Research On Two-Dimensional Shape-Optimization Method Based On Adjoint For Aerodynamic Design

In this paper,an adjoint-based two-dimensional shape-optimization method is introduced.In the optimization frame,couples of theories are used including flow equation,adjoint,gradient computation,parameterization,dynamic grid and optimization algorithms.Two-dimensional Euler equations is employed to solve the flow field with the method of variable reconstruction and Roe scheme included.At last,the equations are solved through implicit pseudo-time stepping.The computation of gradients which are necessary in optimization is carried out with the help of discrete adjoint.It could make the gradients-computation very efficient.Besides,we could solve several adjoint equations simultaneously for saving time.We describe an airfoil by means of Chebyshev polynomials. The parameterization is finished with dozens of coefficients set.In the process of optimization,all the grid coordinates should be changed after the shape of airfoil has deformed.A mesh deformation technique,known as spring analogy,is used to evaluate the displacements of all grid nodes.Finally,we could make the aerodynamic properties of airfoil better through an optimization algorithms in which all the theories shown above are integrated.