Re: Airfoil surface finish

Date:         17 Oct 99 23:30:02 
From:         drela@mit.edu (Mark Drela)
Organization: Massachvsetts Institvte of Technology
References:   1
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In article <airliners.1999.1077@ohare.Chicago.COM>, "davidwells" <davidwells@ozemail.com.au> writes:
> I am having difficulty finding information on the benefits of improved
> surface finish on airfoils in gas turbine engines (ie. fan blades and
> compressor blades and vanes).
>
> Also, someone has suggested that there may be an optimum limit (around
> 12 micro-inches) for airfoils beyond which SFC won't improve.

There is a minimum roughness height below which the
turbulent skin friction is essentially the same as
on a perfectly smooth wall (see Schlichting or White).
This height is about 4 in wall units:

      +
     h  =  h u* / nu  =  4

 u*  =  shear velocity  =  Ue sqrt(Cf/2)
 nu  =  kinematic viscosity
 Ue  =  BL edge velocity
 Cf  =  turbulent skin friction coefficient

So the wall is effectively smooth when the height/chord
ratio is

            4      nu
  h  <  ---------- --
        sqrt(Cf/2) Ue

or equivalently

  h         4       1
  -  <  ---------- ---
  x     sqrt(Cf/2) Rex

 - Mark Drela
 - MIT Aero & Astro