DIMENSIONLESS CURVES IN OPTIMAZING WIND TURBINES CONSTRUCTION WITH HORIZONTAL AXIS

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1 Analele Uniersităţii din Oradea, Fascicula Protecţia Mediului Vol. XXV, 015 DIMENSIONLESS URVES IN OPTIMAZING WIND TURBINES ONSTRUTION WITH HORIZONTAL AXIS Dubău ălin*, ătaş Adriana** *Uniersity of Oradea, Faculty of Enironmental Protection, 6 Gen. Magheru St., Oradea, Romania, calin_dubau@yahoo.com ** Uniersity of Oradea, Faculty of Science, Department of Mathematics and omputer Science, 1 Uniersity St., Oradea, Romania, acatas@uoradea.ro Abstract The present paper establishes the goal function regarding a mathematical model based on the operating cures. This is an important aim called generic desideratum cures, consisting in some steps by means of which the optimization of the blades of turbines with horizontal axis is proided. Physical model of the turbine is a theoretical concept, which allows ealuation analysis of characteristic parameters of wind turbines. The results are applied for different alues of rapidity and are deeloped in a comparatie presentation for two types of turbine. This paper highlights the importance of certain parameters of wine turbine in the process of construction and deelopment of the aero-electrical aggregates and their optimal functioning. Key words: Optimization of the blades turbines geometry, wind turbines, operating cures, dimensionless cures. INTRODUTION Turbine geometry optimization consists in selecting those forms that maximizing the exchange of energy in certain gien conditions (wind speed, engine res). Wind turbine is composed mainly of a rotator fixed on a support shaft, comprising a hub and a moing blade consisting of one or more blades. Actie body of aeolian turbines which made the quantity of conerted energy is the blade (Bej A., 003). The achieing of aerodynamic performances, kinematics and energy cures of the aeolian turbines depend on the choice of certain geometry. Optimum performance is built through iterations geometryperformance in order to maximize the energy extracted from the wind for exploitation. The physical and mathematical associated model inoles the following components: site offer, exchange energy in the aerodynamic engine, optimized geometry of the motor and the functional characteristic cures of the engine in terms of optimized geometries (Gyulai F. and Bej, A., 000). 339

2 MATERIAL AND METHOD By optimizing constructie solution of the blade wind turbine we understand those aerodynamic contours which perform a desired functional characteristic for a certain application. Energy performance representation that produces a wind turbine, as a whole operating area, is materialized by the characteristic cures that are operating in the optimization process. They are of two types namely: operating (exploitation) cures, respectiely dimensionless cures of the type of turbine (Dubau., 003). The characteristic cures associated to the geometry of the blade are calculated by the method of bearing. These are materialized by the two families of cures: operating cures P f ν, n M f ν, n F = f ν, n ; T PT = ( ), = ( ), ( ) adimensional curbes f λ f λ T = ( ), = ( ), = f ( λ) MT F ax Taking into consideration (Dubau., 004), in order to characterize the functionality of arious types of turbines three adimensional coefficients are used, respectiely: power coefficient, moment coefficient or torque coefficients and axial force coefficient, which hae the following calculation expressions: M Fa π n R P = ; ; el 3 M = F = ; ν = a 30 λ ρ Sb ρ S R ρ S where we hae used the following notations: S Area swept by the turbine, R Radius of the turbine, P Power turbine, M The moment at the engine line axis, Axial force, F a ρ Mass density of air [kg/m 3 ], Wind speed [m/s]. The optimization of the turbine designed for an aeroelectrical power station has as a final goal the maximization of the energy extracts from wind, for exploitation in the specific conditions of a certain emplacement. This is translated in achieement of an operating cure of a turbine haing a allure which ensures the maximization of the energy. 340

3 The achieement of such objectie generic called desideratum cures or goal function consists in many steps, by successie corrections, starting with an initial geometry. The characteristic number, namely rapidity of the turbine, is defined by the relation bellow: π n R λ=, 30 where n is the speed turbine [rpm]. There are arious types of wind turbines. Between arious types of wind turbines the rapid axial horizontal wind turbines are the most deelopment ones (Gyulai, F., 000). Many studies are also elaborated taking in consideration the turbines with ertical axes. Such a study regarding the adimensional cures was presented by the first author (Dubau., 009). This paper proides a mathematical simulation on the computer of the output coefficient power for different rapidity, based on the model proposed in the work (Dubău., 007). There are compared two well-known types of turbines namely LM 18 H (DANMARK 36) and AEROTEH-17PI 85. The analyzed turbines are listed in the following table. Turbine code 1 The alues of certain parameters for the analyzed turbines The name of the turbine LM 18 H (DANMARK 36) Installed power [ kw ] Rotor diameter [ m ] Operating speed [ rpm ] AEROTEH-17PI Table 1 Power control Autocapping ontrol blade RESULTS AND DISUSIONS In order to obtain the desideratum cures we hae analyzed certain reference cure of two tested wind turbine and also confirmed as performance, designed by consecrated companies in the field. All the studied operating cures associated to the aboe mentioned cures are measured cures. These types of cures are currently in operation in aeroelectrical power station in different emplacement from the entire world. 341

4 In the table below (table ) are pointed the operating cures for two type of turbine. These are gien for electric power at the electric generator terminals( P el). Table P kw The electric power at the electric generator terminals ( el[ ]) ν [ m / s] Turbine code The type of the turbine 1 LM 18 H (DANMARK 36) AEROTEH-17PI For the constants computation which depends on the type turbine we will use different alues of the rapidity. In order to establish an accurate comparison, the cures were = f λ by the following transposed in terms of dimensionless forms ( ) relations: power coefficient (associated to the power P el ) P = = ; el 3 S π 3 d ρ b ρ π D 1 8 D ur D π D n the characteristic number λ= = ϖ =. ν 60 ν In computations we hae used for the mass density of air [kg/m 3 ] the alue of 1.3 kg/m 3. In the table 3 are presented the determined alues for the power coefficients ( ) and also the determined alues for the characteristic number λ as a function of wind speed ( ) ν ν [ m / s] The type of the turbine LM 18 H (DANMARK 36) AEROTEH-17PI 85 P el The power coefficient ( ) P el λ P el λ P el Table 3 34

5 For two types of turbine we plot below dimensionless cures (Fig.1). Fig. 1 Dimensionless cures ONLUSIONS The presented model permits a better optimization of the parameters of the turbine also the optimization of energy performance of the wind turbines. They are also permitted a good management of the control and automation. REFERENES 1. Bej A., 003, Wind Turbines, Timişoara Polytechnic Press, ISBN , Timişoara, Romania.. Dubău., 003, Study on the usage, storage and technical and economic performance of wind-systems. ollaboration in the Research enter in Aero- Energetical systems of the Faculty of Mechanical of the Uniersity Politehnica, Bucharest. 3. Dubău., 004, Valorization of wind power, Annals of Uniersity of Oradea, Fascicle of Enironmental Protection, ISSN , Vol IX, Year 9. (In Romanian). 4. Dubău,., 007, The Utilization of Micro-Wind Assemblies within omplex Systems, Timişoara Polytechnic Press, ISBN , Timişoara (In Romanian, Ph. D. thesis). 343

6 5. Dubău., 009, omparatie study regarding the energy of turbines with ertical and horizontal axis, Annals of DAAAM International Vienna & Proceedings, ISSN: , January 1, pp Gyulai, F., 000, ontributions on horizontal axis wind turbine theory, Proceedings of the 5th International onference on Hydraulic Machinery and Hydrodynamic, Oct. 000, Timişoara, Romania. 7. Gyulai F., Bej A., 000, State of Wind Turbines in the End of 0th entury and Proposals for Romanian Options, Buletinul Ştiinţific al Uniersităţii Politehnica Timişoara, Romania, Tom 45(59), ISSN