Wind turbine operating principle and aerodynamics (Part 3/4)

Transcription

1 Win turbine operating principle an aeroynamics (Part /4) Ene Win Energy Ville Lehtomäki, VTT Win Power Content Power of the win Betz law 1-D Momentum principle Angular momentum principle 1

2 Pow er [kw] Win spee probability [%] Power of the win consists of: A = rotor area [m^] m = mass flow [kg/s] v = win spee [m/s] ja = air ensity [kg/m^] Power of the win Win spee is solely the most important factor when esigning win farms an - projects. The power of the win is proportional to win spee CUBED i.e. when win spee oubles, the power in the win is 8x!! Power of the win 1 E mu, m U A 1 P U A Win spee istribution: (moerate site) % % % % Power in win at D54m 1000 Win spee istribution 8% % 400 4% 00 % 0 0% Win spee [m/s] Key area: most of prouction (~ 60-70%) one in this area!!!

3 Betz law (1919) backgroun If one coul harvest all of the win s kinectic energy, it woul mean that the win woul be at a total stanstill behin the rotor This woul mean that the win woul pack up an slow own before the turbine thus lowering the prouction. Question: How much can the win spee reuce at the rotor so that a turbine can prouce as much electricity as possible? The answer can be foun with the following physical conitions an limits: Conservation of energy Conservation of mass Conservation of momentum (Liikemäärän säilymislaki) D free stream air flow U,p U,p U w,p w

4 Stream-tube A win turbine steals a part of the wins kinectic energy so win spee reuces immeiately after the rotor (conservation of energy). The stream-tube expans after the rotor because there are as many air molecules before an after the rotor (conservation of mass flow). p p EXTRA INFO: 1-D formulas -Conservation of mass an momentum- Conservation of mass A U A U A U w w Win spee at rotor U U ( 1 a) a = axial inuction factor. Momentum change at rotor ( U Uw) AU U that is create from pressure ifference U a ( p p ) A U ( p p )A (U Uw ) AU ( 1 a ) F (1) F m U 4

5 EXTRA INFO: 1-D Formulas -Conservation of energy- Bernoulli equation assumption (energy conserv.): No gravity & incompressible flow p = p w Upstream Downstream 1 U p 1 U w p U w ( 1 a ) U 1 U p 1 U p 1 ( p p ) (U U w ) () () (1)+() Flow spee is reuce before an after the rotor plane OBS! Bernoulli equation is vali through the stream-tube except precisely at the rotor plane (flow is isturbe by an external rotor) U w ( 1 a ) U 5

6 Power coefficient (Cp) & Betz limit Formulas (1) ja () > Power P FU AU a(1 a) Cp C P C P 4 a( 1 a ) P 1 U A Theoretical surface area A C P 4( 1 a )( 1a ) 0 a a= 1/ 16 C Pmax 0, 59 Which is the Bezt limit Key conclusions 59 % of the wins kinetic energy can be at most transfere into mechanical energy = Betz limit BECAUSE the win cannot be completely stoppe at the rotor plan ue to win packing effect Maximal mechanical energy can be extracte from the win, when the win spee irectly infront of the rotor is / of the unisturbe upstream flow spee U 6

7 Thrust force Thrust coefficient F U A ( U U ) A U w a(1 a) Thrust coefficient C T F 1 U A Dynamic pressure for surface A C C T T 4a(1 a) 0.9 when a 1/ -> Max thrust force for a D100m turbine thrust for a perpenicular football fiel! win F T = F T Wake after the turbine D effects 7

8 Gives a better iea how a win turbine rotor works Air flow rotates the rotor with a moment M at an angular spee P M Angular momentum principle (kulmaliikemääräperiaate) Moment is generate when rotor blaes turn the air flow Thus a tangential flow component (with the axial flow component) is generate An axial {a} AND tangential {a } inuction factors are neee Rotor annular ring (or strip) element r 8

9 EXTRA INFO Flow past a blae profile Win Energy Hanbook, Burton EXTRA INFO Power of an annular ring element P M r M mra' r A U (1 a)a' r Aeroynamics of Win Turbines Martin O. L. Hansen 9

10 EXTRA INFO A correlation between a an a With axial force equation (thrust) P A Ua(1 a) Combining this to angular momentum we get AU a(1 a) A U(1 a) a' r Thus a connection between a an a can be mae U a ( 1 a) a' r Angular momentum simplifications Not vali at rotor circumference because flow conitions become iscontinuous Arbitrary number of blaes Arbitrary blae geometry No D-flow effects No friction or turbulence Maybe BEM coul help?? Angular momentum & momentum theory combine to blae profile effects make it possible to take the above limitations into account -> more in next presentation 10

11 Tip Spee Ratio (TSR) A specific TSR is neee to maintain an optimal aeroynamic efficiency The maximum energy extracte from win can be reache with a certain TSR, that is epenent on the number of blaes. For a - blae HAWT, mathematically Cp,max TSR 7.0. To obtain a esire TSR at increasing win spee, rotor rpm has to increase. Tip spee ratio R U 1 Roottorin kulmanopeus s R Roottorin halkaisija U m Tuulen nopeus s m How many blaes for maximum energy prouction? In theory: infinite amount of infinitely thin blaes the most energy efficient Reality kicks in: the cost Three blaes prouce % more energy but two blaes weigh less an use less material -> cheaper to manufacture Toay, a blae configuration is the most common version in MW-class 11

12 Aing rag force to the equation Summary Betz limit 59 % explains, that even in theory, only a part of the wins kinetic energy (thrust force converter) can be converte to mechanical energy because the win cannot be totally stoppe With 1D axial flow (energy converter) an angular momentum theory one can esign a win turbine rotor with moerate accuracy regarless of the physical simplifications (which are quite extensive!) 1

13 VTT luo teknologiasta liiketoimintaa 1