This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows.General formulation of the continuous ...This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows.General formulation of the continuous adjoint equations and the corresponding boundary conditions are derived.With the adjoint method,the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function,regardless of the number of design parameters.An inverse design of airfoil is firstly performed to study the accuracy of the adjoint gradient and the effectiveness of the adjoint method as an inverse design method.Then the method is used to perform a series of single and multiple point design optimization problems involving the drag reduction of airfoil,wing,and wing-body configuration,and the aerodynamic performance improvement of turbine and compressor blade rows.The results demonstrate that the continuous adjoint method can efficiently and significantly improve the aerodynamic performance of the design in a shape optimization problem.展开更多
This study presented a hybrid model method based on proper orthogonal decomposition(POD) for flow field reconstructions and aerodynamic design optimization. The POD basis modes have better description performance in a...This study presented a hybrid model method based on proper orthogonal decomposition(POD) for flow field reconstructions and aerodynamic design optimization. The POD basis modes have better description performance in a system space compared to the widely used semi-empirical basis functions because they are obtained through singular value decomposition of the system.Instead of the widely used linear regression, nonlinear regression methods are used in the function response of the coefficients of POD basis modes. Moreover, an adaptive Latin hypercube design method with improved space filling and correlation based on a multi-objective optimization approach was employed to supply the necessary samples. Prior to design optimization, the response performance of POD-based hybrid models was first investigated and validated through flow reconstructions of both single-and multiple blade rows. Then, an inverse design was performed to approach a given spanwise flow turning distribution at the outlet of a turbine blade by changing the spanwise stagger angle, based on the hybrid model method. Finally, the span wise blade sweep of a transonic compressor rotor and the spanwise stagger angle of the stator blade of a single low-speed compressor stage were modified to reduce the flow losses with the constraints of mass flow rate, total pressure ratio, and outlet flow turning.The results are presented in detail, demonstrating the good response performance of POD-based hybrid models on missing data reconstructions and the effectiveness of POD-based hybrid model method in aerodynamic design optimization.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.51206003 and 51376009)the National Science Foundation for Post-doctoral Scientists of China(Grant Nos.2012M510267 and 2013T60035)
文摘This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows.General formulation of the continuous adjoint equations and the corresponding boundary conditions are derived.With the adjoint method,the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function,regardless of the number of design parameters.An inverse design of airfoil is firstly performed to study the accuracy of the adjoint gradient and the effectiveness of the adjoint method as an inverse design method.Then the method is used to perform a series of single and multiple point design optimization problems involving the drag reduction of airfoil,wing,and wing-body configuration,and the aerodynamic performance improvement of turbine and compressor blade rows.The results demonstrate that the continuous adjoint method can efficiently and significantly improve the aerodynamic performance of the design in a shape optimization problem.
基金supported by the National Natural Science Foundation of China(Grant Nos.51676003,51206003 and 51376009)
文摘This study presented a hybrid model method based on proper orthogonal decomposition(POD) for flow field reconstructions and aerodynamic design optimization. The POD basis modes have better description performance in a system space compared to the widely used semi-empirical basis functions because they are obtained through singular value decomposition of the system.Instead of the widely used linear regression, nonlinear regression methods are used in the function response of the coefficients of POD basis modes. Moreover, an adaptive Latin hypercube design method with improved space filling and correlation based on a multi-objective optimization approach was employed to supply the necessary samples. Prior to design optimization, the response performance of POD-based hybrid models was first investigated and validated through flow reconstructions of both single-and multiple blade rows. Then, an inverse design was performed to approach a given spanwise flow turning distribution at the outlet of a turbine blade by changing the spanwise stagger angle, based on the hybrid model method. Finally, the span wise blade sweep of a transonic compressor rotor and the spanwise stagger angle of the stator blade of a single low-speed compressor stage were modified to reduce the flow losses with the constraints of mass flow rate, total pressure ratio, and outlet flow turning.The results are presented in detail, demonstrating the good response performance of POD-based hybrid models on missing data reconstructions and the effectiveness of POD-based hybrid model method in aerodynamic design optimization.
