Investigation of the aerodynamics of an innovative vertical-axis wind turbine

Transcription

1 Journal of Physics: Conference Series OPEN ACCESS Invesigaion of he aerodynamics of an innovaive verical-axis wind urbine o cie his aricle: K Kludzinska e al 014 J. Phys.: Conf. Ser iew he aricle online for updaes and enhancemens. Relaed conen - Numerical analysis of he flow around he Bach-ype Savonius wind urbine K Kacprzak and K Sobczak - D compuaions of flow field in a guide vane blading designed by means of D model for a low head hydraulic urbine Z Krzemianowski and R Puzyrewski - Comparison of wo LES codes for wind urbine wake sudies H Sarlak, F Pierella, R Mikkelsen e al. his conen was downloaded from IP address on 07/06/018 a 10:4

2 Invesigaion of he aerodynamics of an innovaive vericalaxis wind urbine K Kludzinska 1, K esch 1, and P Doerffer 1 Gdansk Universiy of echnology, ul. G.Naruowicza 11/1, 80-, Gdansk, Poland Insiue of Fluid Flow Machinery, ul. Fiszera 14, 80-1, Gdansk, Poland krzye@pg.gda.pl Absrac. his paper presens a preliminary hree dimensional analysis of he ransien aerodynamic phenomena occurring in he innovaive modificaion of classic Savonius wind urbine. An aemp o explain he increased efficiency of he innovaive design in comparison wih he radiional soluion is underaken. Several voriciy measures such as ensrophy, absolue heliciy and he inegral of he velociy gradien ensor second invarian are proposed in order o evaluae and compare designs. Discussed crieria are relaed o he vorex srucures and energy dissipaion. hese srucures are generaed by he roor and may affec he efficiency. here are also differen voriciy measure aking advanage of eigenvalues of he velociy gradien ensor. 1. Inroducion he objec of he analysis is he modernisaion of classic design of he urbine (i.e. he Savonius wind urbine), see figure 1. his innovaive design [1] is equipped wih a saor which experimenally shows increased efficiency in comparison wih sandard design. his is rue for wind unnel experimens a leas. Boh urbines have he simples design of all devices convering wind ino oher energy forms, which provides an opporuniy for decrease of is price. he original Savonius wind urbine has numerous advanages such as low noise, simpliciy of design, applicabiliy for a wide range of wind velociies. he bigges problem of he classic design is is relaively low efficiency. he innovaive design, discussed here, is devoid of his disadvanage. Wind urbine research, such as Savonius urbine and is modificaions, are in line wih he general sraegy of developmen of he Polish power indusry. his sraegy ends o quaniaive increase he use of renewable energy sources. One of he limis, as far as he wind energy is concerned, i is high price of wind urbines available. he obained resuls may increase he knowledge of he flow round a whole family of differen ypes of roors whose principle of operaion is based primarily on he use of wind hrus accompanied wih a small share of lif forces. he knowledge gained during he simulaions will enable more effecive designs characerised by increased efficiency and operaional reliabiliy. he flow inside he roor is complicaed and ha is why in pas invesigaions were limied only o laboraory ess [,, 4]. Anoher experimenal mehod was flow visualisaion [5, 6], which allows capuring flow paerns characerisics for seleced insananeous posiions of roor blades wih respec o whom any correspondence should be addressed. Conen from his work may be used under he erms of he Creaive Commons Aribuion.0 licence. Any furher disribuion of his work mus mainain aribuion o he auhor(s) and he ile of he work, journal ciaion and DOI. Published under licence by Ld 1

3 o he wind direcion. Recenly, due o he rapid developmen of compuer hardware and sofware, aemps were made o analyse he srucure of he flow hrough he Savonius roor numerically [7, 8]. his also includes he vorex mehod [9, 10]. Generally, all daa presened on he numerical aspec are mosly wo-dimensional. Also, papers on aemps o modify he shape of he Savonius roor are available [, 11]. he bes shapes of blade ips for a given roor geomery and physical condiions are invesigaed in [1, 1, 14]. Figure 1. Classic (lef) and innovaive (righ) designs.. Mehodology All he numerical calculaions were performed using he commercial CFD code CFX. he urbulen flow of air was reaed as an incompressible medium. he urbulence was modelled by means of he sandard wo-equaion urbulence model k ε. he reason for his choice may be explained by a need of comparison wih oher calculaions found elsewhere. he for his kind of calculaions. he average form of mass conservaion equaion has he form he Reynolds equaion is where he effecive pressure molecular componens p e = d U ρ d k ε model has now become a sandard U = 0. (1) = ρg p e + ( μ D ) e = p + ρ k and he effecive viscosiy is composed of eddy and e μ μ + μ. wo addiional ranspor equaions are hose for modelled kineic energy of velociy flucuaion k which arises from Reynolds sress ranspor equaion d ρ d k 1 k ( μ σ k) ρε = μ D + () and dissipaion of kineic energy of flucuaion ε. his is analogous o k ranspor ( μ σ ε ) ρc ε dε ρ = C1εk μ D + k. (4) d ()

4 he eddy viscosiy is defined as μ = C ρk ε. he five consans in he above equaions should be deduced from experimen for a specific geomery. his sandard se is given by σ 1, σ 1, C = 0.09, C = 1. 44, C = he flow domain was divided ino wo pars: he roaing roor and he seady wind unnel and ambien. Boh pars were merged by means of he domain inerface of he so called ransien roorsaor ype. he ime sep of he ransien calculaions corresponded o wo degree of revoluion and he angular velociy of he roaing domain (roor) corresponded o hree urns per second. he boundary condiions seleced here are: Inle. he mass flow rae was specified here. he specified mass flow rae corresponds o he 1 average velociy 6 m s. he urbulence inensiy defined as τ = U ( k ) 1/ equals k = 5% and he viscosiy raio μ μ = 10. his represens a medium urbulen inensiy. Opening. he so called far field condiion was chosen equal wih prescribed consan amospheric pressure. Symmery. his means han he velociy normal componen equals zero n ˆ U = 0 and all he scalar values ϕ mus fulfil n ˆ ϕ = 0 where nˆ represens a uni vecor normal o he surface. Wall. he flow domain was a wind unnel wih one side open o he amosphere. As for he roor blades and he shroud hey were modelled as no slip wall in he roaing frame of reference.. Coefficiens Among many characerisics of he wind urbines he mos imporan is he orque coefficien. I is commonly defined as C =. (5) 1 ρ U D H 4 he above definiion is valid for boh he seady-sae and ransien flows. For he laer case one should use he ime dependen orque () insead of meaning ha in real case we deal wih he disribuion of C as a funcion of he angular posiion of he roor. he orque coefficien (5) is direcly relaed o he efficiency of he roor. A ypical definiion of he efficiency for he seady-sae case akes under consideraion he wind power N w = m ek = ρ U S U and he power of he roor N = M ω. he wind power is reaed here as he reference power. From he wo above definiions we arrive a he following definiion of he efficiency ω ω DC η s = =. (6) U U ρ HD In he above definiion ω is he angular velociy, ρ represens he densiy, and U - he reference velociy. D is he diameer of he roor, and H is he roor s heigh. he seady-sae efficiency is frequenly referred o as he power coefficien C P. For he ransien case, which is ypical for he Savonius roor operaion, one should consider he oal energy of he wind wihin he ime inerval raher han he insananeous power. his means ha he definiion (6) akes he following form now =

5 + Δ ω D C ( ) d ω DC η = = U Δ U where Δ sands for he ime of ineres (e.g. one urn). Assuming ha he ime sep Δ τ of he ransien CFD calculaions is consan we can approximae he inegral in equaion (7) in he following way +Δ n 1 C ( ) d n Δτ C,i = Δ C (8) n i= 1 where C represens he arihmeical average C = n i = C 1, i and he ime of ineres Δ (e.g. one revoluion) is expressed as Δ = n Δτ. he oal number of ime seps is denoed here as n. he las definiion (7) has an analogical form as he definiion (6). 4. Evaluaion and comparison crieria hese crieria allow for direc evaluaion and comparison of various designs and soluions. As an example of he exising crierion one can recall ensrophy E [15] 1 Ε = d = Ω d = ε d, (9) 1 where ε : = Ω may be again reaed as a specific ensrophy. Here sands for asymmerical par of he velociy gradien ensor U and Ω is he voriciy vecor. he definiion of ensrophy plays imporan role in heory of urbulence. I deermines he rae of dissipaion of kineic energy being a global measure of he dissipaion rae and voriciy measure. One can imagine even simpler voriciy measure e = d = Ω d. (10) Anoher voriciy measure is defined by means of he inegral of he velociy gradien ensor second invarian Q in he following form Q = r U d = r D ε d, (11) n ( ) ( ) where D sands for symmerical par of he velociy gradien ensor. he above definiion is relaed o ensrophy defined in equaion (9) Q = (7) r D d E. (1) he so called heliciy may be reaed as a measure of linkage of vorex lines in he flow. he global heliciy is defined as H = U Ω d. (1) 4

6 ypically, i is beer o ake advanage of absolue heliciy H H = U Ω o avoid cancelling upon inegraion over considered volume. An alernaive definiion of voriciy measure was given by ruesdell ε W = d. (15) r D his measure is combined from wo invarians and equals zero for irroaional flow Ω = 0 and D 0. he measure equals infiniy for roaional flow Ω 0 and D = 0. he former has he larges possible voriciy measure. Discussed crieria are relaed o he vorex srucures and energy dissipaion. hese srucures are generaed by he roor and may affec he efficiency. here are also differen voriciy measure aking advanage of eigenvalues of he velociy gradien ensor. 5. Mesh he boh flow domains, i.e. he roor and he wind unnel, were discreised separaely. Boh domains have an unsrucured grid consising of mosly erahedral elemens. he oal number of elemens covering he flow area is abou 15 million. here are also special elemens around he blades o ensure ha flow near a wall is properly resolved. he wall funcion approach was used o provide near wall boundary condiions for he mean flow. he qualiy of he grid near he blades may be inspeced in + + erms of y disribuion. he average value of y on blades is no greaer han 1 for all he ime seps. d (14) Figure. Flow domain. Figure. Mesh cross secion. Figure presens global view on he compuaional domain consiss of wind unnel and cylindrical par of far field surroundings. he mesh can be inspeced in figure. his figure presens a cross secion which is perpendicular o he roor axis. 6. Resuls of calculaions Figure 4 presens he orque coefficien C disribuion as a funcion of revoluion angle. hese are resuls of ransien calculaions. I has o be poined ou ha mos of he available daa is obained from 5

7 seady-sae calculaions for wo dimensions. he presen calculaions are fully ransien and hreedimensional. he mos visible difference beween presen innovaive design and lieraure daa [,, 16, 6] is ha here are four peaks visible insead of wo. his is because he device consiss of wo roors roaed by an angle relaive o each oher. Addiionally, here is a saor direcing he flow. Figure 4. orque coefficien disribuion C. Figure 5. oriciy measure e disribuion. Figure 5 shows disribuion of voriciy measure e defined by means of equaion (10) ha can be used o compare various designs indicaing he imporance of his equaion. he ime inegral of his measure can be used direcly o evaluae specific urbine. Furhermore, one can anicipae a relaionship beween voriciy measure and efficiency of a urbine. I can be expeced ha he performance of a wind urbine is affeced by vorices generaed during he roor revoluions. hese vorices are complicaed in heir naure and dynamically change heir configuraions and undoubedly inensiies. his may affec pressure disribuion around he blades and accordingly he performance of a roor. Figure 6. Efficiency comparison η. 6

8 From he definiion (7) i may be deduced ha he higher he orque coefficien he more efficien he roor. he calculaed ransien efficiency (7) for he innovaive design is η = 7.%. his value may be easily validaed by means of daa available in he lieraure [17] where expeced performance of he convenional Savonius roor for λ = 0. 4 is esimaed o be 17 %. he roor ip speed raio λ is defined as ω D λ =. (16) U Figure 6 shows he measured efficiency in he wind unnel for he innovaive design (solid line). Black do shows he numerical predicion of he ransien efficiency whereas he red do represens lieraure daa [17] for he classic Savonius design. Even for low wind speed 6 m s he innovaive design if far more efficien. Figure 7. arious voriciy measure disribuion. Figure 7 presens comparison of wo example voriciy measure disribuion. hese are also called vorex cores. In he middle we have r( U ) disribuion which is a par of he inegral of he velociy gradien ensor second invarian Q (equaion (11)). On he righ i is local absolue heliciy U Ω being par of global absolue heliciy H (equaion (14)). 7. Conclusions he innovaive modificaion of classic Savonius shows higher efficiency. his is rue for wind unnel experimens a leas. he increased efficiency is due o presence of he saor which direcs he air and makes i possible o ake beer advanage of is energy. I is believed ha vorex srucures are generaed by he roor and affec he efficiency. Several voriciy measure have been proposed allowing for evaluaion and comparison of various designs. 8. References [1] Doerffer P, Inernaional paen applicaion PC/PL01/00015 and Naional Paen Applicaion P.9705 Akywny wiarak o osi poprzecznej do kierunku wiaru [] Blackwell B F, Sheldahl R E and Felz L 1977 Wind unnel performance daa for wo- and hree-bucke Savonius roor Sandia Laboraories Repor SAND , 105 7

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