Vapor mixing in turbulent vaporizing flows

Scalar mixing and evaporation processes are analyzed in a compressible two-phase homogeneous and isotropic turbulence configuration. To this end, the fully compressible Navier-Stokes equations are solved using a pressure-based method and a mass-conservative interface capturing method (CLSVOF). Temperature and vapor mass fraction transport equations are coupled with the momentum equation via the evaporation rate: i.e. heat and mass transfer has an effect on the flow dynamic through the generation of a Stefan flow at the interface. In this formalism, a pressure equation is developed to include the acoustic, thermal dilatation and compressibility effects. Moreover, the method can consider several gas structures in the same domain, each with independent temperature, density, and thermodynamic pressure. The latter is important to simulate atomization, where interaction among the liquid structures (such as breakup or coalescence) can generate multiple gas inclusions. This work is one of the first to describe with high fidelity the vaporization and turbulent mixing occurring in dense two-phase flows. A statistical analysis of the vapor mass fraction field is performed. The obtained results reveal the influence of the non-homogeneous scalar source at the interface, which depend directly on the local interface temperature, on the PDF shape. Under these conditions, the vapor mass fraction PDF deviates from the Gaussian and beta PDF shapes, frequently used for turbulent combustion modeling. Furthermore, access to the local surface averaged vapor mass fraction and evaporation rate at the interface allows a statistical analysis of these variables. Results show a large dispersion of both quantities, especially at the early times of the simulations, which contradict the usual assumption of a constant vapor mass fraction (or vaporization rate) at the interface used in the literature in standard vaporization models. Finally, the influence of the mean interface curvature on the evaporation rate is quantified and discussed. Large evaporation rate are present when the interface is convex (positive mean curvature). On the contrary, local saturation zones are present near concave interface (negative mean curvature), reducing the evaporation rate magnitude.