were chose to compare the differences between SRT and DRT。 For both

>: 0:44 RepN1000

Rep is the modified relative Reynolds number which considers the effect of turbulence [32]:

ρl 。ug−ul 。d

operating conditions considered here, the typical double circulation flow patterns of the radial flow type Rushton impeller were successfully captured。 What in common is that, both the temporal SRT and DRT flow fields are asymmetrical about the shaft, but the asymmetry is not so obvious for the former。 By comparison, there are more irregularities in

the DRT  flow field。  The most  pronounced difference is  that, for  SRT,

where C is the model parameter。 According to the study of Khopkar and Ranade [28], it was set to 2/9。

3。2。 Turbulence modelling

The turbulent flow was modelled using the standard k–ε turbulence model。 This model finds wide application in simulating the gas–liquid flow when the gas phase concentration is diluted [6,19,27,28]。 Transport equations for this model are well-known to the readers。 For the reason of simplicity, a detailed description is omitted here。 In this model, the turbulent liquid viscosity in Eq。 (6) is given as follows:

the discharge flow of the upper impeller is horizontal, and it is  down-

ward inclined to the horizontal plane for the lower impeller, with the angle of inclination increasing with the increase of the impeller rotational speed。 As for DRT, the discharge flow of the upper impeller is not horizontal but inclined。 Making a qualitative comparison, we

where Cμ = 0。09 is the model parameter。

3。3。 Computational  grid and modelling approach

The computational model was built using the preprocessor Gambit

2。3。 A non-uniformly distributed hybrid mesh consisting of 2441981 cells was generated。 32 and 40 nodes were assigned along the impeller width  and  length,  respectively。  The  minimal  grid  length  equals  to

0。5 mm, which equals to 0。00625D。 The maximum skewness of the

mesh was less than 0。81。 A similar grid resolution (970997 cells for a stirred tank with an diameter T = 0。3 m and Re = 4。17 × 104) was employed by Zadghaffari et al。 [33] in their study of the turbulent flow and mixing in a stirred tank driven by a Rushton impeller, and satisfac- tory results were obtained。 This implies that the grid resolution used here is adequate to resolve the turbulent flow   accurately。

Rotation of the impeller was modelled with the multiple reference frame (MRF) method。 The initial velocities of the fluids, as well as gas holdup in the stirred vessel were assumed to be zero。 The vessel walls, shaft, baffles, sparger and impellers were treated as non-slip boundaries with standard wall functions。 Gas flow at the sparger was defined as velocity inlet boundary with the gas volume fraction equal to 1。 The gas inlet velocity can be computed by piding the gas flow rate with the total area of the sparger holes。 At the liquid surface, only gas was

N=600 r·min–1

allowed to escape and water remained in the tank, and the degassing boundary condition  was  applied。  Water  was  defined  as  the primary

Fig。 2。 Temporal liquid flow fields generated by (a) SRT and (b) DRT at different impeller rotational speeds。

F。 Yang et al。 / Chinese Journal of Chemical Engineering 23 (2015) 1746–1754 1749

can see that due to the alteration of the impeller discharge flow direction, fluid flow in the vessel top and in regions between the two adjacent impellers are enhanced, especially for the higher impeller rotational speed N = 600 r·min−1。 As a consequence, the axial pumping capacity is improved and the interaction between the upper and lower impellers is enhanced。 This is advantageous for gas dispersion in the bulk of the vessel as demonstrated in the following  section。