The aim of this project is twofold. Firstly, we want to gain a better understanding of the behavior of a scalar transported by a turbulent flow. Secondly, this knowledge will be used to develop accurate methodologies to numerically simulate the scalar transport on a broad range of applications.

To achieve these objectives we need to perform simulations of the scalar transport equation in a high-resolution simulation of turbulent flows i.e. we have to develop methodology to overcome the difficulties associated to solving explicitly all the fluid and scalar scales. This project has been split in 4 technical tasks. As already stated, two main approaches will be considered: Large-Eddy Simulations (LES) and remeshed particle methods. The first two tasks will focus on new developments of these two approaches. The third task will be to design a hybrid approach coupling between LES and particle methods. The goal will be to deal with non-diffusive scalar through turbulent flow simulation. Finally the 4th task will deal with specific scalar quantities needed to simulate reacting flows. These quantities are the SGS scalar variance and the SGS scalar dissipation.

The first task is devoted to the improvement of the LES approach in scalar simulations. This is an important point of current research in the field of LES for turbulent flow. The main issue is to develop an accurate SGS model available for any scalar. It means that the model has to be accurate for a broad range of molecular Schmidt number values (from much smaller than one to much higher than one). Few models have been proposed to take directly account the molecular Schmidt number value but no consensus has been found on the exact dependence between the model and this value. In this task, we want to gain a better understanding of the scalar small-scales behavior with the molecular Schmidt number by performing high resolution DNS for various flows. This new knowledge and the generated databases will then be used to develop an accurate SGS scalar flux model. The model development will be based on a systematic procedure using the optimal estimator theory [Moreau et al., 2006] and optimization algorithms. The new model will be used to simulate scalar in various applications.

The second task will focus on particle methods and their coupling with spectral and finite volume flow solvers. We will couple particle schemes first with spectral flow LES solvers, then with finite-volume methods. Coupling with spectral LES methods will be done for homogeneous turbulence experiments, while coupling with finite-volume methods will concern flows in complex geometries. The goal of the task will be the systematic study of the scalar properties with respect to Schmidt number and the respective spatial resolutions used in the flow and particle solvers. An emphasis will be put on the choice of the appropriate plat-forms and algorithms for the flow and particle solvers to obtain the best overall efficiency for the coupling method.

The third task will be directly linked with the first two tasks. Indeed, the objective is to mix the results of these both tasks to develop a hybrid method. For a very weakly diffusive scalar (with a very high Schmidt number) in a high level turbulence, both methods generally tend to fail. This is because the LES meshing does not keep enough large scales to compute the SGS model accurately whereas the number of particles needed for the remeshing method will be too high to discretize until the dissipation scale. We can expect better results by using a remeshing particle method with a SGS model to overcome these limitations. A severe test case will be to be able to perform accurate simulations of a passive scalar without diffusivity (i.e. with an infinite molecular Schmidt number). This is the case when the scalar is an interface capturing Level Set function in multiphase flow simulation.

Finally, the last task will be an extension of the first task where the objective is to develop SGS models for the specific case of reacting flows. In LES of reacting flows, a nonreactive scalar is used. This scalar represents the mixture fraction, i.e. the rate of mixing of fuel and oxidizer. The chemistry reactions are determined from the species mass fractions and the temperature, which are a function of mixture fraction only in the simplest case of infinitely fast chemistry. For example, the filtered mass fraction of the species can be obtained assuming a given filter probability density function of the mixture fraction (FPDF). A classic model for the FPDF is to assume a beta distribution [Cook and Riley, 1994]. To determine this FPDF, the subgrid-scale (SGS) scalar variance is also needed. This quantity has to be modelled in LES. Moreover, in LES of reacting flows, the SGS scalar dissipation rate is also needed and has to be modelled. In fact, it can be shown that the chemical source term is directly proportional to the scalar dissipation rate as long as the chemistry is fast enough [Bilger, 1976]. This quantity therefore appears in essentially all models for non-premixed combustion, such as the flamelet model, the conditional moment closure model, and the transported PDF model (see [Pitsch, 2006] for a review). The goal of this last task is to propose accurate models for these quantities. We want to apply the systematic procedure develop at the first task to achieve this objective. We will thus use the optimal estimation theory on the high-resolution DNS databases previously performed.

Each task focus on a specific objective to be finally able to develop a set of accurate methodologies to simulate the scalar transport in a broad range of applications.