The harmonic adjoint approach to unsteady turbomachinery design

In recent years, there has been rapid progress in aerodynamic optimization methods which use adjoint ow analysis to e ciently calculate the sensitivity of steady-state objective functions to changes in the underlying design variables. This paper shows that the same adjoint approach can be used in turbomachinery applications in which the primary concern is blade vibration due to harmonic ow unsteadiness. The paper introduces the key engineering concepts and discusses the derivation of the adjoint analysis at the algebraic level. The emphasis is on the algorithmic aspects of the analysis, on the iterative solution method and on the role played by the strong solid wall boundary condition, in particular. The novel ideas are exploited to reveal the potential of the approach in the minimization of the unsteady vibration of turbomachinery blades due to incident wakes. Copyright ? 2002 John Wiley & Sons, Ltd.