Aerodynamic Shape Optimization By Stackelberg Game Coupled With The Continuous Adjoint Method

Aerodynamic shape optimization design is a technique that uses numerical methods to mod-ify aircraft's shape automatically in order to improve its perfonnance,which is a major part of flight vehicle design.With the increasing requirements of aircraft design and the improvement of performance,the modern aerodynamic design is supposed to be more sophisticated and efficient.Therefore,critical technologies in the aerodynamic optimization design should be investigated to build an efficient and reliable aerodynamic optimization system.In this paper,on account of the practical engineering design requirements,an aerodynamic optimization framework based on the Stackelberg game strategy coupled with the continuous adjoint method is established,which can solve both steady/unsteady and single/multi-objective optimization problems.The main research issues and achievements in this paper are as follows:1.Based on the continuous adjoint formulation for steady flows,the unsteady continuous ad-joint method is extended and developed.To analyze the effectiveness of the methodology,gradients provided by the continuous adjoint and finite differencing approaches are compared.2.The basic optimizer for efficient single-objective aerodynamic shape optimization design which is suitable for optimizing large number of design variables is proposed.Combined with flow solver,Hicks-Henne/FFD geometry parameterization,mesh deformation,continuous adjoint solver and SLSQP,gradient-based aerodynamic shape optimization design system is established.3.An aerodynamic optimization design framework for conducting both steady/unsteady and single/multi-objective aerodynamic shape optimizations is established,where the Stackelberg game strategy is coupled with the continuous adjoint method.In the framework,the leader and the fol-lower in the Stackelberg game strategy take turns to find its optimum by means of the continuous adjoint method.4.Note that the success of the proposed framework is subject to several influential factors,including the maximal number of iterations for each player,the allocation strategies of design vari-ables and objective functions to different players.In this study,the impacts of these factors are numerically investigated,aimed at providing some useful inferences for the choice of these factors.A set of inferences are obtained:Allocate the objective function that needs more benefits to the leader;Split design variables such that the profile defined by each subset of design variables allo-cated to one player is geometrically continuous;Map the subset of design variables defining the profile with higher surface sensitivities to the leader;Set a moderate or slightly high design cycle to make the optimization of each player basically stable;thus getting acceptable results at bearable computational costs.5.Based on the aerodynamic optimization design framework and a set of inferences estab-lished in this paper,several cases with more engineering interests are processed,i.e.,the steady single/multi-objective optimization of the RAE2822 airfoil,the ONERA M6 wing and the Com-mon Research Model.The optimization results indicate the the usefulness and effectiveness of the proposed method and the inferences obtained in steady single/multi-objective optimization prob-lems with a complex numerical model or a large number of design variables.6.Based on the aerodynamic optimization design framework and a set of inferences estab-lished in this paper,the unsteady single/multi-objective optimization of the NACA 64A010 airfoil is conducted with the baseline and the optimized flow field analyzed by the dynamic mode decom-position.The optimization results indicate the the usefulness and effectiveness of the proposed method and the inferences obtained in unsteady single/multi-objective optimization problems with a complex numerical model or a large number of design variables.