stages and modules and numerical modeling results. In particular, we came to the conclusion that in most cases Craig & Cox method [11] provides quite reasonable accuracy of cascades efficiency estimation.

Figure10. Large steam turbine last (5th) stage efficiency calculated with 1D and axi-symmetric models at different steam volume flow rate

Our experience of computational results validation against experimental data and subsequent modification of the modeling methods assures trustworthiness of the AxSTREAM for the flow path analysis and optimization including off-design operation (Fig.10).

Appendix 2

Procedure for blade twist optimization for a stage with AxSTREAM
At the first glance, the optimization procedures integrated in flow path design process may seem too complex and beyond common end user comprehension. In practice, AxSTREAM operates with conventional turbine designeroriented terminology and "walks" designer through all phases of computations that in particular include the following:
- selection of 1D or axi-symmetric problem formulation, Fig. 11;
- assignment of independent variables and response functions for building the formal models with the help of DoE methodology, Fig. 12;
- selection of parameters variation ranges for creation of quadratic models and estimation the error of approximation, Fig. 13 and 14;
- optimization problems formulation and solution with formal models and subsequent results verification with baseline model, Fig. 15.

In the example discussed here, such blade twist parameters (m1 , β_2mid, m2 and blade lean angles) should be found that could provide maximum efficiency at constrained hub reactivity, Fig. 15.

The results of computation with original model, Fig. 17, and formal, Fig. 16, models at the optimal point have a good convergence.

Figure 11. Selecting problem formulation for stage axisymmetric analysis

Figure 12. Assignment of the type of model and independent variables

Figure 13. Selecting ranges of independent variables variation

In conclusion, a geometric interpretation of the optimal solution on the plain of blade twist parameters m1 и m2 is presented, Fig. 18. It demonstrates how sensitive the efficiency to blade twist variation is, and how seriously a constraint on hub reaction degree impacts the optimal solution.