Available on line at

Association of the Chemical Engineers AChE

www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 16 (4) 379−386 (2010) CI&CEQ

AOYI OCHIENG1 CFD SIMULATION OF THE HYDRODYNAMICS

MAURICE S. ONYANGO2 AND MIXING TIME IN A STIRRED TANK
1
Vaal University of Technology,
Private Bag X021 Vanderbijlpark, Hydrodynamics and mixing efficiency in stirred tanks influence power draw and
1900, South Africa are therefore important for the design of many industrial processes. In the pre-
2
Department of Chemical and Me- sent study, both experimental and simulation methods were employed to deter-
tallurgical Engineering, Tshwane mine the flow fields in different mixing tank configurations in a single phase
University Technology, Pretoria, system. Laser Doppler velocimetry (LDV) and computational fluid dynamics
Private Bag X680 Pretoria, 0001, (CFD) techniques were used to determine the flow fields in systems with and
South Africa without a draft tube. There was reasonable agreement between the simulation
and experimental results. It was shown that the use of a draft tube with a Rush-
SCIENTIFIC PAPER ton turbine and hydrofoil impeller resulted in a reduction in the homogenization
energy by 19.2 and 17.7%, respectively. This indicates that a reduction in the
UDC 66.06:532.51 operating cost can be achieved with the use of a draft tube in a stirred tank and
there would be a greater cost reduction in a system stirred by the Rushton tur-
DOI 10.2298/CICEQ100211040O
bine compared to that stirred by a propeller.
Key words: Draft tube; CFD; solids concentration; stirred tank; simulation.

The performance of a stirred tank depends on meter and that the highest flow per power can be ob-
mixing, which influences many chemical reaction rates tained by this device, especially if used in a fully baf-
as well as the product quality. For this reason, many fled tank. A small draft tube cross-sectional area re-
mixing studies have been conducted in different tank sults in a higher velocity in the core than the annulus.
configurations stirred by various types of impellers. In This leads to an increase in head loss, which is a
most of these studies, conventional impellers such as function of the square of the fluid velocity in the draft
the Rushton turbine [1,2] pitched blade impellers have tube [7]. Ochieng [8] reported that the bottom clear-
been employed[3,4]. Relatively few studies have been ance of the draft tube should be the same as that of
carried out using round or dished-bottomed tanks fit- the impeller, especially if the impeller is a radial pump-
ted with draft tubes [5,6]. ing one.
A draft tube is typically employed to enhance In recent studies, the revelation of many salient
axial mixing in stirred tanks and this promotes homo- mixing features of multiphase systems has been pos-
geneity. In multiphase processes, it is important to at- sible due to the use of computational fluid dynamics
tain bed homogeneity in order to promote interphase (CFD) and laser Doppler velocimetry (LDV) techni-
heat and mass transfer. It has been reported [5] that ques [8,9]. The information obtained from the CFD
draft tubes improve mixing efficiency without causing simulation of the flow field, mixing time and power is
too much shear or turbulence intensity that could lead necessary for the identification of the tank dead zo-
to particle attrition. In this regard, efficient mixing can nes, which affect mixing efficiency in a stirred tank.
be achieved by specifying optimum operating para- The mixing efficiency can be determined from homo-
meters such as impeller speed and phase hold up as genization energy, which is the product of the mixing
well as design parameters. In particular, the bulk fluid time and the corresponding power dissipated [10]. A
flow is influenced by the liquid level above the draft remarkable effort has been expended in simulating
tube. It was earlier reported [7] that the draft tube bot- mixing time and power in flat-bottom tanks stirred
tom clearance should be at least one draft tube dia- using the Rushton turbine [11–14]. Such efforts have
been constrained by the available computational po-
wer. In particular, simulation of mixing time is compu-
Correspondening author: A. Ochieng, Vaal University of Tech-
nology, Private Bag X021 Vanderbijlpark, 1900, South Africa.
tationally expensive and modelling curved surfaces
E-mail: aoyio@yahoo.com such as those of propeller and elliptically bottomed
Paper received: 11 February, 2010 tank just makes the modelling work more complex.
Paper revised: 10 July, 2010
Paper accepted: 13 July, 2010
The previous authors studied the effect of draft tube

379
A. OCHIENG, M.S. ONYANGO: CFD SIMULATION OF THE HYDRODYNAMICS… CI&CEQ 16 (4) 379−386 (2010)

on flow field in a system stirred using either the Rush- Power (P) exerted on the baffles was calculated
ton turbine or a propeller. Most of the studies were as:
done using flat bottomed tanks and, to the best on our
P = 2π MN (4)
knowledge, no comparison was made between flow
field in such systems and in elliptical bottomed tanks where M is the torque and the mean kinetic energy
with regards to impeller and draft tube influence. As a dissipation rate is given by:
result, a lot of work still needs to be done in simu-
P
lating such systems in order to get an insight into the ε= (5)
mixing features therein. VTρ
More recently, Ochieng et al. [14] reported that where VT is the fluid volume. The homogenization
at a low impeller clearance and a draft tube can im- energy (η) was calculated as a product of the kinetic
prove mixing in a tank stirred by a Rushton turbine in energy dissipation rate and mixing time:
a flat bottomed tank. It is of interest, therefore, to
compare the performance of this impeller with the η = ετ 90 (6)
axial one in the same configuration and in elliptical
where τ90 is the time required to achieve 90% homo-
bottom tank. The aim of the present studies is to em-
genization. The mixing time required to achieve 90%
ploy both CFD and LDV techniques to study mixing
homogenization (τ90), for example, is the time it takes
time and power draw in flat and in an elliptically bot-
for the fluctuation of the response signal to be below
tomed tank stirred by axial and radial impellers.
10% of the concentration achieved at perfect mixing.
MODELLING
METHODOLOGY
The hydrodynamics of a stirred tank are gover-
Hydrodynamics and mixing studies were carried
ned by the interaction between the bulk phase (liquid)
out in an elliptically bottomed tank with and without a
flow and the tank geometry, both of which affect mix-
draft tube, using CFD and LDV techniques in single
ing time and energy draw. The flow field is represen-
phase system. Detailed configuration of the mixing
ted by the mass and momentum balance governing
tank is shown in Figure 1. The fluid was water at room
equations. In the present work, the governing equa-
temperature and simulations were run using CFX-
tions are given in a time (Reynolds) averaged form of
-ANSYS codes [15,16]. Figure 2 shows the setup of
the Navier-Stokes equations, for which the conser-
the tank stirred by the standard Rushton turbine and
vation of mass is:
the hydrofoil propeller previously employed by Ochi-
∇ ⋅ ( ρU ) = 0 (1) eng [8]. The impeller diameter (D) was the same
(0.33T) for both the turbine and the propeller, and the
where ρ and U are the density and the mean velocity
vector, respectively. The momentum conservation
equation is given by:
∂ρU
+ ∇ ⋅ ( ρU ×U ) = −∇ ⋅ p +
∂t (2)
+∇ ⋅ μ [∇ ⋅U + (∇ ⋅U )T ] + FB

where p is the pressure, μ is the dynamic molecular

viscosity, FB represents body forces including Coriolis
and centrifugal forces. Mixing time was calculated from
the transport equation in which the transport quantity
(φ) was the tracer mean volume fraction:

∂ρϕ  μT  
+ ∇ (ϕρU i ) = ∇  Γ +  ∇ϕ  (3)
∂t  σT  
where Γ and μT are the molecular and turbulent dif-
fusivities, respectively, σT is the turbulent Schmidt
number. The value of σT is lies between 0.5 and 1,
depending on the flow. In this case, after a few trials,
the value of σT was taken as 0.7. Figure 1. Reactor configuration.

380
A. OCHIENG, M.S. ONYANGO: CFD SIMULATION OF THE HYDRODYNAMICS… CI&CEQ 16 (4) 379−386 (2010)

Figure 2. LDV experimental set-up.

impeller speed (N) was 5 rps, which corresponds to CFD Simulation

an impeller Reynolds number (Re) of 7.81x104. The A quarter of the tank was simulated in the case
tank diameter (T) was 0.38 m and the fluid level (H) of H15T while for the case of R15T, a half of the tank
was 1.3T. The top and bottom clearance was 0.15T, was simulated. For both cases, three grid sizes cor-
and the bottom clearance was the same for both im- responding to half tank were used, with the total num-
pellers. The bottom clearance was taken as the dis- ber of cells being 216000, 436000 and 700000, for
tance from the centre of the hub (or the level of the the coarse, base and fine grids, respectively. The si-
disc, for the Rushton turbine) to the tank bottom. mulations were run on two P4, 2 GB memory, 3 GHz
In the configurations studied, the Rushton tur- PCs using CFX5.7 codes [15,16]. For all the simula-
bine (RT) or the hydrofoil impeller (HI) was employed tion work, the impeller shaft and the gravitational for-
with and without a draft tube. These configurations ce were defined along the x-axis. The blades, disc
are hereafter denoted by R15T for the Rushton turbi- (for the Rushton turbine) and baffles were defined as
ne stirred tank, in which the impeller clearance is thin surfaces, and grids were refined in the wall and
0.15T. Similarly, H15T represents the hydrofoil pro- impeller regions. A free surface boundary condition
peller located at 0.15T from the bottom. The respec- was defined at the liquid surface, where the shear
tive systems with a draft tube (DT) are denoted by stresses were set to zero. On the walls, a no-slip con-
R15T-DT and H15T-DT. dition was specified for the liquid. The standard k-ε
model was employed with both the multiple frames of
EXPERIMENTAL reference (MFR) and sliding grid (SG) approaches,
both of which were developed by Luo et al. [19,20].
Figure 2 shows the LDV experimental setup for
The steady state MFR approach was employed only
which a detailed experimental procedure has been
to generate the initial result for the subsequent use in
described by Wu and Pullum [17]. The LDV probe
the unsteady state SG runs. The semi-implicit pres-
was mounted on a robotic arm as shown in Figure 2
sure linked equation-consistent (SIMPLEC) algorithm
and the measurements of the three velocity compo-
was used to couple the pressure and momentum
nents were taken in the middle of two baffles (θ = 0o).
equations. Equation solvers such as the block Stone
Details of the flow field determined using the LDV and
and algebraic multi-grid [15] were employed with the
mixing time determined using both decolourization
quadratic time differencing scheme. The interconnec-
and conductivity methods for similar configurations
tivity between the rotating and stationary domain was
have been presented elsewhere [14,18]. The working
achieved by the general grid interface (GGI) algorithm
vessel was encased in an outer transparent trough
[15].
with a square cross-section, and both filled with tap
Figure 3 shows the simulation domain meshed
water to a required depth. A conductivity meter [14]
using unstructured grid, which is better than the struc-
was employed to measure the mixing times that were
tured grids for creating domains with high curvature.
used to validate the simulated ones. Consequently,
The initial simulations were run to evaluate the perfor-
the mixing times presented in this work are the simu-
mance of the discretization schemes such as upwind,
lated ones.
hybrid, higher upwind and quadratic upstream inter-

381
A. OCHIENG, M.S. ONYANGO: CFD SIMULATION OF THE HYDRODYNAMICS… CI&CEQ 16 (4) 379−386 (2010)

(a) (b)

Figure 3. Modeled section showing mesh distribution: a) top view; b) side view.

polation for convective kinetics (QUICK). Full hydro- were more precise but those of higher schemes were
dynamic equations were solved for the flow field and more accurate. As a result, the data obtained using
mixing time. Mixing time was obtained from the mean the upwind scheme was used to initialize the simula-
value of the mixing time obtained from five simulated tions for further runs with higher order discretization
probes at different part of the domain. Grid indepen- schemes. The influence of these schemes on the flow
dence studies were carried out using coarse, base field was investigated in the upper (x = 0.8T) and
and fine grids. For the value of the mixing time, the lower (x = 0.21T) regions of the tank. In addition to
difference between based and coarse grid was cal- the convergence of mass residuals, at the end of a
culated and found to be less than 3%. simulation, the total mass of the traced in the domain
was computed and compared with the quantity that
RESULTS AND DISCUSSION was originally introduced into the domain, and it was
found that the total mass remained the same. Further,
Grid independence analysis showed that there it was ensured that the torque on the wall baffle was
was minimal difference between the base and fine constant and the mass imbalance in all sub-domains
grid, consequently. Subsequently, the base grids were was less than 1%.
used for the studies and a reasonable agreement It is shown in Figure 4 that there was a marginal
between the simulation and the experimental results influence of the discretization schemes on the predic-
was obtained. The CFD simulation of the fluid flow tion of the axial velocity profile. Figure 4a shows that
revealed the presence of circulation loops. The orien- the hybrid scheme gave a reasonable prediction in
tation of the loops changed with the impeller clear- the lower region of the tank whilst in the upper region
ance, and the centres of the loops represented dead (Figure 4b), predictions by all three schemes were
zones, which affected both the mixing time and power poor. However, the prediction with the hybrid scheme
draw. The draft tube was shown to improve the flow was, in general, better than the other two schemes.
pattern and consequently, the mixing efficiency by The basis of comparison was the experimental results
suppressing or eliminating the loops. These observa- of the flow field and mixing time as has been shown in
tions are in agreement with the results reported by a previous work [14].
Montante et al. [21] and Ochieng et al. [14]. It is shown in Figure 4 that the predictions in the
Discretization schemes impeller discharge region, in which the cell Peclet
number (Pe) is higher, are better than in the top re-
A very good convergence of the mass residuals
gion. Due to the high cell Peclet number (which is a
up to 1.0x10–6 obtained with the first order discreti-
measure of the relative strengths of diffusion and con-
zation scheme (upwind differencing scheme) was
vection) in the lower region, it is expected that the
lower than that for higher order schemes for which 10-5
hybrid scheme effectively becomes the upwind sche-
was the minimum value obtained. However, the re-
me in this region. However, it is known that this first-
sults obtained using the upwind scheme were a gross
-order scheme (upwind) is prone to numerical diffu-
over-prediction of the velocity field by as much as
sion, especially in high Reynolds flow regions like the
120%. This is an indication that the upwind results
impeller discharge region. The fact that better predic-

382
A. OCHIENG, M.S. ONYANGO: CFD SIMULATION OF THE HYDRODYNAMICS… CI&CEQ 16 (4) 379−386 (2010)

0.4 0.08
(a) x=0.21T (b) x=0.80T
0.2
0.04
0.0
U/Vtip

U/Vtip
0.00
-0.2
-0.4 -0.04

-0.6 -0.08
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
r/R r/R
Figure 4. Effect of discretization scheme on the axial velocity profile: experiments (), higher upwind (), hybrid () and QUICK ().

tions were obtained with this scheme in this region almost the entire liquid height. This is opposed to the
suggests that the discretization schemes were not the double loop flow pattern that is characteristic on flat-
major factors influencing the accuracy of the results. -bottom tanks. The upward velocity was highest in the
The predictions by the higher upwind scheme were region where r/R>0.8 and this can be attributed to the
better in the impeller region than in the upper tank re- effect of the wall jet. In the region where r/R is less
gion. than 0.8, the fluid was moving downwards. Further,
The QUICK scheme, which is third order accu- the axial velocity, which is dependent on the wall jet,
rate, is the most computationally demanding and the decreased with the tank height due to the attenuation
simulations in which it was used could not converge of the momentum generated by the wall jet. The uni-
easily. Even when the residuals finally settled, the le- formity of the upward and downward flow was achiev-
vel of convergence could not go below 4.5x10-4, ed by using a draft tube for which the cross-sectional
which was the worst convergence in comparison to area of the core was the same as that of the annulus.
the other two schemes. This could be attributed to the This geometry results in an equal fluid velocity being
lower diagonal dominance [22], which leads to un- attained in the annulus and draft tube where r/R = 0.7.
boundedness of the solution. A solution is unbound if The flow field for the configuration with a draft tube
it is outside the prescribed boundary conditions. For has been reported elsewhere [14].
the maximum downward velocity, the higher upwind A comparison was made between the flow ge-
scheme gave the highest over-estimation. The maxi- nerated in the flat and elliptically bottomed tanks by
mum upward and downward velocity values give an the Rushton turbine at a clearance of 0.15T. Simu-
indication of the magnitude of the circulation flow. An lation results in Figure 6 show that there was a higher
over-prediction of these parameters is indicative of an (by 16%) axial velocity in the elliptically bottomed tank
over-prediction of the circulation flow. The over-pre- than the flat-bottomed one. This can be attributed to
diction of these parameters with the QUICK scheme the elimination of the minor circulation loop at the bot-
in Figure 4 is in agreement with the work of Brucato et tom edge of the tank. These minor loops act as sinks
al. [23], in which it was reported that the QUICK sche- for the momentum convective transport. In an ellipti-
me over-predicts the circulation rate. The maximum cally bottomed tank, the downward impeller jet is
upward velocity was over-predicted by all schemes. In smoothly deflected upwards rather than being parti-
general, Figure 4 shows that the best predictions ally damped as is the case in the flat-bottomed tank.
were obtained by the standard k–ε model and the hyb-
Mixing time and energy dissipation
rid scheme. Therefore, the standard k-ε model and
the hybrid discretization scheme were subsequently Mixing efficiency was evaluated by calculating
employed. the homogenization energy from the dimensionless
mean kinetic energy dissipation rate,⎯ε. The torque on
Flow field the wall baffles was used to calculate power from Eq.
Figure 5 shows that the secondary circulation (3), and this was in turn used to compute⎯ε from
loop that is typically found below the impellers at the Eq. (4) and the power numbers (Np) in Table 1. The
standard clearance (0.33T) was suppressed. This can power number predictions obtained using this method
be attributed to the low impeller bottom clearance that were much closer to the experimental results than
was used. This observation is in agreement with pre- those obtained from the local simulation values of the
vious findings [9,21]. The upward stream was confi- turbulent kinetic energy dissipation rate. The power
ned to the region closer to the wall, and this can be number for R15T was found to be 3.4, which is in
attributed to the effect of the wall jet, which covered reasonable agreement (12% difference) with the ex-

383
A. OCHIENG, M.S. ONYANGO: CFD SIMULATION OF THE HYDRODYNAMICS… CI&CEQ 16 (4) 379−386 (2010)

(a) (b)

Figure 5. Axial velocity profile in the H15T configuration: a) fringe; b) vector plots between the blades.

perimental value of 3.8 [1]. The under-prediction of circulation, leading to a reduction in the azimuthal mo-
the power number can be attributed to the under-pre- mentum, which is responsible for the torque on the
diction of the torque, which is calculated from the baffles. The use of the draft tube resulted in a reduc-
azimuthal momentum component. An accurate com- tion in the homogenization energy by 19.2 and 17.7%
putation of this momentum depends on the tangential for R15T and H15T, respectively (Table 1). In a flow
velocity component, which has been shown to be generated by H15T, there are relatively less circula-
poorly predicted by the k–ε model [8,20]. In addition, tion loops (Figure 5) to be suppressed by a draft tube
the accuracy of the simulations based on Reynolds as compared to a flow generated by H15T. This could
averaged Nervier–Stokes has been pointed out in many explain the slightly higher reduction of the homoge-
studies. nization energy in the flow generated by R15T com-
pared to that for H15T. The Rushton turbine generally
0.4 generates double loop flow pattern which is charac-
x=0.3T terized by chaotic fluid flow, and this results in high
0.2 energy dissipation. In contrast, the propeller (H15T)
generally creates a smooth flow characterized by one
U/Vtip

0.0
major loop. As a result, the introduction of a draft tube
the R15T system does not change the flow pattern as
-0.2
much as it does for H15T.
-0.4
Table 1. Mixing time and homogenization energy simulation
0.0 0.2 0.4 0.6 0.8 1.0
r/R (η =⎯ετ90) with ⎯ε from Eq. (4); N = 5 rps
2 -3
Figure 6. Comparison of the axial velocity profiles in flat and Configuration τ90 / s Np ⎯ε / m s η / m2 s-2 Δη / %
elliptically bottomed tanks, H15T: elliptical (); flat (). R15T 6.47 3.40 0.09 0.59
R15T-DT 5.94 2.75 0.08 0.48 19.17
It is apparent that⎯ε for R15T was higher than H15T 6.04 1.11 0.06 0.35
that for H15T, and this is due to the higher power H15T-DT 5.65 0.92 0.05 0.29 17.74
number obtained in the R15T configuration. However,
most of this energy was dissipated in the lower region CONCLUSION
of the tank. The power numbers for the system with
the draft tube were lower than those without. This is Hydrodynamics and mixing in a stirred tank was
due to the fact that the draft tube enhances the fluid investigated using computational fluid dynamics (CFD)

384
A. OCHIENG, M.S. ONYANGO: CFD SIMULATION OF THE HYDRODYNAMICS… CI&CEQ 16 (4) 379−386 (2010)

simulation and laser Doppler velocimetry techniques. μ Molecular viscosity, kg m-1 s-1
The influence of a draft tube on mixing time and po- ν Viscosity, m2 s-1
wer draw was studied in flat and in an elliptically bot- ρ Density, kg m-3
tomed tank stirred by axial and radial impellers. In the Γ Diffusion coefficient, kg m-1 s-1
CFD application, the effect of discretization schemes
(first and higher order schemes) on the simulation REFERENCES
results was investigated. The results obtained using
[1] G. Montante, K. Lee, C.A. Brucato, M. Yianneskis, Can.
the hybrid discretization scheme, compared to experi-
J. Chem. Eng. 77 (1999) 649-659
mental data, were as good as or better than those of
[2] M. Kraume, P. Zehner, Trans. Inst. of Chem. Eng. 79A
the third-order accurate upwind scheme (QUICK). This
(2001) 811-818
shows that a higher-order scheme does not neces-
[3] Z. Jaworski, A. W. Nienow, K.N. Dyster, Can. J. Chem.
sarily give better predictions for the systems investi-
Eng. 74(1) (1996) 3-15
gated. The use of a draft tube resulted in higher (19.2%)
[4] B. Kuzmanic, N. Ljubicic, Chem. Eng. J. 84(3) (2001)
homogenization energy reduction in the Rushton tur- 325-333
bine stirred tank than that (17.7%), in the hydrofoil im- [5] A. Cate Ten, J.J. Denksen, H.J.M. Kramer, G.M. van
peller stirred tank. This is an indication that a reduc- Rosemalen, H.E.A. van den Akker, Chem. Eng. Sci. 56
tion in the operating cost can be achieved with the (2001) 2495-2509
use of a draft tube. [6] Z. Wang, Z. Mao, C. Yang, X. Shen, Chin. J. Chem. Eng.
14 (2006) 713-722
Acknowledgement
[7] J.Y. Oldshue, Fluid mixing technology, McGraw Hill, New
Contributions by Prof. Alison E. Lewis and Dr York, 1983, p. 15
Paul Musonge are gratefully acknowledged. [8] A. Ochieng, PhD Thesis, Univ. of Cape Town, 2005

Symbols [9] H. Wei, W. Zhou, J. Garside, Ind. Eng. Chem. Res. 40

(2001) 5255-5261
CFD Computational fluid dynamics [10] M. Bouaifi, M. Roustan, Chem. Eng. Proc. 40 (2001) 89-95
D Impeller diameter, m [11] Z. Jaworski, W. Bujalski, N. Otomo, A.W. Nienow, Trans.
Fc Centrifugal force, N Inst. Chem. Eng. 78A (2000) 327-333
Fce Coriolis force, N [12] G. Montante, M. Moštěk, M. Jahoda, F. Magelli, Chem.
H Fluid depth, m Eng. Sci. 60 (2005) 2427-2437
k Dimensionless turbulent kinetic energy [13] K.H. Javed, T. Mahmud, J.M. Zhu, Chem. Eng. Proc.
LDV Laser Doppler velocimetry 45(2) (2006) 109-112
M Torque, N m [14] A. Ochieng, M.S. Onyango, A. Kumar, K. Kiriamiti, P. Mu-
MFR Multiple frame of reference songe, Chem. Eng. and Proc. J. 47(5) (2008) 842-851
N Impeller speed, s-1 [15] AEAT, CFX5 CFD Services, Harwell, Oxfordshire, AEA
P Power, W Industrial Technology, 2003
p Pressure, kPa [16] ANSYS, CFX5 Flow solver user guide, www.ansys.com,
Pe ρu/(Γ/Δx) 2004
R Ratio of the diameter of the draft tube to that [17] J. Wu, L. Pullum, Trans. Inst. Chem. Eng. 79A (2001)
of the column 989-997
r Tank radius, m [18] A. Ochieng, M.S. Onyango, Chem. Eng. Proc. J. 47 (2008)
SG Sliding grid 1853–1860

t time, s [19] J.Y. Luo, R.I. Issa, D.A. Gosman, ICHEME Symp. Ser.
136 (1994) 549-556
T Tank diameter, m
[20] J.Y. Luo, D.A. Gosman, R.I. Issa, J.C. Middleton, M.K.
U axial velocity, m/s
Fitzgerald, Trans. Inst. Chem. Eng. 71A (1993) 342-344
Vtip Impeller blade tip velocity, m/s
[21] G. Montante, K. Lee, C.A. Brucato, M. Yianneskis, Chem.
xi Cartesian coordinates
Eng. Sci. 56 (2001) 3751-3770
Δx Dimensionless cell width
[22] J. Aubin, D.F. Fletcher, C. Xuereb, Exp. Therm. Fluid Sci.
Greek symbols 28(5) (2004) 431-445
⎯ε Mean specific kinetic energy dissipation rate, [23] A. Brucato, M. Ciofalo, F. Grisafi, G. Micale, Chem. Eng.
m2 s-3 Sci. 53(21) (1998) 3653-368.
η Homogenization energy, m2 s-2

385
A. OCHIENG, M.S. ONYANGO: CFD SIMULATION OF THE HYDRODYNAMICS… CI&CEQ 16 (4) 379−386 (2010)

AOYI OCHIENG1 SIMULACIJA HIDRODINAMIKE I VREMENA MEŠANJA U

MAURICE S. ONYANGO2 SUDU SA MEŠANJEM POMOĆU RAČUNARSKE
1
Vaal University of Technology,
Private Bag X021 Vanderbijlpark, TEHNIKE STRUJANJA FLUIDA
1900, South Africa
2 Hidrodinamika i efikasnost mešanja u sudovima sa mešanjem utiču na snagu mešanja,
Department of Chemical and Me-
tallurgical Engineering, Tshwane pa su zbog toga značajni za projektovanje mnogih industrijskih procesa. Da bi se odre-
University Technology, Pretoria, dila strujna polja u sudovima različite konfiguracije, u ovom radu su korišćene i ekspe-
Private Bag X680 Pretoria, 0001, rimentalne i simulacione metode. Tehnika merenja brzine laserskim Doplerom (LDV) i
South Africa računarska tehnike simulaije strujanja fluida (CFD) su primenjene radi određivanja struj-
nih polja u sistemima sa i bez centralne cevi. Utvrđeno je prihvatljivo slaganje između
NAUČNI RAD simulacija i eksperimentalnih rezultata. Upotrebom centralne cevi u kombinaciji sa Raš-
tonovom turbinskom mešalicom ili propelerskom mešalicom tipa Hydrofoil smanjuje se
potrebna energije za homogenizovanje za 19,2 i 17,7%, respektivno. Ovo ukazuje da se
smanjenje u operativnim troškovima može postići upotrebom centralne cevi u sudu sa
mešanjem, kao i da će se troškovi više smanjiti u sistemu sa Raštonovom turbinskom
mešalicom nego u sistemu sa propelerskom mešalicom.
Ključne reči: centralna cev; CFD; koncentracija čvrste faze; sud sa mešanjem;
simuacija.

386