The Application of Similitude Theory for the Performance Prediction of Radial Turbines Within Small-Scale Low-Temperature Organic Rankine Cycles

For small-scale organic Rankine cycles (ORCs) to be a competitive technology, it is reasonable to assume that the same turbine design will be implemented into a range of different applications. It is therefore critical to be able to predict turbine off-design performance over a range of different operating conditions while utilizing different working fluids. Similitude theory can be used for this purpose, and it has been well validated for ideal gases. However, the same cannot be said for its applications to the organic fluids found within ORCs. This paper considers a candidate subsonic turbine design operating with R245fa and the corresponding turbine performance map. Similitude theory is used to predict the performance of the same turbine operating at different inlet conditions using R245fa, R123, and R1234yf. The similitude predictions are compared to computational fluid dynamics (CFD) results obtained using ansys CFX. The original similitude theory using turbine total inlet conditions was found to only apply within a small range of operating conditions, so a modified similitude theory has been suggested that uses the choked flow conditions instead. This modified similitude theory agrees with the CFD predictions to within 2%, right up until the choked mass flow rate. Further studies considering supersonic turbines are required to establish the applicability of similitude for applications beyond the choked pressure ratio.