Modeling Phase Transition during Primary Breakup of Turbulent Liquid Jets and Sheets

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We consider a Large Surface Structure (LSS) model for the numerical simulation of phase transition during primary breakup of turbulent liquid jets or sheets in three dimensions. To develop and verify the LSS model, Direct Numerical Simulations (DNS) studies of the phase transition effects during primary breakup will be performed. To this end the Level Set/Vortex Sheet (LSVS) method will be extended to include the effects of phase change. Two scenarios representative of engineering applications and consistent with the Large Eddy Simulation (LES) approach of the LSS model will be analyzed: a) the phase change velocity is a constant on the subgrid scale and b) the phase change velocity on the subgrid scale is a function of local subgrid turbulent transport and shear.The first scenario represents a typical LES modeling approach, in that the subgrid phase change velocity is a function of resolved scale quantities only. Its local subgrid PDF is thus a delta function. In the second scenario, local subgrid variations of the phase change velocity due to fluctuations in the subgrid turbulent transport and shear are taken into account. Should these prove to yield significant different DNS results than the first scenario, the use of a non-delta function subgrid PDF of the phase change velocity, dependent on the PDFs, or moments, of transport and shear are required for the LSS model closure.In order to achieve sufficient accuracy for the DNS studies, the partial differential equations will be solved numerically using either a Discontinuous Galerkin method or a Refined Level Set Grid approach employing high-order WENO schemes. Two complimentary strategies will be employed to resolve the wide range of length scales present in the problem. Mesh refinement in the region close to the phase interface ensures the handling of structures of size about one order of magnitude smaller than the Kolmogorov scale. Structures of this or smaller size are then transferred into a Lagrangian spray model. While a localized narrow band approach will ensure that the computational cost remains feasible, parallelization of the whole algorithm will allow access to the high computational power of modern parallel computer systems in order to perform extensive DNS calculations.Practical usefulness of the final LSS method will imply a statistical approach. Turbulence modeling requires the development of appropriate interface based filters and modeling of the unclosed subgrid terms. In the two phase transition cases described above, the modeling strategies developed for premixed turbulent combustion can be applied directly to derive these closure models. The generated LSVS DNS data will be subjected to the same filters in order to validate the closure assumptions. Furthermore, the LSVS method and the final LSS model will be validated using both numerical data obtained by different numerical approaches, specifically the VOF calculations of the French partner, as well as experimental data obtained in the research group and as reported in the literature.