Very fast and accurate flow calculation and performance prediction of multistage axial flow turbines at design and off-design conditions was performed using a compressible steady state inviscid through-flow code with high fidelity loss and mixing models. The code is based on a stream function model and a finite element solution procedure. 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. Optimization was performed using our hybrid constrained optimization code that includes the following modules: genetic algorithm, simulated annealing, modified simplex method, sequential quadratic programming, and a gradient search algorithm. Switching among the modules was performed automatically. By varying a relatively small number of geometric 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. Thus, an optimized meridional flow path can be found that is defined by the optimized shape of the hub and shroud. The multistage design optimization system has been demonstrated using an actual two-stage axial gas turbine as an example. The comparison of computed performance of an already very high efficiency initial design and its optimized design demonstrates more than one percent improvement in the turbine efficiency at design and significant off-design conditions. The entire design optimization process is feasible on a typical single-processor computer workstation or a personal computer.

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