Blade Element Momentum (BEM) for propellers and turbines: part 1 linear and angular momentum
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- เผยแพร่เมื่อ 17 ส.ค. 2024
- blade element momentum theory. mostly from perspective of a propeller in this particular derivation (see my notes for turbine version). linear momentum balance, angular momentum balance, efficiency.
For more detail see the following two references:
Ning, A., “Using Blade Element Momentum Methods with Gradient-Based Design Optimization,” Structural and Multidisciplinary Optimization, Vol. 64, No. 2, pp. 994-1014, May 2021. doi:10.1007/s00158-021-02883-6
Ning, A., “A Simple Solution Method for the Blade Element Momentum Equations with Guaranteed Convergence,” Wind Energy, Vol. 17, No. 9, pp. 1327-1345, Sep. 2014. doi:10.1002/we.1636 - วิทยาศาสตร์และเทคโนโลยี
amazing channel, thank you so much for uploading these lessons professor
Thank you so much for the lectures. Learning so much from them
So from my understanding, for most of the calculations in this video the units are in Torque and Thurst. It is only when you make A_d = 2*pi*r*(dr) and then divide LHS and RHS by (dr) do the equations become Torque per unit length and Thrust per unit length?
There is something wrong with Betz limit if kinetic energy in the wind is 1/2 mass or 50% and Betz limit is 0.5926% then where can the 0.926% come from not the wind ? regards Graham Flowers MEng
At 35:56, you are missing a V_\infty in the equation for torque. Furthermore, in case you would insert the velocity to arrive at the same equation as 34:08, you would end up at torque in terms of units, not torque per unit length. Won't this mess up the integration over the span later on in the calculations?
Good catch, I indeed made a typo on the slide and the V_\infty should be there. With the Vinf include you do get the correct units (torque per unit length, N*m/m or just N). Fortunately, when I combine the momentum and blade element parts in the next video I have the V_\infty term back in so everything else is correct - just a typo on that slide.