Numerical appraisal of the role of heat transfer regimes on transient response of carbon dioxide based supercritical natural circulation loop during power upsurge

Appearance of steep property gradients with change in temperature is a fascinating feature of any supercritical fluid, which can instigate intricate dynamics in supercritical natural circulation loops by modulating the effective forces. While most of the relevant literature focuses on stability evaluation, anticipation regarding the transient response of the system during power transition is of utmost significance, especially in high-power applications. Present study aims at furnishing insight on the same by developing a one-dimensional numerical model of a rectangular loop with supercritical CO${}_2$ as the working medium, and characterizing the temporal trends over a wide range of heating power. Two different profiles of power upsurge have been tested for different regimes of heat transfer, unearthing intriguing characteristics. The combination of initial and final regimes during any transformation is found to be the most crucial factor. Single-step rise in power, in general, is the most vulnerable one, specifically during large-scale change of the order of 1000 W, and better be employed only at low-power regime. Even single-step change $\sim$ 25 W can inflict instability and flow transition within the transition regime. Power transformation following linear ramp profile with transition periods of 5, 10 and 20 s is identified to be the most suitable one across all the regimes. It can successfully mitigate instability even in the later parts of the transition regime, albeit at the expense of greater time requirement to attain the final stable state and possibly a greater period of transformation. Change through multiple small steps (about 250 W for large change in low power regime and 15 W within transition regime) can also be a feasible option for avoiding the growth of unstable oscillations at higher powers.