Aerodynamic Potential Flow Code - Derivation of Panel Method Solution To Potential Flow Problem

Derivation of Panel Method Solution To Potential Flow Problem

  • From Small Disturbances
(subsonic)
  • From Divergence Theorem
  • Let Velocity U be a twice continuously differentiable function in a region of volume V in space. This function is the stream function .
  • Let P be a point in the volume V
  • Let S be the surface boundary of the volume V.
  • Let Q be a point on the surface S, and .

As Q goes from inside V to the surface of V,

  • Therefore:

For :, where the surface normal points inwards.

This equation can be broken down into the a both a source term and a doublet term.

The Source Strength at an arbitrary point Q is:

The Doublet Strength at an arbitrary point Q is:

The simplified potential flow equation is:

With this equation, along with applicable boundary conditions, the potential flow problem may be solved.

Read more about this topic:  Aerodynamic Potential Flow Code

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