Similarity Model of a Rotary Lobe Expander Working with Various Fluids

This paper presents the similarity model of a rotary lobe expander (Roots expander) and calculates its power based on its other reference power. The rotors in these expanders transfer unchanged gas volume within one rotation. In this model, the expander’s construction is represented by the single value of this transferred volume. The derived model concerns the similarity of pressure loss due to the fluid viscosity, which decreases the ideal maximum power of the limiting case of no viscosity. The basic thermodynamic analysis of various fluids is also presented for this case. The novelty is the similarity model of this expander type, which may be used in the analytical and fast engineering calculation of the power before the use of the more precise but expensive numerical calculation. The similarity model is applied to the exemplary rotary lobe expander GGP16XA from Armak Motors. In this paper, the similarity model is applied in two cases. The first application concerns the manufacturer’s data on the power from the compressed air of various inlet pressures and rotational speeds. The second one concerns the numerically calculated power from various fluids: Air, R245fa, SES36, and HFE7100, with the power from Air as a reference. The analyzed fluids are used in Organic Rankine Cycle (ORC) applications. In both cases, the obtained similarity power is in good agreement with the reference, with the same maximum relative error ±5%.