Abstract: Firstly,for the S_2,m streamline-curvature approach,the blade force decomposition method using two stream surface angles in the cylinder coordinates was associated with that using one stream surface angle of the computing station quasi-orthogonal to the streamline;then a control momentum equation suitable for axial-,radial-and mixed-flow type compressors was derived.Secondly,an integrative bypass-turbomachine through-flow inverse design method was proposed,which employs either the convergence strategy of automatically re-positioning the splitter or that of re-calculating the bypass ratio.So an integrative design method for the compression system of fan added by an axial-centrifugal compressor was presented.This method has been applied to a two-channel two-shaft system consisting of a two-stage fan,two-stage booster and a centrifugal compressor.The flow fields of first fan stage and the centrifugal impeller were checked by computational fluid dynamics(CFD),demonstrating the operational feasibility and flexibility of this method.Thirdly,the physical significance of the axial velocity ratio and its application in an axial-flowpath self-adjusting inverse problem were discussed.The simpleness and convenience of the axial velocity ratio as a design parameter are showed by another example.