A Hyperbolic One-Dimensional Model for Two-Phase Flows in Converging–Diverging Nozzles

Abstract

Abstract. Partial-evaporation organic Rankine cycle power systems are a promising technology for power generation from low-temperature heat sources such as waste heat and geothermal heat. A specific challenge in two-phase turbines is converging–diverging nozzle design and performance analysis. Existing one-dimensional methods for two-phase flows in nozzles typically rely on space-marching approaches, which are unsuitable for predicting shock waves and thus limit their application to adapted expansion conditions. To address the limitations of existing models, this article presents a new one-dimensional two-phase flow model suitable for capturing shock waves in converging–diverging nozzles. The model employs a finite volume method to solve the balance equations in a conservative form, using time-marching methods to reach the steady-state solution. The predictive performance of the proposed model is validated against experimental data from converging–diverging nozzles using various working fluids, including organic molecules and CO2. The results indicate that the proposed model formulation is suitable for predicting the performance of two-phase nozzles in terms of pressure distribution, critical mass flowrate, and shock wave characteristics across a wide range of operating conditions. These findings suggest that the developed model can be a reliable tool for the preliminary design and analysis of converging–diverging nozzles in two-phase turbines.