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SUMMARYIn 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.

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The last decade has established the adjoint method as an effective way in Computational Fluid Dynamics of calculating the gradients of an objective functional in a large dimensional design space. This paper addresses the concerns that code developers face when creating a discrete adjoint computer program for design optimization, starting from a nonlinear flow solver and using Automatic Differentiation. Adjoint code development benefits greatly from using Automatic Differentiation but at its current state of maturity, this technology is best applied selectively rather than on entire codes. The paper discusses the practical aspects of using Automatic Differentiation on a large industrial turbomachinery flow solver with the objective of deriving efficient adjoint code. The use of the adjoint gradients is illustrated in an optimization exercise using gradient based methods on the NASA Rotor 37 public testcase.

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