Research On Optimum Aerodynamic Design Using Simulated Annealing Algorithm And POD

The goal of this dissertation is to apply Simulated Annealing Algorithm to aerodynamic shape optimization problems on the CFD-Solver and to develop a new gradient free optimization method that could decrease time cost greatly for aerodynamics problems. The work presented in this thesis comprises of CFD analysis, shape parameterization and optimization algorithm.As a good optimization method Simulated Annealing Algorithm (SAA) has features of simplicity, flexibility, wide application, high efficiency and few initial condition. And it's appropriate to parallel computing. However, the Simulated Annealing Algorithm will expand too much time to estimate the values of objective function when applied to aerodynamics optimizations. The way to remedy this problem in this dissertation is by improving the efficiency of optimizer and the CFD-solver. Our CFD-Solver is base on the modification to the Proper Orthogonal Decomposition (POD) method that can produce a finite series of basis functions or modes through the solution of snapshots. We could construct arbitrary solutions to the Euler equation by these modes with very small computational expense and decreased unknowns and give a quick estimation of objective function. In spite of these advantages, we should concentrate on how to extend the representation of modes, how to apply to unstructured grids, etc. And when combining POD and SAA, it is necessary to know how to represent the shape and how to control the range of seeking and iteration number. Our researches in this paper give the solution to the problems above. And we successfully finish the aerodynamic optimization.The advances achieved in this paper are as follows:Solving the Euler equation with LU-SGS implicit algorithm on unstructured grids, mesh reordering will bring on imbalance. First the amplification factor of the LU-SGS implicit algorithm is analyzed for scalar function. Then we validate the effects through a numerical test we design. The results show that balance is superior to imbalance and imbalance can also achieve convergence.A new method, perturbing airfoil function, of obtaining snapshots in POD method is presented here. It is better than that of adding Hicks-Henne bump...