Stochastic calibration of cavitation model parameters for simulations of 3-phase injector internal flows

Abstract

The work focuses on the calibration of cavitation model parameters for the numerical simulation of three-phase injector flows. Cavitation is modeled through a transport equation for the void fraction closed by the Schnerr-Sauer relation. The vaporization and condensation factors contained in this model are considered for calibration against experimental data available for a test-case characterized by fuel injection in a reservoir filled of air through an axisymmetric channel. In spite of the simplified geometry, this flow configuration is representative of a real injector and contains most of the complex physical phenomena which may be encountered in injector flows, as turbulence, cavitation and hydraulic flip, i.e. a back flow of air from outside the injector along the whole length of the channel replacing the cavitating regions. Since a direct calibration would imply huge computational costs, not affordable in practical applications, response surfaces of the quantities of interest are built through generalized Polynomial Chaos. These response surfaces, which can be obtained starting from only a few deterministic simulations, have been then used to carry out the parameter calibration. The quantities of interest taken into consideration are the critical cavitation point (CCP), i.e. the value of the outlet pressure at which the flow inside the injector can be considered choked (for a fixed inlet pressure), and the mass-flow-rate (MFR) at the CCP. To further reduce the computational costs, calibration is carried out by using axisymmetric simulations. It has been then checked that the obtained cavitation model gives accurate results also in three-dimensional simulations of the actual geometry. Moreover, this set-up has been applied to two different complex one-hole injector geometries, i.e. a sector of real injector geometries, and the results have been compared against available experimental data. The calibrated cavitation model set-up appears to be robust, giving good predictions also in conditions significantly different from those in which it has been obtained.