New algorithm for the numerical simulation of two-phase stratified gas–liquid flow and its application for analyzing the Kelvin–Helmholtz instability criterion with respect to wavelength effect

In this article, the transient condition of two-phase stratified gas–liquid flow was investigated using numerical simulation. The basis of the method involves the one-space dimensional transient solution of the governing equations using the two-fluid model. In this paper, an analogy between the SIMPLE algorithm in two-space dimensional single-phase flow and one-space dimensional two-phase stratified flow is established through the application of a special algorithm created to solve the conservation equations. After the modeling was established and justified, wave growth was examined in two-phase stratified flow in a horizontal duct. The results were then compared with the results of the previously published articles. The results show that the classical criterion for the Kelvin–Helmholtz (K–H) instability is consistent when the long wavelength with small amplitude is considered. In this case (of the K–H instability criterion), the wavelength effect on this instability and pressure variation on the two phases interface was consistent with prior researchers’ correlations. However, as the wavelengths decreased, the results indicated that the K–H instability criterion is over-predicted and must be modified. The application of the present numerical simulation method improved the results, and the consistency with the analytical solution is higher in comparison with other well-known computer codes.