## Relation between CFD and BET velocities

Discuss the theory and modeling of rotor aerodynamics.

Moderator: Bonnie.Jonkman

Abhishek.Chopra
Posts: 1
Joined: Tue May 26, 2020 3:26 pm
Organization: Rensselaer Polytechnic Institute
Location: United States

### Relation between CFD and BET velocities

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)?

Jason.Jonkman
Posts: 5738
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

### Re: Relation between CFD and BET velocities

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,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
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