Aerodynamic Shape Design Methods Based On Data Dimension Approaches

Regards to aerodynamic shape design, design ability, efficiency, robustness anddependence on experience are four main determinant factors. Traditional inversedesign method has shortage of strong experience dependence, poor robustness anddesign ability, but has advantage of high efficiency. Optimization method performswell in robustness and experience, but there are some problems influencingpracticality: efficiency of method based on modern heuristic algorithm isunsatisfactory, and method based on gradient information algorithm has no globalsearching ability. Data involved in aerodynamic shape design is mainlymultidimensional, such as design variables and discrete flow field solution. Higherdimension data always relates to complex problem. Data dimension reduction methodcan realize to reduce data dimension efficiently, and certainly, the retention data canhold the main feature, at last, the problem is simplified.Against the main problems existing in aerodynamic shape design, this paper,considering thought of data dimension reduction and concrete methods, has developedthe following researches.1. Three basic aerodynamic shape optimization design systems have beenestablished for different use. The first system, which evaluates aerodynamicperformance directly, is based on improved differential evolution algorithm and quickevaluation programs for aerodynamic performance and has global optima searchingability. This system is suit for initial design for global optimal problem. The secondsystem, which evaluates aerodynamic performance by prediction approach, is basedon improved differential evolution algorithm and Kriging surrogate model. Thissystem is suit for high accuracy design with less variables in global optima problem.At last, the third system is based on improved gradient descent searching method,discrete adjoint solver and RANS solver. The third system is propitious to highaccuracy design with more variables for local optimal.2. The typical data dimension reduction methods have been studied. In the study oflinear aspect, two methods, POD and SVD, are introdeuced respectively, andequivalence of the two methods has been proved theoretically, meanwhile, thedifference between POD and SVD also is elaborated. In nonlinear data dimensionreduction aspect, properties of ISOMAP algorithm and L-ISOMAP algorithm whichis developed from ISOMAP have been researched. Based on minimum subset coverand SVD, a novel neighborhood parameter and manifold intrinsic dimension estimation method has been developed. This method reduces calculation time atmaximum degree when estimation accuracy is held.3. Gappy POD aerodynamic shape inverse design method has been improved. Indetail, two improvements have been development. Firstly, the optimum snapshotsubstitution sample method is used to replace original random sample method, andthis strengths the ability of samples fitting design target. Secondly, according originalerror of each iteration, a real-time modification on target pressure distribution methodhas been developed for enhancing design accuracy estimation. The tests indicate:above modifications can obviously improve the precision of Gappy POD inversedesign method in case of equal calculation efficiency.4. Inverse design method and optimization design method have been combined inaerodynamic design process to realize their complementary advantages. The basictrain of the idea: the first step is to use improved Gappy POD inverse design methodto design roughly, the second step is using optimization method to design accurately.Test cases indicate that the combination strategy has advantages of strong designability, high efficiency, good robustness and low experience dependency.5. A novel flow field solving accelerating idea, based on initial flow fieldprediction, has been developed for shortening flow field solving time. This paper hascome up with two methods for initial flow filed prediction: the first method is basedon geometric similarity criterion, while the second method is based on combination ofsurrogate model and POD together. The test examples indicate that both of theprediction methods can effectively accelerate flow field solution and the secondmethod performs better. In order to minimum time needed for optimization process,one strategy, which appropriately matches those two methods according to theircharacteristics, has been proposed.6. An idea of filtering and reconstruction design space has been proposed. A newmethod of handling geometric constraints in aerodynamic shape design optimizationhas been established by combining manifold Learning algorithm and manifoldstructure reconstruction technology. Test examples indicate: the unconstrained designspace construction method can effectively improve efficiency of optimization systembased on modern heuristic algorithm which evaluates aerodynamic performancedirectly, and also the system based on gradient information. While the methodproposed above does not work to the optimization system using surrogate model.7. L1T2muti-element airfoil has been optimized by using global optimization system based on surrogate model. Flow field solving accelerating technology basedon initial flow field prediction is used in the process of optimization, so75%time costfor flow field solving has been saved. Compared with original configuration, theoptimization result has a promotion of8.63%in Cl.8. The wing of some long-range wide passenger plane has been designed roughlyby using global optimization system based on evaluating aerodynamic performancedirectly and improved Gappy POD inverse design method respectively, and the designtarget is minimum cruise drag. The results indicate that inverse design result has morepotential in follow-up fine design than optimization result. Based on this conclusion,the inverse design result has been used for fine design by using optimization sysytembased on gradient information. The design space filtering and reconstructiontechnology has been used in the process of optimization. Comparing the optimizedconfiguration with the original configuration, reduction of the drag is up to6.2%,meanwhile, all the geometric constraints are satisfied.