Turbomachinery aerodynamic and aeromechanic design optimization using the adjoint method

Abstract

The thesis documents the investigation of the application of the adjoint method to turbomachinery blading design optimization, with emphasis on blading aerodynamic design optimization in a multi-bladerow environment and concurrent blading aerodynamic and aeromechanic design optimization for a single bladerow. Based on the nonlinear flow equations, a steady adjoint system has been developed using the continuous adjoint approach. The capability of the conventional adjoint system has been augmented by the introduction of an adjoint mixing-plane treatment. This treatment is a counterpart of the flow mixing-plane treatment, enabling the steady adjoint equations to be solved in multi-bladerow computational domains. This allows turbomachinery blades to be optimised to enhance their aerodynamic performance in a multi-bladerow environment with matching between adjacent bladerows dealt with in a timely manner. The Nonlinear Harmonic Phase Solution method, a neat frequency domain method catered specifically for turbomachinery aeromechanics prediction, has been chosen to integrate with the adjoint method to calculate objective function sensitivities efficiently for concurrent aeromechanic and aerodynamic design optimization for single row turbomachinery blades. The Nonlinear Harmonic Phase Solution method, unlike the time-linearized methods, solves the unsteady flow equations at two or three carefully selected phases of a period of unsteadiness. This approach not only can conveniently turn a steady flow solver to one solving the unsteady flow equations efficiently, but also provides a good basis on which the corresponding adjoint system can be formulated and solved in a similar manner by extending a steady adjoint system. In order to resolve the issue of having a good blading performance over a whole operating range at a given operation speed, a multi-operating-point design optimization is implemented by formulating an objective function of a weighted sum of performance at more than one operating point