A lumped element method for modeling the two-phase choking flow through hydraulic orifices

A novel lumped element methodology for modeling the oil-gas two-phase flow through the hydraulic orifice has been presented, focus on the choking condition. The proposed approach consists of a gas cavitation model developed based on "Full Cavitation Model" and a formulation considering the homogenous fluid assumption for evaluating the mass flow rate. The two-phase choking flow occurring at extreme condition is characterized in detail by using the present method, in terms of the critical pressure, sound speed, filling ratio and the critical speed of pump operation in the hydraulic circuit. Mach number is found to be 1 and the critical speed is estimated by the inlet volumetric flow rate at choking condition of the two-phase flow. The effects of different parameters including the orifice diameter, the upstream pressure and the cavitation model coefficient are investigated to find possible ways of improving the operation of the pump circuit. Reducing the cavitation model coefficient is identified to be both advantageous for reducing the critical pressure and increasing the critical speed.