Optimization and Mechanisms of Mistuning in Cascades

Abstract

An inverse design procedure has been developed for the optimum mistuning of a high bypass ratio shroudless fan. The fan is modeled as a cascade of blades, each with a single torsional degree of freedom. Linearized supersonic aerodynamic theory is used to compute the unsteady aerodynamic forces in the influence coefficient form at a typical blade section. The mistuning pattern is then numerically optimized using the method of nonlinear programming via augmented Lagrangians. The objective of the mistuning is to achieve a specified increase in aeroelastic stability margin with a minimum amount of mistuning. It is shown that a necessary but not sufficient condition for aeroelastic stability is that the blades be self-damped. If this condition is met, an optimized mistuning pattern can be found that achieves a given stability margin for a much lower level of mistuning than is required for the alternate mistuning pattern. However, small errors in the implementation of the optimum mistuning pattern severely reduce the anticipated gains in stability margin. These small errors are introduced by the manufacturing process and by the approximation of the optimum mistuning pattern by patterns of a few discrete blade frequencies. Alternate mistuning, which requires only two blade frequencies, is shown to be relatively insensitive to errors in implementation.