MOHAMMED FOUKRACH EFFECT OF IMPELLER BLADE …

Chemical Industry & Chemical Engineering Quarterly

Available on line at Association of the Chemical Engineers of Serbia AChE www.ache.org.rs/CICEQ

Chem. Ind. Chem. Eng. Q. 26 (3) 259−266 (2020) CI&CEQ

259

MOHAMMED FOUKRACH1

HOUARI AMEUR2 1Faculty of Mechanical

Engineering, USTO-MB, El M’naouar, Oran, Algeria

2Department of Technology, University Centre of Naama –

Ahmed Salhi (Ctr Univ Naama), Algeria

SCIENTIFIC PAPER

UDC 544:532.5:621.224

EFFECT OF IMPELLER BLADE CURVATURE ON THE HYDRODYNAMICS AND POWER CONSUMPTION IN A STIRRED TANK

Article Highlights • Performance of curved bladed turbines (CBTs) in cylindrical tanks is investigated • The efficiency of CBT is compared with that of the standard Rushton turbine • The effects of the blade height of the new designed impeller are highlighted • A considerable reduction in power consumption was obtained with increased blade

curvature • Enhanced axial circulation of fluid was obtained with increased height of CBTs Abstract

The performance of curved bladed turbines (CBTs) for the agitation of Newton-ian fluids in cylindrical tanks is investigated. The efficiency of CBT is compared with that of the standard Rushton turbine. Also, effects of the blade height of the new designed impeller are highlighted. The computational fluid dynamics (CFD) study is performed to observe the axial, radial and tangential compo-nents of velocities, flow patterns and power consumption. The obtained results revealed that the increase of blade curvature reduces the power consumption. Also, a slight decrease of power number is observed in the turbulent flow reg-ime within unbaffled tanks. In a comparison between the cases studied, the best axial circulation of fluid is given by the impeller with flat blades. The increase of the height of curved blades has generated a stronger tangential flow and enhanced the axial movement of fluid particles, but with further pen-alty in power input.

Keywords: mechanical agitation, curved bladed impeller, cylindrical tank, hydrodynamics, power consumption.

Mixing is a very crucial unit operation in the chemical, pharmaceutical, biochemical and food ind-ustries. Knowledge of the flow inside the agitated tank is also the background for better understanding of the mixing processes, scale-up modeling, and geometry improvement. Various experimental and numerical studies reported on local flow information, with a view to optimizing the mixing processes (for example see [1-5]). For instance, the flow structures are identified to be highly three dimensional (3D) and complex, with trailing vortices and high-turbulence levels (and dis-sipation rates) in the vicinity of the impeller [6,7]. Correspondence: H. Ameur, Department of Technology, Uni-versity Centre of Naama – Ahmed Salhi (Ctr Univ Naama), P.O. Box 66, 45000, Algeria. E-mail: [email protected] Paper received: 4 August, 2019 Paper revised: 18 October, 2019 Paper accepted: 16 January, 2020

https://doi.org/10.2298/CICEQ190804003F

Among other researchers who studied the com-plexity of turbulent flows in stirred tanks, Devi and Kumar [8] performed a CFD study to observe the spa-tial variations (angular, axial and radial) of hydrodyn-amics (velocity and turbulence field) in an unbaffled stirred tank with a concave-bladed disc turbine (CD-6) impeller. Three impeller speeds (N = 296, 638 and 844.6 rpm) have been considered for this study. Djebbar et al. [9] used impeller boundary condition (IBC) to study the effect of the rotating impeller and stationary baffles on fluid mixing. The processes of mixing described above are determined by hydrodyn-amic parameters. The effect of varying impeller geo-metrical parameters including impeller type, number of impeller blades, blade angle and thickness of pitched blade impellers in turbulent flow have been studied by Wu et al. [10]. Other authors [11,12] intro-duced modifications in the Rushton turbine and they obtained a considerable decrease in power require-

M. FOUKRACH, H. AMEUR: EFFECT OF IMPELLER BLADE CURVATURE… Chem. Ind. Chem. Eng. Q. 26 (3) 259−266 (2020)

260

ments. These modifications concern the introduction of different shapes of cuts in the blade (U-, 2U, V- and W-cuts).

The use of unbaffled stirred tanks in mixing may be desirable, as reported by some researchers [13- -15]. In such cases, surface vortices are formed and the liquid surface can no longer be treated as flat. Accordingly, the free surface deformation must be modeled to obtain a more accurate result. Assirelli et al. [16] and Glover and Fitzpatrick [17] used the same approach for the modeling of a vortex in an unbaffled stirred tank.

The mixing and agitation of fluid in a stirred tank have raised continuous attention. CFD has been applied as a powerful tool for investigating the det-ailed information on the flow in the tank. The code CFD has become an important tool for understanding the flow phenomena, developing new processes, and optimizing existing processes [18]. From other mixing characteristics, the power number Np is an important parameter of the stirred tank, which is generally applied to validate the CFD predictions [19,20]. Bru-cato et al. [21] extended the CFD three dimensional simulations for competitive reactions in a batch pro-cess and the results obtained are based on a macro mixing assumption and they showed that there was a good agreement between simulation results and experimental values. A detailed knowledge of power and velocity distribution of the stirred tank configur-ations is therefore required [22].

The efficiency of mixing depends on the impeller type and the blade curvature is one of the important parameters that should be optimized in design. Ameur [23,24] studied the effect of the blade curved in the radial direction. However, in this paper, we are interested in the study of blades curved in the axial direction. Our objective is to provide a knowledge of the flow structures and power consumption for a new designed impeller with curved blades.

Although it is obvious that curved blades require less torque that the flat ones, it remains necessary to determine the value of torque and power require-ments, as well as the degree of intensity in fluid movements when giving modifications to the impeller blade. Are there considerable or negligible effects of blade curvature?

Stirred tank geometry

The stirred tank geometry employed in this work is a flat bottomed, cylindrical and unbaffled tank with a diameter (D) set to 0.6 m and a height-to-diameter ratio (H/D) equal to 1 (Figure 1). The tank is equipped with a six-blade disc turbine placed at a clearance

from the vessel base c = D/3. Two cases of impeller diameter are considered: d = D/2.5 and D/3.

Figure 1. Stirred tank geometry.

Effects of the impeller blade curvature are stu-died by realizing three geometrical configurations: the first case corresponds to a Rushton turbine with flat blades, however, the second and third configurations are turbines with curved blades (curvature radius r = 3 mm and r = 5 mm, Figure 2). All turbines have six blades mounted on a disc with diameter f = 3d/4, with the following geometrical parameters: blade height h = d/5, blade length l = d/4, blade thickness equal to 3 mm, disc thickness equal to 3 mm and the shaft diameter ds = d/5. The tank was filled with pure water at room temperature 298 K (density ρ = 997 kg/m3, dynamic viscosity μ = 8.90×10-4 Pa∙s). Effects of the blade height (h) of impeller with curvature r = 5 mm are studied by realizing three other geometrical con-figurations: h = d/5, d/3 and 2d/5, respectively.

Figure 2. Models of the impellers used: a) Rushton turbine

(straight blades); b) curved bladed turbine, r = 3 mm; c) curved bladed turbine, r = 5 mm.


261

Theoretical background

The equations describing the fluid flow are der-ived from the conservation of mass and momentum which are also known as Navier–Stokes equations for fluids with constant physical properties.

Conservation of mass:

ρ∇ =( ) 0V (1)

Conservation of momentum:

ττ τρ∂∂ ∂ ∂∇ = − + + +

∂ ∂ ∂ ∂( ) yxxx zxpuV

x x y z (2)

τ τ τρ ρ

∂ ∂ ∂∂∇ = − + + + +∂ ∂ ∂ ∂

( ) xy yy zypuV gy x y z

(3)

ττ τρ∂∂ ∂ ∂∇ = − + + +

∂ ∂ ∂ ∂( ) yzxz zzpuV

z x y z (4)

The Reynolds number for the flow in a stirred tank is defined as:

ρμ

=2

ReNd

(5)

where N is the impeller rotational speed. The power consumption used for agitation, P,

can be calculated using two methods: the first one integrates the viscous dissipation energy, Qv, in the whole tank volume [25]:

η= Vesselvolume

dvP Q v (6)

The element dv is written as:

θ θ=d d d dv r r z (7)

The viscous dissipation energy is given by:

θ

θ

θ

θ θ

= + + +

+ + + + + +

22 2

22 2

dd d2

d d d

dd d d d dd d d d d d

r zv

r r z r z

vv vQR Z

vv v v v vR Z Z R

(8)

The second methodology uses the torque, C, applied on the agitation system as given in the following equation [26]:

π= 2P NC (9)

As found by many researchers, both methods give almost the same results [27]. In this paper, the first method is used.

The power number Np leaves extrapolating power calculations when the diameter of the stirrer

and its speed of rotation N changes. The power number is defined by:

ρ= 3 5

PNpN d

(10)

NUMERICAL DETAILS

The numerical simulation in this study is con-ducted by the CFX 18.0 code which is based on the finite volume method to solve the equations governing the phenomena of momentum transfer. The computer tool Ansys ICEM CFD was used to create the com-putational domain. The grid mesh used is tetrahedral and the global mesh size varies from a geometry to another. To achieve mesh tests, the grid density was increased by a factor of about 2. This approach has been used by other researchers in CFD modeling of the mixing processes [28,29]. As detailed in Table 1, the difference in power number between meshes M2 and M3 does not exceed 2%, so M2 was used to per-form computations.

Table 1. Power number for impeller with curved blades, r = 3 mm, h = 2d/5, d = D/2.5, Re = 4×104 (details on mesh tests)

Property Impeller

M1 M2 M3

Number of cells 425,635 898,138 1,652,635

Np 1.63 1.621 1.624

Time required, s 22,000 54,000 100,800

The Navier-Stokes equations written in a rot-ating, cylindrical frame of references are solved. The centrifugal and Coriolis accelerations are added to the equations because of the choice of a rotating frame. The equations are written in terms of velocity compo-nents and pressure. These variables are discretized on a grid of control volumes, which enables a more precise mass conservation, and a faster conver-gence. A pressure-correction method of the type semi-implicit method for pressure- linked equations- -consistent (SIMPLEC) is used to perform pressure- -velocity coupling.

Constant boundary conditions have been set respecting a rotating reference frame (RRF) appro-ach. Here, the impeller is kept stationary and the flow is steady relative to the rotating frame, while the outer wall of the tank is given an angular velocity equal and opposite to the velocity of the rotating frame. In the case of agitated tanks involving baffles, computational flow could be achieved with the MRF or sliding meshes approaches.


262

The fluid is Newtonian and the regime is station-ary. The flow is turbulent and Reynolds number varies from 104 to 2×105. The k-ε shear stress transport (SST) model is used for modeling the turbulent flow. This modification combines the advantages of k-ε model for bulk liquid and k-ω model for liquid near a tank wall. Results were considered to be converged when the residual target of 10-6 has been reached. The convergence has been reached after about 4000 iterations and 15-17h of CPU time. For further details, please refer to [30].

Validation

Flow fields and power consumption are pre-dicted with the help of a CFD computer program. A comparison and validation are made between our predicted results and the experimental data given by Karcz and Major [31] and Chiti et al. [7]. Figures 3a and b present, respectively, the power number vs. Reynolds number and dimensionless redial velocity along the tank height. As observed in these figures, the numerical results are in a good agreement with the experimental data of these authors.

RESULTS AND DISCUSSION

Hydrodynamics

Effect of impeller configurations In this paper, we focus on the hydrodynamics

distribution and power consumption when introducing changes in the impeller design. The three-compo-nents of velocity as well as the flow patterns are described for each geometrical configuration sug-

gested. As reported by many researchers [25,32-35], the mixing characteristics (mixing time, degree of homogeneity and power input) and the overall per-formance of stirred tanks depend strongly on the flow fields generated in the tank.

Tanks without baffles are also used in many applications, such as fermentation, solid–liquid mass transfer, in the food and pharmaceutical industries, etc. The velocity contours generated by three types of six bladed agitators having the same blade height are presented in Figure 4. The slices on this figure cor-respond to: a Rushton turbine with straight blades,

Figure 3. Validation with experimental data for a standard Rushton turbine d = D/3: a) power number vs. Reynolds number; b) dimensionless radial velocity along the tank height, at R* = 0.33, Re = 1.61×105.

Figure 4. Velocity contours for the three types of agitators, d = D/3, at θ = 0°: a) Re = 4×104; b) Re = 4 ×105.


263

and turbines with blade curvatures r = 3 and 5 mm, respectively. First, we remark that the maximum int-ensity of velocity is located at the end of blades for each case. It can be observed also that the flat blade (case (a)) generates a radial flow directed to the lower part of tank. When the blade becomes curved, the inclination of flow towards the tank bottom is dim-inished. This can be explained by the reduction in the interaction between the fluid flow and the tank walls, which is resulted from the reduction of radial forces of flow impinging from the impeller. At a high Reynolds number, the unbaffled stirred tank equipped with a Rushton turbine produces a discharge flow with a downward direction with increasing impeller rotational speed or the flow becomes more turbulent due to increasing vortex size but in the tank with baffles the discharge flow becomes radial.

To know and illustrate more differences between the three geometrical configurations, we increased the Reynolds number until reaching the value 105 (Figure 4b). Also, the variations of axial, radial and

tangential velocities along the tank height are pre-sented inn Figures 5a–c, respectively.

We notice that the axial velocity (Vz*) is maxi-

mum at the vertical position Z* = 0.2 for the tank agitated by a Rushton turbine and it becomes very weak near the free surface of liquid for curved tur-bines (r = 3 and 5 mm). The radial velocity component is maximum at the blade tip of the Rushton turbine and it is very weak in the upper parts of the turbines. The tangential component velocity is higher for the Rushton turbine (V*

θ,max= 0.34) over than that for impellers with curved blades (V*

θ,max= 0.12 at r = 5 mm). It seems that the flat blade is advantageous in terms of enhancement of the axial circulation of fluid. Although the Rushton turbine is well known by its radial flow, the power of radial jet impinging from the impeller blade causes a strong interaction with the tank walls; the flow is then divided into two parts: one directed towards the tank bottom and the other to the free surface of liquid. The intensified radial flow is accompanied certainly by a powerful axial circulation

Figure 5. a) Axial, b) radial and c) tangential velocity components along the tank height, at R* = 0.25, Re = 4×104, θ = 0°, d = D/3.


264

of fluid particles. However, the increase of blade curvature yields less radial, tangential and axial flows.

Effect of blade height The new suggested design, i.e., a curved bladed

turbine with r = 5 mm, is selected to achieve an investigation on the effect of blade height (h), where three geometrical configurations were realized for this purpose: h = d/5, d/3 and 2d/5, respectively. Figure 6 shows the velocity contours for Re = 4×104. Also, profiles of the axial and tangential velocities are shown in Figures 7a and b, respectively.

The analysis of comparison between the results given in these figures allow us to say that the area swept by the impeller increases with the rise of blade height, resulting thus in increased tangential flows and enhanced circulation of fluid particles in the axial direction.

Power consumption

The agitation power is one of the most important parameters to describe the performance of a mech-anically agitated system. The dimensional analysis

0 30000 60000 90000 120000 150000 180000 2100000

1

2

3

4

Np

Re

Straight blade Curved blade, r = 3 mm Curved blade, r = 5 mm

Figure 8. Power number vs. Reynolds number,

h = 2d/5, d = D/2.5.

enables us to define the power number Np (Eq. (10)). Values of Np are presented in Figure 8 for different values of Re and blade curvature. As observed in this figure, the increase of Re in the turbulent regime yields a slight decrease in the power number, how-ever, the rise of blade curvature requires less power

Figure 6. Velocity contours of the curved turbine for r = 5 mm with various blade heights, at Re = 4×104, d = D/3.

Figure 7. For an impeller with blade diameter d = D/3: a) axial velocity vs. tank height, at R* = 0.233, Re = 4×104; b) tangential velocity vs.

tank radius at Z* = 0.33, Re = 4×104.


265

input. An important gain in power consumption may be obtained with this suggested design (curved blade), where the increased blade curvature provides less power consumption.

Results of the power number for different values of blade height are summarized in Table 2. The vis-cous dissipation is rather high with the rise of blade height, which requires further power input, as obs-erved in Table 2, where values of the power number are provided for the three geometrical cases.

Table 2. Power number for the CBI with r = 3 mm, d = D/2.5, at Re = 4×104

h d/5 d/3 2d/5

Np 1.33 1.47 1.62

CONCLUSION

The purpose of the present paper was to obs-erve the effect of blade shape on the agitation char-acteristics in a cylindrical tank. Three impeller config-urations were studied and compared. The results obtained in this study allow us to draw the following conclusions:

- The increase in blade curvature yields less powerful radial flows;

- The flat blade is more suitable in terms of enhancement of the axial circulation of fluid;

- Less power consumption is required with the rise of blade curvature;

- A slight decrease in the power number is observed in the turbulent flow regime within unbaffled tanks;

- The increase in blade height generates stronger tangential flow and enhanced axial move-ment of fluid particles, but with further penalty in power input.

The modifications introduced in the Rushton turbine have allowed a reduction in the power con-sumption. However, in order to optimize the perform-ance of this new suggested design, further studies of other geometrical parameters and other fluids with different rheological behaviors are required. Also, the determination of other mixing characteristics is needed, such as the mixing time. So, the complete information will be helpful for designers to specify the more appropriate application of the developed design.

Nomenclature

C Torque, N m c Distance between agitator and bottom of the

tank, m D Inner diameter of the agitated tank, m

d Diameter of the agitator, m ds Shaft diameter, m f Disc diameter, m g Gravitational constant, m/s2 l Blade length, m h Blade height, m H Liquid height in the tank, m N Agitator speed, s-1 Np Power number, dimensionless p Pressure, Pa P Power consumption, W Qv Viscous dissipation function, 1/s R Radial coordinate, m R* Dimensionless radial coordinate, R* = 2R/D r Curved blade radius, m Re Reynolds number, dimensionless V Velocity, m/s V*

z Axial velocity, dimensionless (Vz/πND) V*

θ Tangential velocity, dimensionless (Vt/πND) V*

r Radial velocity, dimensionless (Vr/πND) Z* Axial coordinate, dimensionless (Z/D) τ Shear stress, Pa Ρ Fluid density, kg/m3 μ Fluid dynamic viscosity, Pa∙s θ Angular coordinate, degree ω Angular velocity, rad/s

REFERENCES

[1] T. Su, F. Yang, M. Li, K. Wu, Chin. J. Chem. Eng. 26 (2018) 1392–1400

[2] H. Ameur, A. Ghenaim, ChemistrySelect 3 (2018) 7472– -7477

[3] Q. Zhu, H. Xiao, A. Chen, S. Geng, Q. Huang, Chin. J. Chem. Eng. (2018) in press, https://doi.org/10.1016/ /j.cjche.2018.10.002

[4] M. Beloudane, M. Bouzit, H. Ameur, Polish J. Chem. Technol. 20 (2019) 129–137

[5] M. Foukrach, M. Bouzit, H. Ameur, Y. Kamla, Chem. Pap. 73 (2019) 469–480

[6] A. Zamiri, J. T. Chung, Comp. Fluids 170 (2018) 236–248

[7] F. Chiti, S. Bakalis, W. Bujalski, M. Barigou, A. Eaglesham, A.W. Nienow, Chem. Eng. Res. Des. 89 (2011) 1947–1960

[8] T.T. Devi, B. Kumar, Chem. Ind. Chem. Eng. Q. 18 (2012) 535–546

[9] R. Djebbar, M. Roustan, A. Line, Chem. Eng. Res. Des. 74 (1996) 492–498

[10] J. Wu, Y. Zhu, L. Pullum, Chem. Eng. Res. Des. 79 (2001) 989–997

[11] H. Ameur, J. Food Eng. 233 (2018) 117–125

[12] D.A. Rao, P. Sivashanmugam, J. Ind. Eng. Chem. 16 (2010) 157–161

[13] L. E. Aloi, R. S. Cherry, Chem. Eng. Sci. 51 (1996) 1523– -1529


266

[14] J. M. Rousseaux, H. Muhr, E. Plasari, Can. J. Chem. Eng. 79 (2001) 697–707

[15] M. Assirelli, W. Bujalski, A. Eaglesham, A.W. Nienow, Chem. Eng. Sci. 63 (2008) 35–45

[16] G.M.C. Glover, J.J. Fitzpatrick, Chem. Eng. J. 127 (2007) 11–22

[17] J.-P. Torré, D. F. Fletcherb, T. Lasuye, C. Xuereb, Chem. Eng. Sci. 62 (2007) 6246–6262

[18] H. Ameur, ChemistrySelect 2 (2017) 11492–11496

[19] A. Brucato, M. Ciofalo, F. Grisafi, G. Micale, Chem. Eng. Sci. 53 (1998) 3653–3684

[20] C. Bartels, M. Breuer, K. Wechsler, F. Durst, Comp. Fluids 31 (2002) 69–97

[21] A. Brucato, M. Ciofalo, F. Grisafi, R. Tocco, Chem. Eng. Sci. 55 (2000) 291–302

[22] A. Lamotte, A. Delafosse, S. Calvo, D. Toye, Chem. Eng. Sci. 192 (2018) 128–142

[23] H. Ameur, Chin. J. Chem. Eng. 24 (2016) 1647–1654

[24] H. Ameur, Int. J. Chem. React. Eng. 14 (2016) 1025–1034

[25] M. Abld, C. Xuereb, J. Bertrand, Can. J. Chem. Eng. 72 (1994) 184–193

[26] G. Ascanio, B. Castro, E. Galindo, Chem. Eng. Res. Des. 82 (2004) 1282–1290

[27] L. Pakzad, F. Ein-Mozaffari, P. Chan, Chem. Eng. Proc. Process Intensif 47 (2008) 2218–2227

[28] V. Buwa, A. Dewan, A. F. Nasser, F. Durst, Chem. Eng. Sci. 61 (2006) 2815–2822

[29] B. Letellier, C. Xuereb, P. Swaels, P. Hobbes, J. Bertrand, Chem. Eng. Sci. 57 (2002) 4617–4632

[30] H. Ameur, Chin. J. Chem. Eng. 24 (2016) 572–580

[31] J. Karcz, M. Major, Chem. Eng. Process. 37 (1998) 249– -256

[32] H. Ameur, Food Bioprod. Proc. 117 (2019) 302–309

[33] R. Escudié, A. Liné, AIChE J. 49 (2003) 585–603

[34] G. Montante, A. Bakker, A. Paglianti, F. Magelli, Chem. Eng. Sci. 61 (2006) 2807–2814

[35] A. Delafosse, A. Line, J. Morchain, P. Guiraud, Chem. Eng. Res. Des. 86 (2008) 1322–1330.

MOHAMMED FOUKRACH1

HOUARI AMEUR2 1Faculty of Mechanical Engineering,

USTO-MB, El M’naouar, Oran, Algeria 2Department of Technology, University

Centre of Naama – Ahmed Salhi (Ctr Univ Naama), Algeria

NAUČNI RAD

UTICAJ ZAKRIVLJENOSTI LOPATICA MEŠALICE NA HIDRODINAMIKU I SNAGU MEŠANJA U SUDU SA MEŠANJEM

Istraživane su performanse turbina sa zakrivljenim lopaticama (CBT) za mešanje Njutnovskih tečnosti u cilindričnim sudovima. Efikasnost turbina sa zakrivljenim lopaticama je upoređena se sa standardnom Rushtonovom turbinom. Takođe, rasvet-ljeni su uticaji visine lopatica novodizajnirane mešalice. Za analizu aksijalne, radijalne i tangencijalne komponente brzine, obrasca strujanja i snage mešanja korišćena je numerička dinamika fluida. Dobijeni rezultati pokazali su da povećanje zakrivljenosti lopatice smanjuje snagu mešanja. Takođe, neznatno smanjenje faktora snage pri-mećeno je u turbulentnom režimu u sudovima bez odbojnika. U poređenju istraživanih slučajeva, najbolja aksijalna cirkulacija tečnosti je postignuta sa mešalicom sa ravnim lopaticama. Povećanje visine zakrivljenih lopatica je indukovalo snažnije tangencijalno strujanje i poboljšalo aksijalno kretanje čestica fluida, ali bez povećanja snage mešanja.

Ključne reči: mehaničko mešanje; mešalica sa zakrivljenim lopaticama; cilin-drični sud; hidrodinamika; snaga mešanja.

Documents

MOHAMMED FOUKRACH EFFECT OF IMPELLER BLADE …