Session: 34-05 Physics-based and machine learning models

Paper Number: 153250

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

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 the design and performance analysis of converging-diverging nozzles. Existing one-dimensional methods for two-phase nozzles typically evaluate performance under adapted expansion conditions and fail to accurately predict shock waves and their impact on nozzle performance.

In order to address the limitations of existing models, this paper presents a new one-dimensional two-phase flow model suitable for capturing non-equilibrium effects and shock waves in converging-diverging nozzles. The model employs a Finite Volume Method to solve the balance equations in a conservative form, using implicit time integration to reach the steady-state solution. The predictive performance of the proposed model is evaluated by incorporating it into three different models describing the behavior of the two-phase flow and comparing the results with experimental data for converging-diverging nozzles using various working fluids, including refrigerants. The models considered are the Homogeneous Equilibrium Model, the Homogeneous Relaxation Model, and the Delayed Equilibrium Model. The latter two can predict the metastable phase behavior of the mixture by extrapolating the fluid equations of state into the two-phase region, which has an important role in the accuracy of the models.

The results indicate that the proposed model formulation is suitable for predicting the performance of two-phase nozzles in terms of pressure distribution, Mach number, void fraction, and shock waves under a wide range of working conditions. These findings suggest that the proposed model can serve as a reliable tool for the design and analysis of converging-diverging nozzles in two-phase turbines.

Presenting Author: Andrea Cioffi Technical University Denmark

Presenting Author Biography: I am a PhD student at the Technical University of Denmark (DTU), working on the Marie-Curie Doctoral Network Training42Phase: next generation of turbomachinery with two-phase flows.

Authors:

Andrea Cioffi Technical University Denmark
Alberto Bergamin Technical University of Denmark
Roberto Agromayor Technical University of Denmark
Fredrik Haglind Technical University of Denmark