A Mathematical Model for Simulation of Flow Rate and Chamber Pressures in Spool Valves

Abstract

In this paper, a mathematical model to simulate the pressure and flow rate characteristics of a spool valve is derived. To improve the simulation accuracy, the discharge coefficient through the spool valve ports is assumed to be a function of both the Reynolds number and the orifice geometry rather than treating it as a constant. Parameters of the model are determined using the data obtained by computational fluid dynamics (CFD) analyses conducted on two-dimensional axisymmetric domains using ANSYS Fluent 15® commercial software. For turbulence modeling, shear stress transport (SST) k–ω model is preferred after a comparison of performance with the other available turbulence model options. The resulting model provides consistent pressure and flow rate estimations with CFD analyses and a smooth transition between different geometrical conditions. The ultimate aim of this study is to fulfill the need for a model to precisely determine the geometrical tolerances of spool valve components for optimum performance. Estimations of the developed model is compared with the experimental data of a spool valve, and the model is proved to be able to accurately estimate the maximum leakage flow rate, the pressure sensitivity, and the shapes of leakage flow/load pressure curves.