Technology Journal of Energy JET Volume 6 (2013), p.p. 31 - 46 Issue 4, November 2013 http://www.fe.um.si/sl/jet NUMERICAL ANALYSIS OF FLOW OVER A WIND TURBINE AIRFOIL LOPATICNEGA PROFILA VETRNE TURBINE This work presents a comparison of flow conditions over a NACA 4421 two-dimensional airfoil with a closed trailing edge (normal airfoil shape) and a new blade shape with an open trailing edge. The numerical analysis was made using software for an approximate solution of a system of conservation law equations. The results yield a comparison of numerically obtained values of the lift coefficient, as well as diagrams of pressure coefficients and velocity vectors on the airfoil, at different angles of attack. The validity of the method of computation was confirmed with a comparison of computed lift coefficient values for the closed trailing edge profile, with experimentally acquired values from literature. It is reasonable to continue the research of flow conditions with the use of the open trailing edge airfoil. Povzetek Predstavljena je primerjava tokovnih razmer pri obtekanju zraka okoli dvodimenzionalnega profila NACA 4421 z zaprtim izstopnim robom (običajna oblika profila) in novo obliko lopatice z odprtim izstopnim robom. Numerična simulacija je bila narejena s programskim paketom za aproksimativno reševanje sistema parcialnih enačb, ki predstavljajo ohranitvene zakone. Rezultati podajajo primerjavo izračunanih vrednosti vzgonskih koeficientov, ter diagrame tlačnih koeficientov in vektorjev hitrosti na profilu, za različne natočne kote. Pravilnost načina izračuna je bila potrjena s primerjavo izračunanih vrednosti koeficientov vzgona za primer zaprtega m Corresponding author: Janez Bitenc, Tel.: +386 41 800 668, Mailing address: Ul. Janka Kača 2, SI-3310 Žalec, Slovenia E-mail address: jbitenc@icloud.com NUMERIČNA ANALIZA TOKA OKOLI Janez Bitencw, Brane Širok, Ignacijo Biluš Keywords: wind turbine, numerical simulation, airfoil Abstract JET 31 Janez Bitenc, Brane Širok, Ignacijo Biluš JET Vol. 6 (2013) Issue 4 profila, z eksperimentalno pridobljenimi vrednostmi iz literature. Rezultati simulacij kažejo, da je smiselno nadaljevanje raziskav izboljšanja tokovnih razmer z uporabo lopatice z odprtim izstopnim robom. 1 INTRODUCTION Wind turbines are propulsion engines for exploiting renewable energy sources. Wind turbine rotors are divided into drag-based and lift-based or horizontal and vertical, [1]. They are unable to convert the total energy from wind into mechanical work. The theoretical aerodynamic efficiency factor is called the Betz limit and is 59.3%. The motivation for these computations were the current efficiency factors with which conventional wind turbines are operating, which are much lower than the Betz limit and highly dependent on the flow conditions around airfoils. This article discusses the airflow over wind turbine airfoils, for conventional and new blade shapes. Because different angles of attack and blade shapes lead to different flow conditions and thus significantly affect lift and drag coefficients, the discussion is limited to Cl and Cp computation for the profile in external flow. The goal was to show that the new blade type ensures more favourable flow conditions. As a new blade type, a hollow blade, [2], is introduced, with air flow streaming from the trailing edge of the profile, with which we wish to increase the lift coefficient and prevent the intrusion of secondary flow along the blade suction side in the trailing edge area. Numerical simulations of flow conditions were made with Ansys CFX software. 2 WING THEORY The maximum obtainable power of the wind turbine in a free stream, which is independent of the design of wind turbine, is known as Betz's law. It is derived from the conservation laws of the mass and momentum of the airflow that passes through the idealized actuator disk, which extracts energy from the air stream. According to Betz's law, it is impossible for a wind turbine to take advantage of more than 59.3% of kinetic energy of the wind. In practice, wind turbines reach their peak at 75-80% of the Betz limit. 2.1 Betz limit The Betz limit represents the ratio between the maximum achievable power of the turbine and the wind power. It equals, [3]: Vmaks=^L = -^-2 = 0. 592 6 (2.1) tot z' Where g Pmaks = Y7PAV™ (Z2) Pt o t = \pAvl (2.3) 32 JET Numerical analysis of flow over a wind turbine airfoil and vm — wind speed, A — ro tor d isc are a, p — air density. Therefore, this is the maximum efficiency of wind turbines: no more than 60% of the kinetic wind energy can be converted into mechanical work, [3]. Figure 1 shows the efficiency factors of some of the practical implementations of wind turbines. On the abscissa are lined up tip speed ratios , representing the ratio between tip speed and free stream airflow vm, [3]: u 2nnR A = — =--(2.4) Voo Vm From the graph in Figure 1, we can see that the efficiency of wind turbine greatly depends on the tip speed ratio and rotor type. For values , the efficiency is even in optimal conditions greatly lower than the values of A > 5 where we obtain the maximum efficiency factors. This difference is even more obvious in actual wind turbines. The greatest efficiency factors are possible to achieve in the narrow optimal tip speed ratio interval, where the numbers range between rj = 0 . 3 0 and rj = 0 .40, [1]. Figure 1: Comparison of efficiency factors of some of the practical implementations of wind turbines in relation to tip speed ratio, [1] JET 33 Janez Bitenc, Brane Širok, Ignacijo Biluš JET Vol. 6 (2013) Issue 4 2.2 Aerodynamic forces and moments Regardless of complexity of the studied model, the sources of aerodynamic forces and torque on the wing profile in the outer flow, pressure and shear stress distributions are at the airfoil. As shown in Figure 2, the pressure acts perpendicularly, and the shear stress tangentially on the surface. Shear stress is the result of friction between air and body surface, [3]. Figure 2: Distribution of pressure p and shear stress t along the profile, [3] The final effect of the distribution of p and t, integrated over the whole body surface, is the resultant of aerodynamic forces y?and momentum Afonthe body, as shown in Figure 3. Figure 3: Resultant of aerodynamic forces on the profile, its components and momentum The resultant forces R can be divided into components; two pairs are represented in Figure 3. Speed Frc is the free stream speed. In Figure 3, by definition, the marked forces are, [3] L is lift force. It is the component of resultant force R, perpendicular to vm D is drag force. It is the component of resultant force R, parallel to vm N is normal force. It is the component of resultant force R, perpendicular to c A is axial force. It is the component of resultant force R, parallel to c The relation between ¿and N, as well as Z?and Ogives the equations [3] .v D = N sin a — A cos a L = N cos a — A sin a (2.5) (2.6) 34 JET Numerical analysis of flow over a wind turbine airfoil 2.3 Dimensionless coefficients Lift force is the result of change in the momentum of the air as it streams onto the blade. Drag force is the result of friction and pressure differences. Usually, they are represented with lift Cl and drag coefficients Cb,[1] L C ~ T^ (2.7) 2 ^ooPcoà _ D C ~ " (2.8) where L and D are lift and drag forces (Equations 2.5 and 2.6), vœ flow velocity and .iTwing area. Both coefficients are dependent on flow conditions, which are primarily determined by the angle of incidence a, [1]. Another influential dimensionless coefficient is the pressure coefficient Cp P_1 2 (2.9) 2 ^ CO P CO 2.4 Flow separation and the impact on the lift coefficient With increasing air velocity or increasing values of the Reynolds number, the boundary layer along the profile changes. Speed distribution in the boundary layer is dependent on shear forces t, acting along the wall (Figure 4). SihanliW rf .nifal -maximum q><*4 oat if d* tfl Ihr boundary laTO Nwe nmntMPtniBiUiy l»y j i O • 1 C7" ù " 1 Figure 11: Shear stress; a = 14° Figure 13: Shear stress; a = 7.24° From Figures 10 and 12, it is evident that the negative values of pressure coefficient present greater lift force, because the lowering of the pressure on the suction side means a greater pressure difference. Separation points are evident from Figures 11 and 13, in which the shear force equals zero. At absolute values of separation points, the shortening of the blade because of a cut trailing edge needs to be taken into account. Figure 14 shows velocity vectors at angles of attack 14° and 7.24°. A later beginning of flow swirling at the open trailing edge profile is evident, which indicates a movement of the separation point towards the trailing edge of the profile. JET 41 Janez Bitenc, Brane Širok, Ignacijo Biluš JET Vol. 6 (2013) Issue 4 (a) (b) Figure 14: Comparison of velocity vectors along the profile at angles of attack a = 14° (a) and a = 7.24° (b) 4.3 Impact of air velocity change on the results In Table 1 and in Figure 15 andFigure 16, the results of numerical analysis for closed and open trailing edge profiles, at an angle of attack of 3° and three different inlet and outlet air velocities are shown. Table 1: CL at angle of attack a = 3° Velocity vi Velocity V2 Velocity V3 Cl for closed trailing edge profile Cl for open trailing edge profile 0.0486 0.0856 0.0495 0.0916 0.0504 0.0963 42 JET Numerical analysis of flow over a wind turbine airfoil M n M* Figure 15: Pressure coefficient at air velocity v1 Figure 16: Pressure coefficient at air velocity v3 and angle of attack a = 3° and angle of attack a = 3° From the results, it is evident that lift coefficients are raised in accordance to velocity. The difference between Cl for closed and open trailing edge profile is not the same, but rises with the rising of the velocity. Figure 15 and Figure 16 show the comparison of pressure coefficients of close and open trailing edge profiles. Because of the small values of Cl, differences between £^are barely noticeable. 5 DISCUSSION The end results of the numerical analysis of flow over wind turbine airfoil indicate an improvement of flow conditions in case of open trailing edge airfoil, for angles of attack of a >0At angles a < 0 °, the lift coefficients deteriorate, because of the flipped flow conditions on the suction and pressure sides. The values of lift coefficient for closed and open trailing edge profiles give the typical lift coefficient distribution, which raises linearly with an increasing angle of attack and begins to drop when a critical angle of attack is attained. From the presented figures, it is clear that the computationally obtained values correlate well with experimental data. Later flow separation is evident in the case of the open trailing edge profile, especially at greater angles of attack. The average percentage of lift coefficient increase in case of the new blade type is (for the discussed angles of attack greater than 0°): approximately 15%. The results of the numerical analysis at an angle of attack of 3° and three different velocities showed that with proportional increases of air velocity at the domain inlet and the open trailing edge outlet, lift coefficient also increases. Cl in case of open trailing edge profile is on average 52% greater than in case of closed trailing edge profile. Given the above, we can conclude that the open trailing edge profile favourably impacts flow conditions. JET 43 Janez Bitenc, Brane Širok, Ignacijo Biluš JET Vol. 6 (2013) Issue 4 6 CONCLUSIONS At default simplifications (2D model, stationery flow field, ignoring the kinetic energy of flow through the open trailing edge on the Cl formula), it was found that the open edge profile favourably impacts Cl and Cp for positive values of angle a. The use of CFX software for analysis of airflow over wind turbine airfoil was shown to be appropriate. Such a way of studying flow conditions is cheaper, but nevertheless presents an experiment an essential tool for the validation of computations and understanding the dynamics of the phenomenon. The improvement of numerically computed lift coefficients in the case of an open trailing edge airfoil may seem highly significant, but it is necessary to take into account that it is just a two-dimensional numerical computation, for which no kinetic energy necessary for flow through open trailing edge of the profile was incorporated. Thus, a possibility for further research of flow conditions is offered, taking account of three dimensions, a greater number of blades, the rotation of the rotor and the changing angle of attack across the blade into account. It would be intriguing to see how that kind of blade would behave in a laboratory experiment, from which a more realistic picture and validation of the assumed hypothesis could be obtained. References [1] A. Hribernik: Obnovljivi viri energije, Maribor: Založništvo Fakultete za strojništvo, 2010. [2] M. Eberlinc, B. Širok and M. Hočevar: "Patented Hollow Blades of the Axial Fan with Trailing Edge Self-Induced Blowing" Recent Patents on Mechanical Engineering, vol. 2, no. 1, pp. 1-7, 2009. [3] J. D. Anderson: Fundamentals of aerodynamics, 3rd ed., New York: McGraw-Hill, 2001. [4] Aerospace engineering; "Aerospace engineering" February 2013. [Online]. Available: http://aerospaceengineeringblog.com/bio-mimetic-drag-reduction-2/. [5] M. Fike: Eksperimentalna in numerična raziskava tokovnih pojavov v aksialnem ventilatorju, Maribor: Fakulteta za strojništvo, 2013. [6] I. H. Abbott and A. E. Von Doenhoff: Theory of wing sections, Canada: General Publishing Company, 1959. [7] M. Eberlinc, B. Širok, M. Dular and M. Hočevar: "Modification of axial fan flow by trailing edge self-induced blowing" Journal of Fluids Engineering, vol. 131, November 2009. [8] ANSYS, Help, 14.0 ed., 2011. [9] T. Burton, N. Jenkins, S. David and E. Bossanyi: Wind energy handbook, 2 ed., United Kingdom: John Wiley & Sons, Ltd., 2011. [10] E. L. Houghton and P. W. Carpenter: Aerodynamics for engineering students, 5 ed., Butterworth-Heineman, 2003. [11] M. Malgaj: "Obnovljivi viri v EU in položaj Slovenije" February 2013. [Online]. Available: http://www.zelenaslovenija.si/images/stories/pdf_dokumenti/Obnovljivi-viri-energije-v-Sloveniji.pdf. [12] A. Predin: Vetrne turbine, Maribor, 2011. 44 JET Numerical analysis of flow over a wind turbine airfoil Nomenclature (Symbols) (Symbol meaning) A Area A axial force Cl lift coefficient Cd drag coefficient c chord length D drag force Fx axial force L lift force 1 characteristic length M Torque m mass flow rate N normal force Ptot airstream power P Power Pmate maximum power pœ upstream pressure p Pressure R resultant of aerodynamic forces S reference area Su momentum sources t Time u tangential velocity U time averaged mixture velocity vm free stream velocity a angle of attack ^nb maximum coefficient X tip speed ratio v kinematic viscosity pm free stream air density t shear stress; stress tensor JET 45