March 23, 2022

Geometric and thermodynamic considerations of saturated and slightly subcooled water flow through nozzles

By Maksim Oskotskiy

The article created by AIChE DIERS members, including Leonid Korelstein, PASS VP on R&D, is posted in Chemical Engineering Science magazine, Volume 254 (2022).


  • Deviation from equilibrium is recognized as a manifestation of rapid depressurization events including Rapid Phase Transitions, Boiling Liquid Expanding Vapor Explosions, and flow of saturated and slightly subcooled liquids through converging nozzles and sudden contractions.
  • Non-equilibrium effects are attributed to nozzle geometry and the pressure driving force for saturated and slightly subcooled liquid flow through nozzles and sudden contractions.
  • Bubble nucleation theory is used to estimate the deviation from equilibrium and single-phase flow methods are used to estimate the critical mass flux when rapid vaporization occurs at the nozzle throat.


It is well known that homogeneous equilibrium methods for calculating the mass flux of initially subcooled or saturated liquids in short nozzles under-predict the measured values and various methods for estimating non-equilibrium effects have been presented in the past. It is shown in this paper that acceleration effects at the entrance of converging nozzles due to changing cross-sectional area and approach to thermodynamic saturation pressure at the point of maximum fluid acceleration can be the most significant causes of non-equilibrium. By properly accounting for non-equilibrium due to the fluid acceleration, single-phase flow methods can be used to estimate the pressure loss and mass flux in nozzles when rapid vaporization occurs at the nozzle throat. For these cases, choking occurs due to the rapid vaporization while the difference between the inlet pressure and choking pressure determines the nozzle mass flux.

Download the article (pdf)

About the journal

Chemical Engineering Science (CES) has been publishing papers on the fundamentals of chemical engineering since 1951. CES is the platform where the most significant advances in the discipline have ever since been published. Chemical Engineering Science has accompanied and sustained chemical engineering through its development into the vibrant and broad scientific discipline it is today.