Geometric quasi-similarity: Case of nozzles with quadrant-shaped inlet

Abstract

Geometric similarity (i.e. difference only in size scale) is generally believed to be unavoidable condition without which it is impossible to apply the Buckingham π−theorem to two mutually related flowfields. Recently introduced idea of secondary invariants can by-pass this limitation and accept geometric quasi-similarity—i.e. cases with different values of ratios of geometric parameters. In this paper this new approach is demonstrated on an example case of a single-parameter family of nozzles which are mutually not fully geometrically similar.