Non-linear stability analysis of supercritical carbon dioxide flow in inclined heated channel

In this paper, the nonlinear stability analysis of supercritical carbon dioxide (SC - CO2) has been carried out using a reduced order nodalized model for a single inclined heated channel. The primary objective of the present study is to portray the generic view of linear as well as nonlinear stability characteristics of SC - CO2 channel along with the prospect of different types of bifurcation phenomena. The linear stability analysis is carried out with the help of eigenvalues of the Jacobian at steady state conditions, and stability boundary is shown in the parameter plane of pseudo-sub-cooling (N-spc) and pseudo-phase-change numbers (N-tpc). The non-linear analysis includes the detailed study of dynamic and static instabilities. Different types of bifurcation phenomena namely; sub-critical, super-critical and Generalized Hopf are observed; indicating various features of the dynamic instabilities. The first Lyapunov coefficient has been calculated to distinguish between sub-critical and supercritical Hopf bifurcations. Whereas in static instability; Ledinegg excursive phenomena, which is characterized as a saddle-node bifurcation is observed. Additionally, on saddle-node bifurcation curve, Bogdanov-Takens bifurcation points (as interaction with Hopf bifurcation) appear. These bifurcations lead to complex dynamics in the system therefore, several numerical simulations have been carried out around the stability threshold. This type of non-linear analysis is rarely reported for SC - CO2 in the existing literature. To extend this analysis, the dependence of various system design parameters on the bifurcation curve has been investigated along with the shifting of Generalized Hopf (GH) bifurcation point. Furthermore, the effect of the inclination angle of the channel on the stability threshold in parametric space is investigated.