Non-linear stability analysis of uniformly heated parallel channels for different inclinations

Abstract

The linear stability for two phase flow in parallel channels has been studied quite extensively. However, the analysis is valid only for infinitesimally small perturbations. Therefore, there is a need to carry out non-linear stability analysis for small finite sized perturbations. Moreover, earlier studies do not consider inclination of these channels, which exist for various applications. The focus of the present work is to carry out linear as well as non-linear stability analysis of parallel channels for various inclinations (including vertical and horizontal). The bifurcation analysis is carried out to capture the non-linear dynamics of the system and to identify regions in the 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. The analysis shows that, at all inclinations, a GH point and BT point exist. The subcritical and supercritical bifurcations are confirmed by numerical simulation of the time-dependent, nonlinear ODEs for the selected points in the operating parameter space using MATLAB ODE solver. The identification of these points is important because the stability characteristics of the system for finite (though small) perturbations are dependent on them.