Variable wall thickness scroll geometry modeling with use of a control volume approach

In a scroll-type compressor, compression is achieved through relative contact between two spiral curves. Since the scroll invention by Leon Creux (1905), multiple methods have been developed for calculating scroll geometry. What can generally be considered the most classical method, is defining each scroll curve as the involute of a circle. Gravesen and Henriksen (2001) introduced a new method to calculate scroll geometry by deriving each scroll curve from the radius of curvature parameterized with involute angle. This allows a wide range of involute geometries to be considered not included in the classical method. In this paper, Gravesenʹs method is extended to the tip region to include all tip geometries involved in a two arc configuration resulting in a more comprehensive scroll geometry definition. Lastly, with parametric representation of all scroll geometry, the pocket volume can be easily solved using a derived control volume approach.