A Generalized Variational Principle for 3-D Unsteady Transonic Rotational Flow in Rotor Using Clebsch Variables

Via semi-inverse method /1,2/, a generalized variational principle with only 6 independent variables for 3-D unsteady compressible rotational transonic rotor-flow with shocks has been successfully formulated, which has been unknown till the present time, and the matching conditions across all unknown oscillating discontinuities (such as shocks, free surface and free trailing vortex sheets) have been deduced via variable-domain variable principle. This theory aims at rendering a general, rigorous theoretical basis for the finite element method and other direct variational methods.