The three-regime-model for pseudo-boiling in supercritical pressure

Abstract

Supercritical pseudo-boiling (SPPB) refers to the phenomena that when heat is applied to supercritical fluid, bubble-like and vapor-film-like features appear and wall temperature peaks occur, similar to subcritical boiling (SBB). Even though SPPB was reported in 1960s∼1970s, it has not been paid attention and supercritical heat transfer (SHT) is still treated with single-phase fluid assumption, introducing difficulties in accurately describing the flow and heat transfer characteristics. Here, by analogy between SPPB and SBB, a three-regime-model is proposed for SPPB, including liquid-like (LL), two-phase-like (TPL) and vapor-like (VL) regimes. The three regimes are interfaced at an onset of pseudo-boiling temperature T− and a termination of pseudo-boiling temperature T+, determined by thermodynamics. Thermophysical properties of LL and VL phases are evaluated using the two pseudo-boiling temperatures. Pseudo-boiling enthalpy is defined as the enthalpy difference across the temperature span from T− to T+, which is analogous to latent heat of evaporation in subcritical pressure. Pseudo-vapor mass quality x is calculated using bulk fluid enthalpy and fluid enthalpies at T− and T+. Non-dimensional parameters are proposed to reflect interactions of mass, momentum and energy between LL and VL phases. Based on the three-regime-model, SHT is re-analyzed in a different perspective from literature. We show that SHT deviates from that of single-phase convection significantly for 0 < x < 1 corresponding to the TPL regime, indicating that SHT cannot be treated with single-phase fluid assumption under this condition. Reynolds number for LL phase (ReLL) explains the non-monotonic variation of SHT versus heat fluxes. Froude number Fr explains the difference of SHT between top generatrix and bottom generatrix in horizontal tubes. Supercritical boiling number SBO and K number successfully correlate heat transfer and pressure drop for SHT in tubes, and the K number correlation has much smaller error than DB correlation. Our work establishes a new theoretical framework for SPPB and provides a new research direction for heat transfer of supercritical fluids.