Investigationof Discrete Adjoint Optimization For Unstructured Mixed Grid

Shape is crucial for aircraft, because shape determines its aerodynamic characteristics, and in turn determines its flight characteristics. With the development of computer and CFD technology, it is more and more valued to combine CFD and optimizing methods in optimization design of the aircraft aerodynamic shape. Methods without gradient computing, for example, genetic algorithms and simulated annealing, need a huge amount of computation, while many designvariables are used. So the widely using of complex aerodynamic shape optimizationresultes indifficulty. After the introduction of the agent model,the quantity of computation has been decreased. However, the agent model still existscertain similarityin refined aerodynamic optimization.Combined with optimization methods, adjoint optimization method completes aerodynamic shape optimization by solving the adjoint equations of flowfield to obtain sensitive derivative of the objective function indirectly. Because solving adjoint equation doesn’t depend on the number of design variables, there is no relationship between the calculation amount of iterative optimization and the number of design variables. This isthe most significant advantage of adjoint.optimization, avoiding the problem of a great amount of calculation, andmakes it become viable that masses of variable are used in engineering design optimization problems.It is very convenient to distribute grids in complex shape using unstructured grid which has good flexibility, but doesn’t have the limit of nodes, thus, the unstructured grid is widely used in the application of numerical simulation, and has a bright application prospect for three-dimensional complex shape.The discrete adjoint optimization design system for aircraft aerodynamic shapeis established by using mature flowfield solver named MFlow, one dimensional search method and Free Form Deformation technique, based on unstructured grid. The building methods of adjoint equations for Euler equation, RANS equation using SA turbulence model, and RANS equation using SST turbulence model are investigated. The contents of this article are divided into the following eight chapters:The first chapter is an introduction, a brief description of the optimization algorithm development, especially on the discrete ajoint optimization based on unstructured mesh. And the main contents of this article are given.The second chapter is for aerodynamic numerical simulation method. The flowfield solver named MFlow is used:Due to the adjoint equation and flow field equation are tightly coupled, this chapter describes the methods usedfor the system.The third chapter is for the construction and solving of the adjoint equation. Jacobian matrix corresponding to inviscid flux, viscidflux, and the objective function, differenceof inviscid flux Jacobian matrix between firstand secondorderprecision, difference of Jacobian matrix between the boundary and inter cell, simplification strategy of the limiter, the turbulent viscosity coefficient and other parameters, areanalyzed and studied. Jacobi matrices for residual of flowfield and the objective function of drag reduction/increase of the lift to drag ratio are given. LU-SGS method is applied in the solving of the adjoint equation, based onfinite volume, and before and post-scan of the ajoint equation are described. Meanwhile, a parallel multigrid algorithm is implemented to solve discrete adjoint equation in order to improve the efficiency. Appropriate structures of parallel data are proposed. Parallel efficiency and speedup on hundreds of nuclear arestudied.The forth chapter is for mesh deformation and optimization methods.A brief introduction to the Free Form Deformation techniques used in this article is given. And the answer is also described about how to select the design variables. Several deformation examples are given in the section. A brief introduction to the one dimensional search method is givern, with popular search criterion and the search direction calculation methods.The fifth chapter is accompanied by validation and analysisof optimization method, using M6 wing. Simplification strategiseof the limiter and the turbulent viscosity coefficientare studied. Afrer optimization is completed respectively with Euler equation, SA turbulence model and SST turbulence model, difference is compared on the presence and absence of geometric constraint and the differences is given about crosss ectional shape and pressure distribution of the wing. The influence of search criteria and search direction calculation methods on optimization result is researched also.Mixed adjoint methodis advanced in the sixth chapter, include mixing different order and different scheme, and the results are compared and analysised using mixed adjoint method for M6 wing.Optimized instance is given in the seventh Chapter, using established optimization system to achieve the inverse design for EH1590, and to achieve optimization for DLR F6 wing-body and wing shape with the purpose of reducing drag. Optimization status are their cruise, through design variables changing the shape of the wing, and achieving automatic optimization for the objective function.Finally, in closing remarks, the review is given about this work, whit pointing out the deficiencies and future research directions.