**6. Conclusions**

**Figure 2.** Radial mean (a) and fluctuation (b) concentration distribution across the jet. Experimental data (*symbols*) from Ref. [100]: + = 70; ● = 80; × = 90. Simulation results (*lines*) from Refs. [98, 99]: *Solid line*: eddy; *dashed line*: dynamic; *dotted*

**Figures 1** and **2** compare the simulated radial mean and fluctuation distribution of the scalar concentration [98, 99], normalized by the centerline value (*η = r/x*, where *r* is the radial coordinate and *x* is the downstream distance from the nozzle exit), with the experimental

Having in mind the limitations of the eddy diffusivity model, it is noted in **Figure 1** that the mean concentration distribution is predicted reasonably well. On the other hand, **Figure 2** reveals that the three SGS scalar flux models fail to reproduce the concentration fluctuations at higher values of the nondimensional radial coordinate (*η*). Although the LES simulation results of the concentration distribution in radial direction are similar for the tested SGS scalar flux models in **Figures 1** and **2**, the dynamic anisotropy model provides a better perform‐ ance. In LES, a mesh grid refinement would improve the simulation results. Mejía et al. [98] also showed that if the mesh grid is further refined, the dynamic eddy diffusivity improved

**Figure 3.** Streamwise velocity‐concentration correlation across the jet. Experimental data (*symbols*) from Antoine et al. [100]: + = 70; ● = 80; × = 90. Simulation results (*lines*) from Refs. [98, 99]: *Solid line*: eddy; *dashed line*: dynamic; *dotted line*:

*line*: anisotropy; *dashed*‐*dotted line*: FDF.

418 Numerical Simulation - From Brain Imaging to Turbulent Flows

its predictive capabilities.

anisotropy; *dashed*‐*dotted line*: FDF.

data [101].

Large eddy simulation of transport and mixing in high Schmidt flows remains a challenge, in particularfor engineering applications. The appraisal of conventional andadvanced SGS scalar flux models as well as the FDF method has to done based on the object of study. However, some of the merits of the approximations can be highlighted. The SGS scalar flux models have the advantage over FDF methods in that the simplest ones (e.g., eddy diffusivity model) are

available in many CFD solvers. This closure strategy uses the same mesh grid of the flow solver as well as the numerical methods used for the numerical solution of the *N‐S* equations. Therefore, one important consequence is that the programming of advanced SGS scalar flux models is straightforward. Having in mind the computational cost, simple SGS scalar flux models can reproduce important characteristics of the scalar field such as mean quantities on a moderate grid resolution. However, if the application requires a deeper understanding of mesomixing and micromixing (such as combustion and flow instability studies), the use of advanced SGS scalar flux models becomes mandatory. On the other hand, the main advant‐ age of FDF method is that it allows for a detailed description and simulation of the scalar field. The FDF transport equation can be solved using particle‐based methods, which are very simple to implement and to couple to LES solvers. The computational domain can be simpler than the one used by LES, since it only has to account for the spatial domain where the scalar field evolves.
