On the influence of liquid /vapor phase change onto the Nusselt number of a laminar superheated or subcooled vapor flow


The effects of external flow on the evaporation and condensation of a liquid plane surface have not been fully explored despite its extensive applications in various processes. Considering that most of the above applications involve gas mixtures and turbulent flows, it is necessary to solve simple configurations comprising of laminar superheated or supercooled vapor flows both theoretically, numerically and experimentally before moving to complex configurations. In particular, the correlation on the Nusselt number and drag coefficient of the evaporating droplets have been designed based on the interaction between liquid-vapor phase changes and two-phase flows. This has shown the great potential of fully characterizing other configurations.

Elena-Roxana Popescu, Dr. Sebastian Tanguy and Professor Catherine Colin from the Universite de Toulouse investigated the influence of an external flow on the vaporization or condensation of a static liquid pool based on numerical simulations. Specifically, the interaction between a laminar boundary layer of superheated or subcooled vapor flow and the static liquid pool was analyzed at saturation temperature. Thus, a canonical configuration was defined to particularly enhance the physical understanding of the interaction between the laminar flow and vaporization or condensation. The main aim was to present the correlation of the Nusselt number for characterizing both vaporization and condensation for the developed configuration. Their work is published in International Journal of Thermal Sciences.

A full set of simulation was performed. Thus, the correlations of the Nusselt number was obtained depending on the dimensionless numbers: density ratio, Jakob number, Reynolds number and Prandtl number which effectively characterized both the vaporization and condensation. For the configurations involving vaporization and condensation, the Nusselt number decreased and increased respectively. Additionally, for the vaporization configuration, the Nusselt number and subsequently the heat transfer decreased exponentially with Jakob number until a saturation level was achieved. However, the opposite trends were observed for condensation configuration.

It was necessary to determine the behavior of the viscous friction on the vapor flow on the liquid pool. The tangential component of the viscous tensor was observed to be weakly affected by the phase change and especially in cases involving plane interfaces. However, the influence of the phase change on the normal component of the viscous tensor was reported to be even weaker as compared to the tangential component.

Generally, a saturation of the heat flux takes place in configurations involving vaporization whereas a self-amplification of the heat flux occurs if condensation is considered. As such, it was possible to determine the analytical expressions of the integrated heat flux exchanged at the liquid-vapor interface from the known Nusselt number expressions. Furthermore, it was worth noting that even if the profiles were not superimposed, the liquid-vapor change still exhibited little influence on the viscous stress vector components.

In summary, the study by Universite de Toulouse scientists is the first to investigate the interaction between the external vapor flow and the liquid/vapor phase change of a liquid pool. Based on the results and specifically the interaction between the laminar flow and vaporization or condensation, the study will advance not only the academic field but also relevant industrial configurations for improved processes.


Popescu, E., Tanguy, S., & Colin, C. (2019). On the influence of liquid/vapor phase change onto the Nusselt number of a laminar superheated or subcooled vapor flow. International Journal of Thermal Sciences, 140, 397-412.

Go To International Journal of Thermal Sciences

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