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The MRF method was firstly used to obtain a convergedsolution of the liquid flow field, the result of which was then usedas an input for the solution of the scalar transport equation usingthe fully transient SM method in order to predict the time-dependent mixing process. In agreement with the findings of Osman and Varley [9], their predictions were again found to begenerally 2–3 times higher than the experimental value. Bujalskiet al. [11] performed simulations on the same stirred system asthat employed by Jaworski et al. [10] . They used a finer grid inthe regions of high velocity gradients and solved the transient sca-lar transport equation in a stationary reference frame. Althoughimproved results were obtained, discrepancies in the order of100% 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 andthe addition position of a tracer on the mixing time in a baffledstirred tank agitated with a Rushton turbine using the SM method.The former was found to have little effect of the numerical resultbut, the effect of the position of the feed point was very important.When the addition point was close to the stirred tank wall, a largediscrepancy can be observed. By comparison, for the flow with lowReynolds number, the situation ismuch better. Shekhar and Jayanti[13] successfully simulated the flow and mixing characteristics inan unbaffled stirred tank agitated with a eight-blade paddle impel-ler using the SMmethod and the low Reynolds k–emodel for ratherlow Reynolds numbers (up to 480).
Good agreements with theexperimental data and the correlations from the literature wereobtained.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 mixingprocess have been successfully carried out. Yeoh et al. [14] per-formed LES study to characterize the mixing of an inert scalar ina baffled stirred tank agitated with a Rushton turbine. It was foundthat LES can provide a very detailed picture of the spatial and tem-poral evolution of the scalar concentration that cannot be obtainedwith the standard RANS approach. The predicted mixing time com-pared well, on average within 18%, with values determined fromcorrelations reported in the literature. Hartmann et al. [15] per-formed a lattice-Boltzmann based LES study of the flow in a baffledRushton turbine stirred tank at Reynolds number Re = 24,000. Themixing time was found to be significantly influenced by the impel-ler size but, has little effect with the position of the tracer injectionpoint. The simulated mixing times overestimate the experimen-tally determined values but the discrepancies are no more than30%. Min and Gao [16] and Zadghaffari et al. [17] employed thecombination of SM and LES technique to study the mixing processin a baffled stirred tank agitated with a 3-narrow blade hydrofoilCBY 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 requiresenormous amounts of grids and the wall-boundary layers needto be sufficiently resolved and therefore cannot be used in mostpractical settings [18]. DNS can capture all of the relevant scalesof turbulent motion only if the mesh is fine enough to resolve eventhe smallest scales present in the flow. However, the turbulentscales can range from the smallest Kolmogorov scales to the largestscales 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 containthe large eddies. Accordingly, thismodel is computationally expen-sive and has largely been limited to simple geometries. For suchcomplex turbulent flow problem in stirred tanks, DNS is extremelyexpensive and is currently intractable even on modern computers[8]. To the best of the authors’ knowledge, no comprehensiveinvestigation of mixing characteristics in stirred tanks has beencarried out by this technique so far. It is therefore essential to de-velop simulation techniques which can provide reliable mixingtime data and with not so much computational cost. As an alterna-tive, the detached eddy simulation (DES) is adopted to investigatethe mixing process in stirred tanks in this work. It is essentially athree-dimensional unsteady numerical algorithm using a singleturbulence model, which functions as a subgrid-scale model andreduces the eddy viscosity in regions where the grid density is fineenough for LES computations, and as a RANS model in regions nearsolid boundaries, i.e. in the attached boundary layer, and where theturbulent length scale is less than the maximum grid dimension[19].
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