Performance and Wake Comparison of Horizontal and Vertical Axis Wind Turbines under Varying Surface Roughness Conditions

This is a e sion o a publica ion in Please ci e he publica ion as ollows: DOI: Copy igh o he o iginal publica ion: This is a pa allel published e sion o an o iginal publica ion. This e sion can di e om he o iginal published a icle. published by Pe o mance and Wake Compa ison o Ho izon al and Ve ical Axis Wind Tu bines unde Va ying Su ace Roughness Condi ions Mendoza Vic o , Chaudha i Ash inkuma , Goude Ande s Mendoza, V., Chaudha i, A., Goude, A. (2018). Pe o mance and Wake Compa ison o Ho izon al and Ve ical Axis Wind Tu bines unde Va ying Su ace Roughness Condi ions. Wind Ene gy. Pp. 1-15. DOI: doi.o g/10.1002/we.2299 Final d a Wiley Wind Ene gy doi.o g/10.1002/we.2299 © Wiley 2018 This is he pee e iewed e sion o he ollowing a icle (ci ed abo e) which has been published in inal o m a h ps://doi.o g/10.1002/we.2288. This a icle may be used o non-comme cial pu poses in acco dance wi h Wiley Te ms and Condi ions o Use o Sel -A chi ed Ve sions. Pe o mance and Wake Compa ison o Ho izon al and Ve ical Axis Wind Tu bines unde Va ying Su ace Roughness Condi ions VICTOR MENDOZA * Depa men o Enginee ing Sciences, Di ision o Elec ici y, Uppsala Uni e si y, Uppsala 751 21, Sweden ic o [email p o ec ed] ASHVINKUMAR CHAUDHARI CEID, School o Enginee ing Science, Lappeen an a Uni e si y o Technology, P.O. Box 20, 53851 Lappeen an a, Finland ANDERS GOUDE Depa men o Enginee ing Sciences, Di ision o Elec ici y, Uppsala Uni e si y, Uppsala 751 21, Sweden Abs ac A nume ical s udy o bo h a ho izon al axis wind u bine (HAWT) and a e ical axis wind u bine (VAWT) wi h simila size and powe a ing is p esen ed. These la ge scale u bines ha e been es ed when ope a ing s and-alone a hei op imal ip speed a io (TSR) wi hin a neu ally s a i ied ABL. The impac o h ee di e en su ace oughness leng hs on he u bine pe o mance is s udied o he bo h u bines. The u bines pe o mance, he esponse o he a ia ion in he su ace oughness o e ain and he mos ele an phenomena in ol ed on he esul ing wake we e in es iga ed. The main goal was o e alua e he di e ences and simila i ies o hese wo di e en ypes o u bine when hey ope a e unde he same a mosphe ic low condi ions. An ac ua o line model (ALM) was used oge he wi h he la ge eddy simula ion (LES) app oach o p edic ing wake e ec s, and i was implemen ed using he open-sou ce CFD lib a y Open-FOAM o sol e he go e ning equa ions and o compu e he esul ing low ields. This model was i s alida ed using wind unnel measu emen s o powe coe icien s and wake o in e ac ing HAWTs, and hen employed o s udy he wake s uc u e o bo h ull scale u bines. A p elimina y s udy es compa ing he o ces on a VAWT blades agains measu emen s was also in es iga ed. These ob ained esul s showed a be e pe o mance and sho e wake ( as e eco e y) o a HAWTcompa ed o a VAWT o he same a mosphe ic condi ions. Keywo ds: A mosphe ic Bounda y Laye (ABL), Ve ical Axis Wind Tu bines (VAWTs), Ho i- zon al Axis Wind Tu bines (HAWTs), Ac ua o Line Model (ALM), Dynamic S all Model (DSM), La ge Eddy Simula ion (LES) *Co esponding au ho 1 1 In oduc ion The majo i y o he cu en ly deployed wind u bines a e ho izon al axis wind u bines (HAWTs). A enewed in e es has been b ough o e ical axis wine u bines (VAWTs) o o sho e a ays, since hey ha e se e al ad an ages o e he con en ional HAWTs, and hei implemen a ion can po en ially mi iga e he new challenges he o sho e en i onmen p esen s [ 1 , 2 , 3 ]. The omni-di ec ionali y allows hem o ope a e wi h he incoming low om any di ec ion, u he simpli ying he mechanical design, since he e is no need o a yawning mechanism (and o en he pi ching sys em). This cha ac e is ic is conside ably app ecia ed in o sho e en i onmen s whe e ope a ion and main enance a e ele an i ems con ibu ing in he o al ene gy p oduc ion cos . Ano he ad an age o VAWTs is he a ailabili y o place he gene a o a he sea le el, educing he complexi y in ol ed in he ins alla ion and main enance. This imp o es he s abili y o he o e all s uc u e and educes he size and cos o he base, and mo eo e , i minimizes he conce ns ela ed o he dimensions and weigh o he gene a o allowing he ins alla ion o hea y di ec d i e gene a o s wi h pe manen magne s [ 4 ]. On he o he hand, VAWTs ha e a much lowe powe coe icien s and su e om ib a ion p oblems complica ing hei indus ial models p oduc ion. Howe e , his s udy is limi ed o a he ae odynamic issues (powe pe o mance, wake de elopmen and eco e y, e c.) and no o ope a ional ac o s. I is well known ha he gene al s uc u e o a u bine wake is di ec ly ela ed o he in low cha ac e is ics, u bulence p oduced by he u bine, and ope a ional condi ions (blade pi ch, yaw condi ion, ip speed a io [TSR], e c). Conside ing bo h HAWT and VAWT s and-alone u bines, he common p o ile o eloci y de ici is cha ac e ized by a Gaussian-like dis ibu ion (besides in he nea wake) wi h a peak close o he egion whe e he hub is loca ed [ 5 , 6 ]. The nea wake is whe e he main con ibu ion o i s s uc u e comes di ec ly om he u bine, while he a wake is cha ac e ized by (dissipa i e) u bulen s uc u es, he eco e y p ocess, and a Gaussian p o ile o eloci y. The u bulence in ensi y le el in he incoming low con ibu es conside ably o a as e wake eco e y as i has been epo ed in expe imen al [ 7 , 8 , 9 , 10 , 11 ] and nume ical s udies [ 5 , 12 , 13 , 14 ]. In a quali a i e s udy [ 15 ] o e he pe o mance o a la ge wind a m, his e ec showed ha he downwind u bines dec eased conside ably he powe de ici because o an inc easing o he u bulence in ensi y wi hin he incoming low, highligh ing he impo an ole o he a mosphe ic u bulence in he o al powe ou pu . The e a e se e al well known s udies in which he pe o mance and wake cha ac e is ics o HAWTs [ 5 , 16 ] and VAWTs [ 6 , 17 , 18 , 19 ] we e in es iga ed; howe e , hese wo ks ha e been ca ied ou sepa a ely o each ype o u bine. Thus, a di ec compa ison in e ms o ae odynamic pe o mance be ween he wo u bine ypes is pe haps di icul . The p esen ed s udy p o ides esul s o bo h u bines unde he same a mosphe ic low condi ions, wi h he aim o e alua ing he di e ences and simila i ies o hese wo de ices. Tes ing he bo h u bines wi h hei bes ope a ing TSR condi ions as well as unde he same a mosphe ic low condi ions p o ided a ai compa ison in e ms o he ae odynamic pe o mance, esponse o he a mosphe ic u bulence a ia ion, and he esul ing low pa e n. Fo his pu pose, an ac ua o line model (ALM) has been implemen ed using he open-sou ce compu a ional luid dynamics (CFD) oolbox lib a y OpenFOAM [ 20 , 21 ] o sol e he go e ning equa ions and o compu e he esul ing wake. Bo h an HAWT and a VAWT unde a neu ally s a i ied a mosphe ic bounda y laye (ABL) condi ion (i.e., no in luence o e ical empe a u e p o ile) we e es ed o a ying su ace oughness condi ions. These la ge scale u bines ha e simila size and powe a ing, ope a ing a hei op imal TSR. The HAWT employed is a well-documen ed la ge scale u bine NREL-5MW [ 22 ] and he VAWT is a p opo ionally scaled e sion o a 12-kW s aigh -bladed u bine [ 23 , 24 ] wi h almos he same o o p ojec ed a ea as he HAWT. 2 The model is i s alida ed using he wind unnel measu emen s o he powe coe icien s and eloci y low ield (wake) o wo in e ac ing HAWTs [ 25 ]. Addi ionally, he no mal o ces on one blade o a VAWT ope a ing in an open si e ha e been ep oduced and compa ed wi h expe imen al da a [ 23 , 24 ]. The employed model is cha ac e ized by s abili y and accu acy, which makes i a po en ial ool in he design o la ge scale wind u bines. 2 Me hodology An ALM coupled o a dynamic s all model (DSM) has been employed o sol e he blade o ce equa ions and model he u bine ope a ions. The ALM samples he local eloci y om he low sol e and hen i calcula es he angle o a ack and ela i e eloci y o each blade elemen , while he DSM calcula es he uns eady li and d ag o ces, which he ALM impa back as body o ces in o he low sol e . The p esen wo k is ocused on e alua ing he u bines ae odynamic pe o mance and he wake modeling pa . To do his, he lib a y u binesFoam de eloped by Bachan e al. [ 26 , 27 , 28 ] has been used as implemen a ion o he ALM. To o e come he ep esen a ion o a p ope inle bounda y condi ion, he so-called ecycling echnique was used o gene a e he in low u bulence o he low. A de ailed desc ip ion o he ALM and DSM used in he p esen s udy can be ound in [ 27 ] and [ 29 ], espec i ely, since only a b ie explana ion o he ALM is gi en u he in his sec ion. 2.1 Ac ua o Line Model Based on he classical blade elemen heo y, he ALM has been de eloped by Sø ensen and Shen [ 30 ], and i is a h ee-dimensional and ae odynamic uns eady model used o s udy he esul ing low a ound (and wi hin) wind u bines. This echnique di ides he blade in o n -elemen s ha ha e a wo-dimensional ai oil beha io on which (no mal and angen ial) o ces a e de e mined using a DSM commonly based on empi ical da a. The implemen a ion o he ALM equi es he alues o he li and d ag coe icien s o he di e en angles o a ack and Reynolds numbe s locally in ol ed. The geome ical ela ion be ween he angen ial speed o he blade Vblade =Ω , whe e Ω is he angula eloci y and is he adius o he elemen , and he incoming low Vin (which usually is smalle in magni ude han he ee-s eam eloci y V∞ ) is used o he calcula ion o he ela i e low V el and he angle o a ack α, V el =Vin −Vblade (1) The angle o ela i e wind ϕ is ep esen ed by he sum o he angle o a ack α and he blade pi ch angle γ . Figu e 1shows an illus a ion o he eloci ies and ac ing o ces on he c oss-sec ional ai oil elemen o bo h HAWTs and VAWTs. The in low eloci y conside ed in each elemen is he a e aged eloci y alue o a numbe o samples a ound he elemen , which a e symme ically dis ibu ed. Once α and V el a e ob ained (wi h he spanwise componen emo ed om he la e ), he li and d ag o ces pe spanwise leng h uni can be calcula ed as L=1 2ρc CL|V el|2(2) 3 D=1 2ρc CD|V el|2(3) whe e CL and CD a e he li and d ag coe icien s, espec i ely, which a e dependen on α and he local Reynolds numbe . The li componen is pe pendicula o V el and he blade span componen , while he d ag has he same componen as V el. The cho d leng h is ep esen ed by cand he densi y by ρ. The same me hod is employed o ob ain he o ces on he owe s, nacelle ( o HAWTs) and s u s ( o VAWTs). Once all he o ces in he lines o elemen s a e calcula ed, hese a e added as a sou ce o body o ce pe uni o densi y in o he momen um conse a ion equa ion 5. The elemen s a e mo ing in space, o e e y ime-s ep wi hin he ixed olume (domain), as hey a e in a u bine. 2.2 The La ge Eddy Simula ion amewo k In o de o use he LES app oach he o iginal Na ie -S okes equa ions ha e been il e ed, and based on he incomp essible low case a e exp essed as ∂˜ ui ∂xi =0(4) ∂˜ ui ∂ +∂˜ ui˜ uj ∂xj =−1 ρ ∂˜ p ∂xi +ν∂2˜ ui ∂xj∂xj − i ρ−∂τij ∂xj (5) wi h ˜ ui and ˜ p ep esen ing he g id- il e ed eloci y and p essu e alues, espec i ely, ν he kinema ic iscosi y, i he ac ing body o ces (blades) and τij he sub-g id scale (SGS) s ess de ined as τij = g uiuj−˜ ui˜ uj. In o de o pa ame e ize he de ia o ic pa o he SGS s ees, he Smago insky model [ 31 ] was employed as τij −1 3δijτkk =−2(CSe ∆)2|e S|(6) wi h e Sij =1 2∂e ui ∂xj+∂e uj ∂xi ep esen ing he esol ed a e-o -s ain enso , e ∆ is he g id size and CS= 0.1667 as he Smago insky cons an (usually i has a alue be ween 0.1 and 0.2). 2.2.1 The ecycling me hod o simula ing he a mosphe ic bounda y laye (ABL) In LES modelling, he co ec ep oduc ion o ansien in low condi ion is c ucial o a p ope modelling o ABL in e ac ion o wind u bines. P e iously, in many LES s udies dealing wi h ABL modelling (e.g. [ 32 , 33 ]), a sepa a e p ecu so LES calcula ion o ABL low o e a homogeneous e ain has been used o gene a e ansien in low bounda y condi ions. Howe e , his me hod is e y ime consuming as i equi es he en i e simula ion o be pe o med in wo di e en s ages: (1) p ecu so simula ion o ABL low o e a ho izon ally-homogeneous la su ace (i.e. wi hou u bine) o p oduce and s o e he ins an aneous ield da a om each ime-s ep, and (2) o u ilize his ime-dependen da a o he main simula ion (i.e., ABL wi h u bine). In his s udy, he so-called ecycling in low me hod is employed o gene a ing he ully de eloped ABL low p o iles be o e he u bines. Chaudha i e al. [ 34 , 35 , 36 ] ha e s udied he applicabili ies o he ecycling in low me hod o ABL low modelling o e complex e ains, and u he hey ha e shown 4 he alida ion o he me hod agains ield measu emen s. A mo e de ailed desc ip ion o he ecycling me hod can be ound in [34,35,36], and only a b ie explana ion is gi en u he in his sec ion. Using he ecycling app oach, he p ecu so simula ion is combined wi h he main simula ion, as shown in Figu e 2. Du ing he simula ion, he low a iables, mainly eloci y, empe a u e, SGS u bulen kine ic ene gy, e c., a e sampled on a c osswind plane (i.e. ecycling plane in Figu e 2), which is su icien ly downs eam om he in low plane. The sampled da a is hen ecycled back o he in low plane. This p ocess is epea ed o each ime s ep, c ea ing a ecycling sec ion be ween he in low and ecycling planes, in which he low becomes ully de eloped g adually. The me hod is e y sensi i e o he ecycling leng h L and he dis ance be ween he in low and ecycling planes. A e es ing a ious ecycling leng hs, Chaudha i e al. [ 34 , 36 ] sugges ed ha he ecycling leng h L should be a leas 3δ (i.e. L ≥3δ ), whe e δ is he ABL heigh and i is ixed o be δ=5D (since he domain should be high enough o a oid any low dis u bances due o u bine wake [ 37 , 38 ]). This es ic ion is needed o a oid any a i icial u bulence s uc u es wi hin he ecycling sec ion due o oo sho ecycling leng h. In addi ion o ecycling he da a, he me hod also uses he ixed eloci y lux h ough he in low plane (bounda y) in o de o main ain he same amoun o olume low a e h oughou he en i e simula ion. The main ad an age o he me hod is ha p ecu so simula ion is a oided, and he en i e simula ion is pe o med a once on a single compu a ional domain as shown in Figu e 2. The ully de eloped ABL p o iles ob ained using he ecycling me hod a e compa ed wi h he loga i hmic p o ile and a e p esen ed in Figu e 11 in Sec ion 3.2. 2.2.2 Wall- unc ion modeling The su ace bounda y condi ion is also one o he challenges in LES modelling. In o de o a oid massi e compu a ional esou ces equi ed due o he ine mesh esolu ions nea he su ace, he use o he wall- unc ion app oach has become s anda d in LES modeling o ABL lows (e.g. [ 16 , 5 , 34 , 35 , 36 ]). In addi ion, he su ace oughness pa ame e s (heigh o leng h) o a ough su ace a e o en implemen ed ia a wall- unc ion model. In his wo k, a wall unc ion model based on he well-known loga i hmic law o a ough su ace, implemen ed in OpenFOAM by Chaudha i e al. [34,36], is used on he lowe su ace. The loga i hmic law o he wall o e ough su ace is gi en by Vx=Vx∗ κln z+z0 z0(7) whe e z0 is he g ound oughness leng h, κ=0.41 is he on-Ká mán cons an , and Vx∗ is he ins an a- neous ic ional eloci y. Mo e in o ma ion on he implemen a ion o his wall- unc ion can be ound in [34,36,39]. 3 Resul s and Discussion In his sec ion, esul s om he alida ion es s and he s udy o he in luence o a ying su ace oughness condi ions a e p esen ed. Fo he alida ion cases, simila i ies and disc epancies be ween nume ical and expe imen al alues a e discussed. 5 3.1 Nume ical model alida ion Two di e en expe imen al s udies ha e been chosen o alida e he employed nume ical model. The i s case is ocused on he p ope ep esen a ion o he eloci y ield (wake s uc u e) and he pe o mance (powe coe icien s) o wo in e ac ing HAWTs wi hin a wind unnel, while he second one simula es he no mal o ces ac ing on he blades o a 12 kW VAWT, loca ed in an open si e. 3.1.1 Two in-line wind u bines wi h spanwise o se The es case chosen o he powe coe icien ( CP ) and wake alida ion is based on he expe imen epo ed by K ogs ad e al. in [ 25 ]. This wo k has been ca ied ou in a wind unnel acili y and consis s in wo HAWTs, which a e sepa a ed by a dis ance o 3D in he s eamwise di ec ion and a ound 0.415D ( 0.4 m) in he c osswind di ec ion. The downs eam o o has a diame e o D2=0.894 m ( u he deno ed as D in his sec ion) wi h a s epped owe consis ing o ou cylinde s o di e en diame e s while he ups eam u bine has a sligh ly la ge diame e o D1=0.944 m wi h and a owe wi h cons an diame e . The a angemen o he expe imen is such ha he p ojec ion o he a ea om he upwind o o co e s hal o he downwind u bine. The measu emen s o he s eamwise eloci y componen we e done in wo spanwise lines, loca ed 1D and 3D behind he downwind u bine a he heigh o he axis. Figu es 3and 4show mo e de ails abou he wind unnel and he dimensions o he es con igu a ion. In his wo k, wo di e en le els o u bulence ha e been es ed. Fi s , a u bulence in ensi y le el o TI=0.23% in he loca ion o he upwind u bine o o , which co esponds o he measu emen s when he wind unnel is emp y and i is he ea e e e ed o as Case A. Then, in o de o conside he e ec s o a mosphe ic u bulence, a la ge g id was used in he en ance o he chambe (shown in Figu e 3) p oducing a highe le el o u bulence in ensi y measu ed o TI=10% , his is e e ed as Case B. The syn he ic u bulence gene a o u bulen Inle , om he s anda d lib a y o OpenFOAM, is employed o in oduce he di e en le els o u bulence a he inle o he s udied domain. The ABL p o ile is no conside ed o he wind unnel expe imen s, because he dimensions o he expe imen al chambe we e no la ge enough o ully de elop ABL condi ions (see Figu e 4). The employed li and d ag coe icien s in o he ALM a e aken (digi ized) om he wo k o Cakmakcioglu e al. [ 40 ], and hey co espond o he Reynolds numbe equi alen o Re=105 . The upwind and downwind u bine a e u he deno ed as T1 and T2 , espec i ely. The domain has been disc e ized using a mesh opology wi h a uni o m hexahed al dis ibu ion o cells in e e y di ec ion, conside ing a g id esolu ion o 16.8/D cells in he whole domain and a local e inemen o 68/D cells in he egion a ound he o o and behind he u bines in o de o cap u e he de ails o he esul ing wake. This mesh con igu a ion has been chosen based on he c i e ia p esen ed in [ 41 ] (as well o he meshes in subsequen sec ions). The DSM has no been used o hese cases. The speci ica ions o he es ed u bines and expe imen s a e lis ed in Table 1. Powe and h us coe icien cu es Powe coe icien s o he bo h u bines a e e alua ed o e a wide ange o TSRs, bu in he case o he downwind u bine, i s pe o mance has been ob ained while he upwind u bine is ope a ing a i s op imal TSR o design λ1=Ω1R1/V∞=6 , whe e Ω1 ep esen s he angula speed o he upwind u bine o o . The e e ence eloci y conside ed o calcula ions is V∞=10 m/s. The powe and h us 6 coe icien s o he u bines a e de ined as CP=P 1 2AρV3 ∞ (8) and CT=T 1 2AρV2 ∞ (9) wi h P as he a e age powe and T as he a e age h us o he o o ob ained o e one e olu ion. Expe imen al and nume ical esul s o he u bines pe o mance o cases A and B a e depic ed in Figu e 5. Fo he case A, wi h low u bulence le els, i is obse ed ha he e is a good ag eemen in he iden i ica ion o he egion whe e he u bines ope a e a he maximum powe coe icien (op imal λ ), and in gene al, wi h he end o he cu es. The nume ical accu acy has o be highligh ed o he powe coe icien p edic ion in he upwind u bine o λ1≥5 , unlike o he lowe TSRs, whe e disc epancies occu when ep oducing he cu e in he s all condi ion wi h a maximum e o o 28%. The nume ical esul s o he downwind u bine show conco dance wi h he lowe TSRs, while he e is an o e es ima ion o he CP alues o λ2>4 . The in e ac ion o he wake wi h he downwind u bine is also cap u ed and he powe cu e o T2 is cha ac e ized by lowe alues han he cu e o he upwind u bine due o he educ ion in he a ailable kine ic ene gy. The expe imen al h us coe icien da a, which was expec ed o demons a e inc eased CT alues wi h inc easing TSR, was e y simila o bo h u bines, e ealing ha almos he same physical o ces a e applied on he o o s, while di e ing a ailable kine ic ene gy. The upwind u bine has a conside ably good ag eemen wi h he expe imen al alues, while he nume ical h us coe icien cu e o he downwind u bine shows an unde es ima ion o all he es ed TSRs, wi h a maximum e o a ound o 12%. Fo he es case B, wi h high le els o u bulence on he ees eam low, again he e is a good iden i ica ion o he egion whe e he u bines achie e he highes powe coe icien s. A be e nume ical ep esen a ion o he powe cu e is made o λ1>4 o he upwind u bine, and o he downwind u bine, his occu s a λ2≤5 , wi h a maximum e o o 21%. Wi h espec o he h us coe icien s alues, he e is an o e es ima ion in he upwind u bine a λ2≥4 and an unde es ima ion o he downwind one o all he s udied TSRs wi h a maximum e o a ound o 20%. Wake The downwind u bine has been es ed a h ee di e en TSRs, while he upwind u bine is ope a ing a i s op imal TSR λ1=6 , in o de o s udy he esul ing eloci y ield o in e ac ing wakes. The h ee es ed TSR condi ions co espond o pa ially s all, op imal TSR and high TSR wi h λ2=3.5, 4.75 and 8.0 , espec i ely. These condi ions co e om he s all egime o he o o almos wo king as a p opelle . As men ioned ea lie , he s eamwise eloci y componen has been measu ed in a ho izon al line in he c osswind di ec ion a he hub heigh a dis ances x/D=1 and x/D=3 behind he downwind u bine (see Figu e 4), which allows us o iden i y he gene al s uc u e o esul ing low om he in e ac ing wakes. These esul s o he no malized s eamwise eloci y de ici p o iles o all he es ed cases and TSRs a e displayed in Figu e 6, whe e he adius has been used o no malize he spanwise posi ion. 7 In bo h cases, o he sec ion x/D=1 behind he second o o , he nume ical and expe imen al esul s ag ee in he ep esen a ion o he wake geome y and size, as well as he asymme ic beha io . Small disc epancies in some de ails o he eloci y p o ile a e e ealed wi h a maximum e o o 25% o pa icula egions. Th ee di e en egions can be iden i ied in he eloci y p o ile; in −1.5 <y/ < −0.5 whe e he esul ing low comes mainly om he upwind u bine, a −0.5 <y/ <0.5 bo h u bines gi e a con ibu ion o he wake, and 0.5 <y/ <1.5 whe e only he e ec s o he second o o a e p esen . A pa icula condi ion is obse ed o he highes TSR (λ2=8.0) , since he e is a ele an low obs uc ion ( eloci y de ici ) close o he blade ips due o he high o a ional speed o he blades, and in he o he hand, a he oo loca ion he opposi e e ec is no iced. Rega ding he wake a x/D=3 , a change is obse ed om an i egula shape o he eloci y p o ile a x/D=1 o a smoo hly one, speci ically a Gaussian wake de ici p o ile. The e o e, in his sec ion he wake eco e y p ocess al eady s a ed and he di ec con ibu ion om he o o s in o he low is dissipa ed by he u bulen s uc u es. In gene al, he e is also a good ag eemen in nume ical and expe imen al alues in he egions ou side he wake. The e ec s o he added u bulence (Case B) a e no signi ican in he nea wake gene al s uc u e (a x/D=1 ). Mo eo e a his loca ion, i is no iced ha o bo h cases A and B he eloci y p o iles do no di e conside ably, mo e e iden changes a e p esen a he a wake sec ion. The au ho s belie e ha disc epancies be ween nume ical and expe imen al alues mainly can be caused by: • The simpli ied implemen a ion o he u bulence inle gene a o is no ealis ic since i adds andom noise o he speci ied inle mean eloci y om a de ined u bulence le el • Mo e de ailed inpu da a o CL and CD o a wide ange o he Reynolds numbe s is needed. Cu en ly, only da a o Re =105 has been conside ed which can no be app op ia e o all he di e si y o s udied cases, since he employed ALM is highly sensi i e o he inpu coe icien s o a co ec blade o ce p ojec ion • Po en ial imp o emen s o he nume ical simula ions can be achie ed in he ou e wake zones wi h he ully esol ed wall bounda y laye , which was no applied in his wo k 3.1.2 ABL low h ough a 12 kW s aigh -bladed VAWT in an open si e A 3-bladed 12 kW VAWT loca ed in he No h o Uppsala (Sweden) has been chosen o alida e he model unde he in luence o he ABL. The u bine has h ee o o blades p ojec ed om a NACA0021 ai oil p o ile wi h a cho d o 0.25 m and 6.48 m o diame e , he blade leng h is 5 m. This u bine is placed a an open si e and i is su ounded by mild ege a ion which is mos ly composed by g ass and small bushes. The no mal o ces on one blade and i s s u s we e measu ed using ou load cells. The expe imen al ac i i y and esul s as well as mo e de ailed speci ica ions o he de ice a e a ailable in [ 23 ] and [ 24 ]. These o ces ha e been used as he alida ion pa ame e s o a TSR o λ=3.44 (close o he op imal one). Addi ionally, ob ained esul s o he same VAWT unde he in luence o a wind shea (only a cons an mean wind p o ile wi hou u bulence) a e also shown o a compa ison analysis. Fo his s udy, he ope a ing condi ions o he u bine a e such ha he ees eam eloci y a he blade equa o ial plane ( z=5.75 m) is V∞=6.4 m/s. A oughness leng h o z0=0.025 m is conside ed o ep esen ing he place whe e he u bine is loca ed. The li and d ag coe icien s o he ALM a e aken om he epo o Sheldahl and Klimas [ 42 ]. The speci ica ions o he modeled u bine a e lis ed in Table 2. The employed disc e iza ion mesh has a hexahed al cell dis ibu ion o e 8 [47] J. Go schall and J. Peinke, “How o imp o e he es ima ion o powe cu es o wind u bines,” En i onmen al Resea ch Le e s, ol. 3, no. 1, p. 015005, 2008. [48] E. Mölle s öm, F. O e mo, A. Goude, S. E iksson, J. Hylande , and H. Be nho , “Tu bulence in luence on wind ene gy ex ac ion o a medium size e ical axis wind u bine,” Wind Ene gy, ol. 19, no. 11, pp. 1963–1973, 2016. [49] P. K ogs ad and L. Sæ an, “In i a ion o he 2013 blind es 3 wo kshop wo in-line wind u bines wi h spanwise o se ,” Depa men o Ene gy and P ocess Enginee ing, NTNU, T ondheim, No way, 2013. 15 Table 1: Nominal pa ame e s o he es ed u bines and expe imen s. Tu bines Expe imen al cases T1T2A B Numbe o blades 3 V∞[m/s] 10 Diame e [m] 0.944 0.894 TI[%] 0.23 10 Hub heigh [m] 0.817 Blade p o ile NREL S826 Cho d leng h [m] a iable Table 2: Nominal pa ame e s o he modeled 12kW VAWT. Numbe o blades 3 Diame e [m] 6.48 Hub heigh [m] 6 Blade p o ile NACA0021 Cho d leng h [m] 0.25 V∞[m/s] 6.4 TSR 3.44 Table 3: Ae odynamic pe o mance o he es ed u bines o he di e en e ains. Tu bine z0[m] CPP[MW] CTT[MW] VAWT 0.0005 0.346 1.579 0.688 0.402 0.025 0.321 1.500 0.702 0.410 0.1 0.338 1.546 0.673 0.393 HAWT 0.0005 0.558 2.003 0.870 0.399 0.025 0.556 1.997 0.860 0.394 0.1 0.496 1.780 0.761 0.348 16 Figu e 1: Illus a ion o eloci y ec o s and o ces ac ing a he c oss-sec ion ai oil elemen o a HAWT (le ) and a VAWT ( igh ) and a schema ic wi h he lines o elemen s. No e: Fo HAWTs, ˆ θ deno es he angen ial di ec ion o he blade while θis he azimu hal angle o VAWTs Figu e 2: Schema ic iews o he domain and ele an dimensions o he applica ion o he ecycling me hod: pe spec i e (le ), side (uppe igh ) and op (lowe igh ). 17 Figu e 3: Model in he wind unnel [49]: pe spec i e (le ) and om downwind ( igh ) iews. Figu e 4: Schema ic iew o he wind unnel domain: om he uppe pa ( op) and pe spec i e (bo om). The i s wo pe pendicula sec ions (in black) ep esen he o o planes o he u bines, while he wo sec ions a e he u bines (in ed) ep esen he plane whe e he measu emen s we e done, speci ically in a c osswind line a he o o heigh . 18 0.0 0.1 0.2 0.3 0.4 0.5 CP 0 2 4 6 8 10 λ 0.00 0.25 0.50 0.75 CT T1 Expe imen al T2 Expe imen al T1 ALM T2 ALM 0.0 0.1 0.2 0.3 0.4 0.5 CP 0 2 4 6 8 10 λ 0.00 0.25 0.50 0.75 CT T1 Expe imen al T2 Expe imen al T1 ALM T2 ALM Figu e 5: Powe coe icien and h us coe icien o he case A wi h low u bulence le el (le ) and he case B wi h high u bulence le el ( igh ). −2 −1 0 1 2 λ2= 3.5 y/ x/D = 1, Case A Expe imen al ALM x/D = 3, Case A Expe imen al ALM x/D = 1, Case B x/D = 3, Case B −2 −1 0 1 2 λ2= 4.75 y/ 0.0 0.4 0.8 1.2 Ux/V∞ −2 −1 0 1 2 λ2= 8.0 y/ 0.0 0.4 0.8 1.2 Ux/V∞ 0.0 0.4 0.8 1.2 Ux/V∞ 0.0 0.4 0.8 1.2 Ux/V∞ Figu e 6: No malized mean s eamwise eloci y p o iles along a c osswind (ho izon al) line h ough he o o cen e . 19 Figu e 7: No malized ins an aneous s eamwise eloci y a he e ical middle plane: ABL ( op) and wind shea (bo om). 0 45 90 135 180 225 270 315 360 Azimu hal deg ee [◦] −400 −300 −200 −100 0 100 200 300 400 FN[N] Expe imen al ABL Wind shea Figu e 8: The no mal o ce esponse unde he in luence o he ABL and a wind shea . Figu e 9: Illus a ion o he main cha ac e is ic dimensions o he es ed u bines. 20 0 2 4 6 8 10 12 λ 0.0 0.1 0.2 0.3 0.4 0.5 CP HAWT VAWT Figu e 10: CPas uncion o λ o bo h a VAWT and a HAWT in ull scale. Figu e 11: Ve ical p o ile o he mean s eamwise eloci y o he in low condi ions. 21 Figu e 12: No malized ins an aneous s eamwise eloci y in he e ical plane a he cen e o he u bine o di e en e ains. 22 Figu e 13: No malized mean s eamwise eloci y in he e ical plane a he cen e o he u bine o di e en e ains. 23 Figu e 14: No malized s eamwise eloci y a di e en ep esen a i e sec ions pe pendicula o he low o di e en e ains wi h z0=0.0005 m ( op), 0.025 m (cen e ) and 0.1 m (bo om). 24