LES method
In general, turbulence contains a series of eddies with a wide scale range. The transport of the main physical quantities is affected by the large-scale eddies, which are highly anisotropic, in particular in a turbulent stirred tank. The small-scale eddies are not as closely related to the problems solved as large-scale eddies, tending to be isotropic. Thus, in the LES approach, the large-scale eddies are resolved directly by solving Navier–Stocks equations, while small-scale eddies are modeled by subgrid-scale (SGS) models.
For the SGS models, the most popular Smagorinsky-Lilly model, which was first proposed by Smagorinsky15, has been adopted to predict the flow patterns in the stirred vessels by many researchers16,17. In this work, a higher-level SGS model, the dynamic kinetic energy transport model, in which the SGS turbulence kinetic energy (ksgs ) was solved by the corresponding transport equation, was adopted. This model has been successfully applied to study the propagation of the turbulent flame, the swirling diffusion flame18, and to predict the turbulent flow in the stirred tank in our previous work19. The governing equations are summarized in Table 1.
Table 1. Model equations for LES approach