Computational simulation and aerodynamic sensitivity analysis of film-cooled turbines

A computational tool is developed for the time accurate sensitivity analysis of the stage performance of hot gas, unsteady turbine components. An existing turbomachinery internal flow solver is adapted to the high temperature environment typical of the hot section of jet engines. A real gas model and film cooling capabilities are successfully incorporated in the software. The modifications to the existing algorithm are described; both the theoretical model and the numerical implementation are validated.; The accuracy of the code in evaluating turbine stage performance is tested using a turbine geometry typical of the last stage of aeronautical jet engines. The results of the performance analysis show that the predictions differ from the experimental data by less than 3%. A reliable grid generator, applicable to the domain discretization of the internal flow field of axial flow turbine is developed. A sensitivity analysis capability is added to the flow solver, by rendering it able to accurately evaluate the derivatives of the time varying output functions. The complex Taylor's series expansion (CTSE) technique is reviewed. Two of them are used to demonstrate the accuracy and time dependency of the differentiation process. The results are compared with finite differences (FD) approximations. The CTSE is more accurate than the FD, but less efficient. A “black box” differentiation of the source code, resulting from the automated application of the CTSE, generates high fidelity sensitivity algorithms, but with low computational efficiency and high memory requirements. New formulations of the CTSE are proposed and applied. Selective differentiation of the method for solving the non-linear implicit residual equation leads to sensitivity algorithms with the same accuracy but improved run time. The time dependent sensitivity derivatives are computed in run times comparable to the ones required by the FD approach.