Dual Solution and Choked Flow Treatment in a Streamline Curvature Throughflow Solver

Abstract

In most turbomachinery design systems, streamline curvature based throughflow calculations make the backbone of aero design process. The fast, reliable, and easy to understand solution is especially useful in performing several multistage design iterations in a short period of time. Although the streamline curvature based technique enjoys many benefits for subsonic applications, there are some challenges for transonic and supersonic flow applications, which is the focus of this paper. In this work, it is concluded that three key improvements are required to handle transonic flows in a streamline curvature throughflow solver. These are (1) the ability to overcome dual sub and supersonic solutions and guide the solver towards a supersonic flow solution where applicable; (2) a suitable technique to calculate the streamline curvature gradient term, which can avoid singularity at sonic meridional Mach number and high gradient values in transonic flows; and (3) a suitable technique to handle choked flow in the turbomachinery flowpath. Solution procedures for “dualsolutionâ€‌ and choked flow treatment are new and developed as part of this work. However, a procedure for calculating streamline curvature gradient is leveraged from earlier work done by Denton (1978, “Throughflow Calculations for Transonic Axial Flow Turbines,â€‌ Trans. ASME, 100, pp. 212–218) and Came (1995, “Streamline Curvature Throughflow Analysis,â€‌ VDIBer., 1185, p. 291). Implementation of these improvements is performed in a streamline curvature based throughflow solver. Numerical improvements presented here have been tested for a range of compressor and turbine cases (both subsonic and supersonic). It is shown that the numerical improvements presented in this paper resulted in an enhanced version of the streamline curvature throughflow solver. The new code produces consistent solutions for subsonic applications with no sacrifice in the accuracy of the solver. However, considerable robustness improvements are achieved for transonic turbine cases.