Computationally efficient two-regime flow orifice model for real-time simulation

In fluid power system simulation, orifice flow is, in the main, clearly in the turbulent area. Only when a valve is closed or an actuator driven against an end stopper does the flow become laminar as pressure drop over the orifice approaches zero. So, in terms of accuracy, the description of laminar flow is hardly necessary. Unfortunately, when a purely turbulent description of the orifice is used, numerical problems occur when pressure drop becomes close to zero since the first derivative of flow with respect of pressure drop approaches infinity when pressure drop approaches zero. Furthermore, the second derivative becomes discontinuous, which causes numerical noise and an infinitely small integration step when a variable step integrator is used. In this paper, a numerically efficient model for the orifice flow is proposed using a cubic spline function to describe the flow in the laminar and transition areas. Parameters for the cubic spline are selected such that its first derivative is equal to the first derivative of the pure turbulent orifice flow model in the boundary condition. The key advantage of this model comes from the fact that no geometrical data is needed in calculation of flow from the pressure drop. In real-time simulation of fluid power circuits, a trade-off exists between accuracy and calculation speed. This investigation is made for the two-regime flow orifice model. The effect of selection of transition pressure drop and integration time step on the accuracy and speed of solution is investigated.