# Supersonic Airfoil + Bow Shocks

1. Feb 21, 2013

### Pilgrimman

1. The problem statement, all variables and given/known data

Hey all,

In my Gas dynamics class we need to find the lift and drag coefficients of a supersonic airfoil (diamond shaped) for a range of AoA and Mach numbers. I can easily handle any situation where oblique shocks or Prandtl-Meyer expansions occur, but I'm unsure how to handle bow shocks. If the half angle is, say, 5° and the AoA is 15° with a Mach number of 1.1, then observing the top half of the airfoil I would conclude that there is a Prandtl-Meyer fan at the leading edge. However, observing the bottom half, I would conclude that a bow shock exists for the bottom half.

My question is: is it valid to split the upper and lower halves of the flow into two regimes and treat them separately when one regime has a bow shock? I would think in real life that the bow shock from the bottom would screw up the flow on top and make the flow subsonic over the whole airfoil.

2. Relevant equations

There aren't really any... This is conceptual.

3. The attempt at a solution

My gut is telling me that a bow shock would cause both the top and bottom halves of the flow to be subsonic. On the other hand I can't shake the feeling that maybe the bow shock somehow "terminates" near the leading edge and the upper half of the flow can be handled via a Prandtl-Meyer fan. Any insight??

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2. Feb 22, 2013

### Pilgrimman

Anyone? I'm seriously at a loss here...