Subcritical and supercritical bifurcations for two-phase flow in a uniformly heated channel with different inclinations

In the past few decades, the stability of two-phase flow in vertical channels has been studied quite extensively. However, such studies for horizontal channels are relatively limited. Moreover, stability analysis of inclined channels is not available in the literature on two-phase flows. Therefore, linear stability analysis using a reduced order model for two-phase flow in inclined channels is carried out. In addition, bifurcation analysis is also carried out to capture the non-linear dynamics of the system and to identify the regions in parameter space for which subcritical and supercritical bifurcations exist. The study is carried out for different inclination angles in order to characterize the effect of inclination on the stability of the system. It is observed that the stability characteristics of two-phase flow in horizontal and inclined channels are significantly different from those of vertical channels even for the same operating conditions. Furthermore, from the non-linear analysis it is seen that the dynamics of the system for inclined and horizontal channels are quite complex. At an inclination of 45°, three generalized Hopf (GH) points (these points separate subcritical region from supercritical region) have been observed in the stability map. These GH points do not exist for vertical channels. Moreover, numerical simulations of the time-dependent, non-linear ODEs are carried out for the selected points in the operating parameter space to verify the stability behavior as predicted by stability maps.