value of the low-fidelity modeling for the goals of flow path parameters optimization.

Problem formulation of MDO is complicated by the necessity to integrate the fragmented solvers used for the flow, the blade strength/vibration and other computations and the modules responsible for optimization in an uniform system. The modules for control functions parameterization and tools for parameterized blades and interblade channels meshes generation belong to main non-standard components of that system. It is worth to note that the parameterization problem tightly bound to the optimization problem formulation and to the method of 3D profiling of the blade airfoil, either. As a rule, the blade airfoil optimization problem formulations extracted from publications offer to parameterize the blade airfoil using parameters that don’t impact the profile section shapes, i.e. the profile stagger angle in the sections or the blade lean/sweep angles.

We used more flexible parameterization for profiling, including parameters that affect the planar sections configuration (wedge angles, edges stagger angles, profile stagger angle etc.). If design of experiment technique is used in the search for the blade shape optimum, we suppose the following algorithm of multidisciplinary optimization as most adoptable:
1. Selection of m cross-section parameters on which the profiles optimization will be performed (m=3…6).
2. Selection of n cross-sections, in which the parameterized profiles will be built. In practice, three sections are enough for the method of the airfoil profiling used in AxSTREAM.
3. Generation of design of experiment for m*n variables in the frame of assigned ranges of parameters variation with the help of a DoE tool like AxPLAN.
4. Blade airfoil construction by means of embedded in AxSTREAM module in each point of design of experiment with subsequent export of the airfoil stored in one of the standard CAD object transition format (IGES, for instance) to a mesh generation tool for further aerodynamic and strength computations.
5. Aerodynamic, structural and vibration analyses performed with corresponding solvers. At this phase of optimization, each point computation is carried out independently.
6. According to results of computations in AxPLAN, it is possible to restore the response functions (efficiency, stresses, weight, etc.) as quadratic functions and formulate and solve different tasks of the blade airfoil optimization. For example, it is possible to assign such criterions as:
- minimum of aerodynamic loss at allowable stresses and vibration constraints;
- minimum of weight strength and vibration constraints.