Maximizing multistage turbine efficiency by optimizing hub and shroud shapes and inlet and exit conditions of each blade row

Abstract

By matching a well established fast through-flow analysis code and an efficient optimization algorithm, a new design system has been developed which optimizes hub and shroud geometry and inlet and exit flow-field parameters for each blade row of a multistage axial flow turbine. The compressible steady state inviscid through-flow code with high fidelity loss and mixing models, based on stream function method and finite element solution procedure, is suitable for fast and accurate flow calculation and performance prediction of multistage axial flow turbines at design and significant off-design conditions. A general-purpose hybrid constrained optimization package has been developed that includes the following modules: genetic algorithm, simulated annealing, modified Nelder-Mead method, sequential quadratic programming, and Davidon-Fletcher-Powell gradient search algorithm. The optimizer performs automatic switching among the modules each time when the local minimum is detected thus offering a robust and versatile tool for constrained multidisciplinary optimization. An analysis of the loss correlations was made to find parameters that have influence on the turbine performance. By varying seventeen variables per each turbine stage it is possible to find an optimal radial distribution of flow parameters at the inlet and outlet of every blade row. Simultaneously, an optimized meridional flow path is found that is defined by the optimized shape of the hub and shroud. The design system has been demonstrated using an example of a single stage transonic axial gas turbine, although the method is directly applicable to multistage turbine optimization. The comparison of computed performance of initial and optimized design shows significant improvement in the multistage efficiency at design and off-design conditions. The entire design optimization process is feasible on a typical single-processor workstation.