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(SM) and multiple reference frame (MRF) method, were employed,
the prediction of mixing time based on RANS approach is not accu-
rate when compared with the result determined from experiments
or empirical correlations reported in the literature. For example,
Osman and Varley [9] studied the mixing time in an unbaffled stir-
red tank agitated with a Rushton turbine using the MRF method.
The predicted mixing time was found to be two times higher than
the experimental value. Jaworski et al. [10] studied the homogeni-
zation in a baffled stirred tank agitated with a dual Rushton impel-
ler. The MRF method was firstly used to obtain a converged
solution of the liquid flow field, the result of which was then used
as an input for the solution of the scalar transport equation using
the fully transient SM method in order to predict the time-
dependent mixing process. In agreement with the findings of
⇑ Corresponding author. Tel.: +86 531 88396708; fax: +86 531 88392118.
E-mail address: fly@sdu.edu.cn (F. Yang).Osman and Varley [9], their predictions were again found to be
generally 2–3 times higher than the experimental value. Bujalski
et al. [11] performed simulations on the same stirred system as
that employed by Jaworski et al. [10] . They used a finer grid in
the regions of high velocity gradients and solved the transient sca-
lar transport equation in a stationary reference frame. Although
improved results were obtained, discrepancies in the order of
100% still have been found between the predicted and experimen-
tally determined mixing time values. In a further investigation,
Bujalski et al. [12] studied the influence of modeling strategy and
the addition position of a tracer on the mixing time in a baffled
stirred tank agitated with a Rushton turbine using the SM method.
The former was found to have little effect of the numerical result
but, the effect of the position of the feed point was very important.
When the addition point was close to the stirred tank wall, a large
discrepancy can be observed. By comparison, for the flow with low
Reynolds number, the situation ismuch better. Shekhar and Jayanti
[13] successfully simulated the flow and mixing characteristics in
an unbaffled stirred tank agitated with a eight-blade paddle impel-
ler using the SMmethod and the low Reynolds k–emodel for rather
low Reynolds numbers (up to 480). Good agreements with the
experimental data and the correlations from the literature were
obtained.
In order to predict the turbulent quantities at small scales pre-
cisely, large eddy simulation (LES) or direct numerical simulation
(DNS) is needed. In the last few years, LES studies on the mixing
process have been successfully carried out. Yeoh et al. [14] per-
formed LES study to characterize the mixing of an inert scalar in
a baffled stirred tank agitated with a Rushton turbine. It was found
that LES can provide a very detailed picture of the spatial and tem-
poral evolution of the scalar concentration that cannot be obtained
with the standard RANS approach. The predicted mixing time com-
pared well, on average within 18%, with values determined from
correlations reported in the literature. Hartmann et al. [15] per-
formed a lattice-Boltzmann based LES study of the flow in a baffled
Rushton turbine stirred tank at Reynolds number Re = 24,000. The
mixing time was found to be significantly influenced by the impel-
ler size but, has little effect with the position of the tracer injection
point. The simulated mixing times overestimate the experimen-
tally determined values but the discrepancies are no more than
30%. Min and Gao [16] and Zadghaffari et al. [17] employed the
combination of SM and LES technique to study the mixing process
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