Some nonlinear dynamics of a heated channel

Linear stability analysis of flow instabilities with a nodalized reduced order model in heated channel

“…Applying state space approach, these nonlinear ODEs are used to determine the stability of the system. The results of the present model are compared with various existing models [33,34,36] which are closer to exact solutions [31]. The SBs obtained show good agreement with the said models.…”

“…As mentioned [36], linearelinear homogeneous model with invariant density assumption only shows the conventional trend of a typical stability map. The map predicted by the said model is far away from the quadratic models [33,34] which are closer to the exact solution [31] and experimental data [37]. It is seen that the stability map obtained with linearelinear density invariant model by assuming the single phase and two-phase region of the channel to be composed of only 2 nodes each, is far from the quadratic model of Dokhane [34].…”

“…And hence, this impacts the position of stability boundaries. In addition to these, it is evident from previous studies [31,33,36,38] that, stability boundaries obtained with linearelinear approximations of single phase enthalpy and twophase quality; only show the conventional L-fold trend. These SBs are far away from experimental data and exact solutions that lie on the left side of the obtained SBs (forced circulation system) in corresponding parameter plane (N pch eN sub plane).…”

“…It is worth noting that this left shift in stability boundaries due to increase in number of nodes indicates that as the number of nodes increases, the stability boundary become closer to the exact solutions even in the presence of linear approximations of single phase enthalpy and two-phase quality. The shift pattern due to different combinations of approximation techniques and exact solutions can be found in several literatures [31,33,34].…”

“…Achard et al [30] carried out an analytical bifurcation study of DWO with homogeneous equilibrium model (HEM). Rizwan-Uddin and Dorning [31] extended that approach by replacing HEM by drift flux model which results even more complicated nonlinear delay integro-differential equations. In their study they showed the impact of void distribution parameter C 0 and the drift velocity V gj between phases on the sensitivity of stability boundary (SB) in various planes.…”