Vapour Liquid Equilibrium (VLE)

In order to consider phase change,a two phase thermodynamic model is needed for calculating the properties. These thermodynamic models, which are often very complex, can only be used where phenomena are at equilibrium. From the thermodynamic points of view via the second law of thermodynamics, one isolated system owns the maximum entropy at the equilibrium state.

To satisfy the equilibrium constraints, it can be concluded that Ti = Tj , Pi = Pj , μik = μik, which are the thermodynamic equilibrium constraints so that temperature and the pressure as well as the chemical potentials of each component should be the same for each phase of the system(equality of chemical potential of each component+massbalance).


Flow chart of the VLE thermodynamic solver



  1. Evaporation modeling

The process that converts liquid to gaseous is called evaporation. As the number of components grows, especially at various pressure and temperature levels, this modeling approach will become quite challenging. One method to assist in the modeling of evaporation for multicomponent systems is the VLE approach.

2. Cavitation

During the processing of centrifugal pumps, turbines, marine propellers, or even at some high pressure injectors nozzles, cavitation—the creation of vapour bubbles inside a liquid at low-pressure regions—occurs in locations where the liquid has been accelerated to high speeds. Hence, cavitation is a phenomena that occurs when a liquid's static pressure falls below its vapour pressure, causing tiny cavities filled with vapor to form in the liquid. Particularly at various regimes in relation to the multicomponent thermodynamic critical points, this modeling for multicomponent systems will become extremely difficult.

Cavitation modeling of HTHP injector for
 n-dodecane- N2 systems

3. Condensation

Condensation is the process by which any vapor is changed into liquid phase; it's the opposite of evaporation. Condensation is crucial to the cycle because it is responsible for the formation of clouds Particularly at various regimes in relation to the multicomponent thermodynamic critical points, this modeling for multicomponent systems will become extremely difficult. 

Condensing-evaporating jet

Sajad Jafari. Numerical Modelling of transcritical turbulent jets using a tabulated real-fluid approach. Fluids mechanics [physics.class-ph]. Université Paris-Saclay, 2022. English. NNT : 2022UPAST038, PHD manuscript.
[Thesis Link] [Link@ Paris Saclay Universite site]