A Note on Leakage Jet Forces: Application in the Modelling of Digital Twins of Hydraulic Valves

The proper modelling of fluid flow through annular gaps is of great interest in leakage calculations for many applications in fluid power technology. However, while detailed numerical simulations are certainly possible, they are very time consuming, in various cases prone to numerical instabilities and may not even include all physically relevant effects. This is an issue especially in system simulations, where a large set of computations is needed in order to prepare the lookup-tables for the required input fields. In this work, an analytical approximation for the shear force, which is induced by viscous flow between two eccentric cylinders, is presented. This relation, and its derivation, mimics and enhances the well-known Piercy-relation for the corresponding volume flow that is utilized in state-of-the-art system simulation tools. To determine its range of validity, the analytical relation for the shear force is compared to 3D-simulations. Additionally, an application of this approximation for creating digital twins of hydraulic valves is also discussed in this work.