Research On Numerical Prediction Method Of Aerodynamic Flows Based On Model Reduction By Sampling Data Analysis

The fast prediction of aerodynamic flows features prominently in the process of aircraft design and evaluation.With the emergence and rapid development of high-performance computing,computational fluid dynamics(CFD)has shown great potential in flow field prediction and analysis.However,a large number of CFD numerical simulations of flow field still consumes a lot of resources and time,which greatly restricts the design cycle of aircraft.The reduced order model based on data analysis is an effective way to achieve the fast prediction of flow field.In this thesis,the design of experiments(Do E)method of flow field data sampling is systematically analyzed.Combined with dimensionality reduction technology based on the proper orthogonal decomposition(POD),a variety of fast numerical prediction methods of aerodynamic flows are established.A parallel reduced order model(ROM)framework for complex hypersonic flows is developed,and the research work of fast numerical prediction of large-scale flow field that meets the requirements of engineering application is carried out.The main contributes of this thesis are as follows:(1)Based on the analysis and summary of the characteristics of Do E methods,a Delaunay triangulation and gradient-based adaptive sampling method is proposed.A hybrid adaptive sampling method based on Delaunay triangulation is further developed by introducing the entropy weight method and technique for order preference by similarity to an ideal solution.The method can achieve a reasonable trade-off between the space filling of the sampling point distribution and the output characteristics of the function.The biggest advantage of this method is that it can add sampling points one by one without building a surrogate model.By testing three numerical functions,peaks,franke and droplet,the efficiency and robustness of the method are verified,and the aerodynamic prediction of airfoil is carried out with kriging surrogate model.The prediction accuracy of the method is better than that of the full factorial design and other similar sampling methods.(2)An interpolation-based POD ROM is constructed,and a fast prediction method of flow field based on data-fit models is established.The physical space of flow field variables is transformed into POD truncated subspace by POD method,and the order reduction from flow field physical variables to POD basis coefficients is achieved.By using the data-fit surrogate model,the correspondence between the sampling point and the basis coefficients is constructed.The prediction of flow field is done in real time using the method and test results show good precision and efficiency.In order to collect and operate flow data resulting from different grids and achieve the mesh deformation of moving parts in large-scale problems,the efficient parallel algorithms of flow field normalization and mesh deformation are developed based on the datafit models and MPI library.(3)A constrained POD ROM based on Navier-Stokes equations is proposed,and a fast numerical prediction method of aerodynamic flows based on model reduction is established.The constraints in the iteration are formulated by satisfying the physical boundary conditions.To achieve this,a weighting matrix constructed by an improved Gauss weighting function is adopted to determine the contribution of each cell to the constraint term.The result of the interpolation-based POD ROM is chosen as the initial flow field to accelerate convergence of the constrained POD ROM.In the prediction of hypersonic flows,the boundary conditions are effectively constrained,and the convergence problem of Galerkin-POD ROM in predicting complex flow structures,such as shock wave and separation,is solved,which improves the robustness while maintaining high accuracy.Based on the partition parallel strategy of MPI,the parallelization of the method is implemented,which effectively solves the memory overrun problem of 3D complex flow prediction,and lays a foundation for the fast prediction of largescale complex aerodynamic flows.(4)Aiming at improving the efficiency and accuracy of projection-based POD ROM,multistep enhanced ROMs are proposed.1)An enhanced POD ROM based on greedy algorithm is established.The grid samples are selected to approximate the Residual and Jacobian terms.Results show 1/10 of the grid points achieve the same prediction accuracy as the original ROM,and the computation amount of nonlinear terms is greatly reduced.2)A compact POD ROM containing flow field sensitivity information is established.The enhanced POD basis of Jacobi induced inner product is improved,and the prediction accuracy is improved compared with the original ROM.3)A multi-step ROM based on automatic domain decomposition is developed.The two proposed automatic domain decomposition method are based on the information change of flow field and the prediction estimation error respectively.The former is simple and convenient for practical application.(5)Aiming at the practice of engineering application,a practical design optimization platform for supersonic airfoil is built.Based on the analysis of sampling data,a fast evaluation method of hypersonic vehicle aerodynamic performance is established and the corresponding parallel computing software is developed.Class and shape transformation based on B-spline basis function is used combined with wavelet decomposition to enhance the local control and fairing abilities.The fast design optimization of airfoil is achieved.A sequential sampling method and the termination criterion for reentry trajectory of hypersonic vehicle is proposed.According to the given trajectory evaluation conditions,the local POD ROM is constructed to improve the calculation efficiency and prediction accuracy.The results of aerodynamic performance evaluation of typical trajectory show that the computing efficiency is increased by three orders of magnitude compared to CFD.