Supercritical “boiling” number, a new parameter to distinguish two regimes of carbon dioxide heat transfer in tubes

The objective of this paper is to develop a criterion to predict the onset of heat transfer deterioration (HTD) for supercritical CO₂ heat transfer. A new mechanism is proposed by assuming supercritical pseudo-boiling. Before bulk fluid reaches pseudo-critical temperature (T_pc), the tube cross-section contains a vapor layer and a liquid-like fluid. The saturation temperature interface is defined at T = T_pc, inside and outside which are a vapor layer (T > T_pc) and a subcooled liquid (T < T_pc). The subcritical boiling number is extended to supercritical “boiling” number, defined as SBO = q_w/(Gi_pc), where q_w, G and i_pc are heat flux, mass flux, and CO₂ enthalpy at T_pc, respectively. SBO, by coupling the density ratio between “liquid” and “vapor” represents the competition between vapor expansion induced momentum force and inertia force. The experiment of supercritical CO₂ heat transfer is performed in a 10.0 mm inner diameter tube, covering ranges of P = 7.5–21.1 MPa, G = 488–1600 kg/m²s and q_w = 74–413 kW/m². Surprisingly, the onset of HTD is found to occur at a critical SBO which is 5.126×10⁻⁴ and the critical heat flux is expressed as q_CHF=5.126×10⁻⁴Gi_pc. It is shown that our new criterion is also suitable for other experiments reported in literature, providing a general guidance to design and operate S–CO₂ heaters to avoid HTD.