Effect of Agitator’s Types on the Hydrodynamic Flow in an Agitated Tank

The aim of this paper is to study the effect of agitator’s types on the turbulent flows in stirred tanks without and with baffles. The hydrodynamics behavior induced by four different agitator’s types: a Rushton turbine (RT), a circular blade turbine (CBT), a diverging triangular blade turbine (DTBT) and converging triangular blade turbine (CTBT) are numerically predicted by solving the Navier-Stokes equations and RNG κ–ε turbulent model. The simulations are carried out using the Multi Reference Frame (MRF) approach. The numerical results showed good agreement with experiment. We find that the agitator CTBT gives an important profit on the power consumption per report/ratio the others and DTBT give a good reduction of the vortex size of the impeller angles.


Introduction
Mixing is one of the most widely used unit operations in the chemical, bio-chemical, pharmaceutical, petrochemical, and food processing. The objective of mixing is homogenization, manifesting itself in a reduction of concentration or temperature gradients or both simultaneously, within the agitated system [1]. A stirred tank unit typically consists of a rotating impeller in a vessel. Fluid motion is promoted by the transfer of energy from the impeller into the process fluid.
The agitation of liquid in these tanks is an operation more or less simple to realize, but always complex to characterize, because of the nature of the flows and the geometry of the system. Today, the majority of the operations of agitation and mixture are carried out by means of a pendulum agitator turning around a shaft, placed in a tank, generally of cylindrical form. In literature, the study of the systems of agitation started in several works relating to the characterization of the turbulent flows. As an indication, one can quote the work of Refs. [2][3][4][5][6][7].
The agitation system consists of the agitator and the baffles, the baffles are used to break the liquid flow to increase turbulence and mixing efficiency. There are a number of comprehensive studies on baffled tanks that investigate their hydraulic efficiency [8][9][10].
The present work aims to determine the influence of geometrical parameter of a stirred vessel with down pumping direction from a pitched blade turbine (PBT 45°) on the hydrodynamic flow structure. The effect of the addition of a cylindrical bump in the center of dished bottom tank and the reduction of the bottom height with the same distance by realizing four geometries are also investigated. In planes r-z the effect from the reduction on the bottom height for all configurations tank with bump allows good growth parameters mixture for turbulent viscosity, turbulent kinetic energy and mean velocity [11].
They study an effect of the tubular baffles configuration in an agitated vessel with a high-speed impeller on the power consumption. Aqueous solutions of CMC were agitated within transitional range of the non-Newtonian liquid flow in the agitated vessel of inner diameter equal to 0.6 m. Eight different types of the impellers were tested: Rushton or Smith turbines, turbine with straight blades, pitched blade turbines and propeller. The results show that geometry of the tubular (2020) 33:37 baffles mostly affects the power number for the system with radial flow Rushton turbine [12]. Agitating liquids in unbaffled stirred tank leads to the formation of a vortex in the region of the impeller shaft when operating in the turbulent flow regime. A numerical model is presented here that captures such a vortex. The volume of fluid model, a multiphase flow model was employed in conjunction with a multiple reference frame model and the shear stress turbulence model [13].
Power characteristics for an agitated vessel equipped with planar short baffles of length L and pitched blade turbine of pitch β are presented in the paper. The studies were carried out in the vessel of inner diameter D = 0.6 m, where the baffles were located in the distance p from the vessel bottom (p + L = H). The effects of the pitch β and geometrical parameter p/H on the power number Ne were determined mathematically. The results showed that, for the assumed value of the angle β, the function Ne = f (L/H) decreases with the decrease in the baffle length L (i.e., with the increase in the parameter p). The greatest differences between power numbers Ne were observed for the turbine with the flat blades (β = 90°) [14].
They make a comparative study enters of the baffled tanks and other not baffled, these tanks equipped with a mobile with agitation of the Maxblend type. They found that the consumption of energy is higher in the tanks baffled by reports/ratios with the not baffled tanks [15]. He studies the effect of the design of the tanks on the flow models, the size of the tank and the power consumption. The three shapes of different tanks were carried out: a flat-bottomed cylindrical tank, a dished bottom cylindrical tank and a closed spherical tank. The comparison between the results obtained for the three configurations of tank showed that the spherical forms provide uniform flows in all the volume of the tank and require a less of power consumption per report/ratio the others (flat bottom and dished bottom) [16].
They studied by digitally simulates the effect of the curve of the baffles on the power number, they tested several geometrical configurations with the striping curve of baffles vary from 0 up to 7/30, they showed that the baffles curved also influence the stability of the free face [17].
They studied the effect of the baffles on the consumption of energy in a tank agitated by a Rushton turbine. Three types of the tanks were used: without baffles, with baffle and a tank with slits placed at the perimeter external of its vertical wall. The effect the length of the slit was studied. The comparison between numerical results envisaged and the experimental data available shows a satisfactory agreement. They found new indicates tank which minimizes the consumption of energy [18].
They tested by a numerical study the effect of the angle of inclination of the baffles, several angles tested in this work 25°, 32°, 45°, 70° and 90°. They found that the angle of inclination of the baffles 25° ensures a good mixture at a time reduced and with an energy consumption reduced to. In addition, the free face is more stable in the tanks equipped with baffles tilted 25° [19].
They studied a digital simulation of the flow of the fluids pseudo-plastics in a tank mechanically agitated by a Rushton turbine. The presence of the baffles in the tank has an important influence on the vortex size. The width of these baffles must be optimized. The determination of the size of these vortices is highlighted and the influence of the theological and hydrodynamic parameters of the fluids is studied. They concluded when the baffle width is sufficient, the vortex is removed, but the consumption is then a maximum.
The power of agitation increases with the increase in the structural index, because of the viscous forces, and it varies slightly starting from the transitory mode [20]. The technique of particle image velocimetry is used to analyze the vortices of wake and to elucidate their relationship to the properties of turbulence in a tank agitated by four various agitators, Rushton turbine; turbine with a disc with blades: concave, semi elliptic, parabolic [21]. The results showed that more the curve is broad plus the vortex resides longer at the blade tip, a longer distance between the higher and lower vortex, one longer life span and leads to the formation of smaller and more robust vortices.
The turbulent kinetic energy decreases more the curve is large, because of the progressive reduction in the power provided for the same Reynolds number; the area of larger, dissipated power ε and turbulent kinetic energy κ is the zone between the higher and lower vortex; as well as the difference in distribution of κ and ε of the four turbines is associated with different axes from the vortex of wake due to the shape of the blades.
In the present work, single-phase flow patterns in a stirred vessel have been investigated using (CFX 16.0) in a turbulent flow regime using four different agitator's types, a Rushton turbine (RT), a circular blade turbine (CBT), a diverging triangular blade turbine (DTBT) and converging triangular blade turbine (CTBT). Comparisons have been made of the flow fields produced when the impellers are operated in the down-and up-pumping modes. These velocity fields have been assessed by examining the power consumption and vortex sizes.
Hence, the objective of this work is to: • Analyze and determine the effect of the agitator's types on the hydrodynamic flow structure. • Reduce the power consumption and vortex size. • Our attention is focused on the effect: baffle height rotation, impeller angle, circular horizontal cut baffle and impeller clearance ratio.

Description of the Stirred System
The  Table 1.

Theoretical Backgrounds
The working fluid is pure water at room temperature 20 °C with density ρ = 997 kg/m 3 and viscosity μ = 0.89 × 10 −3 Pa·s. They are the same as the experimental study of Ref. [22]. The manner most used to characterize an agitated system is the determination of the dimensionless numbers. These characteristic parameters can be expressed starting from the fundamental units (mass, length, time). The Reynolds number (Re) provides information on the relation between the inertias and the forces viscous acting on a fluid. This value indicates if the fluid has a laminar behavior (Re < 20) or turbulent (Re > 10 4 ).
The Reynolds number of the flow in a stirred vessel is defined as:  where ρ is the density, N is the number of impeller revolutions (ω = 2πN, ω is the angular velocity), μ is the dynamic viscosity of the working fluid. The radial (R) and axis (Z) coordinates are normalized as: The tangential, radial and axial velocities are normalized with the blade tip velocity: In a dimensionless form, the power number is defined by: The power consumption (P) depends on all the parameters characterizing the external geometry of the vessel, the stirrer geometry, flow regime and the rotating speed of the impeller. The power is calculated according to a determination of the couple necessary to make turn the agitator, by the use of an assembly of dynamometer making it possible to measure the cable which is exerted on the shaft actuating the agitator.
The losses with the frictions on the parts moving are evaluated with the no-load tests in which agitation turns in the air.
The consumption is obtained by the equation: where C the couple in load and C 0 the couple in vacuum. (1)

Numerical Details
In this study, the commercial software CFX 16.0 was used to simulate 3D flow fields in stirred vessels equipped with a four agitator's type (RT, CBT, DTBT and CTBT). The geometry was created and meshed the computational domain by tetrahedral cells (Figure 2). The computational grids were defined by unstructured, non-uniformly. Numerical test were carried out to confirm the effect of mesh size on the calculated results. Table 2 shows a total grid of 501312 was enough to get mesh independence resolution.
In unbaffled tanks, the stirrer rotation was modeled by using the Rotating Reference Frame (RRF) method. Here, the impeller is kept stationary and the flow is steady relative to the rotating frame, while the outer wall of the vessel is given an angular velocity equal and opposite to the velocity of the rotating frame. This approach can be employed due to the absence of baffles [23].
The Multiple Reference Frame (MRF) approach was used in baffled tanks; this technique consists of dividing the computational domain into two parts: an inner rotating cylindrical volume enclosing the turbine and an outer stationary volume containing the rest of the tank. Other details of this technique are found in Ref. [18]. Several studies have focused on the MRF approach like Refs. [24][25][26][27].
The multiple reference frames (MRF) method is the most suitable method to simulate impeller rotation in mixing systems. Precise determination of stationary and moving zones in MRF method leads to accurate results in mixing performance [28].
In this study, the Reynolds number is varying from 10 4 to 10 5 . The RANS, RNG κ-ε model used for modeling the turbulent flow in the agitated tanks and gives a good result; we can quote some work on this model by Refs. [29][30][31][32]. The effect of the modeling approach, discretization scheme and turbulence model on mean velocities, turbulent kinetic energy and global quantities, such as the power and circulation numbers, has been investigated.
The type of the turbulence model was limited to the κ-ε and RNG models due to convergence difficulties encountered with a Reynolds Stress Model (RSM) and there was found to be little effect of these models on the mean flow and turbulent kinetic energy [7]. They studied  the effect of three models of turbulence (κ-ε, RNG and RSM) in a stirred tank by using an MRF approach on the tangential velocity field. They found that the RNG model reduced the unphysical reverse swirl region in the upper tank predicted by simulations [33]. The mathematical modeling and numerical simulation of the turbulent, two-phase flow of liquid and gas in a gas induced agitated stirred-tank reactor using computational fluid dynamics (CFD) techniques. A threedimensional (3D), transient, Euler-Euler two-phase flow model is developed and used to investigate the turbulent flow and mixing of liquid and bubbles in the stirred-tank reactor, applying the sliding mesh approach. Turbulence is simulated by means of several available models, the Renormalization Group (RNG) κ-ε model being the one finally recommended as the most appropriate of the ones studied, for the present application [34]. The re-normalization group (RNG) κ-ε model, large eddy simulation (LES) model and detached eddy simulation (DES) model were evaluated for simulating the flow field in the stirred tank.
All turbulence models can reproduce the tangential velocity in an unbaffled stirred tank with a rotational speed of 150 r/min, 250 r/min and 400 r/min, respectively. LES model and RNG κ-ε model predict the better tangential velocity and axial velocity, respectively [35]. Simulations was converted when normalized residuals for pressure and velocities drop below 10 −5 . Most calculations required 1700-2000 iterations and about 8-10 h.

Results and Discussion
In practice, the flow in the stirred tanks is three-dimensional. However, the absence of baffles does not ensure a good quality of mixing, this is due to the fact that the flow is mainly tangential, on the other hand the mixing becomes more efficient if the steering system comprises baffles, and that this translated by the transformation of the predominantly tangential flow into a three-dimensional flow. The different configurations of the agitator types (RT, CBT, DTBT, and CTBT) are shown in Figure 3 for tanks without baffles.
In order to verify the reliability of the calculation code and the simulation method used, reference was made to the work of Ref. [22]. Note that the same geometric conditions as those undertaken as well as the same fluid, were simulated. The numerical predicted results for the power consumed in a cylindrical vessel without baffles on the left and with baffles on the right ( Figure 4) and were compared with those of Karcz and Major [22]: a satisfactory agreement was noticed. Figure 5 illustrates the power number N P in a cylindrical vessel without baffles provided with different agitator's types (RT, CBT, DTBT, CTBT) according to the Reynolds number Re which varies between 10 4 and 2 × 10 5 . From the graph, it can be noted that the tanks which have agitators: DTBT and CTBT are identical with a mean power number about 2.5 and the others (RT and CBT) N P about 1.
When the stagnant areas exist in a stirred tank, mass transfer and heat is lower with higher temperature gradients, which makes it is necessary to eliminate these undesirable regions in the tank [36]. The effect of certain parameters on the flow fields is presented. Figure 6 illustrates the different flow structures obtained for the four agitator's types (RT, CBT, DTBT, CTBT) with Reynolds number Re = 4 × 10 4 . It can be seen that the intensity of the speed is higher at the end of the blades (RT, CBT, and DTBT) and less intense for the CTBT agitator as well as a large swept area up and down the blades for RT and DTBT and low area scanned for the CTBT. These types of turbine split the flow into two streams: one going towards the bottom of the tank and the other towards the free liquid surface, resulting thus is the formation of two vortices above and below the turbine. The power consumption is a global parameter to describe the performance of a mechanically agitated system. Table 3 shows the variation of the power number N P with Reynolds number Re = 4 × 10 4 in a tank with baffles and the other without baffles with four agitator's types: RT, CBT, DTBT, CTBT and we compared our numerical results with the experimental ones of Ref. [18]; one obtains a good value with the experimental one for the agitator RT and a decrease for the others in the baffled tanks and an increase of the NP for the unbaffled tanks (CTB, DTBT, CTBT), it is noted that the CTBT stirrer reduces the power consumption about 43.83% in the baffled tank.

Effect of Baffle Height Ration (L/H)
Experimentally, they studied the effect of baffle height for different agitator's types (Rushton turbine, propeller, radial blade turbine, flat and inclined) on the turbulent energy consumption [22]. They found than the Rushton turbine type characterized by higher energy consumption by comparing to the different mobiles studied.
In this section, the effect of the baffle height is studied.

Effect of Impeller Angle ( θ)
In this part we interested to study the effects of the impeller angle of four agitator's types (RT, CTB, DTBT and CTBT) on the hydrodynamic flow in tanks with vertical baffles, five angles are tested ( θ = 10°, 25°, 45°, 60° and 90°) with Reynolds number Re = 4 × 10 4 . Figure 16 shows vectors speed for baffled tanks with four agitator's types and various angles θ , by comparison, we can notice that the intensity of the vectors raised around the turbine for two agitators (CBT and DTBT) east decreases when moves away because of the baffles which play a role of obstacle which slows down the fluid and formation of the dead zones of recirculation   (2020) 33:37 (stagnant) behind the baffles. The angles θ = 25° and 90° for CBT and DTBT give a better distribution of vectors. The five impeller angles ( θ = 10°, 25°, 45°, 60° and 90°) for baffled tanks with four agitator's types with Reynolds number Re = 4 × 10 4 are studied and drawing the graphs of axial velocities along the vessel radius, at R * = 0.333 as shows in Figure 17. By comparison, between the four graphs, one notes that axial speeds almost identical for the various angles θ of the four agitator's types, one observes a maximum value axial speed approximately 0.035 in the high part of the turbine and almost 0.033 in the lower part of the turbine for agitator DTBT and minimal value for the agitator CTBT about 0.02 and 0.018 tops and low of the turbine for impeller angles ( θ = 25° and 90°) and null in the free face of the liquid. Figure 18 illustrates the vortex size for different agitator's types with various impeller angles with Reynolds number Re = 4 × 10 4 , we can note that the values of vortex size varied with the impeller angles θ . A maximum value of the vortex size is about 0.66 and minimal approximately 0.4 of CTB. The agitator DTBT give a good reduction of the vortex size of the impeller angles by report/ratio the other agitators.
The power number according to the impeller angles of the tanks equipped with four agitator's types is found in Figure 19. We can note that all the graphs constant with all the angles and one observes an important power number value N P approximately of 5.2 of the two agitators (RT and DTBT) who are identical and a minimal value N P = 2.7 for agitator CTBT, therefore, this agitator reduces the power consumption almost half.

Effect of Circular Horizontal Cut Baffle (CHCB)
They find that the cylindrical vessel with cut horizontal circular baffle (CHCB) at an angle of 20° decreases the size of the vortex and reduces power consumption by comparing a cylindrical vessel with four designs (CHCB) is a better design to avoid damage to the agitator [37].
Four configurations have been realized to study the influence of the cut circular horizontal baffle (CHCB) with an angle of 20° in cylindrical tanks with RT, CTB, DTBT and CTBT as shown in Figure 20.  The vortex size and power number are shown in Table 4 in a cylindrical vessel equipped with different agitator's types with CHCB s with an angle of 20°. Our numerical results were compared with the work of Ref. [37], we (2020) 33:37 found similar results concerning the vortex size of the different agitator's types and power number slightly varied, and we also noticed a significant decrease in power number of the CTBT agitator.

Effect of the Impeller Clearance Ratio (c/D)
In a standard tank, the height of the liquid is equal to the tank diameter. The impeller is positioned at a distance c generally measured from lower impeller edge to the vessel bottom; to know the influence of impeller clearance on the hydrodynamic structure, four cases of c/D ratios are tested (c/D = 0.17, 0.33, 0.5 and 0.67) for cylindrical vessels equipped with four agitator's types (RT, CBT, DTBT, CTBT). The evolution of the vector speed in the horizontal plane of the tank with CHCB with an angle 20° and for the four agitators with four impeller clearance ratio c/D with Reynolds number Re = 4 × 10 4 are represented in Figure 23. We can observe that the intensity of the vector speed is higher around the turbines and important in the medium and on the wall of the tanks for the four agitators with ratio c/D = 0. 33   We compare and validate our numerical results with the experimental one of Ref. [38], in Figure 26 the variation of the power number N P versus impeller clearance  ratio c/D was introduced. It can be seen that the power number increases slightly with an increase of the ratio. We deduce also, the agitator CTBT gives an important profit on the power consumption per report/ratio the others, his power number about N P = 2.

Conclusions
The geometrical shape of the baffle and the agitator is a factor very influencing on the performances of a mechanically agitated system. The baffles are essential devices in the construction of the agitated tanks.
The role of the baffles is to transform the tangential flow generated by the mobile of agitation into flow three directional, mainly axial, radial and tangential, and to also avoid the formation of the vortices on the level due to the centrifugal force. In our work, we interested to study four agitator's types (RT, CBT, DTBT, and CTBT) in tanks without and with baffles (VB and CHCB) in a mode of turbulent flow.
Several parameters are tested, such as the effect of: vertical baffles baffle height, impeller angle, and circular horizontal cut baffle and impeller clearance.
In the unbaffled tank, we find that agitator CBT gives the power number similar to agitator RT and the CTBT