Stochastic models in the under-resolved simulations of spray formation during high-speed liquid injection

Abstract

In the under-resolved simulation of the high-speed liquid injection into stagnant air, the attention in subgrid-scale models is focused on events of intense gradients of the velocity in turbulent flow, i.e., on effects of intermittency. Three typical flows are considered—the in-nozzle flow, primary atomization zone, and secondary atomization of spray droplets. In the simulation of the first two flows, the filtered Navier–Stokes equations are forced by stochastic processes with properties which incorporate the statistical physics of fluid acceleration at the high Reynolds number—in this way we update the under-resolved acceleration. In the case of in-nozzle flow, the proposed stochastic subgrid acceleration model is combined with wall-damping function, and the ability in prediction of the velocity statistics is demonstrated. In the simulation of primary atomization, the approach with stochastic subgrid acceleration is combined with the volume of fluid method. This leads to intensification of the interface dynamics, resulting in additional corrugation, with more intense shearing and stretching of liquid structures are observed. Thereby, the experimental profiles of the time-averaged liquid volume fraction distribution for four different axial locations are rather well predicted. The secondary atomization of droplets is simulated by a new stochastic model for the breakup rate along the droplet path. To this end, the breakup rate is expressed as a function of turbulent viscous dissipation which evolves along the droplet path according to the proposed stochastic process. Preliminary assessment performed against the recent experiments shows the correct predictability of this model and its low sensibility to the grid density.