Double Linearization Theory Applied to Unsteady Aerodynamic Analysis of Three-Dimensional Subsonic Cascade Vibrating with Spanwisely Nonuniform Mean Loading

The improved double linearization theory is extended to three-dimensional subsonic cascades to study three-dimensional effects upon unsteady aerodynamic forces for vibrating blades with spanwisely nonuniform mean loadings. It is found that two kinds of unsteady spanwise aerodynamic forces arise due to nonzero mean loading. One is proportional to the blade inclination times steady pressure difference between upper and lower blade surfaces. Another is the aerodynamic force which acts on streamwise component of steady bound vorticies moving with blades relatively to the fluid. Numerical examples are presented, which illustrate the comparison between the present theory and the strip theory and some features of three-dimensional effects of nonuniform mean loadings on unsteady aerodynamic responses are made clear.