Relation between CFD and BET velocities

[Abhishek.Chopra]

Hi everyone,

I'm trying to calculate induction and forces on a wind turbine (modeled using ALM) using the velocities obtained from CFD. The domain is set in such a way that z-direction is streamwise (flow) direction, and x as well as y (x-y plane is where rotor plane) are tangential directions. I was hoping if someone could clarify a few points:-

1. Does the following relation for tangential velocity hold true -> V_tan = sqrt(Vx_r^2 + Vy_r^2) + omega*r*R? where Vx_r is the x-velocity at a node inside the rotor region, Vy_r is the y-velocity at a node inside the rotor region, omega is the rotation speed of a blade in rad/s, r is the distance of the node from the center of the rotor normalized by rotor radius and R is the rotor radius.

2. Does the following relation for tangential induction hold true -> b = sqrt(Vx_r^2 + Vy_r^2)/(omega*r*R)?

Thank you in advance!

[Jason.Jonkman]

Dear Abhishek,

In both equations, I would expect that instead of the vector magnitude, that you'd want to project the tangential flow velocity normal to the blade axis, i.e., replace

Code: Select all

sqrt(Vx_r^2 + Vy_r^2)

with

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{ vx_r*xhat + vy_r*yat } dot nhat

in both equations, where,
xhat = unit vector along x
yhat = unit vector along y
nhat = unit vector normal to the blade axis in the x-y plane
dot = the vector dot product

Best regards,