Preliminary Design Method for Dense-Gas Supersonic Axial Turbine Stages

A fast preliminary design methodology for supersonic organic Rankine cycle (ORC) stator and rotor axial turbine blades with low degree of reaction is presented. First, the stator and rotor blade mean-line profiles are designed by using the two-dimensional (2D) method of characteristics (MOC), extended to gases governed by general equations of state (EOS). We focus more specifically on working fluids with medium to high molecular complexity, operating at thermodynamic conditions such that the fundamental derivative of gas dynamics Γ is lower than one in a significant portion of the flow field. For rotor blades, MOC is combined with a free-vortex method to achieve a smooth deflection of the supersonic incoming flow. A numerical approach is developed for solving the unique incidence problem in the case of gases governed by general EOS. Both stator and rotor blade geometries designed according to the inviscid MOC model are subsequently corrected to account for the development of viscous boundary layers by solving the compressible integral boundary layer equations extended to dense gases. The resulting blade designs are assessed by means of computational fluid dynamics (CFD) simulations based on a high-order finite volume solver equipped with advanced thermodynamic and transport-property models. Properly accounting for dense gas and viscous effects at an early design stage is found to improve the expected performance of ORC turbine rows significantly and delivers valuable baseline profiles for any further optimization.