Geometric Design of Scroll Expanders Optimized for Small Organic Rankine Cycles

Abstract

The application of organic Rankine cycles (ORCs) for small scale power generation is inhibited by a lack of suitable expansion devices. Thermodynamic and mechanistic considerations suggest that scroll machines are advantageous in kilowatt-scale ORC equipment, however, a method of independently selecting a geometric design optimized for high-volume-ratio ORC scroll expanders is needed. The generalized 8-dimensional planar curve framework (Gravesen and Henriksen, 2001, “The Geometry of the Scroll Compressor,” Soc. Ind. Appl. Math., 43, pp. 113–126), previously developed for scroll compressors, is applied to the expansion scroll and its useful domain limits are defined. The set of workable scroll geometries is: (1) established using a generate-and-test algorithm with inclusion based on theoretical viability and engineering criteria, and (2) the corresponding parameter space is related to thermodynamically relevant metrics through an analytic ranking quantity fc (“compactness factor”) equal to the volume ratio divided by the normalized scroll diameter. This method for selecting optimal scroll geometry is described and demonstrated using a 3 kWe ORC specification as an example. Workable scroll geometry identification is achieved at a rate greater than 3 s⁻¹ with standard desktop computing, whereas the originally undefined 8-D parameter space yields an arbitrarily low success rate for determining valid scroll mating pairs. For the test case, a maximum isentropic expansion efficiency of 85% is found by examining a subset of candidates selected the for compactness factor (volume expansion ratio per diameter), which is shown to correlate with the modeled isentropic efficiency (R² = 0.88). The rapid computationally efficient generation and selection of complex validated scroll geometries ranked by physically meaningful properties is demonstrated. This procedure represents an essential preliminary qualification for intensive modeling and prototyping efforts necessary to generate new high performance scroll expander designs for kilowatt scale ORC systems.