Potential Flow Around an Ellipsoid
u / Uinf = ( Umax / Uinf ) . sqrt[ ( 1 - x2 ) / ( 1 - x2 . a2 ) ]
a2 = 1 - r2
Umax / Uinf = 2 / (2 - b)
b = 2 [ ( 1 - a2 ) / a3 ] . ( atanh(a) - a)
u is the surface velocity magnitude
Uinf is the free stream velocity magnitude assumed parallel to x-direction
x is the distance from center assuming overall length is 2
r is the radius at x = 0 (in this case r = 0.2)
Pressure coefficient surface contours.
Normalized velocity comparison between potential flow theory for an ellipsoid and computation.
Pressure coefficient comparison between potential flow theory for an ellipsoid and computation.
Notice the excellent agreement between the computation and the theory.
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