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

•Characterisation of nozzles by invariants of their behaviour is discussed.•New concept introduced of geometric quasi-similarity, applied to a nozzle family.•New invariants based on the idea of boundary layer displacement thickness.••Another set of invariants are based on idea of additive correction term.•Universal characteristic found, valid for any nozzle shape.

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.