Double Multiple Stream Tube Model and Numerical Analysis of Vertical Axis Wind Turbine

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1 Energy nd Power Engineering, 011, 3, 6-70 doi:10.436/epe Published Online July 011 ( Double Multiple Strem Tube Model nd Numericl Anlysis of erticl Axis Wind Turbine Abstrct Hbtmu Beri, Yingxue Yo Deprtment of Mnufcturing nd Automtion, Hrbin Institute of Technology, Hrbin, Chin E-mil: Received April 18, 011; revised My, 011; ccepted My 11, 011 The present pper contributes to the modeling of unstedy flow nlysis of verticl xis wind turbine (AWT). Double multiple strem tube (DSMT) model ws pplied for the performnce prediction of stright blded fixed pitch AWT using NACA0018 irfoil t low wind speed. A moving mesh technique ws used to investigte two-dimensionl unstedy flow round the sme AWT model with NACA0018 irfoil modified to be flexible t 15 from the min blde xis of the turbine t the triling edge locted bout 70% of the blde chord length using fluent solving Reynolds verge Nvier-strokes eqution. The results obtined from DMST model nd the simultion results were then compred. The result shows tht the CFD simultion with irfoil modified hs shown better performnce t low tip speed rtios for the modeled turbine. Keywords: Wind Turbine, Actutor Disk, Momentum Model, Strem Tube, AWT, CFD 1. Introduction Over the pst decde the wind energy conversion to electric power hs experienced significnt progress in the world. This ws mde possible by considerble engineering reserch nd development of wind mchines with emphsis on the erodynmic, structurl, nd systems chrcteristics. The Drrieus rotor AWT offers mechniclly nd structurlly simple method of hrnessing the energy of the wind. Although first ptented in 1931 it hs been intensively developed only since 1970, primrily by the Ntionl Reserch Council of Cnd, Sndi Ntionl Lbortories, nd by others in Europe [1]. In recent yers n incresing demnd in decentrlized power plnts is observed renewing the interest in erticl Axis Wind Turbines (AWT). The AWT offers severl dvntges when compred to the more conventionl Horizontl-Axis (HAWT) mchines. The AWT is inherently Omni-directionl nd hence obvites the need to provide ywing mechnism for keeping the mchine turned into the wind. The trnsmission nd electricl genertion equipment cn be locted t ground level, thus tending towrd simpler, lighter structure. The AWT is lso better ble to withstnd high winds. In one sense, the price pid for structurl simplicity is erodynmic complexity: AWT erodynmics is inherently unstedy, nd highly nonliner. However, the reltively recent development of severl methods cpble of predicting stedystte performnce hs gretly in-cresed our understnding of AWT erodynmics [] Power Obtined from Wind Turbine A simple model, generlly ttributed to Betz (196) cited in [3], cn be used to determine the power from n idel turbine rotor, the thrust of the wind on the idel rotor nd the effect of the rotor opertion on the locl wind field. This simple model is bsed on liner momentum theory. The nlysis ssumes control volume, in which the control volume boundries re the surfce of strem tube nd two cross-sections of the strem tube (see Figure 1). The only flow is cross the ends of the strem tube. The turbine is represented by uniform ctutor disk which cretes discontinuity of pressure in the strem tube of ir flowing through it. Note tht this nlysis is not limited to ny prticulr type of wind turbine. This nlysis uses the following ssumptions: Homogenous, incompressible, stedy stte fluid flow; No frictionl drg; An infinite number of bldes; Uniform thrust over the disk or rotor re; Copyright 011 SciRes.

2 H. BERI ET AL. 63 Figure 1. Actutor disk model of wind turbine;, is ir velocity; 1,, 3 nd 4 indicte loctions. A non-rotting wke; The sttic pressure fr upstrem nd fr downstrem of the rotor is equl to the undisturbed mbient sttic pressure. Applying the conservtion of liner momentum to the control volume enclosing the whole system, it is possible to find the net force on the contents of the control volume. Tht force is equl nd opposite to the thrust, T, which is the force of the wind on the wind turbine. From the conservtion of liner momentum for one-dimensionl, incompressible, time-invrint flow, the thrust is equl nd opposite to the chnge in momentum of ir strem: T A A where ρ is the ir density, A is the cross sectionl re, is the ir velocity nd the subscripts indicte vlues t numbered cross sections in Figure 1. For stedy stte flow, (ρa) 1 = (ρa) 4 = m, where m is the mss flow rte. Therefore: T m () 1 4 The thrust is positive so the velocity behind the rotor, 4, is less thn the free strem velocity, 1. No work is done on either side of the turbine rotor. Thus the Bernoulli function cn be used in the two control volumes on either side of the ctutor disk. In the strem tube upstrem of the disk, 1 1 p1 v1 p v (3) In the strem tube downstrem of the disk, 1 1 p3 v3 p4 v 4 (4) where it is ssumed tht the fr upstrem nd fr downstrem pressures re equl (p 1 = p 4 ) nd tht the velocity (1) cross the disk remins the sme ( = 3 ). The thrust cn lso be expressed s the net sum of the forces on ech side of the ctutor disc s: T A P P (5) 3 Solving for (p p 3 ) using Equtions (3) nd (4) nd substituting into (5), it is possible to obtin: 1 T A1 4 (6) Equting the thrust vlues from () nd (6) nd recognizing tht the mss flow rte is A, 1 4 (7) Thus, the wind velocity t the rotor plne, using this simple model, is the verge of the upstrem nd downstrem wind speeds. If one defines the xil induction fctor, s the frctionl decrese in wind velocity between the free strem nd the rotor plne, then 1 (8) 1 (9) (10) 4 1 From (6), (9) nd (10), the xil thrust on the disk is: 1 T A1 41 (11) The thrust on wind turbine cn be chrcterized by non-dimensionl thrust coefficient s: C T T Thrust force (1) 1 A dynmic force From (1), the thrust coefficient for n idel wind turbine is equl to 4(l ). 1.. Generl Mthemticl Expressions for Aerodynmics Anlysis of Stright Blded Drrieus AWT Stright blded drrieus type AWT is known for its simplest type of wind turbine. However, its erodynmic nlysis is quite complex. Flow velocities in the upstrem nd downstrem sides of the Drrieus-type AWTs re not constnt. The generl mthemticl expressions t specific loction of the blde is described below. From Figure the reltive velocity component ( R ) cn be obtined from the cordil velocity component nd the norml velocity component s follows Copyright 011 SciRes.

3 64 H. BERI ET AL. Figure. Airfoil velocity nd force digrm. sin R cos R (13) where is the xil flow velocity (i.e. induced velocity) through the rotor, ω is the rottionl velocity, R is the rdius of the turbine, nd θ is the zimuth ngle. Normlizing the reltive velocity using free strem wind velocity one cn obtin: R R sin cos (14) Referring bck to (9) nd substituting with nd 1 with, Eqution (14) cn be re-written s: R 1 sin 1 cos (15) where is induction fctor nd λ is tip speed rtio of the turbine. Referring Figure, ngle of ttck cn be expressed s: sin tn cos R Non-dimensionlizing the eqution, tn sin R cos 1 1 sin tn 1cos (16) (17) (18) The norml nd tngentil coefficients cn be expressed s C C cos C sin (19) n L D C C sin C cos (0) t L D where C L lift coefficient nd C D drg coefficient for ngle of ttck α The instntneous thrust force (T i ) on one single irfoil t certin θ is 1 Ti R hcct cos Cnsin (1) where h is blde height nd c blde chord length The instntneous torque (Q i ) on one single irfoil t certin θ is 1 Qi R hcct R () 1.3. Computtionl Models for Drrieus-Type Stright-Blded AWT In the pst, severl mthemticl models, bsed on severl theories, were prescribed for the performnce prediction nd design of Drrieus-type AWTs by different reserchers. According to literture survey, the most studied nd vlidted models cn be brodly clssified into three ctegories (1) Momentum model, () ortex model nd (3) Cscde model. For the purpose of this pper momentum model is chosen to predict the performnce of AWT s it is fst nd provide resonbly ccurte prediction of stedy stte verge turbine output. Momentum models: the first ppliction of momentum theory to the modelling of AWTs is ttributed to Templin [4]. He used single strem tube encompssing the entire turbine within which the momentum blnce ws clculted. The flow velocity within the strem tube ws ssumed to be uniform. Wilson nd Lissmn [5] ssumed sinusoidl vrition in inflow velocity cross the width of the turbine to ccount for non-uniform flow. In order to ccount for this effect more fully, Stricklnd [6] extended the model so tht the flow through the turbine is divided into multiple independent strem tubes s shown in Figure 3. The momentum blnce is crried out seprtely for ech strem tube, llowing n rbitrry vrition in inflow. A single blde psses ech strem tube twice per revolution in the upstrem nd downstem. The instntneous thrust force on one single blde is given in Eqution (1). The time verged thrust force cting in strem tube by N bldes nd twice per revolution cn be expressed s T Ninstntneous thrust (3) π Copyright 011 SciRes.

4 H. BERI ET AL. 65 C p C (7) where D is the dimeter of the turbine Double Multiple Strem Tube Model Q Blde flight pth Figure 3. Principle of multiple strem tube model with 6 strem tubes divided by uniform θ. The verge erodynmic thrust cn be chrcterized by non-dimensionl thrust Coefficient: T CT 1 hrsin (4) NC R cos Ct Cn R π sin The instntneous torque on single bde is given in Eqution (). The verge torque (Q ) on rotor by N bldes in one complete revolution is then given s Q N* m i1 1 R hcct * R m (5) where m is number of strem tube, nd m is number of θ. The torque coefficients (C Q ) nd power coefficients (C P ) re given s C Q 1 Q * Dh R R t m NC D i1 C m (6) The Double Multiple Strem tube (DMST) version developed by Prschivoiu [7] models llowed for the difference between the upwind nd downwind psses of ech blde by dividing ech strem tube into n upwind hlf nd downwind hlf s shown in Figure 4. The turbine s interction with the wind in the upwind nd downwind psses of the bldes seprtely. The ssumption is mde tht the wke from the upwind pss is fully expnded nd the ultimte wke velocity hs been reched before the interction with the bldes in the downwind pss. The downwind bldes therefore see reduced free-strem velocity. This pproch more ccurtely represents the vrition in flow through the turbine. Ech strem tube in the DMST model intersects the irfoil pth twice; once on the upwind pss, nd gin on the downwind pss. At these intersections we imgine the turbine replced by tndem pir of ctutor discs, Figure 4. DMST with ctutor discs nd velocity vectors u is induced velocity t upstrem ctutor disc, e is equilibrium vlue, nd d induced velocity t downstrem ctutor disc. Copyright 011 SciRes.

5 66 H. BERI ET AL. upon which the flow my exert force. The DMST model simultneously solves two equtions for the strem-wise force t the ctutor disk; one obtined by conservtion of momentum nd other bsed on the erodynmic coefficients of the irfoil (lift nd drg) nd the locl wind velocity. These equtions re solved twice; for the upwind nd for the downwind prt of the rotor. Now ccording to the ctutor disk theory shown in (7) bove the induced velocity ( u ) on the upstrem wind will be the verge of the ir velocity t fr upstrem ( ) nd the ir velocity t downstrem equilibrium ( e ). Thus 1 u e or, e u (8) The present pper ttempts to evlute the performnce of fixed pitch verticl xis with three bldes using double multiple strem tube (DMST) model nd D unstedy flow nlysis using CFD. The conventionl irfoils used for Drrieus AWTs were NACA001, NACA0015 & NACA0018. These bldes re of symmetricl geometry with minimum or negtive torque genertions t lower TSRs. Among these bldes profile NACA0018 ws chosen for the nlysis. This is due to the vilbility of experimentl dt s for comprison. The irfoil chosen ws modified to vry t the triling edge from the originl geometry. This mkes the turbine blde to hve two prts with fixed prt nd flexible. The ssumption for the modifiction of the irfoil ws to increse the lift forces for the performnce of the turbine t lower tip speed rtio. The flexible prt ssumed to cse vrition of the wind velocity tht psses on the top nd lower surfce of the irfoil. This cuses pressure differences on irfoil so tht lift force cn be generted for better performnce of turbine t lower tip speed rtio. Once the turbine pssed the negtive torque genertion, the flexible prt ssumed to tke the sme orienttion with the min irfoil for opertion t higher tip speed rtios like the conventionl symmetricl irfoil geometry. In the nlysis, the conventionl NACA0018 symmetricl irfoil ws used for the nlysis of multiple strmtube (DMST) model. The sme NACA0018 symmetricl irfoil ws mde to be divided into two prts t bout 70% of the cord length s shown in Figure 5 for its D unstedy flow nlysis using commercil CFD softwre bsed on Reynolds verged Nvier-stokes (RANS) eqution using moving mesh technique. The triling edge xis inclintion ws set to 15 from the min blde xis.. Methodology.1. CFD Anlysis For the AWT nlysis, the modified irfoil ws set to 0. m chord length with rdius equl to m. Gmbit modeling softwre ws used to crete D model of the turbine. The model nd mesh generted were then red into the commercil CFD code fluent for numericl iterte solution. The RANS equtions were solved using the green-guss cell bsed grdient option nd the sliding mesh method ws used to rotte the turbine bldes. The RNG k-epsilon model ws dpted for the turbulence closure. The boundry conditions re shown in Figure 6. The inlet ws defined s velocity inlet, which hs constnt inflow velocity, while the out let ws set s pressure out let, keeping the pressure constnt. The no slip sher condition ws pplied on the turbine bldes, which set the reltive velocity of the bldes to zero. The flow condition used for the nlysis is shown in Tble 1. Figure 6. Boundry conditions. Tble 1. Flow conditions. TSR(λ) elocity m/s Turbine ng.vel. (rd/s) Figure 5. Modified geometry of NACA0018 irfoil Copyright 011 SciRes.

6 H. BERI ET AL DMST Anlysis Similrly, For the AWT nlysis using DMST, the norml NACA0018 irfoil ws set to 0.m chord length nd the turbine rdius ws set to m. The wind velocity used in the nlysis is 4 (m/s) nd the tip speed rtios (λ) re 0.5, 1, 1.5,, 3, 4, 5, nd 6. The totl number of strem tube used for the nlysis is 1 with θ = 15. The itertive procedure used in the DMST nlysis is shown in Figure 7. A spredsheet is used for esy mngement of the dt. The mesh generted ner the rotor for the numericl nlysis is shown in Figure 8. The induction fctor ws clculted for ll of the strem tube twice, one for hlf upstrem of the turbine nd the other hlf downstrem of the turbine. The lift nd drg coefficients for NACA0018 section used re the dt of Sheldl nd klims [8], corrected by Lzusks (00). Since the momentum eqution in (1) is not pplicble beyond induction fctor of 0.5 the Gluert empiricl formul is used to clculte the thrust coefficient for 0.4 < < Results nd Discussions Assume vlue for induction fctor Clculte Normlized velocity, ttck ngle, lift, drg, norml nd tngentil coefficients Clculte thrust coefficient derived from erodynmics forces Clculte thrust coefficient derived from theory of ctutor disc (momentum loss) Compre erodynmic thrust coefficient with momentum loss Are the thrust coefficients the sme? Yes No Figure 9 shows the coefficient of power (Cp) comprison between computtionl fluid dynmics (CFD) nd double multiple strem tube (MDST) model. The coefficient of power for the modified irfoils ws generted by combining the performnce of turbine triling edge inclined t 15 for TSR 0.1 to 1 nd without inclintion of the triling edge for TSR greter thn 1. The Cp ws obtined from the rtio of the modeled turbine power to the vilble wind power in the ir. DMST Cp curve shows tht the turbine genertes negtive torque for lower tip speed rtios less thn bout.6. Wheres the CFD nlysis for the modified irfoil shows, positive torque t low tip speed rtios. Figure 10 shows the coefficient of moment (Cm) of the simulted model t low tip speed rtio. The Cm vlues were obtined from the verge moment of the three irfoils modeled through CFD computtionl nlysis for the modified irfoil for tip speed rtios 0.1, 0.5, 0.75 nd 1. As cn be seen, Cm ner zero is higher nd seems to reduce up to TSR = 0.5 nd then strts to rise. Figure 11 shows simulted torque vlues for the modeled NACA0018 modified irfoil t lower TSR. It shows the torque vlues t different zimuth ngle in N-m for complete revolution of TSRs 0.1, 0.5, 0.5, 0.75 nd 1. The torque vlues were obtined from coefficient moment (Cm) of the modeled irfoil, ir density, turbine re, free strem velocity chosen nd the rdius of the turbine modeled. The grph shows tht the verge torque vlues t ech of the TSR simulted re positive. Accept vlues of for the strem tube Figure 7. Itertive procedure used to clculte the flow velocity. Figure 8. Mesh ner the rotor. Figure 1 shows the stedy stte torque vlues t TSR 0 for different wind speeds t three different orienttions of the bldes. The blde orienttions were tken t three different zimuth ngles of 0, 45 nd 90. This helps to show the performnce of the turbine t its stedy stte. Copyright 011 SciRes.

7 68 H. BERI ET AL. Figure 9. Cp result for DMST nd CFD. Figure 10. Coefficient of moment t low TSR for modified irfoil. Figure 1. Torque versus velocity t three loctions of bldes. tive torque genertion t lower TSRs. Numerous ttempts were mde to improve self string of AWT by different scholrs. These includes blde offset pitch ngle, nd blde len forwrd (or yw) ngle [9], the use of cmbered blde sections [10,11], use of inclined bldes [1] use of flexible sils [13] Svonius Drrieus hybrid [14], vrible pitch [15,16]. Though the pproches were tend to contribute in the increses of strting torque, reductions in pek efficiencies nd working on the operting rnge were some of the mjor problems. The DMST result is lso in greement with the drw bcks. As cn be seen from the Cp curve comprison between CFD nd DMST result, the CFD simultion result for the modified irfoil hs shown better performnce t low tip speed rtio. The mximum Cp vlue is lso not fr prt from the DMST result. This indictes tht the modified irfoil cn ccelerte t lower TSR which cnnot be possible using conventionl symmetricl irfoil. From the stedy stte simultion result t TSR = 0, it lso indictes tht the turbine cn generte positive torques t ll the selected orienttions. This pper contributes to literture on the performnce improvement of the AWT t low tip speed rtios. 4. Conclusions Figure 11. Torque for triling edge inclined t 15. The simultion result shows tht the torque vlues re positive t ll the orienttions nd increses with increse of wind velocity. Symmetricl irfoils NACA001, NACA0015, nd NACA0018 re the conventionl irfoil sections used in Drrieus type AWTs. However, the min drwbcks with these types of sections re their minimum or neg- AWT with NACA 0018 blde geometry bsed on fixed pitch three bldes ws nlyzed using double multiple strem tube model. D unstedy flow of AWT with the sme irfoil modified t it triling edge ws lso nlyzed using CFD. The stedy stte performnce of the modified irfoil ws lso nlyzed t TSR = 0. The power coefficients obtined from the DMST nd CFD were then compred. The DMST result shows tht the turbine genertes negtive torque for the lower tip speed rtios. However, the CFD simultion result shows tht the turbine genertes positive torque for lower tip speed Copyright 011 SciRes.

8 H. BERI ET AL. 69 rtios. The stedy stte performnce t three different orienttions lso indictes positive torque. The mximum power coefficients show tht both re in the norml rnge of turbine performnce. 5. References [1] I. Prschivoiu, Double-Multiple Strem Tube Model for Studying erticl-axis Wind Turbines, Journl of Propulsion nd Power, ol. 4, No. 4, 1988, p doi:10.514/ [] G. F. Homicz, Numericl Simultion of AWT. Stochstic Aerodynmic Lods Produced by Atmospheric Turbulence: AWT-SAL Code, Technicl Report SAND91-114, Sndi Ntionl Lbortories, Albuquerque, [3] J. F. Mnwell, J. G. McGown nd A. L. Rogers, Wind Energy Explined: Theory Design nd Appliction, John Wiley & Sons, Hoboken, 00. [4] R. Templin, Aerodynmic Performnce Theory for the NRC erticl-axis Wind Turbine, Ntionl Aeronuticl Estblishment Lbortory Technicl Report LTR- LA-160, Ntionl Reserch Council, Cnd, [5] R. Wilson nd P. Lissmn, Applied Aerodynmics of Wind Powered Mchines, Technicl Report NSF-RA- N , Oregon Stte University, Corvllis, [6] J. Stricklnd, The Drrieus Turbine: A Performnce Prediction Model Using Multiple Strem Tubes, Technicl Report SAND75-041, Sndi Ntionl Lbortories, Albuquerque, [7] I. Prschivoiu, Aerodynmic Lods nd Performnce of the Drrieus Rotor, Journl of Energy, ol. 6, No. 6, 1981, pp doi:10.514/3.661 [8] R. E. Sheldl nd P. C. Klims, Aerodynmic Chrcteristics of Seven Airfoil Sections through 180 Degrees Angle of Attck for Use in Aerodynmic Anlysis of erticl Axis Wind Turbines, Sndi Ntionl Lbortories, Albuquerque, [9] L. Lzusks, Three Pitch Control Systems for erticl Axis Wind Turbines Compred, Wind Engineering, ol. 16, 199, pp [10]. G. Dereng, Fixed Geometry Self Strting Trnsverse Axis Wind Turbine, US Ptent No , [11] H. Beri nd Y. Yo, Effect of Cmber Airfoil on Self Strting of erticl Axis Wind Turbine, Journl of Environmentl Science nd Technology, ol. 4, No. 3, 011, pp doi:10.393/jest [1] J. R.Brker, Fetures to Aid or Enble Self Strting of Fixed Pitch Low Solidity erticl Axis Wind Turbines, Journl of Wind Engineering nd Industril Aerodynmics, ol. 15, No. 1-3, 1983, pp doi: / (83) [13] B. Hurley, A Novel erticl Axis Sil Rotor, Proceedings of 1st Wind Energy Workshop, London, 19-0 April 1979, pp [14] T. Wkui, Y. Tnzw, T. Hshizume nd T. Ngo, Hybrid Configurtion of Drrieus nd Svonius Rotors for Stnd-Alone Wind Turbine-Genertor Systems, Electricl Engineering in Jpn, ol. 150, No. 4, 005, pp doi:10.100/eej.0071 [15] H. M. Dreess, Self-Strting Windmill Energy Conversion System, US Ptent No , [16] L. Liljegren, erticl Axis Wind Turbine, US Ptent No , Copyright 011 SciRes.

9 70 Abbrevitions nd Acronyms A C CFD C D C L C m C n C Q C t C T D DMST h m m N p P Q i projected frontl re of turbine induction fctor blde chord length computtionl fluid dynmics lde drg coefficient lde lift coefficient coefficient of moment norml force coefficient torque coefficient tngentil force coefficient thrust coefficient turbine dimeter double multiple strem tube height of turbine number of strem tube mss flow rte number of blde sttic pressure tmospheric pressure instntneous torque H. BERI ET AL. Q R RANS T T T i TSR d u e R w AWT α θ θ λ ρ ω verge torque turbine rdius Reynolds verge Nvier -strokes thrust force verge thrust force instntneous thrust force tip speed rtio ir velocity long freestrem velocity direction induced velocity induced velocity in the downstrem side induced velocity in the upstrem side equilibrium vlue wind velocity reltive flow velocity wke velocity in downstrem side strem wind velocity verticl xis wind turbine blde ngle of ttck zimuth ngle strem tube ngle division vlue tip speed rtio = Rω/ fluid density ngulr velocity of turbine in rd/s Copyright 011 SciRes.