Two-phase non-equilibrium models: the challenge of improving phase change heat transfer prediction

Abstract

This lecture addresses some recent developments in modelling of macroscopic thermodynamic and hydrodynamic non-equilibrium phenomena in convective phase change (boiling and condensation) of pure fluids and mixtures. Proper accounting of such phenomena may hold the key to explain and predict deviations from the classical (equilibrium) phase change convective heat transfer behaviour reported in the literature and yet not fully understood. In the first part of the paper, a detailed qualitative description of the classical heat transfer coefficient behaviour is presented together with two examples of departure from macroscopic equilibrium largely supported by experimental evidence. The second part of the paper reviews successful attempts to model the non-equilibrium phase change phenomena taking place in the two situations. The first example is a thermodynamic non-equilibrium slug flow model (one in which saturated Taylor bubbles become separated by slugs of subcooled liquid) that predicts the peaks in heat transfer coefficient at near-zero thermodynamic quality observed in forced convective boiling of some pure liquids. The occurrence of such peaks is typical of low latent heat, low thermal conductivity systems and of systems in which the vapour volume formation rate for a given heat flux is large. The second example is a comprehensive annular flow calculation methodology that predicts the decrease in the heat transfer coefficient with increasing quality observed in convective boiling of binary and multicomponent mixtures. In this case, as will be seen, coupled mass transfer resistance and hydrodynamic non-equilibrium effects generate concentration gradients between the liquid film and entrained droplets that are responsible for the heat transfer deterioration. In addition, it will be shown that for condensation of mixtures the methodology predicts a heat transfer intensification which has been subsequently confirmed by independent experimental results

Comparison of Experimental Heat Transfer Coefficient with Qualitative Description of Classical Heat Transfer Coefficient at Low Heat Flux Conditions

“…This was not the case in our experiment since we observed a deterioration in the heat transfer coefficient to a minimum peak before an increasing trend. Similar deterioration of heat transfer coefficient at low quality was reported by Barbosa (2005), Kandlbinder (1997) [6], [8].…”

Numerical study of heat and mass transfer of binary mixtures condensation in mini-channels

“…They also mentioned that a more detailed set of experiments is required for the consolidation of the analysis. Moreover, it is stated that the correct prediction of the droplets interchange may hold the key to understanding the deterioration associated with the heat transfer coefficient at high qualities during the mixtures boiling, while there remained the challenge of quantifying the heat transfer gain adequately in mixtures condensation (Barbosa, 2005). Therefore, it is also necessary to make an estimation of the droplets interchange during mixtures condensation and to look into this effect on the heat transfer.…”

“…The final term QDG is the heat transferred by the droplets due to droplets interchange. The above equations are based on the multi-fluid model described by Saito et al (1987) and the heat and mass transfer models given by Barbosa andHewitt (2001a, 2001b). …”

Experimental Study of Flow Boiling Heat Transfer at Low Heat Fluxes

“…Popular among these descriptive maps are Collier (1981), Collier and Thome (1994) and Kandlikar (1991) [6]- [8]. According to Barbosa (2005) [9] and Hewitt (2000) [10] these descriptions have been the basis for design calculation and formulation of various flow boiling correlation for many years. Because of the relevance of this parameter, various flow regimes and transition schemes have been suggested by different authors to represent the characteristics of this parameter during flow boiling under different conditions.…”