Rotodynamic pump scaling.

Abstract

Despite extensive theoretical knowledge of fluid dynamics, the design process for rotodynamic pumps still relies heavily on experimental data. One common technique is to model the design of a new pump based on the design of existing pumps, using the laws of similarity. Another, similar approach frequently used for atypically large or small pumps is to scale a final product design from conveniently sized laboratory prototypes that have been refined to the desired performance in extensive experiments. Both approaches to pump design are usually considered highly reliable. However, for blood pumps, this approach has been questioned. Due to the extremely small size of these pumps and the relatively low Reynolds Numbers, extraneous effects may overwhelm the assumptions made for similarity calculations that are satisfactory for significantly larger models. Three geometrically similar pumps with related scaling factors of 1, 3.2, and 6.4 were tested for the same range of nondimensional flow and pressure. The quality of similitude was determined by comparing the nondimensionalized pump data of the three pumps. It was found that the effects of large linear dimension scaling factors had only a small influence on the quality of similitude (maximum 5.8% error), whereas Reynolds Number effects, especially at high pump flows, had a strong impact on the quality of similitude (maximum 45.4% error). Because Reynolds Number similarity cannot always be achieved simultaneously with geometric similarity, a correction factor for Reynolds Number related departure from similarity was developed. It is based on the Reynolds Number, the Flow Coefficient, the specific speed, and the pump's relative surface roughness. Use of this correction factor reduces the error due to Reynolds Number effects to a maximum of 7.5%. We conclude that the use of scaling techniques in rotodynamic blood pump design is a valid approach, if Reynolds Number similarity is maintained or suitable correction factors are used.