Elsevier Editorial System(tm) for Water Research Manuscript Draft Manuscript Number: WR16241 Title: An approach to improve the separation of solid-liquid suspensions in inclined plate settlers: CFD simulation and experimental validation Article Type: Research Paper Keywords: Keywords: Computational fluid dynamics (CFD), Residence time distribution (RTD), Plug flow, Nonideal flow, Inclined Plate Settlers, Sedimentation. Corresponding Author: Mr. ahmed ibrahim salem, M.Sc. Corresponding Author's Institution: Centre for Environmental Research & Technology (UFT) First Author: ahmed ibrahim salem, M.Sc. Order of Authors: ahmed ibrahim salem, M.Sc.; George Okoth, M.Sc.; Jorg Thöming, Professor Abstract: The most important requirements for achieving effective separation conditions in inclined plate settler (IPS) are its hydraulic performance and the equal distribution of suspensions between settler channels, and which both depend on the inlet configuration. In this study, three different inlet structures were used to explore the effect of feeding a bench scale IPS by a nozzle distributor on its separation efficiency. Experimental and Computational Fluid Dynamic (CFD) simulation analysis were carried out to asses both the hydraulic characteristics and separation efficiency. Comparing the experimental results with the predicted results by CFD simulation imply that the CFD software can play a useful role in studying the hydraulic performance of the IPS by employing residence time distribution (RTD) curves. Also, the results show that the using of nozzle distributor can significantly enhance the hydraulic performance of the IPS which has contributed to improve its separation efficiency.
Cover Letter
Covering latter
Dear Water Research Editor I am pleased to submit a manuscript entitled ‘An approach to improve the separation of solid-liquid suspensions in inclined plate settlers: CFD simulation and experimental validation’ in order to be considered as a new submission for the Water Research Journal. The corresponding paper’s author is me (Ahmed I. Salem) and the following is my contact data: Yours Ahmed I. Salem *
Corresponding Author:
Ahmed I. Salem Department of Chemical Engineering – Regeneration and Recycling, Centre for Environmental Research & Technology (UFT), Leobener Strasse D28359 Bremen, Germany. Tel: +49(0) 421 21863495 & Fax: +49(0) 421 2188297 Emails:
[email protected] &
[email protected]
Abstract Click here to download Abstract: Abstract.doc
Abstract The most important requirements for achieving effective separation conditions in inclined plate settler (IPS) are its hydraulic performance and the equal distribution of suspensions between settler channels, and which both depend on the inlet configuration. In this study, three different inlet structures were used to explore the effect of feeding a bench scale IPS by a nozzle distributor on its separation efficiency. Experimental and Computational Fluid Dynamic (CFD) simulation analysis were carried out to asses both the hydraulic characteristics and separation efficiency. Comparing the experimental results with the predicted results by CFD simulation imply that the CFD software can play a useful role in studying the hydraulic performance of the IPS by employing residence time distribution (RTD) curves. Also, the results show that the using of nozzle distributor can significantly enhance the hydraulic performance of the IPS which has contributed to improve its separation efficiency. Keywords: Computational fluid dynamics (CFD), Residence time distribution (RTD), Plug flow, Nonideal flow, Inclined Plate Settlers, Sedimentation.
Research Highlights
The inlet structure of lamella settler (LS) plays important role in the separation process.
Three inlet structures were examined to explore the hydraulic performance of LS that is fed by a nozzle distributor (ND).
The hydraulic performance is studied through distribution of suspension between settlers and flow patterns of entire LS system.
The results show that using of ND can significantly improve the hydraulic performance of LS which has led to improve its separation efficiency.
Residence time distribution is a crucial method for validation of CFD studies.
*Manuscript Click here to download Manuscript: manuscript.doc
Click here to view linked References
1
An approach to improve the separation of solid-liquid suspensions in inclined plate
2
settlers: CFD simulation and experimental validation
3
A. I. Salem, G. Okoth, J. Thöming
4
University of Bremen, Centre for Environmental Research and Technology (UFT), Department of
5
Chemical Engineering – Regeneration and Recycling, Leobener Strasse D28359 Bremen, Germany
6
Abstract
7
The most important requirements for achieving effective separation conditions in
8
inclined plate settler (IPS) are its hydraulic performance and the equal distribution of
9
suspensions between settler channels, and which both depend on the inlet configuration.
10
In this study, three different inlet structures were used to explore the effect of feeding a
11
bench scale IPS by a nozzle distributor on its separation efficiency. Experimental and
12
Computational Fluid Dynamic (CFD) simulation analysis were carried out to asses both
13
the hydraulic characteristics and separation efficiency. Comparing the experimental
14
results with the predicted results by CFD simulation imply that the CFD software can
15
play a useful role in studying the hydraulic performance of the IPS by employing
16
residence time distribution (RTD) curves. Also, the results show that the using of nozzle
17
distributor can significantly enhance the hydraulic performance of the IPS which has
18
contributed to improve its separation efficiency.
19
Keywords: Computational fluid dynamics (CFD), Residence time distribution (RTD),
20
Plug flow, Nonideal flow, Inclined Plate Settlers, Sedimentation.
21
1. Introduction
22
A gravity settler is a common unit with wide application in treatment of water, domestic
23
wastewater and industrial wastewater. Solid-liquid separation efficiency in this type is
24
directly related to the surface area available for settling, but under limited space
25
conditions as it is in industrial wastewater treatment the using of IPS is preferred. It
1
1
provides high space-time yield due to short settling distance and the available settling
2
area is given by the total area of the plates projected on a horizontal surface.
3
Separation efficiency of IPS is usually much below the theoretical performance due to
4
many factors. Okoth et al. (2008) summarised these factors by modelling of suspension-
5
sediment interaction phenomenologically. In their experimental study, they employed a
6
nozzle distributor to improve the hydraulic performance of IPS which is a one of the
7
factors affecting on the separation efficiency. However, they did not investigate in detail
8
the effect of using this nozzle on both distribution of the total flow between the settler
9
channels and flow patterns of the entire IPS system, and which both have a significant
10
impact on the separation performance of the IPS. The equalized distribution of
11
suspension within each settler is important to obtain an equal overflow velocity on
12
every plate, which contributes in improving IPS efficiency. Both inlet configuration and
13
flow patterns could have an impact on the flow field in the IPS. The inlet structure plays
14
a very important role in determining the flow characteristics in the downstream particle
15
separation zone (He et al., 2008), while the flow patterns are essential to determine the
16
flow characteristics in order to achieve a reliable design (López et al., 2008).
17
To explore operational shortcoming and characterize new separation equipment, it is
18
important to understand the reactor hydrodynamics, which may be done by interpreting
19
the reactor residence time distribution (RTD) (Behin and Aghajari, 2008). The residence
20
time distribution of a reactor is one of the most informative characterizations of the flow
21
pattern in a reactor (Gavrilescu and Tudose, 1999). Knowledge of the liquid RTD is
22
important for a number of reasons, such as allowing for accurate modelling of the
23
system and aiding in reactor design to achieve or preserve a desired flow pattern
24
(Behin and Aghajari, 2008).
25
Flow in tanks always deviates from ideal plug flow or complete mixed flow and usually
26
describes as a non-ideal flow pattern. Levenspiels, (1999) described two methods for the
2
1
characterization of non-ideal flow pattern. One is the longitudinal dispersion (LD)
2
model which represents a flow that deviates from plug flow, and the other is the tanks in
3
series (TIS) model which describes the mixing within a single real reactor as a number
4
of equally sized continuous stirred-tank reactors in series (CSTRs). When the number of
5
tanks in series is 1, the model predicts the performance of an ideal CSTR. As the
6
number of tanks in the TIS model is increased the flow within the reactor approaches
7
that of a plug flow reactor (PFR) (Bircumshaw et al., 2006). Both the LD and TIS
8
models are characterised by dispersion number and the number of tanks in series (NTIS)
9
respectively. The TIS model was used in this study because it is mathematically much
10
simpler than the LD model. Also, the NTIS does not depend on the definition of the
11
inlet and exit boundary conditions.
12
Computational fluid dynamics (CFD) has become a powerful tool to conduct reactor
13
design and provide useful detailed information prevailing in the reactors, such as
14
velocity field, concentration distribution, and phase holdup distribution (Zhang et al.,
15
2007). CFD is used typically in simulation of RTD (Patwardhan, 2001; Choi et al.,
16
2004; Moullec et al., 2008; Aubin et al., 2009). CFD codes used in software package
17
such as Fluent, CFX and Cosmos offer different models for numerical solution of
18
Navier Stokes partial differential equations. Generally, the model should be
19
experimentally verified (Thýn et al., 2002).
20
Two turbulent models (k- model and k- model) were implemented in the present
21
study to predict both velocity flow field and RTD curve. Thereafter, the prediction
22
results were compared with the experimental for evaluation.
23
In this study, we demonstrate the influence of hydraulic performance on the separation
24
efficiency of the bench scale IPS which is fed by a nozzle distributor.
25 26
3
1
2. Material and method
2
Three inlet configurations were used to investigate the impact of feeding the IPS by a
3
nozzle distributor on its hydraulic behaviour. Sketches of the employed inlet structures
4
are shown in Fig. 1.
5
The IPS was made of plexiglas with 15 mm thickness and has internal dimensions
6
(100 mm × 80 mm × 480 mm) and was placed on a ramp with an angle inclination 45°
7
in all tests. Three plates with 300 mm long and 5 mm thickness were used in the IPS
8
and made of polyvinylchloride. The three plates could be fixed at any distance from the
9
nozzle apex, and the spacing between plates was 15 mm.
10
2.1. Experimental set-up and procedures
11
Two techniques were used to identify the hydraulic behaviour of the IPS; the first
12
technique is measurement the velocity within every settler by using the colour velocity
13
measurement (CVM) method (United States Department of the Interior Bureau of
14
Reclamation, 1997). The second method is quantified the hydraulic behaviour of the
15
IPS by using residence time distribution (RTD) experiment. Furthermore, to explore the
16
impact of using distribution nozzle on the separation process, the removal of suspended
17
solids (SS) efficiency for the IPS was determined.
18
A small slug of concentration dye solution (potassium permanganate) was injected
19
impulsively into the IPS inlet, and a high resolution digital camera was used to provide
20
the data for the calculation of mean velocity within every settler by computing the
21
required mean time for the dye to travel a known length.
22
The RTD was measured by injecting quickly 3 mL of tracer (KCL, 3 g/l) into the IPS
23
inlet and the tracer concentration at outlet was measured with conductivity probe every
24
5 seconds, using a data acquisition system. The experimental procedures were repeated
25
five times for every flow rate. Then, the fitting of curve was performed to minimize the
26
deviation between experimental data and simulation data.
4
1
The separation efficiency was determined by specifying the concentration of SS in the
2
samples which were collected from the inlet stream and outlet stream. The samples were
3
filtered under pressure through a 0.45 m pore size cellulose nitrate membrane using a
4
compressed air filter model 16249 from Sartorius AG. This was followed by dry mass
5
concentration analysis using a moisture analyser model MA45 also from Sartorius AG,
6
Germany (Okoth et al., 2008).
7
To carry out these tests an experimental setup was constructed. Process flow diagram of
8
the experimental set-up is shown in Fig. 2, which consists of a 35 L storage tank with an
9
aerator mounted at the bottom denoted A. This tank was filled with tap water in both
10
velocity measurement and RTD experiments, while it was filled with suspension which
11
includes crushed walnut shell particles in the separation efficiency test. These particles
12
have density 1.35 g/cm3 and their size distribution have been analysed using the laser
13
diffraction technique, with Malvern (Mastersizer, 2000) analyser. Particle size
14
distribution parameters like d(0.1), d(0.5), d(0.9) were analyzed and the corresponding
15
values were 35, 115, and 235 µm, respectively, where the d(0.1), d(0.5) and d(0.9)
16
values indicate that 10%,50% and 90% of the particles have diameters which are
17
smaller than or equal to the stated size.
18
The feeding of fluid was achieved by using a centrifugal pump denoted B. The flow
19
rates were regulated by using variable direct current–voltage power suppliers in the
20
range 0–24 volt. Between the pump and the inlet, there is a flow meter denoted C. Both the
21
conductivity meter and data acquisition system -denoted D and E- were used in RTD test
22
only. To determine the separation efficiency, t hree sets of samples were collected for each
23
measurement point, from the inlet stream (section 1) and the outlet stream (section 2).
24 25 26
5
1
2.2. CFD Simulations
2
CFD analysis using CFX-10 from ANSYS was performed by employed the standard k-
3
model and k- model, where k, , denote turbulent kinetic energy, turbulent
4
dissipation rate, turbulent frequency, respectively.
5
For wall-bounded flows, as in IPS, the standard k- model neglects the effects of
6
viscosity in the near-wall region, and it is valid for turbulent core flow (Hrenya et al.,
7
1995). A scalable wall function is adopted in CFX to improve the near wall treatment by
8
limiting the value of the dimensionless distance from the wall (y+) to be ≥ 11.06, (where
9
11.06 is the intersection between the logarithmic and linear near wall profile), which
10
prevents the mesh points falling within the viscous sub-layer. Then, all fine mesh
11
inconsistencies are avoided (Grotjans and Menter, 1998). On the other hand, an
12
automatic near wall treatment is used in the k- model by Wilcox (1988), which
13
provides an analytical solution for in both the logarithmic and the viscous regions.
14
The idea behind the automatic wall treatment is that the model shifts gradually between
15
a viscous sub-layer formulation and wall functions, based on the grid density near wall
16
(Cheng and Tak, 2006).
17
The two models were selected in this study for purposes of comparison, and to find out
18
which model would be closed to experimental results.
19
The governing equations of mass and momentum were determined using the Reynolds
20
averaged Navier-Stokes Eqs. 1 and 2
21
U 0 t
22
U U U p' eff U eff U B t
23
Where is the liquid density, B is the sum of body forces, U is the mean velocity
24
vector, p’ is the modified pressure and eff is the effective viscosity.
(1)
6
(2)
1
The modified pressure is given by
2
p' p
3
While the effective viscosity is estimated by
4
eff t
5
Where t is the turbulent viscosity which is given by
6
t C
7
t
8
Both equations (5) and (6) were employed for k-and k-models respectively.
9
The values of both k and in k- model are estimated from the equation 7 and 8
2 k 3
(3)
(4)
k2
(5)
k
(6)
10
respectively
11
eff k Uk Pk k t k
(7)
12
eff U C 1 Pk C 2 t k
(8)
13
Where Pk is the shear production due to turbulence
14
While the values of both k and in k- model are estimated from the equation 9 and 10
15
respectively
16
k Uk Pk k t k t k3
(9)
17
U Pk 2 t t k
(10)
18
Where Pk is the production rate of turbulence
19
The set of the k- model constants is Cμ = 0.09, Cε1 = 0.1256, Cε2 = 1.92, σk = 0.9,
20
σε = 1.3.
7
5 3 ,= , σk = 2, σ = 2. 9 40
1
While the values of k- model constants are ’ =0.09, =
2
The simulation was performed in two stages. First stage, steady-state turbulent flow was
3
solved, using both the k-ε model and k- model individually to getting velocity profiles,
4
kinetic energy, eddy energy, and eddy diffusivity. Second stage, the information of the
5
flow field and turbulent field obtained was used to solve a non-reacting scalar transport
6
equation, based on the assumption that the tracer is dispersed in the tank by convection
7
and diffusion as follows:
8
U D t t Sct
9
Where is the tracer concentration, / is the conserved quantity per unit mass, S is a
10
volumetric source term, D is the kinematic diffusivity for the scalar and Sct the
11
turbulence Schmidt number, indicating the ratio between the rate of momentum
12
transport and passive scalars (ANSYS Inc., 2005; Zhang et al., 2007).
13
The used tracer was KCL which has molecular diffusivity 1.703x10-9 m2/s (Griffiths et
14
al., 1915).
15
The boundary conditions for the system were as follow, IPS wall, nozzle distribution,
16
and lamella plates were assumed as standard wall boundary conditions with no-slip
17
flow. The boundary condition at the inlet was set as mass flow rate with a value from 55
18
to 97 g/s, whereas the boundary condition at the outlet was set as average static pressure
19
across the outlet area. The mesh structures for LS1, LS2 and LS3 have contained
20
1.09x106, 1.2 x106 and 1.07 x106 elements respectively.
21
By determining the tracer concentration at outlet from the transient results, the
22
residence time distribution could be computed as follow:
23
C t outlet t
S
(11)
(12)
8
1
The normalized concentration E(t) is used to compare RTD curves under different flow rate
2
conditions, and it is defined by the following equation
3
E t
C t
(13)
C t dt 0
4
The mean residence time is given by
5
tC t dt t C t C t C t dt i
0
tm
i
i
i
(14)
i
0
6
The spread of the residence time curve (variance) is measured by
t C t dt 2
7
2
t t C t t C t C t dt
0
2
2
i
m
i
i
(15)
m
i
i
0
8
The normalized variance is calculated from the following equation:
9
2
2
(16)
t m2
10
Finally the next equation estimates the NTIS
11
NTIS
12
3. Results and discussion
13
3.1. Flow distribution study
14
Owing to our hypothesis is that the IPS efficiency depends on the quality of flow
15
distribution within each settler, the velocity through every settler was determined and
16
used for calculating a standard deviation (SD) as criterion for the flow distribution
17
efficiency. Fig (3) shows that the SD increases as the flow rate increases, indicating
18
decreasing in the flow distribution efficiency. Further, the distribution efficiency clearly
19
depends on the type of inlet structure. It was best for LS3. Whereas the inlet structure of
1
(17)
2
9
1
LS1 has shown worst performance and highest dependency of SD on flow rate.
2
Obviously by using the nozzle distributor can be significantly improved the flow
3
distribution within the IPS.
4
3.2. Hydraulic behaviour study
5
3.2.1. RTD Experiments
6
Runs has been carried out at four different flow rates, with values of 200,250, 300, and
7
350 l/h and RTD curves were described as E(t) versus (t).
8
The influence of flow rate on the normalised concentration curves depending on the
9
inlet structure is shown in Figure (4). As expected, the peak of the curve moves to
10
shorter times with increasing flow rate in the three cases (LS1, LS2 and LS3). Also it
11
was observed a strong tail of the RTD curve in all cases. This leads to more deviation
12
from ideal case (i.e. plug flow) which is undesired for the performance of separation
13
process (Kuoppamäki, 1977; Wilkinson et al., 2000). Furthermore, the existence of tail
14
indicates presence of dead space, which gives an indication of stagnant pockets or
15
recirculation regions. These regions reduce the effective volume and should be kept as
16
small as possible.
17
To quantify the hydraulic performance for the IPS, the NTIS is calculated from the RTD
18
curve. Fig. 5 illustrates the impact of both inlet configuration and flow rate on the NTIS.
19
This figure reveals that the NTIS depends strongly on the inlet structure, also the
20
hydraulic behaviour of LS1 is significantly different from the plug flow as expected due
21
to non use of any an effective inlet device to distribute the suspension. In contrast, the
22
NTIS for LS2 and LS3 is about 7 to 10 indicated tendencies to plug flow.
23
3.2.2 Comparison between numerical simulation and experimental results.
24
Comparing the RTD predicted by CFD simulation with experimental results RTD in
25
figure 6 reveal a good agreement. For LS1 an extreme initial peak with average value at
26
~ 0.50 which indicates a short circuiting stream where is dimensionless time [ = ti
10
1
/Tmean; Tmean= theoretical mean retention time]. Contrarily the average values of initial
2
peak for both LS2 and LS3 reached maximum concentration at = 0.78, and =0.90
3
respectively. This means the hydraulic behaviour of LS3 approaches plug flow
4
conditions (Tchobanoglous et al., 2003).
5
Moreover, it can be generally observed from the figure that the simulated results
6
obtained by k- model match better with experimental observation comparing with the
7
k-model. This is especially the case in both the prediction of time at which the peak
8
concentration of the tracer is observed and the end of the tail. On the other hand, the
9
k-model gives wide difference with the experimental observation. These results could
10
be because of the k- model takes into account the effects of viscosity in the near-wall
11
region.
12
Fig. 6 shows the effect of flow rate on RTD curves. It is noticeable that again with an
13
increase in liquid flow rate leads to decreases in the average residence time as discussed in
14
RTD experiments section. Also, the normalized variances values of LS1 increase as flow
15
rate increases for both experiment and simulation results. On other hand, in both the LS2
16
and the LS3, flow rate did not change the normalized variances values significantly,
17
despite the flow rate increases approximately 2-fold. It indicates a wide working range
18
for both LS2 and LS3.
19
The calculated NTIS from CFD simulations also match well with the experimental
20
finding in Fig. 7. Further, it can be seen from this figure; the values of normalized
21
variances equivalent to 2 to 3 NTIS for LS1, 7 to 9 NTIS for LS2 and 9 to 10 NTIS for
22
LS3. These values again reveal that the LS3 significantly provides best hydraulic
23
behaviour than both LS1 and LS2.
24
3.3. Separation efficiency study
25
The impact of flow rate and inlet configuration on the removal of suspended solids is
26
illustrated in fig. 8. The results reveal that the separation efficiency decreases as the
11
1
flow rate increases for the 3 inlet structures. This could be expected based on the
2
previous results, which indicated that, the hydraulic behavior of IPS decreases with
3
increases in the flow rate. Also it can be observed that the separation efficiency for both
4
LS1 and LS2 closed together from flow rate 200l/h to 250l/h which means that the
5
separation efficiency at low flow rate does not depend largely on the configuration of
6
inlet zone. Moreover it can be seen the separation efficiency of LS1 has dropped rapidly
7
after 250 l/h to the contrary the separation efficiency of both LS2 and LS3 which has
8
decreased gradually after 250l/h. It can be said generally the inlet configuration
9
employed in LS3 has improved both the distribution of flow within every settler and
10
hydraulic behaviour of IPS which have led to improve its separation efficiency.
11
.4. Conclusions
12
The impact of feeding the IPS by a nozzle on distribution of the total flow between IPS
13
channels, flow patterns of the entire IPS system and separation efficiency could be
14
clearly demonstrated via CFD simulation and experiments at different flow rates. The
15
comparison between CFD simulation and experiments data showed better agreement for
16
k- than k- model. Furthermore, the results show that the inlet structure which
17
employed in LS3 is crucial in improving both the distribution of flow within every
18
settler and hydraulic behaviour of IPS, and which both have led to improve the
19
separation efficiency of the IPS.
20
Acknowledgements
21
The authors are grateful to Michael Birkner for manufacturing the experimental set-up
22
and assisting in some experiments. Also the authors would like to thank Lydia Achelis,
23
for her support in the particles size analysis. Further, A. Salem gratefully acknowledges
24
the Egyptian government for providing the financial support for his scholarship through
25
the Missions Department in the Ministry of Higher Education.
26
12
1
Nomenclature
2
B
the sum of body forces, N
3
Cμ, Cε1, Cε2
constants in the k- model dimensionless
4
D
Kinematic Diffusivity, m2/s
5
E(t)
residence time distribution, s-1
6
E()
dimensionless residence time distribution
7
K
turbulent kinetic energy, m2/s2
8
NTIS
number of tanks in series model
9
p’
modified pressure, Pa
10
S
11
Sct
turbulence Schmidt number dimensionless
12
tm
mean residence time, s
13
Tmean
theoretical mean retention time, s
14
ti
time interval, s
15
U
mean velocity vector, m/s
16
Greek Symbols
17
turbulent dissipation rate, m2/s3
18
turbulent frequency, s-1
19
Density, kg/m3
20
eff
effective viscosity, Pa.s
21
t
turbulent viscosity, Pa.s
22
σk, σε, ’, , ,σ
constants in the k- model and k- model dimensionless
23
tracer concentration, kg/m3
24
σ
25
σ
volumetric source term
spread of the residence time curve normalized variance of residence time distribution
13
1
2
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Figure Captions
Fig.1 Sketches of the employed inlet structures. Where LS1 is fed by pipe, LS2 is fed by a nozzle distributor which is surrounded by the IPS wall, and LS3 is fed by a nozzle distributor which is surrounded by an additional cylindrical wall. Fig.2 Process flow diagram of experimental set-up with aerator (A), pump (B), rotameter (C), conductivity probe (D), data acquisition system (E), and sample collection points denoted 1 and 2 in the inlet and outlet streams, respectively, while the stream of withdrawal concentration sediment denoted 3. Fig.3 The influence of both inlet configuration and flow rate on efficiency of flow distribution between lamella plates which is quantified by the standard deviation (SD) for the mean velocity within every settler. Fig. 4 Determined the normalised concentration E curves experimentally for (a) LS1, (b) LS2 and (c) LS3 at flow rates [in l/h] of
200,
250,
300 and
350. Fig. 5 The impact of both inlet configuration and flow rate on approaching plug flow quality quantified by the number of tanks in series model (NTIS). Fig. (6) Comparison of RTD prediction by CFD simulation with experimental results. (a)Q= 200 l/h; (b) Q= 250 l/h; (c) Q= 300 l/h; (d) Q= 350 l/h; model, and
experiment,
k-
k- model.
Fig. (7) Prediction of NTIS by CFD simulation compared with experimental results for (a) LS1, (b) LS2 and (c) LS3.where
Experiment,
k- model and
k- model. Fig. 8: Separation efficiency for a suspension of non-cohesive particles [= (SSin SSout) x100/SSin] as a function of both flow rate and inlet configuration
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