Modeling and Simulation of the Steady-State and Transient Performance of a Three-Way Pressure Reducing Valve

This paper deals with modeling and simulation of a class of three-way pressure reducing valves. The study aims to point out the peculiarities of function and operation of this class of valves in the steady-state and transient modes of operation. A comprehensive nonlinear mathematical model is deduced in order to predict the performance of the studied valve in both modes. The proposed model takes into consideration most nonlinearities of the studied valve. A computer simulation, based on the proposed model, is performed to predict the steady-state and transient performance. During the simulation study, it was found that nonlinearity occurs due to the following factors: the transient change in the valve operating pressures and the change in the throttling areas of the valve restrictions and their discharge coefficients. The transient change in the valve operating pressures causes nonlinear velocity changes of the fluid flow passing through the throttling areas of the valve restrictions. These throttling areas usually have nonlinear mathematical formulas. The discharge coefficients of these throttling areas are assumed constant independent of the flow rates, Reynolds number, and dimensions of these areas. However, these parameters affect the discharge coefficient in a complicated manner. The validity of the proposed model is assessed experimentally in the steady-state and transient modes of operation. The results show good agreement between simulation and experiment in both modes. The study shows that the geometry of the throttling orifice, which connects the upstream port to the downstream port, plays an important role in the studied valve steady-state and transient performance. This result implies the need for further investigation of the effect of the dimensions of the throttling orifices on the steady-state and transient performance of hydraulic control valves.