A model for pressure drop of gas-liquid bubbly flow through an orifice or an abrupt pipe contraction

A new physical model is developed to predict the pressure drop of a steady-state gas-liquid bubbly flow through an orifice or an abrupt pipe contraction. The formulation of the model involves balance equations deduced from the macroscopic mass, momentum, entropy and energy conservation laws as well as a balance of forces exerted on the dispersed bubbles phase. The thermal equilibrium between phases is assumed but the gas-liquid slip motion is taken into account. The gas-liquid interaction and the wall shear stress are evaluated from theoretical considerations. The predictions of pressure drop from the model are found to be in good agreement with several experimental data of the literature obtained for bubbly air-water flows through orifices. In agreement with the experimental observations, the theoretical predictions show that the two-phase pressure drop multiplier is not strongly influenced by the pipe diameter and increases slightly with the cross-sectional area ratio of the orifice. An essential feature of the present model is the absence of adjustable constants.