Study On Axial Turbine Airfoil Design Based On Response Surface Method

Axial turbine,as fluid machinery that converts the internal energy of working fluid into mechanical work,has the characteristics of large mass flow and high power,is widely used in the field of energy and power.In the design process of an axial turbine,obtaining the required turbine blades according to the low-dimensional design results is the most important link,and every blade is mainly formed by stacking the airfoils of various sections.This paper studies the relationships between the design parameters and geometric parameters of turbine airfoils.Firstly,use the aerodynamic design principles of axial turbine,a one-dimensional design program for axial turbine is written using MATLAB software.At the same time,the method of parametric modeling of turbine blade is studied.Based on the existing research work of the research group,the parametric modeling program of turbine blade is debugged with C++ software to improve the modeling method.The effectiveness of the one-dimensional design program and blade modeling program are verified by using the NASA TM X-3289 three-stage axial turbine.Secondly,study the principles of Kriging response surface method and Analysis of Variance method,and verify the feasibility of two methods.Take the airfoil design parameters,namely inlet flow angle,outlet flow angle,outlet Mach number,and Zweifel loading coefficient as independent variables,the airfoil geometric parameters of incidence angle,deviation angle,leading edge wedge angle,trailing edge wedge angle,suction surface and pressure surface profile control parameters are used as dependent variables.Adopt the Kriging response surface method to construct the functional relationships between the design parameters and geometric parameters of turbine airfoils,which is the airfoil response surface.Finally,the Analysis of Variance method is used for the airfoil response surface to analyze the contribution of the airfoil design parameters to each geometric parameter.The results show that all four airfoil design parameters are very important.By predicting the unknown points in the airfoil response surface design space,it is proved that the airfoil response surface has better effect,the predicted response surface airfoils are close to the optimized airfoils.But some predicted airfoils do not meet the requirements for selecting the optimal airfoils,therefore,the accuracy of the airfoil response surface needs to continue to be improved.In order to further study the influence of the response surface airfoil and optimized airfoil on the turbine three-dimensional performance,take a three-stage axial turbine as an example,its blade section airfoils which fit the use range of airfoil response surface are replaced with the response surface airfoils,and a three-dimensional numerical calculation is carried out on this basis.The results show that the difference between the response surface airfoil and the optimized airfoil has almost no impact on the three-dimensional performance of turbine if the response surface airfoil meets the requirements for selecting the optimal aifroil.The research results of the airfoil response surface in this paper provide an idea and a tool for the intelligent design of turbine airfoils,which can be used in the design of axial turbine.