Numerical validation of novel scaling laws for air–water flows including compressibility and heat transfer

Air–water flows are among the most important flow types in hydraulic engineering. Their experimental modelling at reduced size using Froude scaling laws introduces scale effects. This study introduces novel scaling laws for compressible air–water flows in which the air is considered compressible. This is achieved by applying the one-parameter Lie group of point-scaling transformations to the governing equations of these flows. The scaling relationships between variables are derived for the fluid properties and the flow variables including temperature. The novel scaling laws are validated by computational fluid dynamics modelling of a Taylor bubble at different scales. The resulting velocity, density, temperature, pressure and volume of the bubble are shown to be self-similar at different scales, i.e. all these variables behave the same in dimensionless form. This study shows that the self-similar conditions of the derived novel scaling laws for compressible air–water flows have the potential to improve laboratory modelling.