Supersonic Convergent-Divergent Vaned Nozzles Design Algorithm and Respective Discharge Coefficient Model

Abstract To continue the series of already published articles on supersonic drilled nozzles GT2022-83387, GT2023-101760, this publication is devoted to another type of supersonic nozzles, which are formed by vanes providing an annular row of convergent-divergent supersonic channels. This type of supersonic vaned nozzles, as well as the drilled nozzles, are used in numerous high-loaded turbine applications. Published data on this type of nozzles and turbine stages with them have very limited information on both the design methodology and calculation methods and thus do not allow these data to be systematized and implemented into the turbine design and calculation tool. The work carried out in this direction includes all the algorithms and models required for the supersonic vaned nozzle design and calculations: (1) The design algorithm of a highly efficient supersonic vaned nozzle, (2) the discharge coefficient model, (3) loss model, (4) flow angle deviation model. In this article, we focus on design model (1) and discharge coefficient (2) items. A list of geometric parameters that uniquely determine the 3D geometry of the nozzle channel that is used in the design algorithm is discussed. The approaches to building convergent and divergent parts of the supersonic nozzle are elaborated. Besides, the model of the discharge coefficient through the critical section of the nozzle is described in detail. The developed discharge coefficient model demonstrated a maximal deviation of 0.6% and an average of 0.18% from CFD results in a wide range of configurations of the nozzle channel.