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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.
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