Airfoil Design for Vertical Axis Wind Turbine Operating at Variable Tip Speed Ratios

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1 Send Orders for Reprints to The Open Mechanical Engineering Jornal, 015, 9, Open Access Airfoil Design for Vertical Axis Wind Trbine Operating at Variable Tip Speed Ratios Mei Yi *,1, Q Jianjn 1 and Li Yan 1 School of Mechatronics Engineering, Harbin Institte of Technology, Harbin, Heilongjiang, 15001, China; School of Engineering, Northeast Agricltral University, Harbin, Heilongjiang, , China Abstract: A new airfoil design method for H type vertical axis wind trbine is introdced in the present stdy. A novel indicator is defined to evalate vertical axis wind trbine aerodynamic performance at variable tip speed ratios and selected as the airfoil design objective. A mathematic model describing the relationship between airfoil design variables and objective is presented for direct airfoil design on the basis of regression design theory. The aerodynamic performance simlation is condcted by comptational flid dynamics approach validated by a wind tnnel test in the stdy. Based on the newly developed mathematic model, a new airfoil is designed for a given wind trbine model nder constant wind speed of 8 m/s. Meanwhile, the comparison of aerodynamic performance for newly designed airfoil and existing vertical axis wind trbine airfoils is stdied. It has been demonstrated that, by the novel indicator, the rotor aerodynamic performance at variable tip speed ratios with the newly designed airfoil is 6.78 higher than the one with NACA0015 which is the airfoil widely sed in commercial H type vertical axis wind trbine. Keywords: Airfoil design, Comptational flid dyanmics, Variable tip speed ratios, Vertical axis wind trbine, Horizontal axis wind trbines, Wind trbine rotor model. 1. INTRODUCTION There is a growing interest in harvesting wind energy within the bilt environment in rban areas with the increasing focs on off-grid energy generation [1-4]. Horizontal axis wind trbines (HAWTs) and vertical axis wind trbines (VAWTs) are two main types of eqipment applied in converting the kinetic energy in the wind into mechanical energy. It has been fond by several researchers, H type VAWTs are particlarly well sited to residential wind power generation for some inherent advantages in comparing with their HAWT conterparts [5-7]. Those merits are: being able to extract energy independently from wind direction, lower prodction costs, qieter in operation, and ease of installation and maintenance. To achieve better wind trbine aerodynamic performance, the selection of the airfoil plays a crcial role. For commercial H type VAWTs, symmetric airfoils from the NACA 4-digit series are commonly employed becase only for these airfoils aerodynamic characteristics are the most well docmented [8]. De to the particlar reqirements, efforts have been made to improve the VAWT airfoil profile based pon the NACA 4-digit series in recent years. In 006, Claessens [9] designed DU 06-W-00 based pon NACA The new airfoil has a mch higher maximm lift coefficient for positive angles of attack, reslting in a wider drag bcket, deep stall occrring at higher angles of attack with a smaller drop in lift coefficient. One year later, Islam et al. [10] developed an airfoil named M1-VAWT1 with the *Address correspondence to this athor at the School of Mechatronics, Harbin Institte of Technology, Harbin, Heilongjiang, , China; Tel: ; darrenymei@gmal.com prpose of ensring the airfoil to generate more torqe at low Reynolds nmber which is the operating condition of VAWT. In 011, Q et al. [11] designed an airfoil named OPTFoil for VAWT in attempt to make the blade obtain higher tangential force dring the rotation. More recently, Sh et al. [1] presented a tailored airfoil on the basis of NACA 001 and reslt shows that tailored airfoil exhibits better stall characteristics than NACA001. The existing research focsed on improving the aerodynamic characteristics of single airfoil. However, an H type VAWT rotor is consisted of mltiple blades, signifying that the improvement of single airfoil aerodynamic performance does not garantee the perfectly better aerodynamic performance of the wind rotor. It is necessary to alter the design goal from individal airfoil to entire wind rotor. Moreover, when applied in rban sites, H type VAWTs enconter the problem that operating at variable tip speed ratios, which is attribted to complex wording condition featred by the matching of rotor and generator, electric storage and consmption, changing of electrical load [13-15]. Ths, sing a power coefficient at fixed tip speed ratio to assess rotor aerodynamic performance at variable tip speed ratios is confsing and an attempt to develop a new aerodynamic performance evalation indicator shold be made. On another aspect, CFD method copled with optimization algorithm has been rotinely applied in wind trbine airfoil design [16, 17]. It shold not be neglected that the CFD calclation, thogh having relatively accrate prediction reslts compared to other aerodynamic calclating tools, tends to be time consming when the stdy object is H type VAWT characterized with complex flow field. Then, how to decrease the comptational cost becomes one of the major challenges dring the airfoil design process X/ Bentham Open

2 1008 The Open Mechanical Engineering Jornal, 015, Volme 9 Yi et al. The present work is dedicated to design an airfoil for H type VAWTs applied in rban sites, contribting better rotor aerodynamic performance in comparison of existing VAWT airfoils. The research is condcted from two aspects: developing a new indicator in order to evalate aerodynamic performance nder a range of tip speed ratios meanwhile selecting this indicator as airfoil design objective, and constrcting a mathematic model describing the explicit fnctional relationship between airfoil design variables and objective for direct airfoil design, looking to redce comptational time in airfoil design process.. THE WIND TURBINE ROTOR MODEL It has been sggested by reference [18] that the vale of height to radis ratio for VAWT applied in rban areas is between to 3. Also, a three-bladed VAWT rotor is strctrally non-directional and tends to rn smoothly becase of lower flctations of energy in each revoltion [19]. Assming the wind speed in rban regions is sally between 6 m/s to 10 m/s [0], the wind velocity vale in this stdy was maintained at 8 m/s. Major geometry specifications of scaled VAWT rotor are categorized and listed in Table 1. Table 1. Major rotor geometry specifications. Parameter Vale Rotor radis, (m) 0. Rotor central shaft radis, (m) 0.01 Blade cord length, (m) 0.07 Blade length, (m) 0.5 Nmber of blade 3 3. METHOD FOR AIRFOIL DESIGN The rotor aerodynamic performance at variable tip speed ratios is selected as the airfoil design objective. A new indicator named averaged effective wind energy tilization coefficient has been developed as represented in section 3.1. Airfoil geometry generation which allows the translation of the variables into the actal airfoil is an important part of the airfoil design, and the geometry generation method is described in section 3.. This paper aims to bild a mathematic model for direct airfoil design on the basis of relatively small amont of CFD calclation by qadratic Fig. (1). Flow chart of airfoil design process.

3 Airfoil Design for Vertical Axis Wind Trbine Operating at Variable Tip Speed Ratios The Open Mechanical Engineering Jornal, 015, Volme regression orthogonal composite design, which is illstrated in section 3.3. Also, details of CFD approach are stated in section 3.4. Fig. (1) shows the flow chart of airfoil design process Design Objective Analysis It is widely acknowledged that the wind trbine harness the kinetic energy contained in flowing air masses. The wind trbine firstly transforms the power available in wind to the power otpt from the rotor. Then the mechanical energy is transformed to the electronic power by the generator. It is physically impossible to technically exploit the entire wind energy, so there is efficiency dring the wind power transformed to mechanical power. Power coefficient C P written as Eq. (1) is an expression of trbine harness wind energy, and torqe coefficient C T described by Eq. () reveals the torqe performance of the rotor. C P = T ave! "SV 3 (1) where T ave is the averaged torqe of wind rotor dring each revoltion, ω is the rotor rotating anglar velocity, ρ is the density of the air, S is the swept area of wind trbine and V is the inlet air velocity. C T = T ave!srv " () The power coefficient reflects the aerodynamic performance of rotor. To evalate the efficiency of rotor extracting wind power, C P of a fixed tip speed ratio is confsing. If the tip speed ratio λ alters dring the trbine operation, the power coefficient changes accordingly. An H type VAWT is spposed to work at wind speed of V between time range [t a, t b ], which means the generator and electrical eqipment are on reglar operation and the otpt power is effective. The fnction of tip speed ratio λ varies with time is denoted as λ(t), and the range of λ is [λ a, λ b ]. Then the effective wind energy tilization coefficient E e in [t a, t b ] can be defined by the ratio of the extracted wind energy on the rotor swept area and the energy provided by the flowing air. The mathematical expression of E e is shown as Eq. (3). E e = 1!SV t 3 b " $ C P [(t)]dt t a 1!SV 3 " t b = $ C P [(t)]dt (3) However, it is not easy to provide the specific expression of λ(t), as the complex reason of rotor operating at variable tip speed ratio. As an eqipment harnessing energy from the wind, the evalation of a rotor aerodynamic performance can be converted to estimate the overall potential of rotor absorbing effective wind energy resorces. Ths, if the effective working range of λ is [λ a, λ b ] nder the wind velocity of V, regardless of the specific vales of λ at any time, the rotor aerodynamic performance can be defined by averaged effective wind energy tilization coefficient E ea, as shown in Eq. (4). t a 1 t b E ea = C P (!)d!! b "! t a a (4) The power performance coefficient vales obtained by nmerical simlation are discrete data corresponding to tip speed ratios. Besides the step size of λ is easy to maintain stable in the calclation, nmerical integration can be applied in solving Eq. (4). Spposing the nmber of tip speed ratio data achieved in nmerical simlation is m, the compting formla of E ea can be written as Eq. (5). Lift type VAWTs generate effective power when λ>1. Also, the noise emission level exceeds 60dB when λ>3, according to Lida s stdy [1]. Ths, the range of λ shold be [1, 3] in practical calclation of E ea. m! 1 E ea = (m!1) [C (" ) + C (" ) + C (" p a p b ) p i ] (5) 3.. Airfoil Geometry Generation According to previos investigation [, 3], thickness and camber are two parameters having major inflence on rotor aerodynamic performance, which shold be selected as design variables. Airfoil geometry generation is that one allows the translation of the design variables into the actal airfoil. The present work is on the basis of NACA 4-digit series airfoil which has been tilized by the majority of VAWTs. Reference [4] gives their shapes based pon rectanglar coordinate system are given by the following eqations: c max " (1! x cmax ) [(1! x ) + x cmax cmax $ x! x y camber = $ c max (x cmax x! x ) $ x cmax where y camber is the y coordinate of the mean camber line, c max is the maximm camber vale, x cmax is the x coordinate of the maximm camber. ±y thick = 5t max (0.969 x! 0.16x!0.3516x x 3! x 4 ) i=1 (6) (0 < x < 1) (7) where y thick is the y coordinate of the thickness distribtion, t max is the maximm thickness vale Mathematic Model for Rotor Aerodynamic Comptation Mathematic model developed in this part is sed to describe the fnction relationship between rotor aerodynamic performance at variable tip speed ratios and the airfoil design variables. A second order nonlinear regression method is applied to bild the model by calclation of data points in conjnction with composite design [5]. The relationship can be written in a general form as follows: p y =! 0 + "! j x j + "! jk x k x j + "! jj x j (8) j=1 k< j p j=1

4 1010 The Open Mechanical Engineering Jornal, 015, Volme 9 Yi et al. where y is the design objective, x k and x j are design variables, p is the nmber of variables, β 0, β j, β jk, β jj are regression coefficients. When applying composite design to obtain experiment data points, in order to ensre the orthogonality of experiment plan, Eq. (8) needs to be transformed into the pattern in the code space as shown in Eq. (9). The encoding formla is given by Eq. (10). The strctre matrix and ndetermined coefficients of Eq. (9) are given by Eq. (11) and Eq. (1). p y = b 0 +! b j z j +! b jk z k z j +! b jj z j (9) j=1 k< j p j=1 z jk = x kj! x 0 j " j (k = 0, 1, ; j = 1,,..., p) (10) where x 0j =(x 1j +x j )/ and Δ j =( x j - x 1j )/, x j and x 1j are the pper and lower limit of x j, separately.! Z = " z 10 z 11 z 1 z 11 z 1 z 11 z 1 z 0 z 1 z z 1 z z 1!!!!!! z 110 z 111 z 11 z 111 z 11 z 111 b 0 =! y i i=1 b j =! z ij y i! z ij i=1 i=1 $ b kj =! z ik z ij y i!(z ik z ij ) i=1 i=1 b jj =! z ij " y i! z ij " i=1 i=1 where is the nmber of experiment. z z 11 $ (11) (1) Once the form of Eq. (9) is confirmed, it is necessary to process regression diagnostics where F-test is applied. Regression diagnostics is consisted of three parts, namely significance test on regression coefficients, significance test on regression eqation and lack of fit test on regression model. The formla of significance test on regression coefficients is written as Eq. (13). If F j >F α (f j, f e ), F jk >F α (f jk, f e ) and F jj >F α (f jj, f e ), the design variables are significant nder level α, or the design variables need to be determined again.! F j = S j S e F kj = S kj " S e F jj = S jj $ S e f j f e f kj f e f jj f e (13) where S e is the residal sm of sqares, S j, S jk and S jj represent the linear term, interaction term and qadratic term sm of sqares, f e is the additional freedom, f j, f jk and f jk represent the degree of freedom for linear term, interaction term and qadratic term. The significance test on regression coefficients is expressed by Eq. (14). If F E >F α (f E, f e ), the regression eqation is significant nder level α. f E F E = S E (14) S e f e where S E is the regression sm of sqares, f E is the degree of freedom for regression. The test for lack of fit on regression model is condcted by Eq. (15), if F lf <F α (f lf, f e ), the fit is good. Otherwise, there can be higher order relation between the design objective and variables, the regression model reevalation is needed. f lf F lf = S lf (15) S e f e where S lf is the sm of sqares for lack of fit, f lf is the residal degree of freedom, S e is the error sm of sqares for zero repetition test, f e is the degree of freedom for zero repetition test. After the reslt of regression diagnostics is confirmed to be positive, Eq. (10) is applied again on Eq. (9) with all determined coefficients to obtain Eq. (8). Then, applying extreme vale analysis method on Eq. (8) can resolve the optimal vales of design variables and the geometry of the new airfoil is achieved CFD Approach for Aerodynamic Simlation The commercial CFD package was sed for the aerodynamic simlations. The code ses the finite volme method to solve the governing eqations for flids. The incompressible nsteady Reynolds Averaged Navier-Stokes eqations were solved for the rotor flow field. The copled pressre based solver was selected with a second order implicit transient formlation for improved accracy. The PISO algorithm was applied for the soltion of the pressrevelocity copled eqations. All soltion variables were solved via QUICK scheme which is a high order p wind method in view of the complexity of the flow. All the residals are set to 10-5 for all the variables. The shear stress transport (SST) k-ω model [6] has been sccessflly applied for many nmerical simlations of H type VAWT [7-9]. Therefore, the SST k-ω model was employed for all the simlations presented in this paper. The geometry of the rotor was created by sing Gambit software. Fig. () is the D schematic of the comptational domain employed for comptations, where Φ is noted as the diameter of the rotor. The domain is created by assembling a circlar rotating region in a rectanglar stationary region ABCD where the rectanglar region is 0Φ in length and 10Φ in width, and the circlar rotating region has a diameter of Φ. For the rectanglar domain, AC side is set as an inlet bondary condition whereas BD side set as a pressre otlet bondary with six no slip bondaries to three blade srfaces, rotor central shaft, AB and CD sides. The bondary where rectanglar region connects to circlar rotating region is set as an interface bondary condition in order to employ the

5 Airfoil Design for Vertical Axis Wind Trbine Operating at Variable Tip Speed Ratios The Open Mechanical Engineering Jornal, 015, Volme sliding mesh techniqe. According to the rotational speed of the rotor, the time for an eqivalent of half degree rotation of the rotor was adopted for nmerical time step size. To ensre a fll development of the flow, several revoltions have to be simlated before converged periodical soltion is achieved. Therefore, when the relative difference of periodic averaged power coefficient over one revoltion is less than 1, the soltion is considered to be converged in this paper. As averaged power coefficient is related to averaged torqe, the relative difference of averaged torqe, r, is r = T ave (i +1)! T ave (i) T ave (i) < 1 (16) Fig. (). D schematic of the comptational domain. Strctred qadrilateral grids were sed for the domain meshing. As shown by Fig. (3a), O type mesh was adapted arond each blade. The height of the first cell sed was m and the growth rate of inflation was implemented as 1.07 to give an average of the y pls vales from the flow soltions of 5 to 10. Fig. (3b) shows the mesh in the domain. To redce comptation time, the stationary domain was relatively coarsely meshed with a maximm edge length of the cells not exceeding a blade cord length. A mesh independent test was also performed nder one rotor tip speed ratio. Several different strctred grids composed of variable mesh size of the entire domain ranging from 100,000 to 700,000 cells have been examined. It has been determined that arond a mesh nmber of 600,000 cells on the domain was the level at which grid independence was attained. (a) where T ave (i) is the averaged torqe at rotor cycle nmber of i. Instantaneos torqe vales can be calclated by Flent dring the simlation process, this makes torqe be a fnction of time. Ths, the averaged torqe T ave dring the time interval [t 0, t n ] is calclated by 1 t n T ave = T (t) t n! t t 0 0 " dt (17) where t 0 represents the time at the beginning of a single rotation of the rotor and t n is the time at the end of a single rotation. As instantaneos torqe vales are recorded in terms of discrete data by Flent, by applying Newtown-Stokes formlas, Eq. (17) can be written as t n "t $ 0 "1 '!t T ave = (t n " t 0 ) T (t!t 0)+ T (t i ) + T (t n )) ) i=1 () (18) where Δt is the nmerical time step size vale, T(t i ) is the compted instantaneos torqe of rotor at t i. Based on the nmerical reslts of instantaneos torqe, the compted vales rotor power coefficient at every individal tip speed ratio can be obtained by combining Eq. (18) and Eq. (1). 4. VALIDATION OF CFD SIMULAITON (b) The CFD simlation shold be checked against experimental data to assess its capability of correctly simlating VAWT aerodynamic performance. The experimental test was condcted in a low speed wind tnnel with an otlet of 1 m 1 m. This tnnel is an open jet type with total length of 13 m, inclding power section, diffser, stilling chamber and contract section. The wind is generated from an axial fan driven by an inverter controlled electric motor, allowing a range of air velocity from 1 m/s to 0 m/s, with a vale of 1 trblence intensity. An experimental platform is settled in front of the contraction. Fig. (4) shows the view of assembled wind trbine test platform in front of the wind tnnel. The major geometric vales of the wind rotor and profile of the blade are consistent with the data listed in Table 1. The height of the fondation has been well designed to ensre that the wind rotor is positioned in the middle of the wind tnnel otlet. Fig. (3). Mesh generation: (a) mesh arond the airfoil; (b) mesh in the domain.

6 101 The Open Mechanical Engineering Jornal, 015, Volme 9 Yi et al. 5. DESIGN RESULTS AND ANALYSIS Fig. (4). Assembled platform. The comparison between the CFD reslts and the experimental data of power coefficient at the constant wind speed of 8 m/s is illstrated by Fig. (5). As shown in the figre, simlation reslts are appeared to be comparatively well matched together with the experimental data. However, some deviations are still observed and the averaged relative error is As far as absolte power coefficient vale is concerned, the validation is not that exact. This is becase the CFD model is D while the actal problem is 3D. Nevertheless, it is not wisely to apply 3D CFD simlation in the airfoil design becase 3D simlation is extraordinary time consming for VAWT. Moreover, the prpose of applying nmerical simlation in airfoil design is progressing comparative analysis of aerodynamic performance, meaning absolte levels of performance are not important and only relative vales of performance are needed. Considering the same tendency of two power performance crves, especially the good agreement in optimm tip speed ratio prediction, the CFD method condcted in this stdy is capable to captre the flow physics and sitable for aerodynamic comptation in airfoil design. According to Eq. (6), five airfoils with different thickness can be obtained by controlling vales of t max at 1, 15, 18, 0 and, noted as T1, T15, T18, T0 and T, separately. According to Eq. (7), five airfoils with different camber can be obtained by controlling vales of c max at 0, 1,, 3 and 4, noted as C0, C1, C, C3 and C4, separately. By CFD simlation, trends of averaged effective wind energy tilization coefficient E ea dependent on different thickness and camber vales are illstrated in Figs. (6, 7). It can be seen from Fig. (6), E ea increases with the rising t max and the maximm vale attains at t max =18 before decreasing to 0.35 at t max =0 by The figre shows a frther drop when t max reaches. Similar trends can be fond in Fig. (7), the maximm E ea achieves at c max =1, bt frther rising of c max leads to a decline of E ea. The decreasing rate is 3.7 when the vale of c max alters from 1 to 4. It can be conclded from those analysis that there is a sharp decline of E ea when t max exceeds 0, and the amplitde range of E ea is smaller when t max [0, 4]. Therefore, the design constraint conditions are as follows: 15 t max 0, 0 c max 4. Fig. (6). E ea dependent on different t max vales. Fig. (5). Comparison of power coefficients obtained by different methods. Fig. (7). E ea dependent on different c max vales.

7 Airfoil Design for Vertical Axis Wind Trbine Operating at Variable Tip Speed Ratios The Open Mechanical Engineering Jornal, 015, Volme Assming t max =x 1 and c max =x and applying Eq. (10), the following exists: x 01 =0.175, x 0 =0.0, Δ 1 =0.0178, Δ = The experimental plan, inclding three zero repetition tests, is shown by Table. Table. Experimental plan. No. x1 x among which, NACA0015 is the widely sed airfoil for commercial VAWT, DU 06-W-00 and OPTFoil are foils designed with the design objective of improving single airfoil aerodynamic performance, and OPTFoil014 is the newly designed foil with the design objective of improving rotor aerodynamic performance at variable tip speed ratios. It is seen from the table, compared to rotor applied NACA0015, vales of E ea obtained by rotors with DU 06-W- 00, OPTFoil and OPTFoil014 are higher and the maximm vale of 0.5 is achieved by OPTFoil014. By sing OPTFoil014, E ea of rotor can increase by 6.78 in comparison of those with NACA0015. Table 3. Effective wind energy tilization coefficients of rotors with for different airfoils Airfoil E ea Having obtained experimental data points by CFD approach and applying Eq. (9) to Eq. (14), the mathematic calclating model of rotor aerodynamic performance at variable tip speed ratios can be written as Eq. (19). Throgh extreme vale analysis of Eq. (19), the maximm E ea obtained at t max =17.45 and c max =1.98. The newly designed airfoil is noted as OPTFoil014. Fig. (8) shows the comparison of airfoil configration between OPTFoil014 and widely sed VAWT airfoil NACA0015. E ea =! t max!13.43t max c max!18.49c max (19) NACA DU 06-W OPTFoil 0.38 OPTFoil Power performance of rotors with varios airfoils is given by Fig. (9). It can be seen from the figre, rotor with DU 06-W-00 has higher power coefficient than others at the region of 1<λ<, while rotors with NACA0015 and OPTFoil014 maintain high power performance at the region of <λ<3. To have a better nderstanding of the differences, instantaneos torqe coefficient (C Tinst ) crves and flow field of rotors with varios airfoils are analyzed at λ=1.1 and λ=.9 (corresponding to positions A and B as signed in Fig. 11) which are selected as representatives of lower and higher tip speed ratios. Fig. (9). Power performance of rotors with for different airfoils. Fig. (8). Airfoil configrations of OPTFoil014 and NACA0015. Table 3 shows the statistics of calclated averaged effective wind energy tilization coefficients of H type VAWT rotors with the for different airfoils, namely NACA0015, DU 06-W-00, OPTFoil and OPTFoil014, Figs. (10, 11) show the instantaneos torqe performance and vortex contors at λ=1.1 and λ=.9, separately. As seen in Fig. (10a), all instantaneos torqe coefficient crves attain the peak vales at θ=60, θ=180 and θ=300, while fall to the bottom at θ=0, θ=10 and θ=40. The major difference of these crves exits in the process C Tinst dropping from the peak to bottom, where C Tinst of rotor with

8 1014 The Open Mechanical Engineering Jornal, 015, Volme 9 Yi et al. (a) (a) NACA0015 (b) DU 06-W-00 (b) OPTFoil OPTFoil014 Fig. (10). Instantaneos torqe performance of rotors with different airfoils at λ=1.1 and λ=.9: (a) λ=1.1; (b) λ=.9. NACA0015 drops faster than others and the slowest decrease comes from the rotor with DU 06-W-00. Flow physics is shown in Fig. (11a) which is featred by dynamic stall and flow separation. Both vortex shedding and flow separate can weaken the aerodynamic performance of blade. For blade 1, flow separation moving toward leading edge can be observed at NACA0015 and OPTFoil, trailing edge separation is seen on OPTFoil014, and no sign of separation can be fond on DU 06-W-00. For blade, vortexes have been separated from the blades of NACA0015 and OPTFoil. Bt the scale of shedding vortex from NACA0015 is larger than the one from OPTFoil, leading to a lower aerodynamic performance. When it comes to DU 06-W-00 and OPTFoil014, the Fig. (11). Vortex contors of rotors with different airfoils at λ=1.1 and λ=.9: (a) λ=1.1; (b) λ=.9. vortex is still developing and abot to shed, leading to a higher aerodynamic performance. Flow separation and vortex shedding at DU 06-W-00 and OPTFoil014 are delayed dring the rotor rotating compared with NACA0015 and OPTFoil, reslting in relatively higher torqe coefficient and power coefficient at lower tip speed ratio. As seen in Fig. (10b), all instantaneos torqe coefficient crves reach the peak vales at θ=100, θ=0 and θ=340, while fall to

9 Airfoil Design for Vertical Axis Wind Trbine Operating at Variable Tip Speed Ratios The Open Mechanical Engineering Jornal, 015, Volme the bottom at θ=40, θ=160 and θ=80. The major difference of these crves also exits when C Tinst dropping from the peak to bottom. It can be observed from Fig. (11b) that the flow field is now featred by significant wake flow. The spreading of wake flow can lead to dissipation of energy which lowers energy extraction efficiency. For blade 1, the largest spreading area of wake flow is observed at DU 06-W- 00 while the smallest one is seen at NACA0015. For blade, which is affected by the wake flow from blade 3, is also fond to generate wake flow and distrb blade 1. The negative inflence is more serios at DU 06-W-00 and OPTFoil than NACA0015 and OPTFoil014. Wake flow generated by NACA0015 and OPTFoil014 have less blockage effect on the flow field than those generated by DU 06-W-00 and OPTFoil, reslting in relatively higher torqe coefficient and power coefficient at higher tip speed ratio. It can be fond by the above analysis that the nsteady flow field featres varies at different tip speed ratios, inflencing the rotor aerodynamic performance. To attain better rotor aerodynamic performance, an H type VAWT airfoil shold strike aerodynamic balance between lower and higher tip speed ratio. Based on the above comparative analysis, only OPTFoil014 achieves the objective while another three airfoils fail. CONCLUSION (1) Based on the analysis of overall potential of VAWT rotor absorbing effective wind energy resorces, a new indicator named averaged effective wind energy tilization coefficient has been defined to evalate the aerodynamic performance of rotor at variable tip speed ratios and selected as the airfoil design objective. () A mathematic model for direct airfoil design has been constrcted on the basis of relatively small amont of CFD calclation by regression design theory. Based on this model, a new airfoil noted as OPTFoil014 is designed for an H type VAWT sed in rban sites nder constant wind speed of 8 m/s. Compared with NACA0015 which is widely sed, the averaged effective wind energy tilization coefficient of rotor with has increased by 6.78 when OPTFoil014 is applied on the rotor. (3) With the changing tip speed ratio, rotor flow field is characterized by different nsteady flow featres which have direct inflence on aerodynamic performance. Traditional H type VAWT airfoil design method is aiming at aerodynamic performance of single airfoil which is not capable to take the nsteady flow field into accont. It is necessary to apply rotor aerodynamic performance at variable tip speed ratios as the airfoil design objective. 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