An orifice flow model for laminar and turbulent conditions
The square root characteristic commonly used to model the flow through hydraulic orifices may cause numerical problems because the derivative of the flow with respect to the pressure drop tends to infinity when the pressure drop approaches zero. Moreover, for small values of the pressure drop it is more reasonable to assume that the flow depends linearly on the pressure drop. The paper starts from an approximation of the measured characteristic of the discharge coefficient versus the square root of the Reynolds number given by Merritt and proposes a single empirical flow formula that provides a linear relation for small pressure differences and the conventional square root law for turbulent conditions. The transition from the laminar to the turbulent region is smooth. Since the slope of the characteristic is finite at zero pressure difference, numerical difficulties are avoided. The formula comprises physical meaningful terms and employs parameters which have a physical meaning. The proposed orifice model has been used in a bond graph model of a hydraulic sample circuit. Simulation results have proved to be accurate. The orifice model is easily implemented as a library model in a modern modeling language. Ultimately, the model can be adapted to approximate pipe flow losses as well.
hydraulic orifices bond graphs library model laminar and turbulent flow treatment of discontinuities and singularities in ordinary differential equations empirical formula