Non-linear Stability Analysis for Supercritical Fluid Flow in Inclined Heated Channel

The nonlinear stability analysis of Supercritical fluids (SCFs) has been carried out using a reduced order nodalized model for the single inclined heated channel. The primary objective of the study is to portray the linear as well as nonlinear stability characteristics of SCFs flow channel along with the prospect of different types of bifurcation phenomena. The linear stability analysis is carried out with the help of the 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 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 super-critical 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 an interaction with Hopf bifurcation) appear. These bifurcations lead to complex dynamics in the system, therefore, various numerical simulations have been carried out around the stability threshold. This type of bifurcation analysis is rarely reported for SCFs in 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 inclination channel on the stability threshold in parametric space is also investigated