Convenient polynomial approximation for calculating the onset of reverse flow in radial-flow centrifugal pump impellers having backward leaning blades

Abstract

This article presents a sixth-order polynomial approximation for calculating the onset of reverse flow in centrifugal pump impellers having backward leaning blades. The polynomial approximation presented here is an easily computable alternative to the exact analytical formulation published in a previous study [1]. In this previous study, an exact analytical solution was given on the basis of potential-flow considerations. This exact solution was formulated in closed-form in terms of a Fourier series expansion, but the slow convergence of the series makes the expression rather inconvenient to evaluate for any given blade angle and/or number of blades. This situation is improved by the correlation presented in the current article. Moreover, it provides an extension to the empirical formulae commonly applied to predict the onset of suction and discharge flow recirculation in radial-flow centrifugal pump impellers [6–13]. The polynomial approximation can be used to calculate the reverse-flow onset capacity for any blade angle between 0 and 90°, with the number of blades varying from 2 to 12. The calculated result will approximate the exact analytical solution [1] with an error <0.5 per cent, and, as such, provides a theoretically sound and a practical engineering tool for evaluating new and existing impeller designs with regard to (avoidance of) reverse flow.