  Modelling the sudden depressurisation of superheated liquids through nozzles
is a challenge because the pressure drop causes rapid flash boiling of the
liquid. The resulting jet usually demonstrates a wide range of structures,
including ligaments and droplets, due to both mechanical and thermodynamic
effects. As the simulation comprises increasingly numerous phenomena, the
computational cost begins to increase. One way to moderate the additional cost
is to use machine learning surrogacy for specific elements of the calculations.
The present study presents a machine learning-assisted computational fluid
dynamics approach for simulating the atomisation of flashing liquids accounting
for distinct stages, from primary atomisation to secondary break-up to small
droplets using the ${\Sigma}$-Y model coupled with the homogeneous relaxation
model. Notably, the model for the thermodynamic non-equilibrium (HRM) and
${\Sigma}$-Y are coupled, for the first time, with a deep neural network that
simulates the turbulence quantities, which are then used in the prediction of
superheated liquid jet atomisation. The data-driven component of the method is
used for turbulence modelling, avoiding the solution of the two-equation
turbulence model typically used for Reynolds-averaged Navier-Stokes simulations
for these problems. Both the accuracy and speed of the hybrid approach are
evaluated, demonstrating adequate accuracy and at least 25% faster
computational fluid dynamics simulations than the traditional approach. This
acceleration suggests that perhaps additional components of the calculation
could be replaced for even further benefit.
