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in a baffled stirred tank agitated with a 3-narrow blade hydrofoil
CBY impeller and a Rushton turbine, respectively. They all con-
cluded that LES is a reliable tool to investigate the unsteady behav-
ior of the turbulent flow in stirred tanks.
Albeit has the ability to study the mixing process, LES requires
enormous amounts of grids and the wall-boundary layers need
to be sufficiently resolved and therefore cannot be used in most
practical settings [18]. DNS can capture all of the relevant scales
of turbulent motion only if the mesh is fine enough to resolve even
the smallest scales present in the flow. However, the turbulent
scales can range from the smallest Kolmogorov scales to the largest
scales the same dimensions as the object characteristic length.
Therefore DNS require grids fine enough to capture the small ed-
dies, but the computational domain must be extended to contain
the large eddies. Accordingly, thismodel is computationally expen-
sive and has largely been limited to simple geometries. For such
complex turbulent flow problem in stirred tanks, DNS is extremely
expensive and is currently intractable even on modern computers
[8]. To the best of the authors’ knowledge, no comprehensive
investigation of mixing characteristics in stirred tanks has been
carried out by this technique so far. It is therefore essential to de-
velop simulation techniques which can provide reliable mixing
time data and with not so much computational cost. As an alterna-
tive, the detached eddy simulation (DES) is adopted to investigate
the mixing process in stirred tanks in this work. It is essentially a
three-dimensional unsteady numerical algorithm using a single
turbulence model, which functions as a subgrid-scale model and
reduces the eddy viscosity in regions where the grid density is fine
enough for LES computations, and as a RANS model in regions near
solid boundaries, i.e. in the attached boundary layer, and where the
turbulent length scale is less than the maximum grid dimension
[19]. This model is also referred to as a hybrid RANS/LES model
in that it combines the advantages of RANS and LES methodologies
and can resolve the flow at less computational cost as well as with
high accuracy [20]. Since its inception the method has been applied
to a range of configurations including simple shapes such as
cylinders, spheres and aircraft forebodies, in addition to complex
geometries including fighter aircraft [21]. The fluid flow in a hu-
manmouth–throat was also studied by DESmodel and good agree-
ment with the LES data was obtained [22].
It has been proved that eccentric agitation can improve the mix-
ing in the laminar, transitional and turbulent flow regime. The
eccentric position of the impeller lead to mixing time reduction
with increasing the impeller eccentricity [23–27]. However, these
investigations were all performed by experimental approaches. In
the present work, an attempt is made to characterize the mixing
of an inert scalar in stirred tanks equipped with four pitched-blade
turbines using the DES model. To the best of the authors’ knowl-
edge, no comprehensive investigation of mixing characteristics
and assessment of mixing time has been performed by this model
so far. The authors’ previous work [28,29] showed that DES model
can predict the hydrodynamics of stirred tanks as accurate as LES
does, can provide considerably improved predictions of the mean
and turbulent quantities compared with those obtained by the
RANS approach. This suggests that a better prediction of mixing
time by DES model should be expected.
The paper is organized as follows: Section 2 presents the stirred
system geometry and the operating conditions. In Section 3, thegoverning equations, computational grid and numerical solution