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