Plotting and application of predominance area diagram of In-S-O system based on topological rules

The mathematical topological rule was proposed to plot the predominance area diagram.Based on the phase rules,the components of In-S-O system were analyzed and the coexisting points of three condensed phases were determined.Combined with the topological rules and thermody namic calculation,four relation diagrams between the coexisting points of three condensed phases,which were denoted as α,β stable plane-topological diagram and unstable plane-topological diagram,were plotted for the In-S-O system.The results show that α stable plane topological diagram is in accordance with the predominance area diagram of In-S-O system plotted by traditional methods,which indicates that the new method is feasible to plot the predominance area diagram of In-S-O system.Meanwhile,β unstable plane-topological diagram can be used to elucidate the indium production with the bath smelting process.

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

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

Plotting and application of predominance area diagram of Me-S-O system based on topological rules

The mathematical topological rule was applied to plot the predominance area diagram.Based on the analysis of the mutually conjugated,only two diagrams were the best topological embryonic graphs to build the predominance area diagram of Me-S-O system.Combined with topological rules and thermodynamic calculation,four relation-diagrams were denoted asαandβstable and unstable plane-topological diagrams,which were plotted for the Pb-S-O system and Zn-S-O system.The results show thatβstable plane-topological diagram of Pb-S-O system andαstable one of Zn-S-O system are in accordance with the traditional predominance area diagram,which indicates that it is feasible to plot the predominance area diagram based on mathematical topological rules.Meanwhile,αunstable plane-topological diagram of Pb-S-O system can elucidate the phenomenon that metallic lead exists in higher oxygen and sulfur pressure area in modern bath smelting furnace.The mathematical topological rules broaden the application scope of the predominance area diagram and enrich the practice of its plotting.

Nonlinearity of initiating and extinguishing boundaries of DBDs with airflows

Various applications of volume dielectric barrier discharges(DBDs)with airflows have attracted significant attention such as in the fields of plasma medicine,surface modification,ozone synthesis,etc.In this work,the nonlinearity characteristics of DBDs in initiating and extinguishing boundaries with airflows are experimentally investigated.It is found that the difference between initiating pulse repetition frequencies(PRFs)and extinguishing PRFs is affected by the addition of airflows.A hysteresis region is produced between these two PRFs.A topological rule of Thom's classification theorem is proposed to investigate the hysteresis phenomenon of discharges with airflows.It is concluded that the discharge state is dependent on the operation route.The discharge state would transit from initiating to extinguishing,or in the opposite direction,while passing along a specific operation route.Based on the topological method,two nonlinear laws of discharge structure transition under the typical operation routes are predicted and verified in the discharge experiments.