Design Optimization of Balancing Holes in a Centrifugal Pump

Abstract

Centrifugal pumps are widely used in fluid transport systems due to their ability to deliver high flow rates in a compact, low-maintenance design. Despite their welldefined performance characteristics, a major operational challenge is the generation of axial force, a force imbalance caused by the pressure difference across the front (suction) and back (pressure) sides of the impeller. If the axial force is not properly investigated during the design process, it can cause bearing failure, increase maintenance requirements, and significantly reduce both hydraulic efficiency and pump lifespan. Balancing holes are commonly introduced to mitigate axial force by reducing the pressure imbalance. While effective in reducing axial force, balancing holes introduce fluid recirculation from the pressure side to the suction side of the impeller, leading to a reduction in hydraulic performance. Therefore, identifying an optimal balancing hole configuration is essential to minimize axial force without compromising overall efficiency.

This study investigates the development of a multi-objective target function using both scalarization and Pareto-based methods to identify an optimal balancing hole design configuration that reduces axial force while maintaining the hydraulic performance. CFD simulations were carried out using a steady-state approach with implicit local time stepping, in conjunction with a non-linear k−ε turbulence model and the frozen rotor approach, to capture the internal flow behaviour and to extract performance metrics—head, power, and axial force—for all generated configurations during the optimization process. To explore the design space effectively, Sobol sequence sampling was used to generate a diverse set of initial configurations. The target function was formulated by normalizing head and power at the Best Efficiency Point (BEP) and axial force across part-load, BEP, and over-load conditions, then iteratively optimized using Bayesian optimization and target function scoring to identify an optimal balancing hole design. A Pareto front analysis was finally conducted to analyze the trade-offs between hydraulic performance and axial force reduction for the generated configurations throughout this study.

The findings revealed that the formulated target function using scalarized method effectively guided the optimization process toward configurations that reduced axial force by up to 40.59 % while maintaining head and power within 99.98 % and 99.87 % of the reference, respectively. Iterative Bayesian optimization and Pareto front analysis consistently led to a key design feature, which was also supported by the flow field visualization.