BIFURCATION ANALYSIS OF THE SUPER-CRITICAL CARBON DIOXIDE FLOW IN HEATED CHANNEL

In several engineering applications, super-critical fluids (SCF) are being used as a heat transfer coolant in fluid flow systems. SCFs are used beyond the physical limit of the pseudo-critical temperature to obtain high conversion efficiency. This high potential property of the SCFs helps reduce the power generation cost due to the high thermal efficiency. SCFs experience dramatic changes in its fluid properties, as the fluid temperature crosses the pseudo-critical temperature. Due to such dramatic changes, higher and lower density fluids flow across the system successively, which eventually causes the power or flow oscillations (instabilities) in the systems. These oscillations make the system unstable and cause mechanical vibrations in the system. The present work aims to analyze this instabilities phenomenon in a single heated channel when supercritical CO2 flow in the channel as a heat transfer coolant. To fulfill the objective, the heated channel is nodalized into N number of nodes and mathematically modeled into a set of one-dimensional mass, energy and momentum conservation partial differential equations (PDEs). These PDEs are converted into corresponding time-dependent non-linear ordinary differential equations (ODEs) by applying the weighted residual method. The linear stability threshold of the system is determined by analyzing eigenvalues of the Jacobian matrix at the steady states of the set of ODEs. The non-linear stability (bifurcation) analysis is carried out to sub-critical Hopf, super-critical Hopf and Generalized Hopf (GH) bifurcation. This type of bifurcation analysis is rarely reported for the SC-CO2 fluid flow systems.