Variable-domain finite element method based on variational principles for solving hybrid problems of fully 3-D compressible rotor flow

Based on a unified variable-domain variational theory (Liu, 1988), a new finite element method (FEM) with self-adjusting nodes for determining the unknown boundaries (shape of the blade and of the annulus walls) in hybrid problems is presented. Two hybrid problem types H(A)xD and [H-C+D]xD are tested numerically by this FEM and the geometry of the rotor bladings thus obtained coincides with the original one quite well. Thus, a new numerical method with great generality and versatility for practical 3-D blading design and/or modification is provided.