teoria bem y calculo de fuerzas xabier munduate wind energy department cener - national renewable...
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TEORIA BEM Y CALCULO DE FUERZAS
Xabier Munduate
Wind Energy DepartmentCENER - National Renewable Energy Centre (Spain)
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Introducción
Teoria BEM y Calculo de Fuerzas
Limitaciones en la aplicación al diseño
Indice
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El campo aerodinámico objeto de estudio en BEM se puede dividir en: la zona local y la zona global y una interface que comunique ambas zonas.
Zona global Zona globalZona local
Escalas espaciales y temporales
t=c/ Ωrt=D/V t=D/V
Cantidad de
Movimiento
Cantidad de
Movimiento
Elemento de pala
(LL)
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BEM=Blade Element Momentum.Teoría de la Cantidad de Movimiento 2D: axial y tangencial + combinada con la Teoria de Elemento de Pala.
TEORIA BEM
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steady incompresible uniforme 2D flujo axial y tangencial : no hay flujo radial por lo
que fuerzas radiales son ignoradas. irrotacional upstream: pero es rotacional al paso por el
rotor y en la estela cercana. no perdidas de energia: no turbulencia, no disipacion. no viscoso en la zona global. El drag se asume en la
zona local flow incorporandolo a traves de coeficientes Cl-Cd.
Simplificaciones del flujo
TEORIA BEM
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TEORIA BEMBase teorica
Conservation of mass flow rate
through concentric annular elements of the disc, A=
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TEORIA BEMBase teoricaDefinitions, axial induction factor
Admiting that
the velocity in the far wake
it may be observed the axial induced velocityfactor in the far wake, 2a, is twice that across the
disc, a.
a>1/2Wake velocity
negative
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TEORIA BEMBase teorica
Conservation of Axial Momentum By applying the axial momentum equation toan annular ring at radius r with width dr,the local thrust is given by
combining with the two previous expressions for velocity
Eq 1
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TEORIA BEMBase teorica
From Angular momentum conservation the local torque Q produced by the tangential force on a circular element at radius r is given by
Considering
Assuming that
and that the wind far upstream is irrotational
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TEORIA BEMBase teorica
rewriting the above Eq gives the torque
Eq 2
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TEORIA BEM
Cx
Cy
Plane of rotation
Plane of rotation
Knowing Cl and Cd as a function of the angle of attack, it is now possible to determine the rotor disc Cx and Cy.
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TEORIA BEMBase teorica
is the number of blades
the chord blade
Equating the elemental thrust and torque obtained via momentum
theory Eqs 1 and 2 to theseexpression given by blade element theory Eqs 3 and 4 results in two
expressions, one for a and a second for a´. The set of non_linear equations
can be solvednumerically in a iterative fashion
Eq 3
Eq 4
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BEM
Debido a estas simplificaciones el método básico BEM sufre las siguientes limitaciones a la hora de aplicación practica:
Para a>1/2 la teoria no es valida: Flujo reverso estela. No tiene en cuenta ni el numero de palas ni la dimensión finita
de estas en el calculo aerodinamico. Es un método estático 2-D, por tanto no admite transitorios
(yaw, dynamic stall) y cada seccion de pala es independiente de la contigua (No ve ningun efecto 3D a lo largo de la pala).
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