Enhanced Quasi-One-Dimensional Modeling and Design Performance Assessment of an ORC with Radial Turbine for Waste Heat Recovery

Organic Rankine Cycles (ORCs) are widely recognized as an effective solution for waste heat recovery (WHR). However, the design and optimization of these systems must address the tradeoff between computational efficiency and the need to capture complex component behavior. This requires moving beyond purely energetic 0D modeling approaches to account for constructional, spatial, and operational constraints. This work presents a novel modeling framework with a specific focus on the expansion device. Radial inflow turbine stages are selected for their capability to achieve high pressure ratios while maintaining compactness and high efficiency. Heat exchangers follow a generic one-dimensional counterflow configuration, with a shell-and-tube geometry adopted for sizing purposes. The turbine stages are modeled by resolving several internal sections in order to capture local thermofluid dynamic conditions. The framework predicts turbine efficiency and incorporates a newly developed formulation for shock-induced losses, improving performance prediction under trans-sonic flow conditions. After validation against experimental data, the model is applied to a WHR system integrated with an internal combustion engine fueled by biofuels. The results highlight the existence of optimal operating conditions arising from competing physical mechanisms. The analysis also shows the transition from single-stage to two-stage turbine configurations at high pressure ratios and emphasizes the role of real gas effects in determining stage performance and optimal expansion distribution. The results of simulations carried out for three different working fluids (ethanol, toluene, and R1234ze(E)) highlight that the available mechanical power ranges from 10 to 22 kW for single-stage turbine configurations and from 24 to 36 kW for two-stage configurations, with total system volumes varying between approximately 600 and 9000 L. Among the working fluids considered here, ethanol provides the best overall performance for the present case study. Overall, the proposed approach provides a reliable and computationally efficient tool for the preliminary design and optimization of ORC-based WHR systems.