The position of the shed vortex sheet is determined iteratively by first 

 solving the boundary value problem with an assumed position, and then aligning the 

 wake with the computed total velocity field for a specified radial contraction. 

 The boundary value problem is then re-solved and the procedure is repeated until 

 convergence (see Figure 4). This process of wake alignment is different from the 

 simple wake model in PUF2, where the trailing vortex wake geometry is defined at 

 the outset by several semi-empirically determined geometric parameters. 



Once a converged solution is obtained, blade forces are computed by applying 

 the Kutta-Joukowski and Lagally theorems. The Lagally theorem is used to compute 

 the forces on the source elements as a modification for the effect of the thickness 

 (source). This modification is equivalent to subtracting the thickness-induced 

 velocity from the total velocity used to compute the Kutta-Joukowski force on the 

 vortex elements. If the thickness-induced velocity were included in the total 

 velocity, the resulting Kutta-Joukowski force would be larger than experimental 

 values. In PSF, as in PUF2 , an empirical suction factor is used to estimate the 



leading-edge suction force at off-design conditions. The reader is referred to 



12 

 Greeley and Kerwin for details of the computation. 



MODIFICATIONS TO PSF 



In PSF, the overall blade load is computed by summing up the elementary loads 

 (the jump in pressure across the surface) acting on each line vortex and source 

 element. The elementary load is computed at the midpoint of each spanwise and 

 chordwise singularity on the key blade by assuming the average velocity over the 

 length of a singularity can be approximated by the velocity at its midpoint. This 

 point is called "load point." Since the total velocity is calculated at each load 

 point to compute the load, it is logical to choose the same point as the "pressure 

 point" for pressure calculation. In the present study, pressure is computed at 

 only the pressure points on the spanwise singularities and Is Interpolated at 

 specified radii. 



The velocity calculated at the load point In PSF is a mean velocity that does 

 not include the self-induced velocity due to the singularity segment where the 

 elementary load is calculated. However, when computing the pressure, not the jump 

 in pressure, the velocity jump across the singularity must be included. 



