Based on the optimal control theory and Navier-Stokes equations, aerodynamic design of airfoil with multi-constraint conditions, such as aerodynamic and geometric constraint conditions, is studied. According to a given problem, the corresponding adjoint equations, boundary conditions and final cost function formulation are derived in the computational space. In order to achieve the requirements of the numerical solution, final formulations in the physical space is also achieved. Numerical methods are developed effectively. By integrating the aspects, such as the flow analysis, the solution of adjoint equations, gradient solution, optimal arithmetic and grid generation etc., an aerodynamic design method involving drag reduction is successfully developed. Testing results show that the method has outstanding merits in the above aspects. It is effective and feasible for aerodynamic design with a large number of design variables. Computational time consumption is less than the conventional aerodynamic design method.

It is interesting for designer how to reduce drag of transonic wing which meets design lift requirement. Based on adjoint equation theory and using Euler equations, an optimization design method of transonic wing with drag reduction and constant lift coefficient is developed. According to the cost function given, three dimensional adjoint equations and their boundary conditions in physical space are dreived, and a numerical method is developed to solve the three dimensional adjoint equations. The sensitivity derivation of objective function with respect to design variables can be obtained by using grid perturbation method, and the quasi-Newtonian algorithms are used. Some numerical tests are made for the drag reduction with constant lift coefficient. The test results show that shock strength on wing surface will become much weaker than that of initial wing, thus drag may be reduced effectively.

The Collar grid method and the virtual grid method are jointly used in the embedding technique to solve the problem of finding the interpolating cells among the internal and external boundary points near the joint regions. With different boundary planes generated along different fixed surfaces, the Collar grid obtained using the hyperbolic partial differential equations can ensure to generate high-quality grids and to provide real interpolating cells for the boundary points on the joint regions. The main purpose of the virtual grid is to convert a solid wall boundary condition into an interface condition while no fluid flow computations are conducted within the virtual grid. The computational results of several configurations show that the currently developed embedding technique with Collar grid and virtual grid can effectively treat the geometrical configuration and can more accurately predict the flow over complex configurations with intersecting surfaces.

The Euler/Kirchhoff method is adopted to calculate the far field noise of UH-1H rotor,and the calculated results are compared with the measured data.The effect of rotor blade tip shape on high speed rotor noise is investigated.The results show that,with the decreasing of airfoil thickness near the blade tip or the increasing of the taper ratio near the blade tip and the sweep of the blade tip, the high speed rotor noise can be reduced to some extent.