Abstract
The design of high-loading and compact modern turbomachines results in strong blade row interactions, which have been found to have a noticeable impact on aerodynamic performances of turbomachines. Therefore, it is necessary to consider unsteady effects arising from blade row interactions in multi-row turbomachinery aerodynamic analyses and design optimizations. In this work, three-dimensional multi-row unsteady aerodynamic design optimizations of turbomachinery blades are performed using a discrete adjoint solver developed by using the automatic differentiation tool--Tapenade. An efficient harmonic balance (HB) method with a complete rotor-stator interface coupling treatment is used to analyze unsteady flow and adjoint fields. To stabilize solution, the one-step Jacobi iteration combined with the Lower-Upper Symmetric Gauss-Seidel (LU-SGS/one-step Jacobi) method is used for an implicit solution of the HB equation systems. For an efficient sensitivity evaluation, the effect of an adjoint solver's root mean square (RMS) residual convergence levels on adjoint sensitivity accuracy is thoroughly studied to find an adjoint solver's convergence criteria. The results from the NASA Stage 35 reveal that when the adjoint RMS residual is reduced by three orders, accurate sensitivity information can be obtained, leading to a 41% reduction in computational cost compared with a fully converged one. The LU-SGS/one-step Jacobi method can stabilize the solution while the solution of the LU-SGS equation system diverges quickly. Furthermore, compared with a steady one, the unsteady optimization can achieve more performance gains.
