Quasi-One-Dimensional Loss Model of Volute Using Boundary Layer Approach for Inward Flow Radial Supercritical CO2 Turbines

Abstract

Inward flow radial sCO2 turbines operate at considerably higher speeds than conventional gas or steam turbines making only the low specific speed designs practically realizable. Low-specific speed designs suffer from significantly higher viscous losses in the volute due to long and narrow flow passages. The volute loss in low specific speed designs results in an 8% to 12% efficiency drop, which is approximately 50% of the total loss. The paper proposes a quasi-one-dimensional (quasi-1D) model to estimate the total pressure loss in a volute with acceptable accuracy while consuming negligible computational power compared to a three-dimensional computational fluid dynamics simulation. The model converts the three-dimensional flow in a volute into an equivalent quasi-1D flow. Boundary layer-based momentum integral method is used on the quasi-1D flow path to calculate the total pressure loss. A computer program is developed to implement the proposed model. The accuracy of the model is tested with three-dimensional computational fluid dynamics results in the kW to MW power scale for different boundary conditions. The validation exercise is performed for two volute cross sections—circular and trapezoidal, to check the universality of the model. The model predicts the total pressure loss with less than 10% error for all test conditions. In contrast, a fully developed pipe flow model shows a considerably higher error (∼50%) in total pressure loss prediction for identical flow conditions. The model can also incorporate the effect of surface roughness of the volute. In addition, the model accurately calculates losses under off-design operations.