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
In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increa...In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increasing number of design variables,it becomes difficult to maintain the smoothness on the surface which consequently makes the optimization process progressively complex.In this paper,smoothing methods based on B-spline functions are studied to improve the smoothness and design efficiency.The wavelet smoothing method and the least square smoothing method are developed through coordinate transformation in a linear space constructed by B-spline basis functions.In these two methods,smoothing is achieved by a mapping from the linear space to itself such that the design space remains unchanged.A design example is presented where aerodynamic optimization of a supercritical airfoil is conducted with smoothing methods included in the optimization loop.Affirmative results from the design example confirm that these two smoothing methods can greatly improve quality and efficiency compared with the existing conventional non-smoothing method.展开更多
The influence of complicated interaction between the flow field and heat transfer in cooled turbines becomes more and more significant with the increasing turbine inlet temperature. However, classical through-flow met...The influence of complicated interaction between the flow field and heat transfer in cooled turbines becomes more and more significant with the increasing turbine inlet temperature. However, classical through-flow methods did not take into account the influence of the interaction caused by air cooling. The aerodynamic design and cooling design of cooled turbines were carried out separately, and the iterations between the aerodynamic design and cooling design led to a long design period and raised the design cost. To shorten the design period and decrease the design cost, this paper proposes a concise aero-thermal coupled through-flow method for the design of cooled turbines, taking into account the influence of the complicated interaction between the flow field and heat transfer in cooled turbines. The governing equations, such as energy equation and continuity equation in classical through-flow method are re-derived theoretically by considering the historical influence of cooling with the same method that deals with viscous losses in this paper. A cooling model is developed in this method. The cooled blade is split into a number of heat transfer elements, and the heat transfer is studied element by element along both the span and the chord in detail. This paper applies the method in the design of a two-stage axial turbine, of which the first stator is cooled with convective cooling. With the prescribed blade temperature limitation and the knowledge of the flow variables of the mainstream at the turbine inlet, such as the total pressure, total temperature and mass flow rate, the convergence of the calculation is then obtained and the properties of the flow field, velocity triangles and coolant requirement are well predicted. The calculated results prove that the aero-thermal coupled through-flow method is a reliable tool for flow analysis and coolant requirement prediction in the design of cooled turbines.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.
文摘In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increasing number of design variables,it becomes difficult to maintain the smoothness on the surface which consequently makes the optimization process progressively complex.In this paper,smoothing methods based on B-spline functions are studied to improve the smoothness and design efficiency.The wavelet smoothing method and the least square smoothing method are developed through coordinate transformation in a linear space constructed by B-spline basis functions.In these two methods,smoothing is achieved by a mapping from the linear space to itself such that the design space remains unchanged.A design example is presented where aerodynamic optimization of a supercritical airfoil is conducted with smoothing methods included in the optimization loop.Affirmative results from the design example confirm that these two smoothing methods can greatly improve quality and efficiency compared with the existing conventional non-smoothing method.
基金supported by the National Natural Science Foundation of China(Grant No.51276093)
文摘The influence of complicated interaction between the flow field and heat transfer in cooled turbines becomes more and more significant with the increasing turbine inlet temperature. However, classical through-flow methods did not take into account the influence of the interaction caused by air cooling. The aerodynamic design and cooling design of cooled turbines were carried out separately, and the iterations between the aerodynamic design and cooling design led to a long design period and raised the design cost. To shorten the design period and decrease the design cost, this paper proposes a concise aero-thermal coupled through-flow method for the design of cooled turbines, taking into account the influence of the complicated interaction between the flow field and heat transfer in cooled turbines. The governing equations, such as energy equation and continuity equation in classical through-flow method are re-derived theoretically by considering the historical influence of cooling with the same method that deals with viscous losses in this paper. A cooling model is developed in this method. The cooled blade is split into a number of heat transfer elements, and the heat transfer is studied element by element along both the span and the chord in detail. This paper applies the method in the design of a two-stage axial turbine, of which the first stator is cooled with convective cooling. With the prescribed blade temperature limitation and the knowledge of the flow variables of the mainstream at the turbine inlet, such as the total pressure, total temperature and mass flow rate, the convergence of the calculation is then obtained and the properties of the flow field, velocity triangles and coolant requirement are well predicted. The calculated results prove that the aero-thermal coupled through-flow method is a reliable tool for flow analysis and coolant requirement prediction in the design of cooled turbines.
