AN APPLICATION OF TOPOLOGICAL ANALYSIS TO STUDYING THE THREE-DIMENSIONAL FLOW IN CASCADES;PART I—TOPOLOGICAL RULES FOR SKIN-FRICTION LINES AND SECTION STREAMLINES

摘要

Based on the working of Lighthill and Hunt et al.,in the present paper the author hasestablished the topological rules adapting to analysing the skin-friction lines and the sectionstreamlines in cascades.These rules are(1)for a rotor cascade without shroud band,thetotal number of nodal points equals that the saddle points on the skin-friction line vectorfields in eachpitch range;(2)for an annular or straight cascade with no-clearances at bladeends,the total number of saddle points is two more than that of nodal points on the skin-friction line fields in a pitch;(3)the total number of saddles in the secondary flow fields oncross-sections in cascade is one less than that of nodes;(4)in the section streamline vectorfields on a meridian surface penetrating a flow passage,and on leading and trailing edgesections,the total number of nodes is equal to that of saddles;(5)on the streamline vectorfields of a blade-to-blade surface,the total number of nodes is one less than that of saddles.