A unified theory of various hybrid problems for blade-to-blade compressible flow is developed herein via the functional variation with variable domain. Two variational principle (VP) families for three typical hybrid problems are derived, following a systematic approach (Liu, 1990a). Full advantage is taken of the natural boundary condition and suction/blowing along the blade surface are accommodated. This theory is aimed at offering a new theoretical basis for the finite element method (FEM) and various ways for blade design and/or modification, and it also constitutes an important part of optimal cascade theory (Liu,1987b). Based on these VPs, a new FEM with self-adjusting nodes is also suggested, and the numerical tests yield good results.

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