Application of computational fluid dynamics models to aerodynamic design and optimization of wind turbine airfoils

1 Applica ion o compu a ional luid dynamics models o ae odynamic design and op imiza ion o wind u bine ai oils E. Cas iñei a-Ma ínez, I. Solís-Gallego, J. González, J. Fe nández O o, K. A güelles Díaz and S. Vela de-Suá ez Á ea de Mecánica de Fluidos, Depa amen o de Ene gía Uni e sidad de O iedo Edi icio Depa amen al Es e, Campus Uni e si a io, 33203 Gijón, España (Spain) Phone: +0034 985 182101, e-mail: sa[email p o ec ed] Abs ac In his wo k, he capabili y o simple nume ical models wi h coa se g ids o p edic pe o mance coe icien s in wind u bine ai oils is explo ed. A wide ange o simula ions we e pe o med o a ypical wind u bine p o ile, unde he main c i e ia o design simplici y and low calcula ion ime. The solu ions we e compu ed o e di e en mesh sizes using a wo-dimensional Reynolds-A e age Na ie -S ockes (2D- RANS) app oach. Spala -Allma as, k-ε and k-  u bulence models we e un in he simula ions. Li , d ag and momen um coe icien s we e compu ed o ou inciden angles, anging om -2.5 o 12.5, o each mesh size and u bulence model, compa ing hem la e wi h expe imen al da a. Resul s show a use ul model which gi es a good ag eemen be ween nume ical and expe imen al esul s and can indeed be used as a i s app oxima ion p e ious o a mo e de ailed and expensi e s udy. Key wo ds Wind u bine ai oils, CFD, 2D-RANS nume ical models, u bulence models. 1. In oduc ion. The s a e o he a in he de elopmen o wind ene gy con e sion sys ems s ill poses some ques ions on he de ailed ae odynamic phenomena in ol ed in he low a ound he u bine blades, gene ally go e ned by qui e a iable low condi ions and a om he design ones. One o he pa icula e o s being ca ied ou is based on he use o Compu a ional Fluid Dynamics (CFD) echniques o handle he low s udy a ound he blade ai oils, e en in a design s age, p e ious o he blade cons uc ion. Fo such kind o app oach, i is essen ial a good selec ion o he main pa ame e s depending on he low condi ions such as he spa ial disc e iza ion o nume ical g id quali y, he u bulen closu e scheme, he nume ical unce ain y, he uns eady ea men , e c. Se e al wo-dimensional Reynolds-A e age Na ie -S ockes (2D-RANS) nume ical models ha e been employed in o de o p edic he ae odynamic pe o mance o wind u bine ai oils wi h sa is ac o y esul s. Fo ins ance, Yu e al. [1] ha e been applying his kind o me hodology o s udy he dynamic s all o an ai oil unde going sinusoidal pi ch oscilla ions, inding p omising esul s in p edic ing li , d a and momen um coe icien s. In he cases o eal blades a high angles o a ack, 2D simula ions a e known o o e p edic d ag, due o ip e ec s in he spanwise dis ibu ion o d ag. These e ec s appea o be mo e p onounced a high incidence angles and can be adequa ely p edic ed by a 3D-RANS model (So ensen e al. [2]). When a ull de ailed desc ip ion o he uns eady low is needed, such as he case o gene a ion and p opaga ion o ai oil noise, la ge eddy simula ion (LES) schemes mus be used (Fleig. e al. [3]), wi h he subsequen highe compu a ional cos s. In his wo k, he capabili y o simple nume ical models wi h coa se g ids o p edic li and d ag In e na ional Con e ence on Renewable Ene gies and Powe Quali y (ICREPQ’14) Co doba (Spain), 8 h o 10 h Ap il, 2014 Renewable Ene gy and Powe Quali y Jou nal (RE&PQJ) ISSN 2172-038 X, No.12, Ap il 2014 h ps://doi.o g/10.24084/ epqj12.342 370 RE&PQJ, Vol.1, No.12, Ap il 2014 2 in wind u bine ai oils is explo ed. The main goal is o de elop a simple and as me hod which could be employed in he design s age wi h a low compu a ional cos , in o de o selec he bes al e na i e be ween se e al op ions, and p e ious o mo e de ailed and e ined simula ions which will be needed in u he s ages o he ai oil de elopmen and cons uc ion. The s udy s a s wi h he CFD nume ical s udy o a ypical ai oil geome y used in wind u bines, in o de o de e mine he main c i e ia o choose he op imum model and nume ical pa ame e s, depending on he low condi ions. The s udy co e s he ollowing wo main aspec s: sensi i i y s udy o he de eloped compu a ional g id and e i ica ion o he be e u bulence model o cap u e he main physical phenomena. In o de o con as he ob ained nume ical esul s, he expe imen al public da abase o he Na ional Renewable Ene gy Labo a o y (NREL) a Golden, Colo ado, USA (Selig e al. [4]) has been conside ed. 2. Me hodology The esea ch begins wi h he nume ical s udy o a ypical ai oil geome y used in wind u bines. Fo all he cases p esen ed in his s udy, a FX 63-137 ai oil model was used. Simula ions we e un combining di e en pa ame e s, while some o hem ha e been main ained cons an such as he inciden eloci y, compu ed o a Reynolds numbe o 350,000 based on he ai oil cho d leng h. Th ee pa ame e s we e modi ied: he numbe o mesh cells, he inciden angle o he low and he u bulence model employed in he simula ion. Fo he sake o compa ison, he nume ical esul s achie ed we e alida ed wi h he expe imen al public da abase o he NREL (Na ional Renewable Ene gy Labo a o y) a Golden, Colo ado, USA (Seling e al. [4]). 2.1. Geome y and mesh gene a ion. GAMBIT meshing so wa e was used o geome y and mesh gene a ion. This so wa e is associa ed wi h Fluen , whe e la e simula ions we e made. Fou mesh densi ies we e c ea ed o a oid high skewed elemen s: a coa se mesh wi h 2,992 cells, a middle densi y mesh wi h 12,451 cells, a high-densi y mesh wi h 48,780 cells and one ex a mesh o he k- SST case wi h 111,105 cells. In he ollowing, a simple nomencla u e is used o e e he di e en meshes, named G1, G2, G3 and G4, espec i ely. The pu pose o he chosen shape is o c ea e a meshing ha is adap ed o he geome y om a simple and e ec i e way as shown in Fig.1. Howe e , o he ines meshes i was necessa y o make some changes in he geome y o he mesh o keep he s abili y in he simula ions. . Fig. 1. Simple scheme o he geome y o he mesh o coa se and middle mesh. In Fig. 2, a de ail o he middle densi y mesh is shown, allowing a be e app ecia ion o he ai oil and he geome y o he mesh a ound i . Fig. 2. De ail o middle mesh (G2). 2.2. Inciden angles. In his pape , ou di e en inciden angles we e conside ed o he simula ions: -2.5°, 2.5°, 7.5° and 12.5°, as ep esen a i e o nega i e, low, medium and high angles. These ha e been selec ed owing o i s dis ibu ion along he expe imen al cu e, enabling a wide ange o esul s, wi hou excessi ely inc easing he calcula ion ime, which is e y impo an in his s udy. h ps://doi.o g/10.24084/ epqj12.342 371 RE&PQJ, Vol.1, No.12, Ap il 2014 3 2.3 Tu bulence models. Simula ions we e ca ied ou o h ee di e en u bulence models: Spala -Allma as, k-ε and k- using he comme cial CFD code, ANSYS FLUENT. De aul cons an s p o ided by he p og am we e used o he k-ε and he Spala -Allma as models. In pa icula , he k-ε model employed he e is he ReNo maliza ion G oup (RNG), a a ian o he s anda d. Va ia ions in he wall unc ions ha e been also conduc ed, unning simula ions wi h S anda d Wall Func ions (SWF) and Enhanded Wall T ea men (EWT). Finally, ini ials pa ame e s (k and ) calcula ed as exposed by So ensen e al. [2] and using NREL expe imen al alues we e used o he k-  model. Fo his model, wo a ia ions we e conduc ed. Fi s ly, he simula ions we e un wi h he s anda d model and la e he k- SST model o Men e was used, included in his la e he op ion o ansien lows. I is wo h no ing ha a con e gence s anda d o 10-6 o he esidual pa ame e s was employed. A Semi Implici Me hod o P essu e Linked Equa ions (SIMPLE) algo i hm was applied o en o ce he p essu e- eloci y coupling o he h ee models and he spa ial de i a i es a e disc e ized using a second o de upwind app oach. In Table 1 he p essu e in e pola ion schemes employed a e summa ized. Table 1. P essu e in e pola ion schemes used o each mesh and model. 2.4 Es ima ion o e o s Dimensionless coe icien s ob ained nume ically a e compa ed o he expe imen al da a p o ided by he bibliog aphy, calcula ing he a e age e o o he whole ange o inciden angles conside ed. As only he simula ion o ou angles has been pe o med, he mos a ional p ocedu e o ob ain an es ima ion o he e o is o ob ain om he expe imen al dis ibu ion he exac alues o each o he simula ed angles h ough a polynomic equa ion o he endency line. A e wa ds, he global a e age e o is ound wi h equa ion [1] . ∑| | | | [1] whe e Rglobal is he a e age e o o a speci ic mesh size and u bulence model, N is he o al numbe o inciden angles o which his calcula ion is made, Ciexp is he app op ia e coe icien (li , d ag o momen um) ob ained o he expe imen al s udy and Cinum is he coe icien ob ained by nume ical simula ion. 3. Resul s and discussion 3.1 Spala -Allma as u bulence model. The g aphs shown in Fig. 3 co espond o his one-equa ion u bulence model. The e olu ion o he li coe icien p esen s a no able ag eemen wi h he expe imen al da a, e en in he case o coa se meshes. As can be seen, esul s wi h G2 appea o be he closes o he e e ence da a, while G3, supposed o be close o he e e ence alues, has a simila beha iou o G1. Tha could be because he hi d g id in ol es an excessi e amoun o nea wall cells o a Spala -Allma as u bulence model, as his model does no include any wall ea men . On he o he hand, an accu a e es ima ion o he d ag coe icen is mo e di icul o ob ain by nume ical simula ion, and esul ing alues a e usually o e p edic ed ega ding o expe imen al da a. O e all esul s appea o imp o e wi h he inc ease o numbe o cells. The momen um coe icien is in pe ec co espondence wi h he expe imen al cu e o low angles o a ack, de ia ing g adually wi h an inc easing o he angle o a ack. 3.2. k-ε u bulence model. Fo his model, he g aphs a e plo ed in Fig. 4. The li coe icien shows an accu a e p edic ion o he alues and he endencies, especially using medium and e ined g ids, epo ing he bes alues wi h high inciden angles wi h he S-A k-ε k- G1,G2 G3 G1,G2 G3 G1,G2, G3,G4 PRESTO! Second O de Second O de S anda d S anda d h ps://doi.o g/10.24084/ epqj12.342 372 RE&PQJ, Vol.1, No.12, Ap il 2014 4 enhanced wall ea men (EWT) model. Fo his u bulence model, he d ag coe icien alues a e excessi ely away om he expe imen al cu e in all ype o meshes and condi ions, hus poin ing ou ha his is no a good model o p edic he d ag coe icien . Fig. 3. Li , d ag and momen um coe icien s o Spala -Allma as model. Fo he momen um coe icien , a good accu a e p edic ion o he alues is shown, especially a low angles o a ack . Fig. 4. Li ,d ag and momen um coe icien s o k-ε model. 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 -5 0 5 10 15 CL coe icien Incidence Angle [] Exp Num(G1) Num(G2) Num(G3) 0 0,05 0,1 0,15 0,2 -5 0 5 10 15 CD coe icien Incidence Angle [] Exp Num(G1) Num(G2) Num(G3) -0,25 -0,2 -0,15 -0,1 -0,05 0 -5 0 5 10 15 Cm coe icien Incidence Angle [] Exp Num(G1) Num(G2) Num(G3) 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 -5 0 5 10 15 CL coe icien Incidence Angle [] Exp Num(G1) Num(G2) Num(G3) Num(G1)-EWT Num(G2)-EWT Num(G3)-EWT 0 0,05 0,1 0,15 0,2 -5 0 5 10 15 CD coe icien Incidence Angle [] Exp Num(G1) Num(G2) Num(G3) Num(G1)-EWT Num(G2)-EWT Num(G3)-EWT -0,25 -0,2 -0,15 -0,1 -0,05 0 -5 0 5 10 15 Cm coe icien Incidence Angle [] Exp Num(G1) Num(G2) Num(G3) Num(G1)-EWT Num(G2)-EWT Num(G3)-EWT h ps://doi.o g/10.24084/ epqj12.342 373 RE&PQJ, Vol.1, No.12, Ap il 2014 5 3.3. K-  u bulence model In his u bulence model only he SST e sion is shown, because i is he model which has p esen ed he bes esul s, excep o he middle mesh (G2), whe e he s anda d model had sligh ly be e esul s wi h espec o he d ag coe icien . The s anda d model has shown o ep oduce he expe imen al cu e wi h a good accu acy, excep o high angles o a ack in he ines meshes. Fig. 5. Li ,d ag and momen um coe icien s o he k- SST model. Looking a he li coe icien cha , shown in Fig. 5, i can be no iced ha in he mos e ined mesh exis s a la ge accu acy a high angles, al hough he coe icien is o e p edic ed o he lowes angles. In his case, he middle mesh (G2) is he one showing he bes ag eemen wi h he expe imen al da a. In he g aph o he d ag coe icien , o he ines meshes, he nume ical cu e p esen s he highes accu acy wi h espec o he expe imen al one o he en i e nume ical da abase. Finally, he momen um coe icien has an accu a e p edic ion o alues and endencies; qui e simila wi h he expe imen al cu e, especially o he ines meshing (G4). 3.4 A e age uni a y e o s. Summa y ables o a e age uni a y e o s o each u bulence model and o each mesh size a e p esen ed in his sec ion. The compu a ional ime o each simula ion is also shown. These esul s show ha e ined meshes and complex u bulence models a e no equi ed o he li coe icien . To ob ain an accu a e app oxima ion, jus a mesh wi h a ela i ely low numbe o cells (G2) and wi h a one-equa ion model as he Spala -Allma as can be used. Ne e heless, o he d ag coe icien , i is e y di icul o ob ain accu a e nume ical esul s conce ning expe imen al ones. A mo e complex u bulence model, such as k- SST, and high densi y meshes a e equi ed o achie e an accep able e o . Resul s o he momen um coe icien a e be e o k- s anda d model wi h a ela i ely e ined mesh (G3), al hough low e o s a e also ob ained o middle meshes and wi h a one equa ion u bulence model. Table 2. A e age uni a y e o s o he Spala - Allma as model. 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 -5 0 5 10 15 CL coe icien Incidence Angle [] Exp Num(G1)-SST Num(G2)-SST Num(G3)-SST Num(G4)-SST 0 0,05 0,1 0,15 0,2 -5 0 5 10 15 CD coe icien Incidence Angle [] Exp Num(G1)-SST Num(G2)-SST Num(G3)-SST Num(G4)-SST -0,25 -0,2 -0,15 -0,1 -0,05 0 -5 0 5 10 15 Cm coe icien Incidence Angle [] Exp Num(G1)-SST Num(G2)-SST Num(G3)-SST Num(G4)-SST Spala -Allma as Tes ed G ids Max. Compu a ion imes A e age uni a y e o s CL CD Cm G1 10 seconds 0.08 1.93 0.18 G2 2 minu es 0.03 0.73 0.10 G3 2 hou s 0.08 0.68 0.14 h ps://doi.o g/10.24084/ epqj12.342 374 RE&PQJ, Vol.1, No.12, Ap il 2014 6 Table 3. A e age uni a y e o s o he k-ε model wi h SWT. Table 4. A e age uni a y e o s o he k-ε model wi h EWT. Table 5. A e age uni a y e o s o he k- s anda d model. Table 6. A e age uni a y e o s o he k-Ω SST model. 4. Conclusions 2D-RANS nume ical models a e able o p edic global pe o mance o wind u bine ai oils wi h easonable accu acy and compu a ion imes o ew hou s (maximum) unning in a con en ional desk op pe sonal compu e . Li and momen um coe icien s a e accu a ely p edic ed wi h a simple one-equa ion Spala - Allma as u bulence model using medium meshes and compu a ional imes o a ew minu es, o all he incidence angles es ed. In hese condi ions, he nume ical esul s o d ag coe icien ep oduce he global endency o he expe imen al ones, bu uni a y e o s a e excessi ely high. D ag coe icien is accu a ely p edic ed o all he incidence angles es ed using he k- SST u bulence model wi h an adequa e e ined mesh, esul ing in compu a ional imes o some hou s. In hese condi ions, he esul s o li and momen um coe icien s a e also accu a e. Global endencies o li , d ag and momen um coe icien s a e well cap u ed wi h hese ela i ely simple models, hus allowing he compa ison o al e na i e ai oil geome ies in he design s age. Acknowledgemen This wo k has been suppo ed by P ojec “Ca ac e ización y p edicción de la gene ación ae odinámica de uido en pe iles de u binas eólicas”, DPI2011-25419. Minis e io de Economía y Compe i i idad, España. Re e ences [1] Yu, G.H.; Zhu, X.C.; Du, Z.H., 2010, "Nume ical simula ion o a wind u bine ai oil: dynamic s all and compa ison wi h expe imen s", P oceedings o he Ins i u ion o Mechanical Enginee s, Pa A: Jou nal o Powe and Ene gy, Vol. 224, 657-677. [2] So ensen, N.N.; Michelsen, J.A., 2004, "D ag P edic ion o Blades a High Angle o A ack Using CFD", Jou nal o Sola Ene gy Enginee ing, Vol. 126, 1011-1016. [3] Fleig, O.; Iida, M.; A akawa, C., 2004, "Wind Tu bine Blade Tip Flow and Noise P edic ion by La ge-eddy Simula ion", Jou nal o Sola Ene gy Enginee ing, Vol. 126, 1017- 1024. [4] Selig, M.S.; McG anahan, B.D., 2004, "Wind Tunnel Ae odynamic Tes s o Six Ai oils o Use on Small Wind Tu bines", NREL/SR-500-34515. K-ε S anda d Wall Func ion Tes ed G ids Max. Compu a ion imes A e age uni a y e o s CL CD Cm G1 10 seconds 0.19 3.92 0.16 G2 1.5 minu es 0.02 3.01 0.14 G3 2.5 hou s 0.03 3.28 0.15 K-ε Enhanced Wall T ea men Tes ed G ids Max. Compu a ion imes A e age uni a y e o s CL CD Cm G1 10 seconds 0.19 3.93 0.16 G2 1.5 minu es 0.03 3.07 0.12 G3 2.5 hou s 0.06 2.96 0.22 K- S anda d Tes ed G ids Max. Compu a ion imes A e age uni a y e o s CL CD Cm G1 45 seconds 0.22 2.50 0.17 G2 5 minu es 0.07 0.95 0.08 G3 2.5 hou s 0.09 0.53 0.07 G4 2.75 hou s 0.06 0.55 0.06 K- SST Tes ed G ids Max. Compu a ion imes A e age uni a y e o s CL CD Cm G1 45 seconds 0.23 2.27 0.15 G2 5 minu es 0.08 1.08 0.11 G3 2 hou s 0.12 0.27 0.16 G4 4 hou s 0.09 0.19 0.14 h ps://doi.o g/10.24084/ epqj12.342 375 RE&PQJ, Vol.1, No.12, Ap il 2014