Optimal Inverse Method for Turbomachinery Design

An adjoint optimization method based on the solution of an inverse problem is proposed. In this formulation, the distributed control is a flow variable on the domain boundary, for example pressure. The adjoint formulation delivers the functional gradient with respect to such flow variable distribution, and a descent method can be used for optimization. The flow constraints are easily imposed in the parametrization of the controls, thus those problems with many strict constraints on the flow solution can be solved very efficiently. Conversely, the geometric constraints are imposed either by additional partial differential equations, or by penalization. Constraining the geometric solution, the classical limitations of the inverse problem design are overcome. Two examples pertaining to internal flows are given.