PROFILES WITH COANDA EFFECT, NECESSARIES TO WIND TURBINES

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1 PROFILS WITH COANDA FFCT, NCSSARIS TO WIND TRINS Mircea Dimitrie CAZAC*, Mireille Sorina ANGHL** *Corresponding author POLITHNICA niversity of ucharest, Hydraulics and Hydraulic Machines Department **Technical School Group Videle Teleorman DOI: / Abstract: The air flow separation around profiles and the wind turbine rotor vibration leading to the blade breaking is a well known phenomenon based on which the present work is conceived. The paper is focused on theoretic and experimental researches effectuated on any profiles with Coanda effect, which are followed with the patenting of three similar profiles. In the frame of theoretical researches the molecular attraction forces of adhesion and cohesion in the numerical integration of viscous fluid flow around a breaking plate even to the angle of 45 o are introduced, highlighting the advantageous Henri Coanda effect. The experimental researches are effectuated on a profile with Coanda effect, measuring with a two-component strain gauge balance the lift and aerodynamic drag forces for different profile attack angle, highlighting the increasing of the attack angle from the usual value of 11 o to over the 7 o for that profile when the flow separation takes place. Key Words: Henri Coanda effect. Molecular attraction forces of adhesion and cohesion. Wind turbines. 1. INTRODCTION To explain the well known Henri Coanda effect we shall introduce in this paper the molecular attraction forces of adhesion and cohesion (fig.1), considered by us for the first time in the theoretical and experimental study of the patented rotational biphasic contactor [1-3] and also in paper [4] and the patent invention [5]. J = 6 y = 31a = y 6 5 u = J = 43 = 1a D 1 D 3 D 5 1 J = 38 = 7a D D 4 D 6 D 7 Current parallel to = 0 J = 31 the 0x axis 0 D D 4 L x D 1 D 3 D 8 D 8 D 9 J = 1 D 10 I = D D 9 J = 1 = - 1 Fig. 1. The molecular forces domains and the knots numeration INCAS LLTIN, Volume, Number 4/ 010, pp x'

2 Mircea Dimitrie CAZAC, Mireille Sorina ANGHL 74. TH VISCOS FLID FLOW QATIONS The flow equations [6, p. 38 and p. 5] completed with the molecular attraction forces can be written taking into account that i = I 1 and j = J, I being the column number and J the line number in this network, in which we have for the points comprised in the domains D 1, D and D 5, D 6, that the angle tgβ 1 i,j i,j sin β, cosβ, tgβ D1,, β arc tg, D 1tg β 1tg β 5,6 i,j 13, i,j 13, 3, 3, marking the straight line inclination, that joins the point from the calculus net with the attraction points from the plate extremity and the fluid mass conservation being the equation (3) 13, 1 3, V P υ f a 1 cosβ, 13,, ρ 3, Δ 13, 3, f c 1 cosβ, 13,, 3, δ D,D 6, D,D 1 5 (1) 13, 1 3, V VV P υv V fa1 fc1 f a 1 sinβ, 13,, ρ Δ δ 3, D 3 D Δ 4 fc 1 13, 3, δ sinβ, 13,,, 3, D,D 6 V 0 D,D 1 5. (3) () 3. TH INTRODCTION OF TH STRAMLIN FNCTION To eliminate the equation of the fluid mass conservation, unstable in the iterative numerical calculus, we introduce the streamline function by the expressions: Ψ şi V Ψ (4) and consequently calculating their partial differentials, which intervene in the motion equations (1) and (), and eliminating the pressure function unknown on the all domain INCAS LLTIN, Volume, Number 4/ 010

3 75 Profiles with Coanda effect, necessaries to wind turbines boundaries in the virtue of Schwarzs commutative relation P P of mixed second order, the motion equations become: 13, 13, β cosβ,, IV IV IV 3, 3, ΨΨ Ψ 3 ΨΨ Ψ 3 υψ 4 Ψ Ψ 4 f a 1 Δ βsinβ, 13,, 3, βsinβ, 13,, 13, 3, 3, f c 1 δ β cosβ, 13,, 3, D,6, ( 5) D1,5 4. DIMNSIONLSS FORM OF TH STRAMLIN FNCTION QATION For a greater generalization of the numerical solution we obtained the dimensionless form of the equation (5) choosing as characteristic magnitudes: the calculus domain width, the fluid flow velocity and its pressure P in the plate exterior, the dimensionless variables and functions being: x, y, u =, V v =, P p =, P ψ (6) and the similarity criteria: and cohesion attraction forces. Thus the equation (5) becomes Re / υ of Reynolds number and F f of adhesion a,c a,c y cos x 13, 13, x13, y x x x x y 3, 3, 1 IV IV IV 3, ψ yψ +ψ 3-ψ xψ +ψ 3 ψ +ψ 4+ψ 4 xy x x y y x y y x Fa1 Re x x 13, 3, sin x x13, y 3, x x13, 3, sin x x13, y x x13, y 3, 3, Fc 1 y cos x x13, x x13, y 3, 3, D,6 D1,5 (5') 5. TH STRAMLIN ALGRAIC QATION Developing in our proper series [7] the streamline function after the different steps: aδx δ and b δy δ of a rectangular grid we obtain INCAS LLTIN, Volume, Number 4/ 010

Mircea Dimitrie CAZAC, Mireille Sorina ANGHL 76 0 4 4 4 1 1 4 4 4 4 ab ab a b a b 1 1 1 1 ψ5 ψ8 ψ6 ψ7 ψ1 ψ3 ψ 5 ψ6 ψ7 ab ψ8ψ ψ4 a b u0 v0 1 1 ψ 3 3 ψ1 ψ9 ψ11 1 1 a ψ4 ψ ψ10 ψ 1 3 b y cos I1,J xi1

4 Mircea Dimitrie CAZAC, Mireille Sorina ANGHL ab ab a b a b ψ5 ψ8 ψ6 ψ7 ψ1 ψ3 ψ 5 ψ6 ψ7 ab ψ8ψ ψ4 a b u0 v0 1 1 ψ 3 3 ψ1 ψ9 ψ a ψ4 ψ ψ10 ψ 1 3 b y cos I1,J xi1 x13, J 3, xi 1 x13, xi 1 x13, y 1 I1 y J 3, J 3, J I1,J 8 Fa 1 ab xi 1 x13, J 3, Re 6 sin 4 a xi 1 x13, y I1 J 3, J D1 6 D5 4 b xi 1 x 13, J 3, xi 1 x 13, sin J 3, xi 1 13, I1 y x y I1,J J 3, J Fc 1 y cos I1,J xi 1x13, xi 1x13, y I1 J 3, J 3, J D D6 ψ 1+ψ +ψ3 ψ4 ψ 5+ψ 6+ψ 7+ψ8 ψ 1+ψ3 ψ +ψ4 ψ 9+ψ11 ψ 10+ψ1 and by elaborating the calculus program and by streamline drawing, one can observes in figure the fluid flow cling on the broken plate even at an angle of 45 o, due to the Henri Coandas effect, considering the attraction molecular forces of adhesion and cohesion. (6) 6. PRIMNTAL RSARCHS The experimental installation, figured in figure 3, consists of a metallic support, with a strain gauge balance fixed to its upper side equipped with four groups of double marks for the measuring of the aerodynamic two resultant components, having fixed the blade profile with Coanda effect (fig. 4) shown bellow. Fig.. The aspect of the streamline function INCAS LLTIN, Volume, Number 4/ 010

5 77 Profiles with Coanda effect, necessaries to wind turbines Fig. 3. View of the little free jet wind to determine the profile polar and the used measuring apparatus between the two limited discs. The profile rotation angle is indicated by a protractor and has in the shaft extension two plaques, submerged in a vase full with valvoline to damp the oscillations caused by the whirls induced by the fluid flow turbulence, produced by an electro-ventilator and diminished by an uniformity calming. Leading edge parabola maximal size parabola trailing edge V The angles generated by the two parabolas Fig. 4. The straight anti shock profile, realized by the intersection of the two parabolas INCAS LLTIN, Volume, Number 4/ 010

6 Mircea Dimitrie CAZAC, Mireille Sorina ANGHL 78 On the experimental research basis one obtains the following special result, the lift downfall having place slowly after an angle of about 7 o (fig. 5), instead of the usual angle of 11 o, which can be obtained at the best profile. In this zone the curve evolution is permanently growing, as well as the linear downfall after the flow separation, that permits a good flow stability of the air current. Drag resistance Fx and the lift Fy Fx Fy Atack angle Alfa (degrees) Fig. 5. The variation of the drag resistance F x and lift force F y with the attack angle (degrees) An other patented profile [5] with Coandas effect is the following represented in figure number 6. 1 A Fig. 6. A normal profile with Coandas effect, having in the neighbouring of the profile maximal wide a two separation angle in the regions between the upstream surfaces and 3 rounded in the attack edge 1 and the two downstream surfaces 4 and 5, united in a sharp downstream edge 7. CONCLSIONS Considering the molecular attraction forces of adhesion and cohesion one can theoretically explain the so called Henri Coandas effect, the efficiency of the authors patented profiles and laboratory tested, having the angle of flow separation over 7 o, being possibly to be used with success for the wind turbines, due to the fact that the wind blows in gusts, in which case the blade vibration can be eliminated and thus the wind turbines life can be extended. On this occasion we wish to express our gratitude to renowned fellow compatriot Henri Coanda, the brilliant inventor of the first jet aircraft in INCAS LLTIN, Volume, Number 4/ 010

7 79 Profiles with Coanda effect, necessaries to wind turbines 8. RFRNCS [1] M. D. Cazacu, R. M. R. Neacşu, Iuliana Monica oiangiu. Metoda si dispozitiv de pulverizare a unui lichid (Method and device to spraying a liquid). Patent nr / [] M. D. Cazacu, Iuliana Monica oiangiu. xperimental study of heavy and viscous liquid motion, generated by a rotational cone. The 3 rd Conference professors Dorin Pavel of the Hydroenergetics in Romania, 8-9 May 004, Polytechnic niversity of ucharest, Vol. I, [3] M. D. Cazacu, Iuliana Monica oiangiu. fficient surface aerator for waste water treatment. The 3 rd International Conference on nergy and nvironment CIM, June 8 July 4, 007, Section 5 Wastes Management. Polytechnic niversity of ucharest. CD, 6 p. [4] M. D. Cazacu, Mireille Sorina Anghel. The effect of the molecular attraction forces in hydraulics. Sc. ull. Polytechnic niversity of ucharest, Series D: Mechanical ngineering, Vol.70, 008, Nr. 4, [5] M. D. Cazacu, Mireille Sorina Anghel. Profil hidrodinamic şi aerodinamic antişoc (Anti shock hydro and aerodynamic profile). Patent registered with the nr. A/0065/ [6] Th. Oroveanu. Mecanica fluidelor vascoase (Viscous Fluid Mechanics). Publish. House of Romanian Academy, [7] M. D. Cazacu. etter numerical solution stability by using the function developments in Cazacus proper series. International Conference on Theory and Applications of Mathematics and Informatics ICTAMI 005, September th, Albac-Alba Iulia, Romania, Acta niversitatis Apulensis, Nr. /010, pp INCAS LLTIN, Volume, Number 4/ 010

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