A three-dimensional inverse method using Navier-Stokes equations for turbomachinery blading

A new numerical method for solving fully three-dimensional inverse shape de sign problem of turbomachinery blading has been developed. The general inve rse problem refers to the problem in which the pressure distributions on su ction and pressure surfaces of blade are given, but the corresponding blade profile is unknown. In this paper, the calculations are based on the 3D Na vier-Stokes equations expressed in terms of nonorthogonal curvilinear coord inates and corresponding nonorthogonal velocity components, and the explici t time marching algorithm and Baldwin - Lomax turbulence model are adopted. A special treatment for boundary conditions on blade surfaces is employed to satisfy the given pressure distribution. In computational process, an in itial blade profile is supposed at starting, and then the blade surfaces wi ll move regularly with time steps in the time marching process until the co nvergence is reached. The movement velocities at every point of blade surfa ces are obtained from the solution of the Navier-Stokes equations. After ea ch revision of the blade profile, the grid is reconstructed, and the aerody namic parameters need to be transferred between the old and new grid points by an accurate interpolation method. Thus the viscous inverse problem is s olved in a new process. The computational results for two test cases indica te that the method presented in this paper is very effective.