Aerodynamic Shape Optimization Methods With Discrete Adjoint And Data-driven Techniques

Aerodynamic shape optimization plays an important role in improving aircraft efficiency,comfort,and safety.With the development of large-scale parallel computational techniques,different kinds of aerodynamic shape optimization methods have been applied in different stages of aircraft design,which shortens the design cycle.This thesis conducts researches on gradient-based aerodynamic shape optimization and gradient-free aerodynamic shape optimization with automatic differentiation,machine learning,and active subspace methods.In order to improve the optimization efficiency,global convergence,and robustness,a two-step aerodynamic shape optimization method is proposed based on the combination of the domain-decomposition reduced-order method,the adjoint method,the surrogate model,and the gradient-based algorithm.The main contributions of this work are summarized as follows:(1)A discrete adjoint method for a three-dimensional structured-mesh RANS solver is developed using automatic differentiation(AD)techniques,and a gradient-based aerodynamic shape optimization framework is established for aerodynamic shape optimization.The adjoint method only involves the AD code in the cell level,and then cycles all cells to construct the whole Jacobian matrix to avoid memory surges.The adjoint equation is solved via GMRES to increase the efficiency.The optimization framework couples the adjoint method with SLSQP,RBF mesh deformation method,and kinds of parameterization methods.The validations with finite difference gradient values demonstrate the accuracy of the adjoint solver,and two airfoil design cases show the robustness of the optimization framework.(2)An aerodynamic database for airfoils is constructed with the camber-thickness shape mode method,and an accurate online aerodynamic analysis model is developed based on the database and machine learning techniques.Coupled with a gradient-based algorithm,a fast airfoil design method is proposed.Camber-thickness mode method is proposed in order to efficiently control airfoil shapes.The bounds of higher-order modes are defined using an interpolation method based on dominant modes,which makes the design space both large and filtered.With the CFD sampling of the design space,a big aerodynamic database is constructed with more than 100,000 airfoils.A mixture of experts strategy coupled unsupervised clustering algorithms with supervised classification algorithms is adopted to construct the aerodynamic model.Local aerodynamic models are trained in clusters,and all local models are combined as a global model based on weights provided by the classification model.Based on a number of airfoil tests,the global aerodynamic model is validated to be almost as accurate as RANS.Airfoil shape optimization with the aerodynamic model is done in real time,and the optimization result is almost the same with that by RANS-based optimization.(3)A fast evaluation method of the aerodynamic active subspace is developed with sample smoothing and discrete adjoint methods,and a new global efficient optimization method,ASM-EGO,is proposed to increase the optimization efficiency for high dimensional problems.ASM-EGO reduces the number of design variables in high-dimensional optimization via the active subspace method and thus avoid the “curse of dimensionality”issue.The smoothing procedure based on the Laplacian method significantly decreases the sampling number in the determination of the active subspace,and the adjoint method ensures the efficiency in gradient evaluations which further reduce the cost.ASM-EGO is used in the optimization of the ONERA M6 wing with 220 shape variables,and the result indicates its high efficiency in high-dimensional problems.(4)A data-driven constraint methodology is proposed for high-fidelity gradient-based optimization.This methodology converts design experience to continuous and differentiable functions with data analysis,which is used to make the design optimization more robust.Based on mode analyses and correlation analyses of a large number of designs,the useful feature is captured using the Gaussian Mixture Model(GMM),and then the probability function of GMM is used to detect how much an airfoil or wing section satisfies the feature.In order to solve the thin leading edge issue in the gradient-based optimization of airfoils and wings,a data-driven constraint for thickness modes is proposed based on the analysis of the UIUC airfoil database.The optimization results show that this constraint significantly addresses the thin leading edge issue and improves the design robustness.(5)A hybrid two-step aerodynamic shape global design optimization method is proposed based on the proper orthogonal decomposition(POD)reduced-order model,automatic domain decomposition method,and the adjoint method,which improves the optimization efficiency for detailed design.POD with the Petrov-Galerkin projection is investigated to provide fast flow predictions.In order to improve the prediction accuracy,an automatic domain decomposition method based on the estimation of POD error is developed,and the POD predication in the sensitive domain is further corrected by the CFD solver.The adjoint method of this flow evaluation method is developed to solve the gradient efficiently.In the hybrid two-step method,gradient-free algorithm coupled with surrogate models is used as a first global search,and then a gradient-based optimization is followed up to improve the convergence efficiency.POD model is constructed with the snapshots collected in the first-step optimization,and the POD and automatic domain decomposition techniques are adopted to accelerate flow and adjoint solutions in the second-step optimization.The optimization results of a two-dimensional airfoil design test and a three-dimensional wing design test highlight the efficiency of the proposed method and show its strict convergence.