An Improved Positive Displacement Pump Model Accounting for Suction Cavitation

Positive displacement (PD) pumps are widely employed in industrial settings due to their inherent simplicity and reliability, serving a variety of applications from slurry transport to jet washing. Although their operational principles are straightforward, the fluid dynamics of the pumped medium exhibit nontrivial characteristics, including intricate transient phenomena. Consequently, a comprehensive fluid dynamic description, such as a three-dimensional fluid analysis, presents challenges due to its demanding computational requirements. While simpler analytical PD pump models are available, they often fail to adequately represent the primary system behaviors, particularly when dealing with cavitation. Motivated by these challenges, this study aims to develop a novel one-dimensional model for PD pumps, offering a representation of essential fluid phenomena without imposing significant computational burdens. After assessing the relative importance of the fluid dynamic behaviors that the model must capture, we construct a pump model based on a one-dimensional fluid description and solve it using a second-order in time and space monotone upwind scheme for conservative law and total variation diminishing (MUSCL-TVD) scheme. The model's validity is confirmed by its application to both single-chamber and three-chamber diaphragm PD pumps, which are instrumented for experimental validation. The results of the one-dimensional model exhibit strong agreement with physical experiments, both in controlled laboratory environments and field conditions. This success suggests a promising approach for industrial applications.