Abstract: An optimal velocity distribution on the wall of a two-dimensional diffuser has been obtained by means of the optimal control theory and the experimental formula Which can be used to predicate the separation of turbulent boundary layer. According to it, then, by solving an inverse problem in the Φ-Ψ plane, we yield an optimal shape of the diffuser. In order to avoid the boundary layer separations in the diffuser, the parameter Γ, should be given a value of about-0.04～-0.05. The comparison between the calculations and experimental results shows that the optimal design method provided in the paper is fairly satisfactory and can be used in the engineering practices.

Key words: 极大值原理, 扩压器, 紊流边界层, 最优控制