Geometry (cm²)

JSXGraph v0.94 Copyright (C) see http://jsxgraph.org
Athroat
50
50
50
75
25
100
0
50
75
25
100
0
Aexit
50
50
50
75
25
100
0
50
75
25
100
0
Ainlet

Mach Number

JSXGraph v0.94 Copyright (C) see http://jsxgraph.org
2
2
2
3
1
4
0
2
3
1
4
0
2
2
2
3
1
4
0
2
3
1
4
0
Min

Pressure (kPa)

JSXGraph v0.94 Copyright (C) see http://jsxgraph.org
50
50
50
75
25
100
0
50
75
25
100
0
50
50
50
75
25
100
0
50
75
25
100
0
Pb

Notes:

  • Click and drag the red dots to change the geometry, inlet Mach number or back pressure
  • Once the boundary conditions are accounted for and the flow regimes are distinguished (subsonic or supersonic), Flozzle uses analytic expressions to compute the flow variables
  • Analytic quasi-1D Euler solution:
      • \frac{A}{A^*} = \frac{1}{M}\bigg[\frac{2+(\gamma-1)M^2}{\gamma+1}\bigg]^{\frac{\gamma+1}{2(\gamma-1)}} " alt=" \frac{A}{A^*} = \frac{1}{M}\bigg[\frac{2+(\gamma-1)M^2}{\gamma+1}\bigg]^{\frac{\gamma+1}{2(\gamma-1)}} " border="0" class="latex" />
    • Remember, this admits two Mach number solutions (subsonic & supersonic) for a given area ratio! A numerical bisection method is used to obtain the Mach number in the desired regime.
  • Normal shock relation:
      • M_y^2 = \frac{2+(\gamma-1)M_x^2}{2\gamma M_x^2 - (\gamma-1)} " alt=" M_y^2 = \frac{2+(\gamma-1)M_x^2}{2\gamma M_x^2 - (\gamma-1)} " border="0" class="latex" />
 

© Philip Caplan 2016