My XROTOR.DOC file from October 1988 reads:
<--- snip --->
Like CL, profile CD is defined piecewise in alpha such that in the unstalled
region, CD has a quadratic dependence on CL (after Prandtl-Glauert scaling)
and a power-law dependence on Reynolds number as follows.
| 2| f
CD = |CD + b (CL - CL) | (Re/Re )
| o o | ref
CD = minimum drag coefficient ; Fortran name: ( CDMIN )
CL = CL at which CD = CD ( CLDMIN )
b = CL weighting coefficient d(CD)/d(CL**2) ( DCDCL2 )
Re = Reynolds Number at which CD formula applies ( REREF )
f = Reynolds Number scaling exponent. ( REXP )
f = -0.1 to -0.2 for high-Re turbulent flow
f = -0.3 to -0.5 for low-Re airfoils
Only the above parameters are supplied by the user, and the program
figures out the CD(alpha) function in SUBROUTINE CDCALC.
<--- snip --->
So we run XROTOR once with realistic drag data and once again with the same propeller but all drag coefficients set to zero. Since I last used XROTOR in the last millennium, I have only my old MacOS version which I run in Sheepshaver. It took me a while to get familiar again, and I took Mark Drela's Daedalus propeller file as the input. Copy-Paste from the old to the new OS doesn't work, so I have pasted screenshots here:
Next, I use the AERO submenu to set the drag parameters and redo the calculation at the same RPM:
What a surprise, without airfoil drag our efficiency equals the ideal efficiency. Looks like I did everything right to isolate viscous effects. The difference is a jump in efficiency from 0.886 to 0.94, a bit more than 5%. This is for a very lowly loaded prop at a very low Reynolds number, so the viscous effect is rather large. Expect less for larger props at higher speed, so your factor k will range between 0.943 and 0.984. The last number is valid for a 6-bladed prop driven by an AE2100 engine, the input file of which I also had at hand.