I think these two equations are showing something slightly different. In the Durham paper, they are computing a (critical) aerodynamic damping ratio and in the PCA/ANSYS paper they are computing an aerodynamic damping coefficient.
We typically don't recommend using the work per cycle or aero damping directly for forced response calculations, since you will lose the stiffness component. You would be best off to follow the procedures shown in this section of the help documentation:
But if that caveat does not scare you, then you could use work per cycle. In that case what ANSYS is going to need for the forced response calculation is the modal force. The relationship for this as shown in the help documentation is
Modal Force = -Wcyc/(PI*scaling)
There is no 2 with the PI, as it is cancelled out in the calculations between Wcyc, critical damping, and modal force.
The scaling is essentially undoing any scaling that happened between structural and CFD.