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.