Practical Use of Similarity and Scaling Laws for Centrifugal Compressor Design

This article focuses on the practical use of the similarity principle for centrifugal compressor design, i.e. geometrical scaling of existing impellers to meet new specifications. Basic principles of similarity are first used to derive scaling laws. Then, the analysis of typical specifications and the use of partial similarity (neglecting the Reynolds-number effects) allows the use of the pressure ratio-specific speed diagram so that a compressor can be scaled along its best-efficiency operating line. A practical method is proposed to use these scaling laws in a design context, in order to define the scaling potential of an existing stage as the ensemble of specifications that can be met by scaling. Finally, the scaling potential of an industrial compressor is evaluated and represented as a surface in the 3D space defined by the similarity variables, with the associated efficiency variations.