Application of a general discrete adjoint method for draft tube optimization

Automatic optimization is becoming increasingly important in turbomachinery design to improve the performance of machine components and Evolutionary Algorithms (EAs) play a very important role in this task. The main drawback of EAs is the large number of evaluations that are required to obtain an "optimal" result. Consequently, in order to keep the computational time in an affordable frame for design purposes, either the mesh size has to be limited, thus reducing the resolution of the flow phenomena, or the number of free parameters must be kept small. Adjoint optimization does not suffer from these restrictions, i.e. the optimization time is not affected by the number of parameters. The computational effort for the adjoint method scales only with the grid size and is usually in the range of two times the CFD simulation alone. In this paper, a discrete adjoint method based on a coupled pressure based RANS solver is presented and applied to draft tube optimization. The adjoint solver is general and can therefore deal with any turbulence model supported by the CFD solver as well as any boundary condition, including mixing planes and mesh interfaces needed for multi-stage simulations. Furthermore, there is no restriction on the choice of objective function. The adjoint method is first applied to a baseline draft tube geometry and then again to its EA optimized geometry where the objective function was the minimization of losses in the draft tube. To reduce the complexity for this proof of concept but still including multiple operating points in the optimization, only peak efficiency and full-load were optimized simultaneously. The adjoint optimization can significantly improve the draft tube performance in both cases (baseline and EA optimization). The interplay between local and global optimization seems to be a promising strategy to find optimal geometries for multi-operating point/multi-objective optimization and will be further investigated in subsequent research.