Euler S2 stream surface calculation for arbitrary curvilinear coordinate system

To adapt the complex geometry of the turbine profile and improve the computing capability, an Euler S2 stream surface calculation strategy is proposed in the body-fitted coordinate system, the governing equation for Euler S2 stream surface calculation in the arbitrary orthogonal curvilinear coordinate system is derived in detail, and the mathematical model for the third order total variation diminishing (TVD) difference scheme is developed. The implicit time marching method and the Riemann solver are also employed to solve the aerodynamic parameters of a flow channel with bump and a linear cascade, and to predict the performance of a 3-stage low pressure turbine. The results show that the proposed strategy is able to capture the shock wave with high resolution. The solution to the linear cascade coincides well with the experimental data with a credible accuracy for the flow field calculation.