Stratified smooth two-phase flow using the immersed interface method

The immersed interface method is used to derive a numerical method for solving fully developed, stratified smooth two-phase flow in pipes. This sharp interface technique makes the representation of the interface independent of the grid structure, and it allows for using an arbitrary shaped interface. The two-dimensional steady-state axial momentum equation is discretized and solved using a finite difference scheme on a composite, overlapping grid with local grid refinement near the interface and near the pipe wall. A low Reynolds number k-ε turbulence model is adopted to account for the effect of turbulence. A level set function is used to represent the interface. Numerical results are presented for laminar and turbulent flows. The numerical method compares well with analytical solution for laminar flow, and it shows acceptable agreement with experimental data for turbulent flow. A few examples are given to demonstrate the capability of the method to solve flow problems with a complex shaped interface.