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Chapter 7

SUMMARY, CONCLUSIONS ANDRECOMMENDATIONS

7.1 SUMMARY

In the present research work a new approach to predict the

pressure at various sections in the jet pump from the fundamentals of

engineering has been proposed. The five essential pre-requisites for the

analysis of flow through jet pump, which form the backbone of the

present approach are as follows:

(i) Solid-fluid interaction – drag coefficient (CD),

(ii) Particle diffusion under generalized flow field,

(iii) Friction factor-Reynolds number equation,

(iv) Two-phase (Solid-fluid) flow through ducts, and

(v) Mixing of coaxial jets (primary and secondary jets).

A theoretical model has been developed for the mixing of coaxial

jets. The approach of Wang & Tullis [134] for boundary layer growth in

pipe entry was extended to predict the decay of the primary core and

the growth of the secondary core in the mixing region of the jet pump

which helps in the prediction of pressure variation at various sections

in the jet pump. The extensive experimental data of several research

workers supported the new approach. The works of Sanger [107], Rose

& Duckworth [104] and Shih [117] with a wide variation in parameters

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were of immense help in validation of mathematical model developed by

the present investigation.

Further, to validate the theoretical model proposed in the present

investigation for two-phase flow and to study the parametric effect of

different variables like the area ratio, flow ratio, s/dt ratio, and particle

size etc., on the performance of the jet pump, experimental

investigations are carefully planned and performed. The results were

discussed in the previous chapter. Some of the important conclusions

are as follows:

7.2 CONCLUSIONS

1. A simple workable solution to the problem of finding the drag

coefficient for particles of any sphericity at any Reynolds number

has been proposed. The method was tested using published data

of Brown [9] and was found to be in very good agreement. The

RMS error was in the range of 3.08% to 7.10%. Details are given

in section 3.1.1.2.

2. Taylor’s assumption of the particle diffusion coefficient to be

equal to the linear momentum diffusion coefficient was found to

be correct. The same method was used in the present analysis

and discussed in section 3.1.2.

3. Swamee & Jain’s equation is found to predict friction factor for

published and present experimental data with lowest standard

deviation in comparison with other existing correlations in the

literature. The error was within ±1.0%.

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4. A mathematical model for mixing of co-axial jets based on

boundary layer theory and from fundamentals of fluid flow has

been developed. The mathematical model was tested using

Sanger’s experimental data (NASA Labs, USA) and also by the

data generated on a specially designed test-rig of the present

investigation and was found to be in good agreement.

5. The theoretical model developed by the present investigation

predicted in close agreement with experimental values of

pressure coefficient (Cp) for the data of Sanger [107] with a

standard deviation of 13.19% and an average error of 10.62%.

6. The particle dynamics approach to predict the pressure

distribution along transport line was found to predict with close

agreement with published data of other researchers and that of

present investigation. The max error was 9.06% and standard

deviation of 11.09. The error analysis is given in table 6.3 in

section 6.1.2.

7. In the experimental investigation of water-water pumping and

water-solids pumping through the jet pump the flow behaviour

was found to depend strongly on the parameters (i) primary flow

velocity, (ii) Nozzle diameter, and (iii) nozzle dimensionless

distance from throat entrance (s/dt). After a detailed parametric

study and analysis of the experimental data the following

conclusions are drawn:

a) Higher the primary velocity, lower the pressure at throat

entrance and vice-versa at the exit of the diffuser.

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b) Higher the nozzle diameter, lower the pressure at throat

entrance and vice-versa at the exit of the diffuser.

c) Higher the s/dt ratio, higher the pressure at throat

entrance and vice-versa at the diffuser exit.

However, it is also found that, the mean particle size does not have

a significant effect on the pressure variation in the jet pump and in

the transport pipe within the range of particle size of 150 µm to

1000 µm.

8. The pressure at the throat entrance for water-solids pumping is

slightly higher than water-water pumping for all three sizes of

sand particles. This is due to the additional frictional resistance

due to the presence of solids.

9. The experimental data of present investigation is in good

agreement with the predicted values of the mathematical model

developed by the present investigation with a standard deviation

of 5.46% and a maximum error of 10.39% for water-water

pumping and with a standard deviation of 5.46% and a

maximum error of 12.55% for water-solids pumping.

10. A jet pump with area ratios of 0.223 (6 mm nozzle) and 0.304 (7

mm nozzle) produced a maximum efficiency of 13.63% and

13.89% respectively at a s/dt of 1.5

11. For jet pump with area ratio of 0.397 (8 mm nozzle) the

maximum efficiency of 13.88% was found at an s/dt of 1.0,

indicating shorter mixing length is sufficient for larger area ratio.

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12. Low efficiencies exhibited at low flow ratios are due to inefficient

mixing whereas low efficiencies at high flow ratios are due largely

to frictional losses.

7.3 RECOMMENDATIONS AND SCOPE FOR FURTHERWORK

It is a well known fact that, abundant amount of minerals are

available on the seabed. Economic realisation of which is still a dream

to mankind. In order to achieve this, as a first step in the research the

experimental data for different polymetallic nodules is to be obtained.

The present investigation restricted its study to only transport of sand

particles of different sizes. However the data for polymetallic nodules is

going to be different and needs to be obtained for commercial operation

of deep sea mining.

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Though the present experimental data forms a basis for transport

of sand in dredging operations, further work with different capacities of

jet pump is recommended for large scale commercial operations.

For other applications such as aircraft fuel pumping, chemical

plant circulating systems, oil well pumping, Boiling-water-re-circulating

pumps in nuclear reactors, deep sea mining etc., the Indian

experimental data is scarce. Because of its immense industrial

importance researchers may focus on experimental research in this

field.

While doing the extensive theoretical studies on Solids Handling

Jet Pump and supported by carefully designed test-rig, some

extensions on the job done so far could be undertaken. They are as

follows;

(1) In the present work sand of three sizes were used. One can

easily select sand of some other sizes and add to the data-set

thus generated so far.

(2) In a similar manner, in place of sand some other material like

iron-ore fines (blue dust) could be tested on the same test-rig.

(3) Another important study on the same test-rig could be to test

the efficacy of using polymers of some kind (like guar-gum

etc), mixed with the solid-liquid mixture for drag reduction.