The two-phase compressible scalar filtered mass density function (FMDF) model is further developed and employed for large-eddy simulations (LES) of turbulent spray combustion in internal combustion (IC) engines. In this model, the filtered compressible Navier-Stokes equations are solved in a generalized curvilinear coordinate system with high-order, multi-block, compact differencing schemes for the turbulent velocity and pressure. However, turbulent mixing and combustion are computed with a new two-phase compressible scalar FMDF model. The spray and droplet dispersion/evaporation are modeled with a Lagrangian method. A new Lagrangian-Eulerian-Lagrangian computational method is employed for solving the flow, spray and scalar equation. The pressure effect in the energy equation, as needed in compressible flows, is included in the FMDF formulation.The performance of the new compressible LES/FMDF model is assessed by simulating the flow field and scalar mixing in a rapid compression machine (RCM), in a shock tube and in a supersonic co-axial jet. Consistency of temperatures predicted by the Eulerian finite-difference (FD) and Lagrangian Monte Carlo (MC) parts of the LES/FMDF model are established by including the pressure on the FMDF. It is shown that the LES/FMDF model is able to correctly capture the scalar mixing in both compressible subsonic and supersonic flows.Using the new two-phase LES/FMDF model, fluid dynamics, heat transfer, spray and combustion in the RCM with flat and crevice piston are studied. It is shown that the temperature distribution in the RCM with crevice piston is more uniform than the RCM with flat piston. The fuel spray characteristics and the spray parameters affecting the fuel mixing inside the RCM in reacting and non-reacting flows are also studied. The predicted liquid penetration and flame lift-off lengths for respectively non-reacting and reacting sprays are found to compare well with the available experimental data. Temperatures and evaporated fuel mass fractions as predicted by the LES-FD and FMDF-MC for both reacting and non-reacting cases are shown to be consistent inside the RCM.Several non-reacting and reacting flows relevant to IC engines are also simulated with the new two-phase LES/FMDF model. The non-reacting flows in three geometrical configurations are considered: (1) a poppet valve in a sudden expansion, (2) a simple piston-cylinder assembly with a stationary open valve and harmonically moving flat piston, and (3) a realistic 3-valve single-cylinder direct-injection spark-ignition engine. The first and the second configurations are considered for validation of LES and for better understanding of the large-scale unsteady flow motions around the valve in the cylinder as generated by the piston movement. The predicted flow statistics by LES for the first two configurations compare well with the available experimental data. The LES results for third flow configuration show significant cycle-to-cycle variations (CCV) in the velocity field but insignificant CCV in the thermodynamic variables. During the intake stroke, the in-cylinder flow is highly inhomogeneous and turbulent, but during the compression stroke the flow becomes more homogeneous as turbulent decays. Turbulent mixing and combustion (with and without spray) in the 3-valve engine are simulated using the new two-phase compressible LES/FMDF model. Consistency of LES and FMDF results for single-phase reacting flows without spray but with flame ignition and premixed flame propagation, and two-phase reacting flows with spray, mixing and non-premixed combustion indicates the applicability and accuracy of the LES/FMDF model for complex turbulent combustion systems with moving boundaries.
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