Computationally Efficient Two-Regime Flow Orifice Model for Real-Time Simulation

Mainly in fluid power system simulation the orifice flow is clearly in turbulent area. Only when a valve is closed or an actuator driven against end stopper the flow becomes laminar as pressure drop over an orifice is approaching zero. So, in terms of accuracy, the description of laminar flow is hardly necessary. Unfortunately, when purely turbulent description of the orifice is used, numerical problems occur when pressure drop becomes close to zero. They do because the first derivative of flow with respect of pressure drop approaches infinity when pressure drop approaches zero. Also the second derivative is discontinuous. This causes numerical noise and also infinite small integration step when variable step integrator is used. In this study a numerically efficient model for the orifice flow is proposed by using a cubic spline function for describing the flow in the laminar and transition areas. Parameters for the cubic spline are selected such that its first derivative is equal to first derivative of pure turbulent orifice flow model in the boundary condition. The superiority 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 there exists a trade-off 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.