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A new scheme for calculation with the discrete-vortex method and boundary-fitted coordinate systems is presented to analyze the two-dimensional jet flow issuing from the metering orifice of oil hydraulic valves. The advantage of the present scheme is that, the jet flow at high Reynolds numbers in the boundaries of arbitrary shape can be treated without conformal mapping between the physical-plane and complex potential-plane.In the present study, the boundary-fitted coordinates are generated as the solution of two elliptic partial differential equations with Dirichlet boundary conditions, and the potential-flow solution without vortices is calculated numerically by solving Laplace equations using the boundary-fitted coordinate system. Furthermore an array of discrete vortices is introduced into the flow field at appropriate time intervals at some points near the separation points. The vortices are moved by a time marching scheme using the rectangular transformed plane, after the velocity of any vortex is obtained.The present scheme is employed to simulate the two-dimensional jet flow issuing from the metering orifice of the spool valves commonly used for hydraulic power applications. A prediction of the vortex pattern of the jet flow and the pressure distribution is undertaken. The simulated results of the pressure distribution on the spool land are compared with the experimental results obtained using the three-dimensional valve model.

Discrete-vortex simulation of a two-dimensional flow in oil hydraulic valves.