Hydraulic Efficiency Conversion From a Model to Prototype Pump Based on Effects of Reynolds Number and Surface Roughness

Abstract

New equations for hydraulic efficiency conversion from a model to a prototype centrifugal pump including mixed and axial flow types have been developed and proposed in this paper. In order to establish a set of conversion equations applicable for all type numbers of pumps, the following factors related to the conversion equations were examined. 1) The ratio of scalable loss to total hydraulic loss was examined by using CFD (Computational Fluid Dynamics) analysis. The ratio is related with the effect of actual complex velocity distributions in the flow passages in the impeller and diffuser/volute casing. 2) The conversion equation was constructed by two terms dealing with flow passages in two major hydrodynamic components, impeller and diffuse/volute separately, where contributions of each component to the efficiency step-up was expressed explicitly. 3) The friction coefficient ratio between a model and prototype pump was expressed in a simplified equation, applicable for both hydraulically-smooth and transitional surfaces. This expression was found to be useful to determine the relationship between equivalent machined surface roughness and uniform sand roughness, as the friction coefficient diagram expressed for uniform sand roughness is used for conversion of hydraulic losses between the model and prototype pumps. 4) The difference between the friction coefficients for decelerating flow and for a flat plate with uniform flow was examined by CFD analysis, and it was found that the friction coefficient for a flat plate can be used for the conversion without causing any substantial deviation.