The two-phase filtered mass density function (FMDF) method is employed for large eddy simulation (LES) of high speed evaporating and combusting nheptane sprays using simple (global) and complex (skeletal) chemical kinetic mechanisms. The resolved fluid velocity and pressure fields are obtained by solving the filtered compressible Navier-Stokes equations with high-order Eulerian finite difference methods. The liquid spray and gas scalar (temperature and species mass fractions) fields are both obtained by Lagrangian stochastic models. The chemistry calculation is accelerated by incorporating the parallel in situ adaptive tabulation (ISAT) method. There are two-way interactions among Eulerian and Lagrangian fields. Simulations of evaporating sprays with and without combustion indicate that the two-phase LES/FMDF results are consistent and compare well with the available experimental data at different gas temperatures and oxygen concentrations. The spray controlled flame tends to move away from a diffusion flame structure toward a premixed one as the oxygen concentration decreases and/or the ambient gas temperature increases because of changes in spray-induced turbulence and mixing. The LES/FMDF results for ignition delay show more sensitivity to the chemical kinetic model at lower gas temperatures due to slower reaction and stronger turbulence-chemistry interactions. The liftoff length is less sensitive to the kinetics.

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The scalar filtered mass density function model is further extended and employed for large-eddy simulations of high-speed turbulent mixing and reacting flows. The model is implemented through a hybrid mathematical/ computational methodology. In this methodology, the filtered compressible Navier-Stokes equations in a curvilinear coordinate system are solved with a generalized, high-order, multiblock, finite difference scheme for the turbulent velocity and pressure. However, the scalar mixing and combustion are computed with the compressible scalar filtered mass density function. The pressure effect in the energy equation, as needed in high-speed flows, is included in the filtered mass density function formulation. The new compressible large-eddy simulation/filtered mass density function model is used for the simulations of flows in a rapid compression machine, in a shock tube and in a supersonic coaxial jet. The numerical results indicate that the model is able to correctly capture the scalar mixing in compressible subsonic and supersonic turbulent flows.

This paper describes a new computational model developed based on the filtered mass density function (FMDF) for large-eddy simulation (LES) of two-phase turbulent reacting flows. The model is implemented with a unique Lagrangian–Eulerian–Lagrangian computational methodology. In this methodology, the resolved carrier gas velocity field is obtained by solving the filtered form of the compressible Navier–Stokes equations with high-order finite difference (FD) schemes. The gas scalar (temperature and species mass fractions) field and the liquid (droplet) phase are both obtained by Lagrangian methods. The two-way interactions between the phases and all the Eulerian and Lagrangian fields are included in the new two-phase LES/FMDF methodology. The results generated by LES/FMDF are compared with direct numerical simulation (DNS) data for a spatially developing non-reacting and reacting evaporating mixing layer. Results for two more complex and practical flows (a dump combustor and a double-swirl burner) are also considered. For all flows, it is shown that the two-phase LES/FMDF results are consistent and accurate.

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A new computational methodology is developed and tested for large eddy simulation (LES) of turbulent flows in internal combustion (IC) engines. In this methodology, the filtered compressible Navier-Stokes equations in curvilinear coordinate systems are solved via a generalized, high-order, multi-block, compact differencing scheme and various subgrid-scale (SGS) stress closures. Both reacting and nonreacting flows with and without spray are considered. The LES models have been applied to a piston-cylinder assembly with a stationary open valve and harmonically moving flat piston. The flow in a direct-injection spark-ignition (DISI) engine is also considered. It is observed that during the intake stroke of the engine operation, large-scale unsteady turbulent flow motions are developed behind the intake valves. The physical features of these turbulent motions and the ability of LES to capture them are studied and tested by simulating the flow in a simple configuration involving a stationary valve. The flow statistics predicted by LES are shown to compare well with the available experimental data. The DISI configuration includes all the complexities involved in a realistic single-cylinder IC engine, such as the complex geometry, moving valves, moving piston, spray and combustion. The spray combustion is simulated with the recently developed two-phase filtered mass density (FMDF) model.

This paper provides a brief review of the scalar filtered mass density function (FMDF) model. The FMDF is a subgrid-scale probability density function (PDF) model for large eddy simulation (LES) of turbulent combustion and is obtained by the solution of a set of stochastic differential equations by a Lagrangian Monte Carlo method. The applicability and the validity of the LES/FMDF are established by simulating various low and high speed, single-and two-phase turbulent reacting flows. The LES/FMDF results are found to be consistent and comparable to DNS and experimental results for different flows.

In this work, parallel solution of the Navier-Stokes equations for a mixed convection heat problem is achieved using a finite-element-based finite-volume method in fully coupled and semi coupled algorithms. A major drawback with the implicit methods is the need for solving the huge set of linear algebraic equations in large scale problems. The current parallel computation is developed on distributed memory machines. The matrix decomposition and solution are carried out using PETSc library. In the fully coupled algorithm, there is a 36-diagonal global matrix for the two-dimensional governing equations. In order to reduce the computational time, the matrix is suitably broken in several sub-matrices and they are subsequently solved in a segregated manner. This approach results in four 9-diagonal matrices. Different sparse solver algorithms are utilized to solve a mixed natural-forced convection problem using either fully-coupled or semi-coupled algorithms. The performance of the solvers are then investigated in solving on a distributed computing environment. The study shows that the iteration run time considerably decreases although the overall run time of the fully coupled algorithm still looks better.