4 THE EFFECT OF GEOMETRICAL PARAMETERS ON MIXING …iaeme.com/MasterAdmin/UploadFolder/THE EFFECT OF GEOMETRICAL... · investigations were carried out to evaluate the parallel and

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

ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 1, Number 1, Sep - Oct (2010), © IAEME

92

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: [email protected]

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

International Journal of Advanced Research in Engineering

and Technology (IJARET), ISSN 0976 – 6480(Print),

ISSN 0976 – 6499(Online) Volume 1,

Number 1, Sep - Oct (2010), pp. 92-111

© IAEME, http://www.iaeme.com/ijaret.html

IJARET © IAEME



93

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.

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.

Figure 2 Locations of parallel, vertical and

circumference secondary fluid ports

Top Ports TP1, TP2, TP3, TP4

Down Ports

Side Ports

1,2,3,4

Parallel Port P1

Parallel Port

Parallel Port P3 Parallel Port P4



95

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



96

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 ).



98

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/s

2 when the DN=50 mm and all the parallel ports are opened

and 1.27x10 m2/s

2 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.



99

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.

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.

Down Ports VS Efficiency

60

65

70

75

80

85

90

95

100

-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

Mix

ing

Eff

icie

ncy %

D1 open

D2 open

D3 open

D4 open

D1,D2,D3&D4 open



100

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.



101

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.



102

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

position, DN=50mm.

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.

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

DN

(mm)

Discharge

Q1

(lph)

Mixed fluid conductivity

( mS/cm)

Std

Conductivity

(mS/cm)

Mixing efficiency

mη

[%]

50

2600 5.45 6.1 89.4

50 3100

6.89 7.3 94.5

50 3600 9.1 9.4 96.7

Mixing efficiency VS Circumference ports

70

75

80

85

90

95

-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

Mix

ing

eff

icie

nc

y %

D1,SF1,UP1

& SB1 ports

open

D2,SF2,UP2

& SB2 ports

open

D3,SF3,UP3

& SB3 ports

open

D4,SF4,UP4

& SB4 ports

open



103

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



104

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



105

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

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

Opened port DN, mm COV

P2 & P4

open

50 0.0017661

D1, D2, D3,

& D4, open

50 0.0008814

P1, P2, P3 &

P4 open

50 0.0004417



107

the entrance of throat and the experiments were repeated for the few best conditions

which were obtained during the experiments.

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.

Driving Nozzle position(DN) VS Mixing efficiency with & with

out insert

70

75

80

85

90

95

100

0 10 20 30 40 50 60DN position in mm

Mix

ing

eff

icie

nc

y %

D1 to D4

open &

without

insert

D1 to D4

open &

with

insert

P1 to P4

open &

with out

insert

P1 to P4

open &

with

insert



108

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



109

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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