Turbulence subgrid-scale

The ability to resolve the dissipation structures allows a more detailed understanding of the interactions between turbulent flows and flame chemistry. This information on spectra, length scales, and the structure of small-scale turbulence in flames is also relevant to computational combustion models. For example, information on the locally measured values of the Batchelor scale and the dissipation-layer thickness can be used to design grids for large-eddy simulation (LES) or evaluate the relative resolution of LES resulfs. There is also the potential to use high-resolution dissipation measurements to evaluate subgrid-scale models for LES. 

It is then assumed that due to this separation in scales, the so-called subgrid scale (SGS) modeling is largely geometry independent because of the universal behavior of turbulence at the small scales. The SGS eddies are therefore more close to the ideal concept of isotropy (according to which the intensity of the fluctuations and their length scale are independent of direction) and, hence, are more susceptible to the application of Boussinesq s concept of turbulent viscosity (see page 163). 

Subgrid-scale modeling for turbulent reacting flows. Combustion and Flame 112, 593-606. 

Cook, A. W., J. J. Riley, and G. Kosaly (1997). A laminar flamelet approach to subgrid-scale chemistry in turbulent flows. Combustion and Flame 109, 332-341. 

Meneveau, C., T. S. Lund, and W. Cabot (1996). A Lagrangian dynamic subgrid-scale model of turbulence. Journal of Fluid Mechanics 319, 353-385. 

Wall, C., B. J. Boersma, and R Moin (2000). An evaluation of the assumed beta probability density function subgrid-scale model for large eddy simulation of nonpremixed, turbulent combustion with heat release. Physics of Fluids 12, 2522-2529. 

DesJardin, P. E., and S. H. Frankel. 1998. Large-eddy simulation of a turbulent nonpremixed reacting jet Application and assessment of subgrid-scale combustion models. J. Physics Fluids 10(9) 2298-314. 

Reveillon, J., and L. Vervisch. 1998. Subgrid-scale turbulent micromixing Dynamic approach. AIAA J. 36(3) 336-41. 

Moin, P., K. Squires, W. Cabot, and S. Lee. 1991. A dynamic subgrid-scale model for compressible turbulence and scalar transport. J. Physics Fluids 3(ll) 2746-57. 

Liquid fuel sprays are not yet fullj understood [310]. The atomization process of a liquid fuel jet [376 332 345 293 309], the turbulent dispersion of the resulting droplets [256 253 262 333 319], their interaction with walls [259 365], their evaporation and combustion [290] are phenomena occurring in LES at the subgrid scale and therefore require accurate modeling. 

In the context of LES, a new modeling issue appears for two-phase flow simulations, either in the EL or EE formulation, and is linked to the subgrid scale model for the turbulent droplet dispersion. This problem has already been addressed in [278 279[ but is still an open question. However in the case of reacting flows, turbulent droplet dispersion occurs in a very limited zone between the atomizer and the flame and it is greatly influenced by the flame dynamics, therefore limiting the impact of the subgrid scale model. 

The turbulent viscosity i/j is determined using the WALE model [330], similar to the Smagorinski model, but with an improved behavior near solid boundaries. Similarly, a subgrid-scale diffusive flux vector Jfor species Jk = p (uYfc — uYfc) and a subgrid-scale heat flux vector if = p(uE — uE) appear and are modeled following the same expressions as in section 10.1, using filtered quantities and introducing a turbulent diffusivity = Pt/Sc], and a thermal diffusivity Aj = ptCp/Pr. The turbulent Schmidt and Prandtl numbers are fixed to 1 and 0.9 respectively. 

In turbulent reacting cases the Dynamically Thickened Flame model [311 321 355 361] is used, where a thickening factor F is introduced to thicken the flame front and the efficiency function developed by Colin et al. [269] is used to account for subgrid scale wrinkling. 

---