13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Optimal design in inner loop Parametric structural model Feature-based parametric FE modeling DOE Strength analysis Sub 1 database Sub 1 Object and constraints approximation Fluid-solid closely coupled analysis System optimization Object: design obiect Constrainte: disciplinary compatibility constraints Strength opt Object: compatibility constraints Constraints: structural constraints Aerodynamics opt Object: compatibility constraints Constraints: structural constraints = Strength analysis Aerodynamics analysis Strength Scale function No Aerodynamics scale function Update database Update Convergenc e ？ Yes No Optimal value DOE Parametric aerodynamics model Fluid FE model Aerodynamics analysis Sub 2 database Sub 2 Object and constraints approximation Update = Update database Figure.2 Multiple-precision optimization strategy The figure 2 shows the multiple-precision optimization strategy which is the CO strategy referring the couple on the turbine blade MDO. This strategy will employ the coupled analysis into the CO strategy by using VCM technology. The way does not only improve the precision, but also makes the optimization results with the higher feasibility. The system level optimizer connects two sub-system optimizers which are used for processing the structure strength optimization and the fluid optimization. The database of the discipline 1 and discipline 2 contains their discipline analysis response and the corrected result at every DOE points. The object and constraint function in the sub-system optimizer is gain by the least square method at the database. The characteristic of fig.2 is nesting a CO strategy in the systemic loop. The optimal value of the CO will accept the aerodynamics analysis, the structure analysis and the flow-solid closely coupled analysis. The former two belong to the medium precision analysis. The latter's response data provides the scale function for the former two. Therefore the CO strategy is skeleton. The various precise methods are the core, and the VCM is the organization mode joining each element. The difference value of the high precision analysis, 3 h 1 h ( ) ( ) 10 i i f x f x ∗ ∗ − + − ≤ , is less than 3 10− as the convergence criterion. 4. Coupled Analysis and MDO on the turbine blade 4.1. Model Parameters The structure includes a shroud and a blade whose parameters are shown in figure 3 [16]. The nine shroud parameters are empirically chosen in this optimization, while this paper chooses six blade parameters which are the axial length ( 1 DZ , 2 DZ and 3 DZ ) and installation angle ( 1γ , 2γ and 3γ ) on three sections of the hub, middle, and tip are blade parameters, as shown in fig.4. They have more influence on the aerodynamic performance. Constructing approximation of the fluid discipline needs at least 28 DOE points for the aerodynamics analysis. The approximate equations of the structure discipline need at least 136 DOE points. Design variables are { } 1 2 , X X X = , including:
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