## Research projects

Laboratory for computational transport phenomena is conducting research projects in field of turbulence and combustion which are sponsored by NASA, NSF, AFOSR. Some of the projects are presented below.

### FILTERED DENSITY FUNCTION

A methodology termed the ‘‘filtered density function’’ (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability densityfunction (PDF) of subgrid scale (SGS) scalar quantities. A transport equation is derived for the FDF in which the effect of chemical reactions appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The FDF transport equation is solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of the equivalent stochastic differential equations (SDEs) are obtained. These solutions preserve the Ito-Gikhman nature of the SDEs. The consistency of the FDF approach, the convergence of its Monte Carlo solution and the performance of the closures employed in the FDF transport equation are assessed by comparisons with results obtained by direct numerical simulation (DNS) and by conventional LES procedures in which the first two SGS scalar moments are obtained by a finite difference method (LES-FD). These comparative assessments are conducted by implementations of all three schemes (FDF, DNS and LES-FD). In non-reacting flows, the Monte Carlo solution of the FDF yields results similar to those via LES-FD. The advantage of the FDF is demonstrated by its use in reacting flows. In the absence of a closure for the SGS scalar fluctuations, the LES-FD results are significantly different from those based on DNS. The FDF results show a much closer agreement with filtered DNS results.

### Filtered Density Function for Large Eddy Simulation of Turbulent Reacting Flows on Unstructured Meshes

A computational filtered density function (FDF) methodology is developed for large eddy simulation (LES) of turbulent reacting flows. This methodology is based on a Lagrangian Monte Carlo (MC) FDF solver constructed on a domain portrayed by an unstructured mesh. The base filtered transport equations on this mesh are solved by a finite-volume (FV) method. The consistency of the hybrid FV-MC solver and the realizability of the simulated results are demonstrated via LES of a different test problems. The overall performance of the model is appraised by comparison with direct numerical simulation (DNS) data. The algorithmic implementation in the commercial software ANSYS-FLUENT facilitates future FDF-LES of turbulent combustion in complex configurations.Filtered density function simulator on unstructured meshes.

### An Irregularly Portioned Filtered Density Function

A new computational methodology is developed for large eddy simulation (LES) with the filtered density function (FDF) formulation of turbulent reacting flows. This methodology is termed the “irregularly portioned Lagrangian Monte Carlo finite difference” (IPLMCFD). It takes advantage of modern parallel platforms and mitigates the computational cost of LES/FDF significantly. The embedded algorithm addresses the load balancing issue by decomposing the computational domain into a series of irregularly shaped and sized sub-domains. The resulting algorithm scales to thousands of processors with an excellent efficiency. Thus it is well suited for LES of reacting flows in large computational domains and under complex chemical kinetics. The efficiency of the IPLMCFD; and the realizability, consistency and the predictive capability of FDF are demonstrated by LES of several turbulent flames.

### Hybrid Discontinuous Galerkin/Monte Carlo Solver

A new computational scheme is developed for large eddy simulation (LES) of compressible turbulent reacting flows via the filtered density function (FDF) subgrid scale closure. This is a hybrid scheme, combining the discontinuous Galerkin (DG) Eulerian solver with a Lagrangian Monte Carlo FDF simulator. The methodology is shown to be suitable for LES, as a larger portion of the resolved energy is captured as the order of spectral approximation increases. Simulations are conducted of both incompressible and compressible flows. The consistency and the overall performance of the DG-MC solver, and the realizability of thesimulated results are demonstrated via LES of a temporally developing mixing layer under both non-reacting and reacting conditions. It is also shown that the scheme is capable of accurate simulation of shock dominated flows

### Self-contained filtered density function

The filtered density function (FDF) closure is extended to a “self-contained” format to include the subgrid-scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy,the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large-eddy simulation (LES) of flows at both low and high compressibility levels. A transport equation is developed for the joint pressure-energy-velocity-composition filtered mass density function (PEVC-FMDF). In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation for each of the transport variables. This yields a self-contained SGS closure. For demonstration, LES is conducted of a turbulent shear flow with transport of a passive scalar. The consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.

### high order unstructured mesh Turbulent Combustion

Work in process…