Special Challenges in the Computational Fluid Dynamics Modeling of Transonic Turbo-Expanders

High pressure ratio turbo-expanders often put a strain on computational fluid dynamics (CFD) modeling. First of all, the working fluid is usually characterized by significant departures from the ideal behavior, thus requiring the adoption of a reliable real gas model. Moreover, supersonic flow conditions are typically reached at the nozzle vanes discharge, thus involving the formation of a shock pattern, which is in turn responsible for a strong unsteady interaction with the wheel blades. Under such circumstances, performance predictions based on classical perfect gas, steady-state calculations can be very poor. While reasonably accurate real gas models are nowadays available in most flow solvers, unsteady real gas calculations still struggle to become an affordable tool for investigating turbo-expanders. However, it is emphasized in this work how essential the adoption of a time-accurate analysis can be for accurate performance estimations. The present paper is divided in two parts. In the first part, the computational framework is validated against on-site measured performance from an existing power plant equipped with a variable-geometry nozzled turbo-expander, for different nozzle positions, and in design and off-design conditions. The second part of the paper is devoted to the detailed discussion of the unsteady interaction between the nozzle shock waves and the wheel flow field. Furthermore, an attempt is made to identify the key factors responsible for the unsteady interaction and to outline an effective way to reduce it.