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Mixing time4.2.1. Time evolution of the scalar concentrationAbove analysis indicates that a performance improvement inmixing time prediction should be expected and this will be provedin this section. The numerically determined evolutions of the tracerconcentration at the selected monitoring positions for the casee = 0.5 are shown in Fig. 5. In these plots, the concentrations weremade dimensionless by piding the concentration under a fullymixed condition. It can be seen that there are large fluctuationsof the tracer concentrations in the initial stages of mixing. The larg-est instantaneous value can be as high as 40 times the equilibriumvalue. Then there is a rapid decrease and it approaches the equilib-rium value asymptotically. For the concentric (e = 0) and othereccentric agitation configurations (e = 0.2, e = 0.3), similar timeevolution trend of the scalar tracer concentration can be obtained.4.2.2. The effect of monitoring positions and eccentricity on mixingtimeFromthe plots of time variations of the scalar concentration, thet95 mixing time for the concentric and eccentric agitations can beobtained and the results are listed in Table 1. We can see thatthe mixing time is a local variable, which depends on the positionof the monitoring point. For concentric agitation, the mixing timeis higher than that of the eccentric agitation. By contrast, the vari- ations in the mixing time for different eccentric agitation configu-rations are small, which shows that eccentric agitation canimprove the mixing uniformity and has better mixing performancethan concentric agitation. Besides, it can also be observed that, asthe eccentricity increases, the mixing time decreases. Hu et al.[24] also drew such conclusion. Numerically determined variationof mixing time with the eccentricities is given in Fig. 6. We can seethat, for concentric agitation, the average mixing time is 17.06 s.when the eccentricity is increased from e = 0.2 to e = 0.3, the aver-age t95 mixing time decreases from 13.93 s to 9.88 s and the reduc-tion is about 29.07%. With the increase of eccentricity from e = 0.3to e = 0.5, the average t95 mixing time is decreased from 9.88 s to9.28 s and the reduction is about 6.07%. This indicates that furtherincrease of eccentricity will not shorten the mixing time dramati-cally. For comparison, the experimental results of Hu et al. [24] arealso presented. It can be found that the numerical results are largerthan the experimental data and the maximumdeviation is no morethan 29%.As can be seen from above section, eccentric agitation canshorten the mixing time compared with the concentric agitation.The reasons for reduction in mixing time can be given below:(a) Eccentric configuration of the impeller breaks the geometri-cal symmetry of the stirred tank system and the periodicityof the fluid flow. The axial circulation flow capacity wasgreatly improved and the manifold structure was changed by such modification [8,23]. Accordingly, the scalar addedfrom the top of the stirred tank can be quickly transportedinto the other regions.(b) The distance between the impeller blade and the tank wall iscontinuously varying, which induces successive stretchingand folding of the fluid filaments, bringmore dynamic pertur-bations on the homogenization of the fluid in the tank, andgive rise to enhancement of the spatial energy distribution.As a result, the whole fluid volume is efficiently utilized formixing instead of the majority of energy dissipation occur-ring in the impeller discharge region alone [23,29].4.2.3. Comparison of mixing time with experimental resultsIn the reported literature of Hu et al. [24], experimentally pre-dicted mixing time of the concentric agitation (e = 0) and theeccentric agitation e = 0.5 were presented in the form of plot. Thenumerically predicted mixing time was compared with the exper-imental data and the results are given in Fig. 7. In general, thenumerical results are in reasonable agreement with the experi-mental results, with an average over-prediction of within 20%. Bestagreement (within 9%) was found for the case e = 0.5. The maxi-mum deviation is 30% from the measured values for the concentricagitation.Nevertheless, there is still discrepancy between the numericalpredictions and the experimental results. In the authors’ opinion,this can be most likely attributed to the following reasons:(a) Inaccurate representation of the top liquid surface of thestirred tank. The top surface of the computational domainwas set as flat surface, while the actual condition is thatthere is deformation and free surface vortex at the top liquidsurface due to the agitation.(b) Differences in the modelled and actual impeller blade widthand thickness. It was found that thinner blade thicknessresulted in higher flow number [40], which consequently isexpected to affect the mixing time.(c) Experimental error associated with the time recording of theconcentration field and difference in the scalar injectionmethod. A total amount of 2 ml scalar was added into thestirred tank by a syringe pump with the injection velocityVinj = 1 ml s 1(i.e., the injection time was 2 s).
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