The K number, a new analogy criterion number to connect pressure drop and heat transfer of sCO2 in vertical tubes

Highlights: • sCO₂ flow and heat transfer were experimentally studied coving wide parameter ranges. • Friction pressure drops are significantly larger when heat transfer deterioration HTD occurs. • K is identified as the similarity criterion number to connect pressure drops and heat transfer. • The orifice contraction effect introduces additional pressure drop for HTD. • A new correlation of friction factors is developed based on Reynolds number and K. Pressure drop and heat transfer are important for design and operation of power plant using supercritical fluid, but they were investigated independently previously. The objective of this paper is to make a connection between pressure drop and heat transfer for supercritical carbon dioxide (sCO₂). Experimental data of pressure drop and heat transfer were obtained in our sCO₂ convective test loop, covering pressures, mass fluxes and heat fluxes in the ranges of 7.5–23 MPa, 500–1500 kg/m²s and 15–400 kW/m², respectively. Different from classical single-phase fluid assumption for supercritical fluid, pseudo-boiling is introduced to deal with flow and heat transfer in supercritical domain, including a wall-attached gas-like layer and a liquid-like fluid in tube core. Supercritical boiling number SBO and K number are developed to characterize the gas-like layer thickness. Friction factors and heat transfer are found to display the two regimes distribution: a normal heat transfer (NHT) regime with smaller friction factors at smaller SBO, and a heat transfer deterioration (HTD) regime accompanying sharply increased pressure drops beyond a critical SBO. We conclude an orifice contraction effect due to the strong vapor expansion, explaining the HTD induced rise of pressure drops. We show that K can be the similarity criterion number to connect pressure drops and heat transfer. A new correlation of friction factors is developed for sCO₂, which is suitable for NHT and HTD, having mean relative error, mean absolute relative error and root-mean-square relative error of −6.2%, 18.1% and 21.2%, respectively, which are significantly smaller than those predicted by the correlations in the literature.