Model assessment for direct contact condensation induced by a sub-cooled water jet in a circular pipe

In this paper, the condensation induced by a sub-cooled water injection in a circular horizontal pipe with a two-phase stratified flow is investigated. The focus of the work is to review the physical models or correlations predicting the condensation heat transfer coefficient and assess them against an experimental database. Three experiments, namely COSI, TOPFLOW-PTS and UPTF, are consolidated in a substantial database. They have different configurations and complexity, covering a wide range of injection mass flowrate, temperature and pressure. A thermal-hydraulic analysis is performed, resulting in reliable and coherent experimental data. The condensation models found in the literature are based on the modelling of the Nusselt number through several dimensionless numbers. The assessment of these correlations against the experimental database provides poor results. Thus, a new approach is proposed. The cold jet is modelled as a heat exchanger, which is described by a condensation potential. The analytical formula of the potential is found starting from an energy balance at the injection, showing that the condensation depends on the jet geometrical shape and a parameter η. A new correlation for the parameter η is calibrated against the COSI and TOPFLOW-PTS experiments, significantly reducing the average standard deviation between evaluations and experimental data. The new correlation is then applied to an independent database, i.e. the UPTF experiments. The results show good agreement between the calculated and experimental values, proving the capability of the new model to accurately predict the condensation at the injection.