Aerodynamic Inverse Design Optimization, Multi-objective and Multidisciplinary Design Optimization for Turbomachinery Cascades Zhenping FENG Institute of Turbomachinery, School of Energy & Power Engineering, Xi’an Jiaotong University, No. 28, Xianning West Road, Xi’an 710049, People’s Republic of China [email protected] Keywords: Turbomachinery Cascade, Inverse Design Optimization, MDO, Data Mining Turbomachinery cascade plays an important part in energy-work conversion process, and much attention has been paid to the cascade design in order to achieve the objective of high performance and high reliability. Because the internal flows in turbomachinery cascades are very complicated which are governed by non-linear Navier-Stokes equations, the optimization design method and system for turbomachinery cascades are still the challenging issues in this area. This paper presents some progresses in turbomachinery cascade aerodynamic inverse design optimization, multi-objective and multidisciplinary design optimization performed by author’s team. With the number of design variables in the inverse design of turbomachinery cascades increasing, and the design requirements being more sophisticated, the adjoint method based on the control theory becomes one of the competitive design methods in aerodynamic optimization design, because its sensitivity analysis can be implemented independent of the number of design variables. The adjoint method can be classified into the continuous and the discrete one in accordance with the construction mode of their adjoint systems. By using the continuous and discrete adjoint methods, the implementation issues for each module are studied, which includes blade geometry parameterization based on NURBS, grid generation and grid perturbation technique, numerical solving of the adjoint equations, CFD technique and optimization algorithms, thus an auto-design system of axial turbine blade aerodynamic design is set up. Based on the shape design system, several cases are carried out to verify the accuracy and ability of the adjoint method for the inverse design. A multi-objective and multidisciplinary design optimization method (MDO) is studied. And a high-performance self-adaptive multi-objective differential evolution algorithm named SMODE is programmed and tested for MDO by coupling with the constraint handling method. Based on non-uniformed B-spline, a 3D blade parameterization method is developed. By applying SMODE as the global optimizer and integrating the 3D blade parameterization method, RANS Solver technique and FEM, a MDO of NASA Rotor 37 blade is carried out for the maximization of isentropic efficiency and the minimization of maximum stress. Similarly, by integrating the load-fitting transfer algorithm in parameterization space, a MDO of a typical transonic turbine stage is carried out. Detailed aerodynamic and mechanical comparisons for both cases indicate that the performance of optimized designs is significantly improved. Furthermore, a MDO of a gas turbine blade profile (C3X) and cooling system is performed and an exploration method is developed and applied in this case by using the self-organization map (SOM) based on data mining technique. Detailed analysis indicates that the thermal performance of optimized blades is greatly improved without deteriorating the related aerodynamic performance. Then, insights into the design space are obtained by exploring the interactions among objective functions and design variables with SOM-based data mining.
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