Modelling analysis of partial evaporation Organic Rankine Cycle with volumetric expander

Abstract

Partially Evaporated Organic Rankine Cycles (PE-ORCs) can improve thermal matching with low-grade sensible heat sources by reducing the isothermal evaporation zone and the associated exergy losses. However, two-phase conditions at the expander inlet require volumetric expanders and modelling approaches that go beyond black-box isentropic-efficiency assumptions. This paper presents a semi-empirical, lumped-parameter model of a micro-scale PE-ORC equipped with a reciprocating piston expander. The expander sub-model integrates an Interface Exchange Model (IEM) to describe non-equilibrium flash evaporation during two-phase expansion. Heat exchangers are modelled using a moving-boundary formulation coupled with the ε-NTU approach, while the feed pump is represented through experimentally derived characteristic curves. The sub-model parameters are calibrated against 27 steady-state operating points from a kW-scale test bench operating with R134a. Validation against an independent experimental dataset covering heat source temperatures from 40 °C to 75 °C and expander inlet vapour qualities from 0.2 to 1 yields Relative Root Mean Squared Errors (RRMSE) below 10% for all primary output variables – including working fluid mass flow rate (RRMSE = 2.6%), expander power output (6.5%), and evaporator thermal power (5.1%). The largest deviations are associated with expander rotational speed, highlighting residual uncertainty in leakage, recompression, and mechanical-loss modelling. A parametric analysis reveals that the most favourable operation occurs at high expander-inlet vapour qualities, between 0.7 and 0.9. The maximum expander power is about 1500 W, while pump consumption can reach up to 1200 W at low vapour quality. Expander efficiency, gross second-law efficiency, and net second-law efficiency reach approximately 25%, 18%, and 8%, respectively. These results indicate that PE-ORC operation is a controllable strategy, but the attainable performance is mainly constrained by expander and pump efficiencies.