I am tyring to make a simple mathematical model to describe the velocity of air in the 2D plane that a wind turbine rotor rotates in.
I am concentrating my project on turbine configurations where the rotor is located upwind of the tower, because the flow upstream of the cylindrical tower is far more stable then the flow downstream.
I am currently only concentrating on the airflow around the tower, and I can then effectively stick the rotor into the aerodynamic conditions near the tower.
I understand well how to model the upstream 2D flow around the cylindrical tower, I have used 2D potential theory to do this.
I guess the flow around the main part of the tower might be fairly accurately modelled with 2D flow, although I am interested in the region close to the top of the tower.
If I only incorporate 2D velocity changes from the tower in the part of the rotor plane which is below the hub, a a discontinous velocity jump occurs across the horizontal. Clearly this would not occur in the real world.
I was thinking of assuming the 2D velocity change at a location along the tower axis could be elliptical, in which case I would simply mutilpy the velocity defecit from the uniform freestream value by the value of an elliptical function at that point.
As usual though, I am expecting it to not be so simple.
If anyone could give me some guidance I would really appreciate it.