Comment on page
Example simulation of an ellipsoid
An ellipsoid with dimensions (semiaxes)
m at an angle of attack of
deg and sideslip angle of
deg is considered. The magnitude of the freestream velocity is
m/s. An unstructured mesh of 14924 elements is used. Similarly to the sphere, an analytical solution for the perturbation and total potential around the ellipsoid exists . The perturbation (doublet) potential is given by:
are integrals given by:
The solution of the
integrals is obtained with the aid of the incomplete elliptic integrals as explained in [2,4]. When the potential is evaluated at the surface of the ellipsoid
is set to 0. Numerical values of the incomplete elliptic integrals, along with values of the
integrals for any combinations of
are given in . The total potential is given by:
is the total potential,
is the perturbation (doublet) potential,
are the semiaxes of the ellipsoid,
are the centroid coordinates of an element on the ellipsoid surface,
are velocity components relative to the ellipsoid. The image blow shows the ellipsoid pressure coefficient.
The images below compare the perturbation potential and the total potential with the analytical solution.
As there is no analytical solution for the pressure coefficient at
deg, the analytical solution for the pressure coefficient at
deg is compared to the one from a simulation at the same conditions.
Good agreement between the simulation and the analytical solution is observed.
 Craig, T., "On the Motion of an Ellipsoid in a Fluid", American Journal of Mathematics, Vol.2, No.3, 1879, pp. 260-279  Byrd, P.F., "Handbook of Elliptic Integrals for Engineers and Scientists", Springer-Verlag, 1971, pp. 1-7, pp. 8-41  Jones, R.T., "Classical Aerodynamic Theory", University Press of the Pacific, 2005  Viana, F. and Fuanda, T. and Joseph, D.D. and Tashiro, N. and Sonoda, Y. "Potential flow of a second-order fluid over a tri-axial ellipsoid", J. Appl. Math., Vol.4, 2005, pp. 341-364