Energy efficiency of different impellers in stirred tank reactors

Energy efficiency of different impellers in stirred tank reactors

Energy 93 (2015) 1980e1988 Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Energy efficiency of di...

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Energy 93 (2015) 1980e1988

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Energy efficiency of different impellers in stirred tank reactors Houari Ameur* ^ma, 45000, Algeria Institute of Science and Technology, University Center Ahmed Salhi, Naa

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 February 2015 Received in revised form 19 October 2015 Accepted 21 October 2015 Available online xxx

The flow energy efficiency of different impellers for stirring rheologically complex fluids (yield stress fluids) in cylindrical tanks has been investigated in this paper. Four impellers have been used: a Maxblend, an anchor, a gate and a double helical ribbon impeller. Our investigations were achieved via numerical simulations with the help of a CFD (computational fluid dynamics) computer program CFX 13.0. It was found from the predicted results that the Maxblend impeller gives the best performance. The effects of some design parameters on the flow energy efficiency and the power consumption have been also studied; it concerns the Maxblend impeller: its grid size and its paddle curvature. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Energy efficiency Maxblend impeller Yield stress fluid CFD simulations Stirred tank

1. Introduction The efficient mixing of liquids is very important in most industrial technologies. When designing a stirred system it is desirable to provide the required transport characteristics (i.e. mixing intensity, heat and mass transfer, gas hold-up, etc.) at the lowest possible energy consumption. The performance of such systems depends on many variables, such as the geometry of the equipment, physical properties of the liquid and operating conditions [1]. With the development of computer performance in the last decades, many researchers have turned to CFD (computational fluid dynamics) for several applications. Yu et al. [2] described, with CFD simulations, the suspension and settling in the bio-waste particles flow in a bioreactor. Baigmohammadi et al. [3] studied numerically the behavior of methane-hydrogen/air pre-mixed flame in a micro reactor. Benajes et al. [4] studied the exhaust gas recirculation and miller cycle strategies for mixing-controlled low temperature combustion in a diesel engine. Hashimoto and Shirai [5] performed numerical simulations of mixed combustion of bituminous and sub-bituminous coals. Sharma et al. [6] predicted syngas composition in a continuous stirred-tank reactor by using extents of major reaction. Zhang et al. [7] studied the mixing phenomena in a fermenter of starch to bio-ethanol. Isfahani et al. [8] studied the effect of micromixing on the performance of a membrane-based

* Tel.: þ213 770343722. E-mail address: [email protected] http://dx.doi.org/10.1016/j.energy.2015.10.084 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

absorber. El-Askary et al. [9] investigated the hydrodynamics characteristics of the hydrogen-generation process through electrolysis. Jin et al. [10] explored the fluid flow and heat transfer characteristics in a solar air heater duct having multi V-shaped ribs on the absorber plate. Modlinski [11] performed numerical simulations of flow with combustion in a coal-fired grate boiler. Ma et al. [12] studied the feasibility of using longitudinal vortex generators to enhance the heat transfer in a thermoelectric power generator. Ye et al. [13] explored numerically the effects of the blade tip grooving on the efficiency on an axial flow fan. For stirred tank reactors, Achouri et al. [14] simulated numerically the fluid flows in a in a vessel stirred by a PBT (Pitched Blade Turbine). For a Newtonian fluid, Ammar et al. [15] achieved a numerical investigation of turbulent flows generated in baffled stirred vessels equipped with three different turbines in one and twostage systems. Aided by CFD simulations, Ameur and Bouzit [16] developed a new correlation for predicting the power required for stirring shear thinning fluids by two-blade impellers in cylindrical tanks. For Newtonian fluids, Rao and Sivashanmugam [17] presented experimental and simulation investigations on the power consumption for a new energy saving turbine agitator. These authors performed modifications by introducing single and double rectangular and V cuts in the conventional turbine agitator. Bao et al. [18] established correlations for calculate the mixing time and the power consumption for mixing CMC (Carboxy Methyl Cellulose) solutions by four coaxial mixers. They combined with either Pfaudler or CBY turbine as the inner stirrer, and helical ribbon or anchor as the outer one. Liu et al. [19] studied the power

H. Ameur / Energy 93 (2015) 1980e1988

consumption of a coaxial mixer formed by an outer wall-scraping frame and double inner turbines. Their predicted results indicated that the power consumption of the outer frame increases in counter-rotation mode and decreases in co-rotation mode. A new impeller design called Maxblend (see Fig. 2), is one of the most promising new generation wide impellers due to its good mixing performance, lower dissipation rates and simple geometry. However, only few studies have been performed and reported in the literature, especially for the agitation of shear thinning fluids with yields stress. The majority of non-Newtonian fluids are naturally opaque; therefore, visualizing the flow fields of these fluids inside a mixing vessel is a challenging task. Patel et al. [20] interested to the Rushton turbine and the Maxblend impeller and demonstrated an efficient method to visualize the non ideal flows such as dead zones in stirred tank reactors. Fontaine et al. [21] studied with experiments the flow dynamics of Newtonian, shear thinning and viscoelastic fluids in a Maxblend impeller system. They reported that elasticity in the laminar regime produces a reversal flow and a solid body rotation in the bottom region of the tank. With Newtonian fluids, Iranshahi et al. [22] investigated experimentally and numerically the flow and mixing in a vessel equipped with a Maxblend impeller in the laminar and transition regimes for baffled and unbaffled configurations. Ameur et al. [23] performed 3D numerical simulations of a Maxblend impeller system with viscoplastic fluids possessing yield stress. They focused on the effect of fluid rheology, impeller rotational speed, impeller clearance from the tank bottom and impeller blade size on the fluid flow and power consumption. Devals et al. [24] performed a CFD characterization of the hydrodynamics of the Maxblend impeller with viscous Newtonian and non-Newtonian inelastic fluids. They found that the bottom clearance plays a significant role on the power consumption, and that the value of the Reynolds number and the power law index strongly affect the axial pumping efficiency and the shear rate profile. The best performance was obtained when the impeller Reynolds number is superior to 10. Physical investigations have been carried out by Fradette et al. [25] to characterize the power consumption and the mixing time in a vessel equipped with a Maxblend impeller. These authors investigated laminar, transitional and turbulent flow regimes using viscous Newtonian and non-Newtonian shear-thinning fluids. Based on data from the literature, a comparison with many

1981

Fig. 2. Characteristics of the stirred system.

different large impellers indicated that the Maxblend technology makes a better use of the mixing power in the upper part of the laminar regime and in the low turbulent regime. The power consumption was found almost identical as that of an anchor but far lower than that of a double helical ribbon impeller. Aided by numerical simulations, Iranshahi et al. [26] investigated and compared the mixing characteristics of the Ekato Paravisc with those of an anchor and a double helical ribbon. For Newtonian and shear thinning fluids, they found that the Paravisc mixer characteristics lie between that of the other impellers at low Reynolds number. For shear thinning fluids possessing yield stress, Patel et al. [27] showed by experiments that the Maxblend impeller is more efficient than the axial-flow impeller (Lightnin A320), radial-flow impeller (Scaba 6SRGT), and close-clearance impeller (anchor) in terms of reducing the extent of dead zones inside the mixing vessel with a lower power consumption. Stobiac et al. [28] investigated the accuracy of the extrapolation method for the lattice Boltzmann simulation of Newtonian fluid

Fig. 1. Geometries of all impellers studied.

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H. Ameur / Energy 93 (2015) 1980e1988

flows in a Maxblend impeller system. Their results showed that the standard bottom clearance is not optimum in the transitional regime. Stobiac et al. [29] examined numerically the pumping mechanisms generated by the Maxblend impeller for Newtonian fluids (Re ¼ 2 e 140) and strongly shear-thinning fluids (Reg ¼ 0.1 e 50). Their results indicate a small pumping capacity in the deep laminar regime followed by its sharp increase in the transitional regime. In the case of the strongly shear thinning fluids, the flow fields and socalled pumping volumes revealed, similarly to the Newtonian case, a change in the structure of the axial and (secondary) radial flow when the Reynolds number is increased. Guntzburger et al. [30] introduced a new experimental method to determine the global pumping capacity of four impellers, namely: a Maxblend impeller, a RT (Rushton turbine), a three-blade HP (hydrofoil propeller) and a four PBT (pitched blade turbine). Their results showed that the Maxblend impeller performs better than the other three turbines in the transitional regime, and it has a similar pumping capacity than that of the RT and the PBT in the turbulent regime. Liu et al. [31] investigated the micro mixing characteristics of a novel LDB (Large-Double-Blade) impeller based on Maxblend and FZ (Fullzone) impellers. They compared the performance of LDB impeller with that of FZ and DHR (double helicon ribbon) impellers. The LDB stirrer is found to be the most efficient for the same power consumption per unit volume. It is often advantageous to increase fluid flow velocities at the tank walls or in the bulk flow in order to improve the heat transfer, to reduce the rate at which scale grows at the tank wall surface, and to increase the metal extraction rate [32]. The best challenge is to increase fluid flow velocities within constraints of the available power input, as it is expensive to alter larger scale motors to obtain an additional power. Therefore, it seems important to improve the impeller flow energy efficiency. From our search in the literature, it was found that most studies focused on the flow structure, the mixing time and turbulence parameters, with less attention to the flow energy efficiency. Therefore, the main purpose of this paper is to study the flow energy efficiency of different impellers for stirring shear thinning fluids possessing yield stress. The impellers considered are: a Maxblend, an anchor, a gate and a DHR (double helical ribbon). Some design parameters of the Maxblend impeller are also investigated. The four impellers studied belong to the same kind, is that of the close clearance impellers. These stirrers are widely used for mixing highly viscous and non-Newtonian fluids. But, which is best mixer? 2. Stirred system The mixing system used in this paper is a flat-bottomed cylindrical unbaffled vessel equipped with a rotating impeller. Four impellers are used: a Maxblend (Fig. 1a), an anchor (Fig. 1b), a gate (Fig. 1c) and a double helical ribbon impeller (Fig. 1d). We note that the following parameters are taken with all geometric configurations: the vessel diameter D ¼ 130 mm, the vessel height H/D ¼ 1, the impeller clearance from the tank bottom c/ D ¼ 0.2, the impeller blade height h/D ¼ 0.6, impeller blade diameter d/D ¼ 0.6, the shaft diameter ds/D ¼ 0.4. For the Maxblend impeller (Fig. 2), the paddle height is h1/D ¼ 0.23 and the grid height is h2/D ¼ 0.38. In the purpose to examine the effect of impeller design, four geometrical configurations were realized, it concerns the Maxblend grid size: d1/D ¼ 0.30, 0.45, and 0.60, respectively. The design of the Maxblend paddle has also been modified by realizing three shapes as will be shown later (on Fig. 2).

3. Theoretical considerations Shear thinning fluids with yield stress were modeled in this work, the Xanthan gum solution was considered. Rheological properties of the materiel simulated are summarized on Table 1, which are based on measurements conducted by Galindo and Nienow [33]. It's rheology can be described by the Herchel Bulkkley model [34]: :n

t ¼ ty þ Kg

(1)

where ty is the yield stress, K is the consistency index, g_ is the shear rate and n is the flow behavior index. According to the Metzner and Otto's correlation [35], the average shear rate can be related to the impeller speed by: :

gavg ¼ Ks N

(2)

The average shear rate can be used to evaluate the apparent viscosity (h) of the solution, which is a HerscheleBulkley fluid.



:

t

gavg

¼

ty þ KðKs NÞn t ¼ ks N Ks N

(3)

The Reynolds number can be given as:

Rey ¼

Ks N 2 D2 r ty þ KðKs NÞn

(4)

The impeller pumping flow rate could be expressed as (refer to Wu et al. [36]):

NQ



!

1=3

P0

P 4 D r

1=3 (5)

where Q is the flow rate, r the fluid density and P the power consumption. The power number Np is determined according to this equation:

NP ¼

P rN 3 D5

(6)

The flow number NQ is calculated as:

NQ ¼

Q ND3

(7)

The factor NQ/P1/3 0 is defined as the impeller flow efficiency index [32]: Based on Eq. (5), the averaged velocity at impeller exit can be calculated as:



!  1=3 4 NQ 2=3 P 4 D D p P 1=3 r 0

(8)

To estimate the velocities at the tank walls at a given power input, we may normalize Eq. (8), to obtain a non-dimensional efficiency coefficient h: Table 1 Rheological properties of Xanthan gum solution. Concentration (%)

K [Pa sn]

n [e]

ty [Pa]

3.5

33.1

0.18

20.6

H. Ameur / Energy 93 (2015) 1980e1988

NQ V h ¼   1=3 ¼ j 1=3 2 P0 P rD

(9)

where j is a non-dimensional parameter dependent on impeller and tank diameters and locations of the impeller(s). The significance of h is that the increase of h yields higher flow velocity per unit power input. Thus, the energy efficiency of various impeller designs for a given vessel size should be compared in terms of this coefficient (h) [32].

1983

Np

Exp [27] Num [Present work]

100

10

4. Numerical simulation Simulations were performed by using the computer code (CFX 13.0) which is based on the finite volume method to solve the equations of momentum and energy. Since the stirred tank is not provided with baffles, a RRF (rotating reference frame) approach was used. 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 technique has been used by other researchers [37,38] for different mixing systems and accurate results were found. For solving the equations of momentum and to perform pressureevelocity coupling, a pressure-correction method of the type SIMPLEC (Semi Implicit Method for Pressure Linked Equations Consistent) is used. Geometries of the mixing systems were realized with the help of the preprocessor (Ansys ICEM CFD 13.0). The flow domain was divided into tetrahedral meshes. When creating meshes, an increased mesh density was performed near the impeller and the tank walls to capture the flow details. Mesh tests were performed by checking that the numerical results were grid independent. Mesh density was increased until the additional cells did not change the energy efficiency and the power consumption in regions with high gradients by more than 2.5%. Calculations were run in a platform with Core i7 CPU 2.20 GHz with 8.0 GB of RAM. Numerical results were considered converged when the residual target drop below 107. Most simulations required 2500e3000 iterations and 5e6 h for convergence. 5. Results and discussion First, we have checked the validity of our numerical results by a comparison with the experimental data given by Patel et al. [27].

Np

1 1

100

Rey

Fig. 4. Power number for the anchor impeller.

Both numerical and experimental results for the power number are depicted on Figs. 3 and 4; the comparison shows agreement. 5.1. Flow energy efficiency of the four impellers The ability of an impeller to convert its power input to the fluid flow is referred to as its hydraulic efficiency h. The higher this quantity, the higher the energy transferred by the impeller to the agitated material, resulting in higher intensity of the flow [39]. As a comparison, the energy efficiency of four impellers operating in viscoplastic fluids with yield stress is considered. For a Reynolds number Rey ¼ 100 and an angular position q ¼ 90 (i.e. the plane orthogonal to the impeller), simulation results of the flow energy efficiency along the tank wall surface are depicted on Fig. 5. We note that the origin of the angular position (q ¼ 0 ) is taken at the prolongation of the blade for each impeller. We remark from this figure that the flow energy efficiency profiles follow the same trend for the anchor, the gate and the Maxblend impellers. However, the maximum is reached with the Maxblend agitator. For the double helical ribbon impeller (DHR), we remark that the maximum of h is reached in the area swept by the blade arms but with small amplitude when compared with the Maxblend. On Fig. 6 we present the variations of the coefficient h along the vessel radius for two locations: (a) Z* ¼ Z/D ¼ 0.075 near the vessel base, (b) Z* ¼ 0.83 near the free surface of liquid. For more visibility, we present on Figs. 7 and 8 the spatial distribution of the flow energy efficiency on horizontal cross section planes for different vertical positions.

Exp [27] Num [Present work]

100

10

Z

*

Anchor impeller Gate impeller Helical ribbon impeller Maxblend impeller

1.0 0.8 0.6

10

0.4 0.2 0.0

1 1

10

Fig. 3. Power number for the Maxblend impeller.

100

Rey

0.00

0.01

0.02

0.03

0.04

0.05

η

Fig. 5. Flow energy efficiency near the vertical vessel wall, Rey ¼ 100, q ¼ 90 .

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H. Ameur / Energy 93 (2015) 1980e1988

η

η

Anchor impeller Gate impeller Helical ribbon impeller Maxblend impeller

0.12 0.11 0.10

Anchor impeller Gate impeller Helical ribbon impeller Maxblend impeller

0.18 0.16

0.09

0.14

0.08

0.12

0.07 0.06

0.10

0.05

0.08

0.04

0.06

0.03 0.02

0.04

0.01

0.02

0.00

0.00

-0.01 0.0

0.2

0.4

0.6

0.8

1.0

*

R

0.0

0.2

(a) Z* = 0.075

0.4

0.6

0.8

1.0

R

*

(b) Z* = 0.83

Fig. 6. Flow energy efficiency, Rey ¼ 100, q ¼ 90 .

Fig. 7. Contours of the flow energy efficiency for Rey ¼ 100, at Z* ¼ 0.3.

The conclusions drawn from the analysis of these figures are as follows: In the whole vessel volume, the anchor impeller is the less efficient impeller (Figs. 6e8). Adding a vertical arm to this impeller for obtaining a gate can improve mixing in the lower part of the vessel, but it seems insufficient for the upper part of the vessel (Fig. 8). The anchor and gate impellers create tangential flows, as a result, a vortex is formed at the free surface of liquid and the fluid begins rotating with the stirrer rather than being pumped. At higher stirrer rotational speeds, the vortex increases in size and the rotational movement entrains the fluid in the whole vessel volume, consequently, the pumping effect of the stirrer is reduced. The paddle design of the Maxblend impeller seems the best efficient in the lower vessel volume (Fig. 8). The shape of the paddle creates large pressure variations inside the vessel and it can be considered responsible for the efficient flow motion, as reported by

Fradette et al. [25]. The front side of the paddle creates an overpressure near the vessel base and pushes the fluid close to the wall in the upward direction. The fluid at the upper part of the vessel is sucked by the low pressure created at the bottom of the tank; the fluid goes downward along the impeller shaft. Mixing is achieved and enhanced by axial pumping. However, the grid mounted on the Maxblend cannot provide sufficient homogenization energy near the free surface of liquid. The DHR impeller can remedy this issue as remarked on Fig. 8 and this is due to the size of the arm blade. Electric energy consumption is an important parameter for the stirred tank design. It is defined as the amount of the electric energy necessary (in a period of time) to generate the fluid circulation within a tank by means of mechanical agitation [40]. The costs associated with power drawn contribute significantly to the overall operation costs of industrial plants. Therefore it is desirable to

Fig. 8. Spatial distribution of the flow energy efficiency for Rey ¼ 100.

H. Ameur / Energy 93 (2015) 1980e1988

Np

η

Maxblend impeller Anchor impeller Gate impeller Double Helical ribbon impeller

14 13 12 11 10 9 8 7 6 5 4 3 2 1

1985

d /D = 0.30 d /D = 0.45 d /D = 0.60

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00

10

20

30

40

50

60

Rey

-0.05 0.0

Fig. 9. Power number for vessel size ¼ 0.6.

0.2

0.4

0.6

0.8

1.0

1.2

*

R

1.4

Fig. 11. Flow energy efficiency at Z* ¼ 0.75, Rey ¼ 100, q ¼ 90 .

Table 2 Values of Np in the deep laminar regime.

Np

Re

Maxblend

Anchor

Gate

DHR

26

0.1 1 10

706.90 71.69 7.300

853.75 84.88 8.59

951.72 95.95 9.734

1304.73 130.92 13.13

25 24

perform efficiently the mixing process with a minimum expense of energy [41]. Here, we estimated the energy consumption for the four impellers. As shown on Fig. 9, the lower the Reynolds number, the greater the energy required to achieve the agitation operation with any kind of impellers. The energy required diminishes continuously with increasing Reynolds number. This reduction is strong in the deep laminar regime (Re < 10), however a fairly reduction is remarked in the transitional regime. The trend of the power number curve obtained in this study is similar to that reported in the literature [27]. It has been shown that the Np*Re is constant in the laminar regime and the power consumption (P) changes to some extent in the transitional regime. Fig. 3 and Table 2 show that at Re < 10, the power curve with a slope of 1 fits the data, which implies that Np*Re is constant and the flow is in the laminar regime. In the transitional regime, the power number changes slightly with Re. Fradette et al. [25] and Iranshahi et al. [26] reported that the laminar region ends for Re in the range between 35 and 40 for the Maxblend and anchor impellers. *

Z

1.4

23 22 21 20 19 0.30

0.35

0.40

0.45

0.50

0.55

0.60

d1/D

Fig. 12. Power number for Rey ¼ 10.

As a comparison, the Maxblend impeller seems to be the best efficient in term of power consumption. Following a descending order in the power consumption for the four agitators: DHR > gate > anchor > Maxblend. The DHR impeller was found to be efficient to improve mixing near the free surface of liquid but with more power drawn.

d /D = 0.30 d /D = 0.45 d /D = 0.60

1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

η

Fig. 10. Flow energy efficiency near the vertical vessel wall, Rey ¼ 100, q ¼ 90 .

Fig. 13. The different geometrical configurations realized to examine the effect of the Maxblend paddle design.

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H. Ameur / Energy 93 (2015) 1980e1988

Z

mixing in this region. In this work, we tried to examine the effect of the impeller grid diameter. For this purpose, three geometric configurations are realized and which are: d1/D ¼ 0.30, 0.45 and 0.60, respectively. Variations of the circulation energy efficiency along the tank wall surface are followed and depicted on Fig. 10. As observed, the maximum flow energy efficiency is h ¼ 0.037 for d1/D ¼ 0.60 compared to h ¼ 0.032 for d1/D ¼ 0.45 and h ¼ 0.029 for d1/D ¼ 0.30. The circulation energy efficiency profiles follow the same trend for the three geometric configurations; however this parameter (h) spreads more in the upper part of the vessel with increasing impeller grid size. More illustration is given on Fig. 11 where h is presented along the vessel radius for a vertical position of Z* ¼ 0.75 (area swept by the grid). It can be said from these results that, the higher the impeller grid size, the higher the energy efficiency with additional power drawn (Fig. 12).

*

Geometry A Geometry B Geometry C

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045

η

Fig. 14. Flow energy efficiency near the vertical vessel wall, Rey ¼ 100, q ¼ 90 .

η

Geometry A Geometry B Geometry C

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

*

R

Fig. 15. Flow energy efficiency at Z* ¼ 0.22, Rey ¼ 100, q ¼ 90 .

5.2. Effect of the Maxblend grid diameter In the case of the Maxblend impeller, we remarked that the flow energy efficiency is pretty low at the top of the vessel, which corresponds to a quasi-solid body rotation. Devals et al. [24] reported that the distance between the upper part of the impeller and the liquid surface in the vessel must be adjusted if one wants to ensure

5.3. Effect of the Maxblend paddle design When mixing highly viscous non-Newtonian shear thinning fluids with yield stress, velocities in the tank tend to decrease with an increase in the viscosity and the flow behavior index. It is very important to increase fluid flow velocities through impeller modifications at a constant power input, where it is often not feasible to increase the motor power for vessels with large geometrical dimensions [42]. In this part of the paper, another modification to the Maxblend impeller design is done. It concerns the impeller bottom shape. Three geometries are realized in the purpose of maximizing the flow energy efficiency at the lower part of the vessel (see Fig. 13). Predicted results of the flow energy efficiency are presented along the tank wall (Fig. 14) and along the vessel radius at a vertical position Z* ¼ 0.22 (near the vessel base) (Fig. 15). To give a different perspective on the type of deformations induced by the impeller, we show in Fig. 16 the spatial distribution of the flow energy efficiency h at an horizontal cross section corresponding to Z* ¼ 0.18 of level. As clearly illustrated, the geometry denoted C seems to be the best design in term of maximizing the flow energy efficiency near the vessel walls. However, an additional power is required to achieve the mixing operation in the laminar regime (Fig. 17). 6. Conclusion This paper provided a 3D numerical simulation of yield stress fluid flows generated by different impellers within cylindrical vessels. The flow energy efficiency of four impellers is investigated,

Fig. 16. Spatial distribution of the circulation energy efficiency at Z* ¼ 0.18, Rey ¼ 100.

H. Ameur / Energy 93 (2015) 1980e1988

Np

Vz Vq Vr R R* Z Z*

27 26 25 24

22 A

B

C

Geometry

Fig. 17. Power number for Rey ¼ 10.

namely: a Maxblend, an anchor, a gate and a double helical ribbon impeller. Following a descending order in the power consumption for the four agitators: DHR > gate > anchor > Maxblend. The DHR impeller was found to be efficient to improve mixing near the free surface of liquid but with more power drawn. As a comparison in term of circulation energy efficiency, it was found that the particular shape of the Maxblend impeller (paddle at the bottom surmounted by a grid) proved to be very efficient for generating efficient mixing at a low power consumption. The modifications performed to the Maxblend impeller design allowed to choose the geometry denoted C as the best design in the purpose of maximizing the flow energy efficiency. To ensure great flow energy efficiency, the design of the lower part of the impeller must follow the shape of the vessel base. For a low impeller rotational speed, a low clearance from the tank bottom is also needed. A better mixing quality and more energy savings can be achieved by considering these concluding remarks in the design of continuous-flow mixing of shear thinning fluids with yield stress. More studies on the subject may be very interesting, especially for viscoelastic fluid flows with the heat transfer phenomenon. Nomenclature

h

Rey V

axial velocity (m/s) tangential velocity (m/s) radial velocity (m/s) radial coordinate (m) dimensionless radial coordinate, R* ¼ 2R/D vertical coordinate (m) dimensionless vertical coordinate, Z* ¼ Z/D

Greek letters : average shear rate (1/s) gavg r fluid density (kg/m3) t shear stress (Pa) ty suspension yield stress (Pa)

23

c d d1 d2 h1 h2 h1 n D ds H K Ks N P Np Q NQ

1987

impeller off-bottomed clearance (m) impeller diameter (m) Maxblend paddle diameter (m) Maxblend grid diameter (m) paddle height (m) grid height (m) impeller height (m) flow behavior index (dimensionless) tank diameter (m) shaft diameter (m) vessel height (m) consistency index (Pa sn) MetznereOtto's constant (dimensionless) impeller rotational speed (1/s) power (W) power number (dimensionless) flow rate (m3/s) flow number (dimensionless) flow energy efficiency (dimensionless) yield stress Reynolds number (dimensionless) velocity (m/s)

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