Modified scaba 6SRGT impellers for process intensification: Cavern size and energy saving when stirring viscoplastic fluids

Mixing of a shear-thinning fluid with yield stress using Scaba 6SRGT impellers in a cylindrical unbaffled vessel is studied. Cuts are introduced in each blade of the impeller in order to reduce power requirements. The effects of the cut-height (five geometrical configurations: h2/D = 0, 0.015, 0.04, 0.065 and 0.09, respectively), cut-length (four shapes: l/D = 0, 0.06, 0.12 and 0.18, respectively) , and of the number of cuts (nb = 1, 2, 3, 4, and 5) on the hydrodynamics and power consumption are explored. From the simulations, it can be inferred that the introduction of cuts is an interesting technique to obtain an energy-saving impeller. The suggested designs, compared to the classical Scaba 6SRGT impeller, display a reduction in power number by about 20%, 19.9% and 66.6% when the cut-height, cut-length and number of cuts are changed from h2/D = 0 to 0.09, l/D = 0 to 0.18 and nb = 1 to 5, respectively. However, the increased surface area of cuts in the blades is accompanied by a reduction in the size of radial jet of fluid, resulting thus in a weakened axial flow and a decrease in cavern size. As a result, the best trade-off between the reduced power consumption and enlarged cavern size correspond to the case nb = 3, l/D = 0.12. The reduction in power number for this case is estimated to be as about 15%.


Introduction
Mechanical agitation of fluids in cylindrical tanks is a fundamental operation in to achieve a wide variety of tasks, such as gas dispersion into liquid to form foams or for mass transfer, powder dispersion or solid blending, dispersion of immiscible liquids for emulsification, preparation of ingredients, etc. Various shapes of impellers have been developed for mixing complex non-Newtonian fluids encountered in different industries and the control of complex fluid flows is highly required to optimize the processes. Shear-thinning fluids with yield stress present the most common class of this kind of fluids, and they are characterized by a great increase in viscosity when the shear stresses are less than the yield stress. For this reason, many challenging problems are encountered during the mixing process such as higher mixing time, low heat transfer, fouling and buildup on the walls, formation of gel, formation of well-mixed regions near the stirrer (the so-called caverns) with stagnant/dead regions elsewhere (Rudolph et al., 2009;Bao et al., 2011). The product quality is highly affected by the formation of these glitches; so, a sophisticated designed impeller should be selected to overcome, i.e. eliminate or at least minimize, the above-mentioned issues.
Radial flow is the main source of mising intensification in stirred tank reactors. Ameur (2016a) and Zhao et al. (2011) reported that trailing vortices generated behind flat-bladed impellers are the main source of energy dissipation. In aerated agitation, these vortices (filled with gas) are also responsible for the formation of cavities, which yields a reduction in mass transfer and unstabilities in power consumption (Zheng et al., 2017). This issue has been overcome by the development of impellers exhibiting semi-circular tube blades (CD), and the evolution of the flow field between the CD-6 impeller and Rushton turbine (RT) has been deeply analyzed by Devi and Kumar (2013). Since then, engineers and researchers have been more and more interested in the development and the use of impellers with deeper concaved blades (Pakzad et al., 2008a(Pakzad et al., , 2008bGhotli et al., 2013Ghotli et al., , 2016Cortada-Garcia et al., 2017;Malik and Pakzad, 2018). Impellers with different shapes of blades have been compared by Zhao et al. (2011): namely, the flat (Rushton turbine), half-elliptical, concave, and parabolic shapes. These authors found an increase in the residence time of vortex at the impeller tip with the rise of blade curvature, which yields also stronger and smaller vortices in this region. The space between the lower and upper vortices presented the location of high turbulent kinetic energy. Recently, Zheng et al. (2018) also designed a new fan-shaped impeller assembled with annular-sector-shaped concave blades. With this new design, they found a reduction in power number by 26% compared to that of the Bakker turbine. For shear-thinning fluids with yield 3 stress, research have been focused on the Scaba impellers under different operating and geometrical conditions, including the coaxial, multistaged, and the multiple eccentric configurations (Pakzad et al. 2013a(Pakzad et al. , 2013b(Pakzad et al. , 2013cKazemzadeh et al., 2016aKazemzadeh et al., , 2016bKazemzadeh et al., , 2017Ameur, 2016b, Ameur andGhenaim, 2018).
Thus, the main purpose of this paper is to propose an original way to save mechanical power when curved-bladed impellers (Scaba 6SRGT) are used for mixing shear-thinning fluids with yield stres: this consists in introducing cuts in the impeller blades, the geometry of which must be optimized. As a result, the effects of the cut size (including the cut-length, cut-height and the numbers of cut) on the flow patterns, caverns size and power consumption have been investigated in detail in the next sections.

Experimental setup
The mechanically stirred tank under study is a flat-bottomed cylindrical unbaffled vessel equipped with a Scaba 6SRGT impeller (Fig. 1). The impeller has six curved blades mounted on on a disc with a thickness t/D = 0.02, where D is the vessel diameter (D= 0.4 m). The impeller shaft has a diameter ds/D = 0.05. The shaft is inserted at the central position of impeller and the off-bottom clearance is c/D = 0.33. The liquid level is kept equal to the vessel height H, where H/D = 1. All other details are summarized in Table 1.
Cuts have been introduced in the impeller blade in order to reduce power supply. For this purpose, fourteen geometrical configuration were investigated to assess the effects of the geometry of the cuts: namely, five geometries with changes in the height of cut (h2/D = 0, 0.015, 0.04, 0.065 and 0.09, respectively), four geometries with changes in the length of cut (l/D = 0, 0.06, 0.12 and 0.18, respectively) and five geometries with changes in the number of cuts (nb = 1, 2, 3, 4 and 5).

Mathematical equations
A xanthan gum solution was utilized as the working fluid in this paper. Based on the experimental measurements reported by Saeed et al. (2007) and Pakzad et al. (2008b), the rheological propeties of this fluid are: concentration 10.5%, consistency index K = 3 [Pa s n ], power law index n = 0.11, yield stress τy = 1.79 [Pa] and density ρ = 991.8 [kg/m 3 ]. The behavior of this fluid is shear-thinning with yield stress and it can be modeled using the Herschel-Bulkley model (Macosko, 1994): In the flow regime, the average shear rate can be related to the stirrer rotational speed by the Metzner and Otto's approach (Metzner and Otto, 1957): . avg s KN  = (2) 5 Thus, the apparent viscosity of the fluid, η, can be evaluated from the average shear rate, as follows:

( )
. n ys ss avg For this class of fluids, the Reynolds number is defined as: The pumping flow rate (Qp), also called the pumping capacity or the delivery rate of the impeller, is the amount of liquid that leaves the impeller blade per unit of time. It is calculated as: where Vr is the radial velocity at the blade tip and Z is the position of a point at the height of the blade.
The power consumption (P) can be deduced by numerical integration on the tank volume of The element dv can be written as: But it can also be deduced by numerical estimation of the torque estimated on the surface of the 6 impeller. The power number and flow number are calculated respectively as: In the dimensionless form, we can define the dimensionless radial and axial coordinates, respectively, as: The dimensionless velocity is also expressed as: and the axial, radial and tangential velocity components can be adimensionalized using the same equation.

Numerical methods
The study was conducted using CFD (Computational Fluid dynamics) with the help of the software commercial software package CFX, which is based on the finite volume method and solves the Navier-Stokes equations. Geometry and mesh of the computation domain were created using computer-aided design and meshing software ICEM CFD. The continuity and momentum equations written in a cylindrical and rotating frame of references were solved. Due to the absence of baffles, the Rotating Reference Frame (RRF) approach was used, i.e. the mixer is kept stationary and the vessel is given an angular velocity equal and opposite to the velocity of the rotating frame.
The efficiency of this technique was proved by many researchers (Beloudane et al., 2018;Foukrach et al., 2019). Coriolis and centrifugal accelerations are added to the governing equations because of the choice of a rotating frame. Thus, the flow is supposed to be steady, laminar, and isothermal. The pressure-velocity coupling is performed using the SIMPLEC (Semi-Implicit Method for Pressure-Linked Equations-Consistent) algorithm.
Tetrahedral grid elements were used to discretize the computational domain and increased mesh density was created near the impeller and vessel walls in order to determine the details of the fluid boundary layer. After mesh tests, the selected mesh which did not give changes in power consumption higher than 2.5%, had about 0.8 million cells. With a machine (INTEL® i7 processor 7 with 8 Gb RAM) and for a residual target 10 -7 , the convergence was achieved after about 700−800 iterations, which corresponds to about 4−5 hrs. CPU time.

Validation of simulations with experimental data
The validation of some of the predicted results with the available experimental data is discussed in this section. To validate the simulations, we referred to the experimental work performed by Pakzad et al. (2008b) and we simulated the same geometry as in this paper. The

. Effect of the height of cut in blades (h2)
In the first part of our investigation, we explored the effect of the height (h2) of cut in blade son the flow patterns and power consumption. For this purpose, the five geometrical 8 configurations described in section 2 with h2/D between 0 (i.e. a plain blade without cut) and 0.09 have been investigated.
The tangential velocity (Vθ * ) is presented in Fig. 3  Consequently, two recirculation loops are formed, respectively above and below the impeller.
it must be pointed out that the cuts do not alter this flow pattern, but the interesting phenomenon illustrated by the slices of this figure is the evolution of the size of eddies yielded by the turbine: The smaller h2/D, the wider eddies. This is mainly due to the reduction of radial flow with the raise of h2/D, as claimed above. Consequently, the limited axial circulation of the fluid is another consequence of the increased height of cut in blade, since the area swept by the turbine is more and more reduced, resulting thus in a reduced size of the cavern (well-stirred region), as observed in Fig. 6. But as observed in Fig. 3 and Fig. 4, this effect is weak when h/D< 0.015.
What about the other factors determining of the performance of a stirred system? Here, we can focus first on the change in the power requirements with cut height. Power number (NP) data is summarized in Fig. 7 for the five geometrical configurations; the values are NP = 9.5, 9 9.1, 8.5, 7.9 and 7.6 for h2/D = 0, 0.015, 0.04, 0.065 and 0.09, respectively. The analysis of these results reveal a reduction in power consumption by 4.2%, 10.5%, 16.8 and 20.0% for h2/D = 0.015, 0.04, 0.065 and 0.09, respectively, compared to the classical Scaba 6SRGT impeller.
As a conclusion, it appears that if the objective is to maintain similar mixing properties, cut height must remain small (h2/D < 0.04) and the power saving in comparison to is limited to the Scaba 6SRGT impeller is limited to about 10%.

Effect of the length of cut (l)
In the second part of this section, the influence of the cut length (l) is studied. The different cases investigated are: l/D = 0 (i.e. a blade without cut), 0.06, 0.12 and 0.18, respectively. The evolution of the velocity magnitude along the vessel height (Z * ) is plotted at the radial position R * = 0.6 for the four cases (Fig. 8). Similarly, the tangential component of velocity is monitored 12 along the vessel radius at the vertical position Z * = 0.41 and plotted in Fig. 9. To capture further details on the effect of cut length on the hydrodynamics, the 2D streamlines are plotted for the four cases in Fig. 10. It is clearly illustrated that the cuts do not strongly alter the flow pattern, characterized by two recirculation loops, but that the axial circulation of the fluid and the radial jet impinging the wall are both weakened when the length of the cut is increased in comparison to the conventional impeller. As a consequence, the size of the recirculation loops which are formed above and below impeller is decreased with the raise of l/D. Near the free surface of liquid, a vortex is formed due to the absence of baffles.
This vortex is intensified and enlarged with the increase of l/D, which is mainly due to the reduced of axial circulation of the fluid. Another consequence is that the size of the well-stirred region just around the impeller decrease progressively with the raise of l/D, as depicted by Fig.   11, even though this decrease is slower when l/D>0.12. Conversely, the increase of l/D seems to promote the intensification of fluid circulation in the area between consecutive baffles, which could be helpful (Fig.12).
However, it emerges from these results that an excessive increase in cut length is not beneficial in terms of cavern size and axial circulation of fluid in the whole vessel volume, but they could contribute to decrease power requirements. Thus, the results of power consumption displayed in Fig. 13 reveal an interesting decrease in NP when cut length is increased. The values of NP for l/D = 0, 0.06, 0.12 and 0.18 are 2.68, 2.37, 2.24 and 2.20, respectively, which corresponds to a decrease by about 11.56%, 16.4%, and 17.9%, compared to the blade without cut. Considering that NP tends to a final value about 2.15 when l/D, these trends at Rey = 100 can be fitted using the following equation:

Effect of the number of cuts (nb)
In this subsection, the effect of another geometrical parameter on the flow pattern and the power consumption due to the impeller is explored: it concerns the number of cuts (nb). For the same cut length cut as in section 6.2 (l/D = 0.12) , five geometrical configurations were considered, which are: nb = 1, 2, 3, 4 and 5. The tangential velocity field, the radial velocity field, and the streamlines calculated in the simulations are presented along the vessel radius, 16 the vessel height and in the vertical plane passing through the impeller in Fig. 14, 15 and 16, respectively. It seems that the increased number of cuts is beneficial in terms of intensification of the movement of fluid particles, the radial jet of fluid is becoming powerful and the axial circulation is highly enhanced. Consequently, the size of the well-stirred region is increased, as observed in Fig. 17. As in section 6.1, when the cut height is small, the fluid tends to follow the same velocity profile as in the conventional impeller design. So, a possible method to increase the total cut height without changing too significantly the flow pattern may consist in using several cuts. This strategy seems very efficient when nb is increased from 1 to 2 in Fig. 14, 15 and 17, but increasing nb appears to be useless when nb > 4.
However, the price to pay to maintain the flow field close to the conventional impeller is necessarily higher power consumption or, in practice, lower power saving. Thus, power number data are depicted in Fig. 18, and the values are as follows: NP = 1.62, 2.2, 2.34, 2.5 and 2.59 for nb = 1, 2, 3, 4 and 5, respectively. The analysis of these results reveals an increase in NP by about 60% from the first case nb = 1 to the last case nb = 5, but in comparison to the classical blade without cut (NP = 4.86), the case nb = 1 reveals a decrease in NP until 66.6%. As a conclusion, even when nb = 3, this makes it possible to approach the flow pattern of the conventional impeller with a decrease in NP approaching 50%.

Conclusion
Mixing of a complex non-Newtonian fluid (a shear thinning fluid with yield stress) in a cylindrical unbaffled vessel has been numerically studied. The impeller used for agitation was a six curved-blade device, the so-called Scaba 6SRGT. Cuts have been introduced in each blade in order to save power requirements. The effects of the geometry of these cuts (including the height, length and number of cuts) on the flow patterns and power consumption have been 19 determined. Fourteen geometrical configuration were studied to better understand the influence of these parameters both on the flow pattern and on power requirements: namely, five cases for the height of cut (h2/D = 0, 0.015, 0.04, 0.065 and 0.09, respectively), four cases for the length of cut (l/D = 0, 0.06, 0.12 and 0.18, respectively), and five cases for the number of cuts (nb = 1, 2, 3, 4 and 5).
The results derived from the simulations based on CFD revealed that the introduction of cuts is an interesting approach to save mechanical energy in the mixing process. However, the optimization of the cut size is not an easy task: if the increased size of cuts in blade is obviously accompanied by a reduction in power requirements, the radial impinging jet and the axial circulation of the fluid are also impaired, resulting thus in the reduction of cavern size, i.e. of the well-mixed regions. So, the overall achievements are as follows: • The increase in cut-height from h2/D = 0 to 0.09 yielded a reduction in power number from 4.21% to 20% compared to the classical Scaba 6SRGT impeller without cut, but it impaired strongly the flow pattern and, therefore, the mixing effectiveness.
• The increase in cut-length from for l/D = 0, 0.06, 0.12 lead to a decrease by about of power number 11.56%, 16.4%, and 17.9%, compared to the blade without cut; thus, the effect of l/D is less significant than that of height, and a further increase in l/D lead to insignificant changes.
• The increase in the number of cuts from nb = 1 to 5 yielded a decrease by about 60% and the comparison between the case nb = 1 and the classical blade without cut revealed a reduction in NP until 66.6%, but to approach the mixing features of the conventional impeller, nb > 2 must be preferred, whereas nb > 4 leads to insignificant changes.
The analysis of these findings allows us to select the case with nb = 3 and l/D = 0.12 as a trade-off between reduced power consumption and enlarged cavern size. In comparison to the conventional Scaba 6SRGT impeller, a reduction in power number by about 50% is achieved, whereas the features of the field are only slightly affected.