Lift and dag coefficients In ode to obtain the full 36 o lift and dag coefficients which ae needed in the BEM computation, the C L and C D shown in Fig. ae extapolated using Vitena method. Moe detail infomation about the method can be found in efeence [7]. The othe input data used in computation ae shown in the following table Table. Computation input data Paametes Unit Paametes Unit Numbe of Blade (B) 3 Chod (C).3 m Radius (R) 5.3 m Pitch angle () degee Root Extension (hub).5 m Twist angle degee Rotational Speed (N) 7.3 pm As shown in the Table, the computed blade has unifom chod length and no twisted angle (untapeed and untwisted blades). 5. Computational Results and Discussion A compute pogam based on the fomulation and pocedues descibed in the peceding section is developed. Using the input data shown in Table, the computation is pefomed. The computation esults in tems of axial and angula induction factos ae shown in the following figue

6 8 Faisal Mahmuddin / Enegy Pocedia 5 ( 7 ) 3 9 axial induction facto (a) V=4 m/s developed BEM V=8 m/s developed BEM V=8 m/s developed BEM V=4 m/s QBlade V=8 m/s QBlade V=8 m/s QBlade angula induction facto (a') V=4 m/s developed BEM V=8 m/s developed BEM V=8 m/s developed BEM V=4 m/s QBlade V=8 m/s QBlade V=8 m/s QBlade (a) Radial Position (m) Axial induction facto (b) Radial Position (m) Angula induction facto Figue 3. Axial and angula induction factos computed by the developed BEM and QBlade softwae In Fig. 3 above, the axial and angula induction factos ae shown fo vaying adial position. It can be obseved fom the figue that slight diffeences of the esults computed by developed BEM and QBlade can be noticed especially fo highe wind speed egion. The diffeences ae caused by the slight diffeences of lift and dag data extapolation method implementation in the developed BEM and QBlade softwae. The value of a and a shown in Fig. 3 ae used to compute the popelle blade powe. The computation esults ae shown in Fig. 4 below. 5 4 Powe (watt) 3 Developed BEM QBlade 5 5 Wind Speed (m/s) Figue 4. Compaison of popelle blade powe with tip and oot losses It can be noted fom the figue that thee is also a slight discepancy of esults especially aound high wind speed egion. The discepancy is the effect of slight diffeences of the a and a obtained peviously. Howeve, it could be summaized fom the figue that the oveall tendency and magnitude of the esults ae shown to be in a good ageement.

7 Faisal Mahmuddin / Enegy Pocedia 5 (7 ) Conclusion The pesent study developed a computational method based on (BEM) theoy. A popelle blade which uses NACA45 aifoil shape was chosen to demonstate the computation pocedues and esults. Tip and oot losses poposed by Pandtl wee also implemented. The developed BEM computation esults ae validated using the ones computed fom QBlade softwae whee they wee found to be in a good ageement. Acknowledgements This wok was suppoted by Unggulan Peguuan Tinggi (UPT) eseach gant fom Indonesian Diectoate Geneal of Highe Education and Hasanuddin Univesity, Makassa fo fiscal yea 6. Refeences [] Glauet H. Aiplane Popelles. In: Duand WF, edito. Aeodynamic Theoy, Belin: Julius Spinge; 935, p [] Snel H. Sectional Pediction of 3-D Effects fo Stalled Flow on Rotating Blades and Compaison with Measuements. Petten: Nethelands Enegy Reseach Foundation ECN; 993. [3] Henandez A, Cespo J. Aeodynamic calculation of the pefomance of hoizontal axis wind tubines and compaison with expeimental esults. Wind Eng 987;(4): [4] Maten D, Wendle J. QBlade Guidelines. Belin: Belin Technical Univesity; 3. [5] Moiaty PJ, Hansen AC. AeoDyn Theoy Manual. Coloado: National Renewable Enegy Laboatoy; 5. [6] Ceyhan O. Aeodynamic Design and Optimization of Hoizontal Axis Wind Tubines by Using BEM Theoy and Genetic Algoithm. Ankaa: Middle East Technical Univesity; 8. [7] Mahmuddin F. The Effect of Flat Plate Theoy Assumption in Post-Stall Lift and Dag Coefficients Extapolation with Vitena Method. J. Subsea Offshoe 6;6:9 3. Biogaphy Faisal Mahmuddin is a senio lectue and eseache at Maine Engineeing Depatment, Hasanuddin Univesity, Makassa Indonesia. His eseach topics ae Maine Hydodynamics and Renewable Enegy.