Numerical simulation of two-phase flow within sudden expansion in horizontal channel pressure and velocity distribution

In this paper, we will study the flow of two immiscible fluids (air/water) through a sudden expansion in a horizontal channel. The first part of the paper will be a detailed bibliography study of sudden expansion problems followed by a mathematical and numerical study where detailed equations and numerical methods used for the numerical simulation are presented. The second part of the paper represents the numerical results obtained. First, we will validate our numerical model with the experimental results obtained by Chalfi and Ghiaasiaan (Int J Multiph Flow 34(1):2–12, 2008. https://doi.org/10.1016/j.ijmultiphaseflow.2007.09.004 ). The validation will be for the pressure distribution in the channel and the pressure jump over the sudden expansion. A comparison will be also done with the experimental results from Chalfi and Ghiaasiaan (2008) and the theoretical model from Armand-type void-quality expression for the pressure with different Reynolds numbers. After that, a numerical study will be done with a different ratio of the same geometry, pressure and velocity parameter will be studied and the jump over these variables is captured at the sudden expansion. The numerical part is done with the FEniCS platform which is a powerful finite-element computational open-source scientific platform.