Semi-analytical bifurcation analysis of two-phase flow in a heated channel

Using a drift flux representation for the two-phase flow, a new reduced order model has been developed to simulate density-wave oscillations (DWOs) in a heated channel. This model is then used to perform stability and semi-analytical bifurcation analysis, using the bifurcation code BIFDD, in which the stability boundary (SB) and the nature of Hopf bifurcation are determined in a suitable two-dimensional parameter space. A comparative study is carried out to investigate the effects of the parameters in the drift flux model (DFM) - the radially void distribution parameter C₀ and the drift velocity V_gj -on the SB as well as on the nature of Hopf bifurcation. It is the first time that a systematic analysis has been carried out to investigate the effects of DFM parameters on the nature of Hopf bifurcation in a heated-channel two-phase flow. The results obtained show that both sub- and super-critical Hopf bifurcations are encountered. In addition, it has been found that, while the SB is sensitive to both C₀ and V_gj, the nature of Hopf bifurcation for lower values of N_sub is more sensitive to V_gj than to C₀. Numerical integration of the set of ODEs is carried out to confirm the predictions of the semi-analytical bifurcation analysis.