Boundary layer and mesh refinement effects on aerodynamic performances of horizontal axis wind turbine (HAWT)

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1 Bondary layer and mesh refnement effects on aerodynamc performances of horzontal axs wnd trbne (HAWT) YOUNES EL KHCHINE, MOHAMMED SRITI Engneerng Scences Laboratory, Polydscplnary Faclty Sd Mohamed Ben Abdellah Unversty (pt Tmes New Roman, centered) BP 3 Road of Oda, Taza MOROCCO yones.elkhchne@smba.ac.ma Abstract: - The desgn of rotor blades has a great effect on the aerodynamcs performances of horzontal axs wnd trbne and ts effcency. Ths work present the effects of mesh refnement and bondary layer on aerodynamcs performances of wnd trbne S809 rotor. Frthermore, the smlaton of fld flow s taken for S809 arfol wnd trbne blade sng ANSYS/FLUENT software. The problem s solved by the conservaton of mass and momentm eqatons for nsteady and ncompressble flow sng advanced SST k-ω trblence model, n order to predct the effects of mesh refnement and bondary layer on aerodynamcs performances. Lft and drag coeffcents are the most mportant parameters n stdyng the wnd trbne performance, these coeffcents are calclated for for meshes refnement and dfferent angles of attacks wth Reynolds nmber s 0 6. The stdy s appled to a S809 blade arfol % thck, specally desgned by NREL for horzontal axs wnd trbnes. Key-Words: - Aerodynamc performances, S809 arfol, CFD Smlaton, SST k-ω trblence model, Bondary layer. Introdcton The comptatonal fld dynamcs (CFD) approach s the most approprate method to nvestgate the mechancal power of wnd trbne, ths approach provdes a best descrpton of flow arond wnd trbne rotor, and gves a detaled descrpton of trblence phenomenon. Wth the ncreasng comptng capacty, the CFD approach s becomng a practcal tool to model and smlate the aerodynamc performances of wnd trbne n threedmensonal. Althogh many stdes have been pblshed on the sbect of horzontal-axs wnd trbne blades CFD smlaton, whch are the effects of mesh refnement and adaptve grds on the aerodynamc performances over NACA 00 arfol [,]. Ths smlaton based on the Reynolds Averaged Naver- Stokes eqatons sng fnte volme method wth a range of meshes. The roghness effects on aerodynamc characterstcs of a wnd trbne arfol. s performed by nmercal smlaton of the trblent flow arond arfol wth a resolton the Reynolds Averaged Naver-Stokes eqatons (RANS) wth k-ε trblence model sng qadrlateral strctred mesh [3]. The mesh s very fne near of arfol srface to satsfy the trblence model condtons and n order to predct the natre of flows, pressre and velocty gradent arond arfol srface. The smlaton was made for a rogh and smooth profle to nvestgate the effects of the roghness characterstcs of arfol. The near wall grd spacng nvestgatons for the SST k-ω trblence model was stded for aerodynamc behavor of horzontal axs wnd trbne [4]. Eght dfferent cases were nvestgated for the near wall grd spacng and all cases whch the total nmber of nodes s fewer than An expermental stdy was performed of aerodynamc performances nvestgaton of a NACA 45 arfol by varyng attack angles at low Reynolds nmber. Ths stdy showed that as the angle of attack ncreased, the separaton and the transton ponts moved towards the leadng edge at all Reynolds nmber. Frthermore, as the Reynolds nmber ncreased, stall characterstc changed and the mld stall occrred at hgher Reynolds nmbers whereas the abrpt stall occrred at lower Reynolds nmbers [5]. Three models for predctng flow transton mplemented n a D crvlnear, aerodynamc Naver Stokes CFD code. These are Mchels ISSN: Volme, 07

2 emprcal model, the en model, and a newly proposed transton model (K V model) [6]. The effect of the transton models on the arfol aerodynamc characterstcs at dfferent Reynolds nmber and ncdence angle are stded nmercally. Both these parameters, when ncreased, promote the growth of flow pertrbatons. The test case s a D ncompressble, low trblence ar flow arond a smooth NACA00 arfol. The effects of trblence models on aerodynamc performances of the S809 and NACA 00 arfols developed by NREL were stded [7-0]. The flow modelled sng nsteady ncompressble Reynolds Averaged Naver-Stokes eqatons sng dfferent trblence models to close the RANS eqatons wth adaptve mesh refnement. The fld flow smlated at dfferent attack angles. Lft and drag coeffcents calclated at each angle of attack. The performance of dfferent trblence models compared, and the reslts show that the best reslts gven by SST k-ω of Menter trblence model. A new stdy of D nmercal smlaton of the steady low-speed flow for S-seres wnd-trbneblade profles, sng Comptatonal Fld Dynamcs (CFD) method based on the fnte-volme approach []. The flow s governed by the Reynolds- Averaged-Naver-Stokes (RANS) eqatons. The man obectve s to extract the lft and drag forces at each secton of arfol, and to determnate the slde raton (L/D) for each blade profle and at dfferent wnd speed. The optmm angle of attack for each blade profle s determned at the dfferent wnd 0 p f speeds, the nmercal reslts are benchmarked aganst wnd tnnel measrements. In ths work, an extended analyss to perform D smlaton of S809 wnd trbne rotor s presented and dscssed. The S809 arfol s sed n the trbne, whch has % thckness wth a sharp tralng edged and s desgned specfcally for HAWT and tested arfol n hgh qalty wnd tnnels and the arfol aerodynamc data are avalable n lteratre. The two-dmensonal smlaton of bondary layer and mesh refnement effects s performed. Dfferent strctred mesh sze s stded by applyng dfferent nmber of nodes at the normal and tangental drectons arond the S809 arfol. In all cases of smlatons, the problem was descrbed by the Reynolds Averaged Naver- Stokes eqatons combned wth SST k-ω trblence model of Menter [] n order to enclose the bondary layer. Lft, drag and power are the most mportant parameters n stdyng the wnd trbne performance. These coeffcents are calclated for dfferent meshes sze and angles of attack. The smlaton gve the accrate reslts compared wth those presented by wnd tnnel experments of Delft Unversty of Technology (DUT). Mathematcal Formlaton The wnd flows arond the arfol descrbed by solvng the Naver-Stokes eqatons for nsteady and ncompressble flow, the governng eqatons can be wrtten as: () () Where s the velocty, p s the pressre, t s the tme, and are the drectonal components, ρ s the fld densty, υ s the knematc vscosty and f are the external body forces. Fg.. Geometrc parameters of arfol secton ISSN: Volme, 07

3 For the D, nsteady and ncompressble flow, the contnty eqaton for secton of arfol as shown n Fg. s obtaned by: v 0 (3) y v p v v ( ) y y v v v p v v v ( ) y y To accont the trblence effects, the nstantaneos Naver-Stokes eqatons are averaged, ths later s based on statstcal approach appled on varables flow and decomposes velocty nto an average and a flctaton components p ( v ) ( ) ( y y Momentm eqatons for vscos flow over arfol secton n x and y drectons as shown n Fg. are, respectvely: (4) (5) and respectvely. The methodology appled s to solve the Reynolds Averaged Naver-Stokes eqatons RANS n two-dmensonal for nsteadystate ncompressble flow. The method of Reynolds s to decompose each physcal varable n an average vale and a flctatng vale: v v v and p p p Replacng the Reynolds decomposton n the contnty and momentm eqatons, we obtaned the Reynolds Averaged Naver-Stokes eqatons (RANS) whch are gven n Eqs. (6) and (7): v ) y (6) v v v p v v v v ( v ) ( ) ( y y y v Wth s the trblent shear stress The closre of the governng eqatons s based prmarly on modellng flctatng terms traned by addtonal varables and v. Therefore, we sed the SST k-ω trblence model proposed by Menter [] n 993, ths model sed near the wall bt swtches to a k-ε model away from the wall. It s obtaned from a combnaton of k- and k- models. Ths last, the most sed; s a model for two eqatons, t provdes the trblent length scale n k k k P k ( k ) P ( k Where P, k ) ( F ) v ) y (7) the near-wall regon. By aganst the k-, based on the Wlcox model [3], s very senstve to free stream vales otsde the shear layer. Several stdes and applcatons have shown ts effcency n case of hgh flow pressre gradents. It s a two eqatons model; one for the trblent knetc energy k and other for the rate of trblent dsspaton energy ω. The orgnal eqatons of SST k-ω model are gven by Eqs. (8) and (9): k (9) k F = nsde the bondary layer and 0 n the free stream. and Table. Constants for SST k-ω trblence model k (8) The constants appeared n above eqatons are gven n Table below: β β β σ k σ k σ ω σ ω γ γ k ISSN: Volme, 07

4 3 Mesh topology The CFD approach s sed to predct the aerodynamc performances of horzontal axs wnd trbne for S809 arfol. It provdes a good precson to nvestgate effects of the mesh refnement and the bondary layer on the obtaned reslts. Generally, a nmercal solton becomes more precse wth mesh refnement, bt sng the addtonal grds also ncreases the reqred memory and comptng tme. The approprate nmber of grds can be ncreased ntl the mesh s sffcently fne so that frther refnement does not change the reslts. The mesh qalty and the doman sze n the CFD calclaton drectly nflence on the comptaton accracy and the convergence tme. A good mesh shold be large enogh to avod bondary effects, there are many types of meshes n CFD smlaton the flow arond arfol wnd trbne. The most poplar mesh topology s the C- type mesh, whch s desgned to have a C-type topology arond the arfol. The dmensons of comptatonal doman mst be sffcent to predct the trblence phenomenon, pressre and velocty dstrbton, then the doman sze mst be stded accrately. Doman sze as shown n Fg. s generated sng ANSYS/WORKBENCH, the arfol s located n the centre of a comptatonal doman that extends to a dstance of 6 tmes the chord length, n all drectons from the arfol aerodynamc centre, except at the wake, the arfol s located of tmes chord length to correctly reprodce the wake effect. Fg. 3. Strctred mesh area The D mesh s a strctred C-type generated. The mesh contans 8386 grds wth 300 grds arond the arfol srface, 50 grds normal to arfol srface and 50 grds extendng from tralng edge. The refnement s very condensed near the arfol srface n order to enclose the bondary layer approach, a large nmber of grds arond the arfol srface are sed to captre the pressre gradent accrately. Fg.. Geometry and dmensons of comptatonal Doman The doman dscretzaton was made sng a strctred qadrlateral mesh, as llstrated n Fg. 3. Fg. 4. Mesh arond tralng edge In the near-arfol regon, a stable resolton of the mesh n the orthogonal drecton to the sold walls s conventonally recommended to compte the bondary layer arfol (y + ). In ths work, we sed the advanced SST k-ω trblence model of Menter, t need a very fne mesh near the wall wth y + vales essentally lower than one as shown n Fg. 4 reqred by k-ω trblence model. In order to satsfy the SST k-ω trblence model lmtatons mst be y + < was obtaned and defned by Eq. (0). y y (0) ISSN: Volme, 07

5 Where y s the dstance of the frst grd pont from the rotor, s the frcton velocty. It s possble to get a frst attempt vale of y by mposng y + < n Eq. () y y () By sbstttng y + = n Eq. () gves y= m. Where p 4 Bondary condtons The bondary condtons have a sgnfcant nflence on the reslts of smlaton. In the present work, the velocty components at the nflow bondary are calclated based on the desred Reynolds nmber and chord length, the pressre s restrcted to the zero-gradent condton. The velocty components along x and y drectons are calclated as follow: V x V cos and V y V sn Where α s angle of attack The free stream velocty V =4.6 m.s - based on Reynolds nmber eqals to 0 6. No-Slp bondary condtons are appled along the arfol srface, and at the otflow bondary, the ambent atmospherc pressre condton s appled and the velocty s set to the zero-gradent condton. The nlet trblence ntensty s set to the level of.84%, the free stream temperatre s 88.5 K, whch s same as the envronmental temperatre and hydralc dameter D h s eqal to the chord length m. FLUENT solver ses a fnte volme method to solve the Reynolds Averaged Naver- Stokes eqatons. Frthermore, pressre based solver COUPLED was sed as the pressrevelocty coplng algorthm, and the dscretzaton of trblence model eqatons k-ω was made sng the dagram second order pwnd. For obtaned heght precsons, the convergence crterons for the absolte resdals of eqaton varables are set below 0-5. All these parameters gven n Table are sed n FLUENT. Table. Flent parameters Trblence model k-ω SST Fld Densty (ρ).5 Dynamc vscosty (µ) Trblence Intensty.84% Inlet velocty V 4.6 Atmospherc pressre (P atm) 035 Chord length (c) Dscretzaton scheme Reynolds nmber 0 6 CFD algorthm 5 Reslts and dscssons A grd ndependency stdy s performed by refnng the mesh arond the arfol srface and ncreasng Ar, ncompressble, nsteady Pressre (second order pwnd) Momentm (second order pwnd) Copled the nmber of grds n the streamwse and normal drectons represented by geometrc parameters m, p and q gven by Table 3. Table 3. Lft and drag coeffcents for for meshes refnement Mesh nmber Mesh m, p, q parameters sze m=50, p=75, q=50 Nmber grds 676 of y + 93 ISSN: Volme, 07

6 Mesh Mesh 3 Mesh 4 m=00, q=00 m=00, q=50 m=00, q=300 p=00, p=50, p=00, The lft and drag coeffcents presented n Fgs. 5 and 6 are calclated for dfferent meshes sze at each angle of attack 0, 6.6, 8.,,.3 and 4.3. Lft coeffcent Cl Fg. 5. Lft coeffcent for dfferent meshes sze as a fncton of angle of attack for R e=0 6 Drag coeffcent Cd angle of attack [ ] Mesh Mesh Mesh3 Mesh4 Exp-DUT Mesh Mesh Mesh3 Mesh4 Exp-DUT Angle of attack [ ] Fg. 6. Drag coeffcent for for meshes sze as a fncton of angle of attack for R e=0 6 Fgres 5 and 6 shows the effect of nmber grds on lft and drag coeffcents at dfferent angles of attack. Ths stdy has revealed that the meshes 3 and 4 have the same reslts at stall angle and are n good agreement wth the expermental data. To ths pont the reslts becomes ndependent wth the nmber grds. Therefore, we choose the mesh 3, whch gves best reslts wth a mnmm calclaton tme. Table 4 presents the lft coeffcent and dmensonless wall y + vales for dfferent meshes szes. Table 4. Dmensonless wall y + and lft coeffcent C l dstrbton verss nmber of grd at angle of attack 6.6 Nmber of y grds + C l Mesh Mesh Mesh Mesh Table 4 shows that the lft coeffcent obtaned by the meshes 3 and 4 s greater than those obtaned by the meshes and becase the mesh refnement arond the arfol srface s very fne and have the vales of y + are less than one and converge to 0, whch makes to solve the problem of bondary layer. We conclded that the reslts obtaned by the SST k- ω trblence model are very senstve to the resolton of the bondary layer. Usng SST k-ω trblence model, the vale of y + mst be less than for the frst grd mesh arond arfol srface (y 0=.50-5 m), y 0 s the dstance between arfol srface and mddle of frst grd. 6 Conclsons The flow analyss arond a wnd trbne arfol has been carred ot sng the nsteady ncompressble Reynolds Averaged Naver-Stokes eqatons. For stdyng bondary layer and mesh refnement, for meshes are compared. The lft and drag coeffcents are calclated for each angle of attack. The calclaton showed that the mesh refnement n area bondary layer has a sgnfcant effect on the reslts qalty, n partclar the lft and drag coeffcents, whch have drect conseqences on the aerodynamc performance of S809 arfol. ISSN: Volme, 07

7 The Cl/Cd rato ncrease wth ncreasng the angle of attack p to 6.5, after that decrease, ths angle called optmal angle of attack. References [] Swanson, R.C. ; Langer, S, Steady-state lamnar flow soltons for NACA 00 arfol, Compters and Flds, 6, 06, 0-8 [] Zho, L.; Ynn, Y.; Anlong, G. and Weang, Z, Unstrctred adaptve grd refnement for flow featre captre, 04 Asa-Pacfc Internatonal Symposm on Aerospace Technology, 99, 05, [3] Bekht, A.; Gerr, O, Inflence de la rgosté sr les caractérstqes aérodynamqes d n profl de pale déolenne, Reve des Energes Renovelables, 5(), 0, [4] Moshfegh, M.; Song, Y.J. and Xe, Y.H, Effects of near-wall grd spacng on SST k-ω model sng NREL Phase VI horzontal axs wnd trbne, Jornal of Wnd Engneerng and Indstral Aerodynamcs, 07-08, 0, [5] Genç, M.S.; Karas, I. and Açıkel, H.H, An expermental stdy on aerodynamcs of NACA45 aerofol at low Re nmbers, Expermental Thermal and Fld Scence, 39, 0, 5 64 [6] Kapsals, P.C.S.; Votsnas, S. and Vlachos, N.S, Comparng the effect of three transton models on the CFD predctons of a NACA00 arfol aerodynamcs, Jornal of Wnd Engneerng and Indstral Aerodynamcs, 57, 06, [7] Gerr, O.; Bohadef, K. and Harhad, A, Trblent Flow Smlaton of the NREL S809 Arfol, Wnd engneerng, 30(4), 006, [8] Elen, D.C.; Athanasos, T.I. and Donssos, M.P, Evalaton of the trblence models for the smlaton of the flow over a Natonal Advsory Commttee for Aeronatcs (NACA) 00 arfol, Jornal of Mechancal Engneerng Research, 4, 0, 00- [9] Ba, C.J.; Hsao, F.B.; L, M.H.; Hang, G.Y. and Chen, Y.G., Desgn of 0 kw Horzontal- Axs Wnd Trbne (HAWT) Blade and Aerodynamc Investgaton Usng Nmercal Smlaton, 7th Asan-Pacfc Conference on Aerospace Technology and Scence, 67, 03, [0] S ong, Y.; Perot, J.B, CFD Smlaton of the NREL Phase VI Rotor, Wnd engneerng, 39(3), 05, [] S ayed, M.A.; Kandl, H.A. and A. Shaltot, Aerodynamc analyss of dfferent wnd-trbneblade profles sng fnte-volme method, Energy Converson and Management, 64, 0, [] M enter, F.R, Two-Eqaton Eddy-Vscosty Trblence Models for Engneerng Applcatons, AIAA Jornal, 3 (8), 994, [3] W lcox, D.C, Formlaton of the k-omega Trblence Model Revsted, AIAA Jornal, 46 (), 008, ISSN: Volme, 07