The effect of geometrical parameters on mixing and parallel jets mixing in a liquid static mixer

International Journal of Advanced Research in and Technology (IJARET)
International Journal of Advanced Research in Engineering Engineering
ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 1, Number 1, Sep - Oct (2010), © IAEME
and Technology (IJARET), ISSN 0976 – 6480(Print),
ISSN 0976 – 6499(Online) Volume 1,
IJARET
Number 1, Sep - Oct (2010), pp. 92-111 © IAEME
© IAEME, http://www.iaeme.com/ijaret.html

THE EFFECT OF GEOMETRICAL PARAMETERS ON
MIXING AND PARALLEL JETS MIXING IN A LIQUID
STATIC MIXER
D.S.Robinson Smart
School of Mechanical Sciences, Karunya University
Coimbatore-641 114
E-Mail id: smart@karunya.edu
ABSTRACT
Experimental investigations and computational analysis were carried out to
predict the effect of parallel, vertical liquid jets mixing and the geometrical parameters
which are effecting the mixing in a liquid static mixer. The computer analysis was carried
out by using commercially available CFD software package FLUENT computational
fluid dynamics (CFD) methods [7].An experimental set up was designed and
investigations were carried out to evaluate the parallel and vertical fluid jets mixing in a
static liquid mixer. Conductivity probe technique was used to evaluate the mixing [3].
The results obtained by experimental investigation and computer analysis were compared
and discussed in detail to decide upon the effectiveness of parallel and vertical liquid jets
mixing. The investigations and computer analysis revealed that the mixing efficiency
increases with the opening of parallel ports and the primary fluid nozzle position reaches
50mm with mixing inserts.
Keywords: Parallel jets; Liquid mixing; Static mixing
1. INTRODUCTION
Mixing of two or more ingredients is essential in number of different process
industries such as chemical, pharmaceutical petroleum, plastics, and food processing,
water and waste water treatment plants. There are two major types of mixers are available
namely dynamic and static mixers. The efficiency of mixing depends on the efficient use
of energy to generate flow of the components .Stirred tanks perform the mixing by a
motor driven agitator. This type of mixer is generally employed when the mixing are

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International Journal of Advanced Research in Engineering and Technology (IJARET)

undertaken in successive batches. Static mixers are in-line mixing devices generally
consisting of mixing elements inserted into a pipe. Mixer of this type is used in
continuous operation, with the energy for mixing being derived from the pressure loss
incurred in the process of fluid flow through the elements [7].Over the years there has
been increasing emphasis in the process industries towards continuous type of liquid
mixing wherever practical or feasible and innovative designs for mixing became
apparent. Hence the process industries are in need of a mixing system, which mixes the
liquids, which are having different properties to produce various liquid products with less
power requirement. In the present work an experimental test facility is designed,
developed and the experimental investigations and computational analysis have been
carried out to predict the efficiency of parallel, vertical liquid jets mixing, the effect of
geometrical parameters such as position of driving nozzle, cone angle of divergent
nozzle, position of mixing insert and position of secondary fluid inlet on mixing with a
view to optimize them [10].
2. EXPERIMENTAL SET UP
The experimental set up consists of a centrifugal pump, reservoirs, rotameter, mixing
nozzle, four U tube manometers, control valves and conductivity meter . The primary
fluid is stored in a tank. A control valve is used to regulate the primary fluid discharge.
A centrifugal pump is used to supply the primary fluid from the tank to the mixer.

Figure 1 Experimental set up of parallel and vertical jets mixing nozzle

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As the primary fluid passes through the driving nozzle the velocity of flow
increases as the area of flow decreases as it passes through the driving nozzle.
Consequently there is a decrease in pressure. This drop in pressure creates a suction
pressure in the converging area and the secondary fluid will be drawn. The suction
pressure at the inlet ports of secondary fluid is measured using the manometers. There are
four sets of secondary fluid ports in the mixing nozzle. The ports which are on the left
side of the converging portion are called parallel ports. Ports on the top of the converging
portion are called top ports and ports on the bottom are called bottom ports. Ports which
are normal to the plane of top and bottom ports are called side ports. The position of the
various secondary inlet ports is shown in Figure 2.Three suction nozzles (convergent) are
fabricated with different cone angle 21deg, 23deg and 25 deg.

Top Ports TP1, TP2, TP3, TP4

Parallel Port P1

Side Ports
1,2,3,4
Parallel Port
Down Ports

Parallel Port P4 Parallel Port P3
Figure 2 Locations of parallel, vertical and
circumference secondary fluid ports

Two types of inserts are made and it is braced to a long screw in order to move
the insert to the desired location. Conductivity probes are used to measure the
conductivity of mixed fluid.
EXPERIMENTAL PROCEDURE
The aim of the experiment is to find out the extent of mixing of the two fluids by
providing parallel jets, varying the geometrical parameters like, position of the driving
nozzle, position of the insert and position of the secondary suction inlet and to evaluate
the effect in on mixedness of the mixing nozzle.

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3.1. Experimentation and mixing efficiency
Conductivity or specific conductance is the measure of the ability of the water to
conduct an electric current. Conductivity depends upon the number of ions or charged
particles in water. The specific conductance is measured by passing a current between
two electrodes (one centimeter apart) that are placed into a sample of water. In solution,
the current flows by ion transport. Therefore, an increasing concentration of ions in the
solution will result in higher conductivity values. The Conductivity Probe is actually
measuring in ohms, conductance is measured using the SI unit, siemens (formerly known
as a mho). Since the siemens is a very large unit, aqueous samples are commonly
measured in micro siemens, or µS.
Initially the discharge of primary liquid is kept as 2600 lit/hr by adjusting
the ball valve and the 21º convergent portion is connected with the throat. Parallel port 1
is opened and all the other ports are closed. The secondary fluid discharge is obtained by
noting down the time required for the suction of 500 ml of secondary fluid. The suction
pressure is noted down from the manometer. Mixed fluid samples are collected from the
samples points and the average electrical conductivity of the samples is measured. This
is referred as the mixed fluid conductivity. Standard solution is prepared by taking a
proportion of primary and secondary fluids which is having a ratio of the mixed fluid.
This proportion of primary and secondary fluid will be well mixed by using a stirrer and
the conductivity of mixed fluid is measured. This is referred as the standard conductivity.
The closeness of mixed fluid conductivity with standard conductivity can be taken
as a measure of mixing efficiency. Mixing efficiency is calculated as the ratio of mixed
fluid conductivity and standard conductivity. The effectiveness of mixing of each port is
obtained experimentally by finding out the mixing efficiency (mixing
efficiency=Conductivity of mixed fluid /Standard conductivity of mixed fluid).
The experiment is repeated by opening the parallel ports P1,P2,P3,P4
individually, P1&P3 , P2&P4, P1&P2&P3&P4 combine and the down ports
D1,D2,D3,D4 individually & D1&D2&D3&D4 combine .Samples are collected at the
points 450mm,900mm & 1800mm from the throat entrance . The whole experiments
were repeated by varying the discharge of secondary fluid as 3100lpm & 3600lpm and

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the distance between the tip of the driving nozzle and the throat entrance as 10mm,
20mm, 30mm, 40mm & 50mm.
5. COMPUTER MODELING AND ANALYSIS
5.1. Effect of Voticity and inserts on mixing
Different models have been created by varying geometrical parameters such as
secondary fluid inlet position, cone angle (convergent) of suction nozzle and driving
nozzle position [5,6]. Similarly Each case has been analyzed by keeping port open and
other ports have kept closed and also by varying the position of driving nozzle away from
the throat entrance. Another set of models have been created by providing an inserts in
the throat of the nozzle. All these models have been created by using a pre-processor
called ‘Gambit’. The computer analysis is done by exporting the meshed or grid
generated model form GAMBIT software to the FULENT 6.0 [7].
The Figure 3 shows that the vorticity magnitude reaches the maximum value of
9.56(1/s) thus increases the mixedness, when the driving nozzle position DN is 50 mm &
all the parallel ports are opened. The value of vorticity magnitude reduces to 8.08(1/s)
when all the down ports are opened and leads to less mixing.

Figure 3 Contours of vorticity when all the parallel ports are open.
It can be observed from the vorticity contours that the vorticity is more when the
DN=50 mm and all the down ports are opened. The increase in vorticity leads to more
interaction of mixing fluids and increasing the mixing efficiency. However near the

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inserts the values of vorticity is fluctuating and it is higher near the inserts and low
without inserts .Hence the presence of inserts enhances the liquid-liquid mixing in a static
mixing nozzle and the efficiency of mixing can be increased.
The Figure 3 shows that the vorticity magnitude reaches the maximum value of
9.56(1/s) thus increases the mixedness, when the driving nozzle position DN is 50 mm &
all the parallel ports are opened. The value of vorticity magnitude reduces to 8.08(1/s)
when all the down ports are opened and leads to less mixing. Also the COV is nearing
zero [3] due to more interaction of fluids and more mixing.
5.2. Effect of driving nozzle position on vorticity magnitude

Figure 4 Comparison of experimental, computational and literature results of Vorticity
magnitude when DN=50 mm.

Figure 5 Contours of turbulent kinetic energy distribution with inserts (Lobes ).

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5.3. Effect of Turbulent kinetic energy

Figure 6 Contours of turbulent kinetic energy when parallel ports are opened

Figure 7 Contours of Turbulent kinetic energy when all the down ports are open

It can be seen that the turbulence kinetic energy is maximum in case when the
parallel ports P1 &P2 & P3 & P4 are opened simultaneously and the driving nozzle
position DN is 50mm as it can be observed in Figure 5&6
From the contours of turbulent kinetic energy it is observed that the turbulent
kinetic energy is 1.87x10 m2/s2 when the DN=50 mm and all the parallel ports are opened
and 1.27x10 m2/s2 when DN=50 mm & down ports are opened. The turbulent kinetic
energy is found to be still reducing when any ports is opened individually or combines
with any other port.

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The computational analysis of Belovich [25] also proved that ,the parallel jets
mixing is more effective .The increase of turbulent kinetic energy and vorticty are
responsible for good mixing of fluids. Hence the mixing efficiency increases when
DN=50 mm and all the parallel ports are opened.
5.4. The effect of DN position & LDNP on mixing efficiency when down
ports are open.

Down Ports VS Efficiency
100

95

D1 open
90
Mixing Efficiency %

D2 open
85

D3 open
80

D4 open
75

D1,D2,D3&D4 open
70

65

60
-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50

LDNP ( Distance between tip of the DN to port side wall ) in mm

Figure 8 The effect of DN position & LDNP on mixing efficiency when down ports are
open
Experiments were conducted as mentioned in the section above by opening the
ports alternately by changing the distance between the tip of the driving nozzle to the
entrance of the throat (DN) as 10 mm, 20 mm, 30 mm, 40 mm & 50 mm. When the DN is
changed the distance between tip of the driving nozzle to side wall entrance which is
facing the entrance of the throat(LDNP) also changes as -40 mm(as it is behind the
driving nozzle), -30 mm, -20 mm, -10mm and 0 respectively. Negative sign indicates that
the corresponding port is behind the tip of the driving nozzle.

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It is clear that the mixing efficiency increases with decrease in LDNP when the
D1, D2 opens .Further the LDNP increases and becomes more than 20 mm the mixing
efficiency starts reduces. The mixing efficiency is found to reduce when the D3 & D4
opens and the LDNP becomes 31 mm ,35mm & 45mm as the chance of interaction of
secondary fluid with primary fluid becomes very less (since the tip of the driving nozzle
becomes away from the port side wall).
When the down ports D1, D2, D3 & D4 are opened simultaneously as the area of
contact of the secondary with primary fluid becomes more, the mixing efficiency is found
to be more than the efficiency when individual ports are opened. When the driving nozzle
position (DN) is adjusted to at 10mm, only port D4 is partially open and exposed to the
main stream of primary fluid, hence the efficiency is found to be low. As the DN is
adjusted to 20mm, port D4 is fully exposed to the primary fluid stream and there is an
increase of efficiency. Further there is an increase of mixing efficiency when the DN
becomes 30mm, and the ports D3 and D4 are fully exposed to the primary fluid stream
.When the DN is changed to 40mm, efficiency has increased more than above said three
conditions, as the ports D3&D4 are exposed fully and D2 is partially exposed to the
stream of primary fluid.
The mixing efficiency has reached to 95.4% when the ports D2, D3, D4 are fully
exposed and D1 is partially exposed the stream of the primary fluid and the DN is
adjusted to 50mm.From the above analysis it is clear that the mixing efficiency is
increasing when the LDNP is between 0-20mm.

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5.5. The effect of driving nozzle position (DN) & LDNP on Mixing
Efficiency when Parallel ports are open

Figure 9 Effect of DN position & LDNP on mixing efficiency when parallel ports are
open
Parallel ports discharges the secondary fluid, parallel to the primary fluid stream.
When the parallel ports P1, P2, P3 & P4 are opened alternately one by one, it was
observed that the efficiency is all most same.
When the distance between the tip of the driving nozzle to exit of the secondary
fluid parallel ports(LDNP) increases the mixing efficiency reduces and it is increasing
with the decrease of LDNP .The increase of efficiency occurring due to the more contact
of secondary fluid with the primary fluid in all the four direction when the LDNP
decreases.
The mixing efficiency decreases with increase in LDNP as the contact between
the primary and secondary fluids getting reduces due the increase of distance between the
tip of the driving nozzle to the exit of secondary fluid outlet. Hence the mixing
efficiency is inversely proportional to the LDNP.

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Table.1. Parallel Port 1(PP1) , 2(PP2), 3(PP3) & 4(PP4)are Open &Driving Nozzle
position, DN=50mm.

Discharge Mixing efficiency
Mixed fluid conductivity Std
DN Q1
( mS/cm) Conductivity ηm
(mm) (lph)
(mS/cm) [%]
50 2600 5.45 6.1 89.4

50 3100 6.89 7.3 94.5

50 3600 9.1 9.4 96.7
Table.1 shows that the conductivity of mixed fluid nearing the conductivity of
standard mixed fluid and which leads to the maximum efficiency when the parallel ports
P1, P2, P3&P4 are opened simultaneously when the driving nozzle position DN is
50mm.Figure 9 shows that, when the LDNP reduces from 60mm to 12mm the mixing
efficiency reaches 96.7 at DN is 50mm.
5.6. Effect of driving nozzle position (DN) & LDNP on Mixing
Efficiency when the down ports, side ports & upper ports are open.

Mixing efficiency VS Circumference ports D1,SF1,UP1
95 & SB1 ports
open
90 D2,SF2,UP2
M ix in g e f f ic ie n c y %

& SB2 ports
85 open
D3,SF3,UP3
80 & SB3 ports
open
75 D4,SF4,UP4
& SB4 ports
70 open
-50 -40 -30 -20 -10 0 10 20 30 40 50
LDNP(Distance between tip of the driving nozzle to side wall of the
ports) in mm

Figure 10 Effect of driving nozzle position (DN) & LDNP on Mixing Efficiency when the down
ports, side ports & upper ports are open.
The Figure 10 shows that the mixing efficiency reduces to 94.3% when all the
down ports and the circumference ports are opened. But the efficiency is increasing to

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95.4% when all the parallel ports open. Hence it is clear that the parallel jets jets mixing
improve the performance of the static liquid mixer.
5.7. Effect of sample location and l/d ratio on mixing.
Samples were collected at l/d = 18, l/d = 36 and l/d = 72 i.e. .450mm, 900mm &
1800mm from the entrance of the throat during the experiments. The Conductivity of
mixed fluid was found out and the mixing efficiency calculated. Figure 11 shows the
results.

Figure 11 Effect of mixing length (l/d ratio or sample point) on mixing efficiency
It can be observed that there is only a slight increase as l/d ratio changes [10] from
35 to 72 and there is an increase of efficiency only 5% as there is no mechanism available
to increase the energy for mixing or to add the energy for mixing.
5.8. Effect of discharge of primary fluid (Q1) on mixing.

Figure 12 Effect of primary fluid discharge on mixing efficiency when parallel ports are
open

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Figure 13 Effect of primary fluid discharge on mixing efficiency when the down ports are
open
Mixing experiments were conducted by varying primary fluid discharge as
2600 lph ,3100 & 3600 lph for various conditions . From the Fig.12 & 13 it is clear that
the mixing efficiency increases with increase in secondary fluid and primary fluid
discharge (Q1&Q2) as the velocity increases more energy being added to the mixed
stream and leads to more mixing and the mixing of fluids take place with greater impact.
The experimental analysis of Ahmed [17] also proved that the velocity and discharge
influences the mixing of coaxial and parallel liquid jets.
5.9. Influence of primary fluid discharge Q1 on Coefficient of variation-
Experimentation
The mean value and standard deviations are calculated for every set of mixed
fluid density values. And the COV calculated (COV=standard deviation of concentration
measurements/mean concentration). This is also called the intensity of mixing or degree
of segregation

104


Figure 14 Influence of primary fluid discharge Q1 on Coefficient of variation-
Experimentation
At least three samples of mixed fluid were collected by changing the primary
fluid discharge Q1, driving nozzle position DN and opening the various ports during the
experiments. Densities of samples were measured. The Figure 14 shows that the mixing
efficiency increasing gradually as the COV reducing when the DN=40mm and D3
opened=50mm and P2 and P4 are open, all the down ports are opened simultaneously and
DN=50mm and opening all the parallel ports.
From the experimental result shown in Figure 14 it is clear that COV is a function
of primary fluid discharge Q1[1] and driving nozzle position DN. When the Q1 increase
from 2600 lph to 3600 lph, DN is 50mm and all the parallel ports are opened, COV
decreases from 0.001169 to 0.000441 as the fluids interacts more and increase in
efficiency. Similarly the density distribution found to be more uniform and the COV is
nearing zero when the DN=50 mm & all the parallel ports are opened. Hence there is an
increase of mixing efficiency.

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Figure 15 Influence of primary fluid discharge Q1 on Coefficient of variation &
Comparison between experimental and computational results
Table 2 Coefficient of variation- COV by computational
Opened port DN, mm COV

P2 & P4 50 0.0017661
open
D1, D2, D3, 50 0.0008814
& D4, open

P1, P2, P3 & 50 0.0004417
P4 open

Figure 15 and Table 2 shows the comparison of COV obtain by experiment and
computational .In both the cases it is clear that the COV approaches zero hence increase
in mixing efficiency when the parallel ports are opened and parallel jets are getting
mixed. There is a good agreement between COV obtained from the computational and
experimental results.
5.10.Effect of mixing insert on mixing efficiency
To evaluate the influence and effect of mixing insert on mixing efficiency, helical
and plate type of mixing inserts have been provided at 900 mm (l/d=36 mm) away from

106


the entrance of throat and the experiments were repeated for the few best conditions
which were obtained during the experiments.

Driving Nozzle position(DN) VS Mixing efficiency with & with
out insert
100 D1 to D4
open &
without
95 insert

D1 to D4

Mixing efficiency %
90 open &
with
insert
85
P1 to P4
open &
80 with out
insert

75 P1 to P4
open &
with
insert
70
0 10 20 30 40 50 60
DN position in mm

Figure 16 Effect of mixing insert on mixing efficiency
The samples are collected at the outlet and whose conductivity was measured.
The Figure 15 shows the trend of mixing efficiency with and without inserts. The
mixing efficiency is found to be increased by 2 to 3 % by addition of helical type of
mixing insert. Hence it can be concluded that the addition of mixing insert improves the
mixing efficiency. The sample points can be changed as l/d=18 mm, l/d=36 mm & l/d=72
mm (mixing length as 450mm, 900mm & 1800mm). The absence of mixing insert does
not have much influence on mixing efficiency even though there is an increase of mixing
length (l/d ratio or sample point). By introduction of mixing insert the mixing efficiency
is found to be increase as it adds more energy for mixing when fluid flow through the
helical path of insert. Hui Hu [24] has studied the effect of mixing insert on mixing
experimentally and proved that ,mixing inserts improves the mixing.
5.11.Effect of driving nozzle position on vorticity magnitude

The Figure 6.10 shows the comparison between the vorticity magnitude obtained
by the computation and literature data’s. The vorticity magnitude reaches the maximum
value of 9.56(1/s) thus increases the mixedness, when the driving nozzle position DN is
50 mm & all the parallel ports are opened and due to the inserts.

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Figure 17 Vorticity magnitude when DN=50 mm
Also the COV is nearing zero due to more interaction of fluids and more mixing
The value of vorticity magnitude reduces to 8.08(1/s) when all the down ports are opened
and leads to less mixing. The results were found agreeing with the literature data.
6. FINDINGS AND CONCLUSIONS
In the present work a mixing nozzle was designed, fabricated and its performance
was evaluated experimentally. Theoretical analysis is also carried out by using CFD
method. The influencet of geometrical parameters on mixing and the parallel jets mixing
were evaluated. The mixing efficiency was evaluated by using conductivity which is
simple and reliable technique to evaluate the mixing efficiency of the mixing nozzle. The
effect parallel jets mixing in a static mixing nozzle on various conditions have been
analyzed and the results are reported.
An experimental set up was fabricated and experiments were carried out to predict
the performance on the mixing by varying the locations of secondary fluid inlet to 5mm,
15mm, 20mm&40mm, driving nozzle position 10mm, 20mm, 30mm, 40mm&50mm,
cone angle of the suction nozzle to 21deg, 23deg & 25deg and the location of the insert to
50mm, 100mm&150mm from the entrance of the throat.
The investigations revealed that the change in sample point (l/d) does not have
much effect on mixing efficiency without adding mixing insert. The addition of mixing
insert improves the mixer performance. The mixing efficiency depends on the direction
of fluids entry. The increase of primary fluid discharge Q1 influences the suction of
secondary fluid which in turn has an effect on mixing efficiency. When the driving

108


nozzle was kept at 50mm and the all the parallel ports are opened and the parallel jets
mixing taking place the mixing efficiency was increasing as vorticity magnitude and the
turbulent kinetic energy are increasing and the fluids interaction becomes more which
intern increases the mixedness.
Computational modeling and the analysis shows that COV is found to be
minimum and gives more effective mixing when all the parallel ports ie., P1, P2, P3 & P4
are opened at DN = 50 mm. The COV obtained by the experimentation and computation
were compared and found to be in good agreement.
7. SCOPE OF FURTHER WORK
Further this study can be extended by studying the effect of temperature, viscosity
of fluids and twisting angle of inserts on mixing. Mapping methods can be used to study
the distributive mixing processes. Further the standard models can be developed to
predict the drop size evolution during the flow in the static mixer.
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