Machine-learning accelerated turbulence modelling of transient flashing jets

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.