# Bm Theory: The Blade Elements Momentum Theory

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The blade element momentum theory is used to evaluate the loads on each blade once the rotor is subjected [***].The BEM theory has been proofed to give good accuracy regarding the time cost [0].The BET relies on two significant conjecture: The force on the blade elements are merely determined exactly by the drag as well as lift coefficient [000]. No aerodynamic interactions between different blade elements Both assumption methods are considered to discuss. It consists of the blade element theory which split the rotor blades into element sections so as to determine the torque as well as thrust contribution of each segment. The momentum theory is introduced by the rotational and axial induction factors. The BEM is generally used for modeling wind turbines rotors [000].…show more content…
Remember that the blade attachment is disregarded. As BET cannot constrain the position of the blade elements along their chord, the determination of J at the design step permanently conveys hesitation [**]. Hence, the above equation can be amended as follows: J/(N ρ_b )=∫▒r^2 dx dy dr+∫▒y^2 dx dy dr=J_1+J_2 It is crucial to find J_1and J_2 in order to determine the moment of inertia. So, we have: J_1=A∫▒〖(cr)〗^2 dr In which A (A=t^'/c) is dimensionless outcome of dividing the area of the aerofoil section by the square of the chord. t^' is the thickness of blade section. The values of A are accessible in Handbooks. J_2≈∫_0^R▒dr ∫_(-c/2)^(c/2)▒dy' ∫_(-t^'/2)^(t^'/2)▒〖(sin⁡〖θ_p x^'+cos⁡〖θ_p y') dx'〗 〗 〗 As it can been seen, the estimated expression is expressed by supposing blade segment is rectangular with thickness of t^' and the centroid is along the z-axis and the moment of inertia is along x-axis. Now, J is: J= A N ρ_b R^5 [∫▒〖(cr)〗^2 dr+A/12 (c^4 〖cos〗_(θ_p)^2 dr+A^2 ∫▒〖c^4 〖 sin〗_(θ_p)^2 dr〗)] Applications of CFD along